Solutions Set for 4th

Edition of CA. Parag Gupta

Cost Accounting & Management: 1. CVP Analysis 1 – 12 2. Activity-based costing management 13 – 33 3. Target Costing, Value Chain analysis & Life Cycle Costing

34 – 42

4. Service Sector 43 – 59 5. Standard Costing & Variance Analysis 60 – 133 6. Budget & Budgetary Control 134 – 175 7. Transfer Pricing 176 – 218 8. Decision Making 219 – 298 9. Miscellaneous Theory Chapters 299 – 308

Operations Research: 10. Linear Programming Problems 309 – 330 11. The Transportation Problem 331 – 359 12. The Assignment Problem 360 – 373 13. Network Analysis-PERT/CPM 374 – 397 14. Simulation 398 – 410 15. Learning Curve Theory 411 – 416

Selling Price per unit = 187500/7500 =Rs. 25 Profit Rs. Sales 10000 x 25 2,50,000 Less: Total Cost 1,93,75

Profit 56,250 P/V Ratio Profit/Margin of Safety

56250/187500

30% BEP Sales 2500 x25 Rs. 62,500 Fixed Cost 62500 x 30%= Rs.

Alternative Answer 2

Ans. 13 (Pg. 11): Margin of Safety(%) = MoS Units/Actual Sales Units CVP

= 7500/(7500+2500) = 75%

Total Sales = 187500/0.75 = Rs.2,50,000/- Profit = Total sales – Total Cost

= 250000 – 193750 = Rs.56250

P/V Ratio = Profit/MoS (Rs.) x 100

= 56250/187500 x 100 = 30% BEP Sales = Total Sales / (100 – MS)

= 2,50,000 x 0.25 = Rs.62,500

Fixed Cost = Sales x P/V Ratio

= 250000 x 0.30-56250 = 18750

Alternate Answer 1

Margin of Safety = Selling Price per unit x ( 7500 units) Rs. 187500 = Selling Price per unit x ( 7500 units) Therefore ,

Selling price = Rs 187500/ 7500 = Rs.25

Total Cost at Break Even point=Rs.25 x 2500 = 62500 = Break Even Sales

(Total Cost – Total Cost of BE)/(Total Units – Break Even Units) = Variable Cost per Unit

(93,750 – 62,500)/(10,000 – 2,500) = 1,31,250/7,500 = Rs.17.50 per unit

Selling Price = 25.00 Variable Cost = 17.50 Contribution = 7.50 P/V Ratio = 7.50/25 = 30% Fixed Cost = 7.50 x 2500 units = Rs.18750.

Profit = 7.50 x 7500 = Rs. 56,250 Ans. 12 (Pg. 11)

(1) P/V Ratio

1

In year 2, additional NP which means additional contribution 8,000

Additional sales 40,000

P/V Ratio 20%

Fixed cost = Contribution – NP = (2,40,000 * 20%) – 18,000 48,000 – 18000 30,000 BEP = FC/PV Ratio 30,000/0.20 1,50,000

(3) Margin of Safety

Year 1

2,40,000 – 1,50,000

90,000

Year 2 2,80,000 – 1,50,000 1,30,000

( ) fi

(Contribution*PV Ratio) – Fixed Cost (2,00,000 * 20%) – 30,000 10,000

OR

Cap Sales

(-) BEP Margin of Safety

(-) PV Ratio NP

2,00,000

1,50,000

50,000

20%

10,000 5) Sales Required

BEP

Margin of Safety Req (100/20*40,000) Sales Required

100/20 ( 30,000(FC) + 40,000(NP))

OR

3,50,000

1,50,000

2,00,000 3,50,000

2

(6) a) 20% decrease in sale Qty

Reduction in Contribution & in net profit

20% *(2,80,000*20%)

20% (56,000)

Reduction in Contribution & in net profit Rs.11,200

(b) Revenue Sales ( 2,80,000*80%) *110% 2,46,400

(-) Revenue Cost (2,80,000*80%) * 80% 1,79,200

Revenue contribution 67,200

(-) Revenue Fixed Cost (26,500)

Revenue NP 40,700

(-) Given NP

Increase in NP

(26,000)

OR

14,700

3

(b) Revenue Sales (2,80,000*80%) *110% 2,46,400

P/V Ratio (now) 100-80 = 20

(new) 3/11 110–80 =30

(Reconciliation of NP change)

Change Effection NP

1) Reduction in Sales Qty (as per (a))

2) Increase in Sales Price (2,80,000*80%*10%)

3) Reduction in Fixed Cost Increase in NP

(11,200)

22,400

3500

14,700 Ans. 3 (Pg. 14) (1) Evaluation of proposal to replace product Z with product S. a: net profit if we continue with product Z.

X (5,00,000*40%/20)*(20-10) 1,00,000

Y (5,00,000*35%/25)*(25-25) 70,000

Z (5,00,000*25%/30)*(30-18) 50,000

Total contribution 2,20,000

(-) Fixed Cost 1,50,000

Net Profit 70,000

b) Net profit if we replace with S X (4,50,000*50%/20)*10 1,12,500 Y (4,50,000*30%)/25*10 54,000

Z (4,50,000*20%)/28*14 45,000

Total contribution 2,11,500

(-) Fixed Cost 1,60,000

Net Profit 51,500

The company should continue with product Z because the replacement of ‘Z’ with ‘S’ would result in reduction net profit.

2) Statement showing the overall breakeven point of the 2 alternatives.

XYZ XYZ

4

Contribution 2,20,000 2,11,500

Sales 5,00,000 4,50,000

Fixed cost 1,50,000 1,60,000

BEP 50/22*1,50,000 3,40,909 3,40,426

The above calculation are based on the presumption, in addition to the usual presumptions that the sales of products X, Y & Z would always be in the ratio of Rs.40:35:25 and that of X, Y & Z would be in the ratio of 50:30:20

Ans. 6 (Pg. 15)

a) Statement showing the budgeted net income for 2003

Fees collected (4,000 *50)

Less: Budgeted cost

G.B 4000* 10

Evaluation 4000*20

Hall rev.

Hon. To Chief Adm.

Super changer (50*4 * 4000/100)

Total

2,00,000

80,000

40,000

8,000

6,000

8,000

1,48,000

Budgeted N.I 52,000

b) (i) Calculation of supervision cost Fees per student

Less: Variable cost + semi variable cost

Evaluation

QB Semi- variable

(supervision)

Gross contribution

Gross Fixed Cost

Gross BEP

Therefore, no. of Supervisory required.

Therefore, Supervision Cost

Net fixed cost

20

10

50

32

18

20,000

1111.11

12

2,400

22,400

30

2

20,000/18

12*200

20,000+2,400

5

(ii)

BEP

Fixed Cost 22,400

Net CTR per student

Fees 50

(-) Variable Cost (30)

20

BEP 1,120

(C) (i) Calculation of total contribution required

Gross contribution per student

Gross Fixed Cost

Net Profit Required

Gross Total Contribution Required

Gross no. of students (40,000/18)

No. of Supervision required

Supervision cost (23*200)

Net Fixed Cost (20,000+4,600)

Net Contribution Required (20,000+24,600)

Net Total Contribution required

Net Contribution per Student

Fees 50

(-) Variable Cost (30)

No. of Students required

18

20,000

20,000

40,000

2,222.22

23

4,600

24,600

44,600

44,600

20

2230 Ans. 7 (Pg.15): (i) Statement of profitability of Special Health Care

Department (for the years 2001 and 2002) Year Year 2001 2002 Rs. Rs. Total contribution : (A) 8,225 bed days × Rs. 260 21,38,500

6

8,225 bed days × Rs. 243.50 20,02,788 (Refer to working notes 1, 2, & 3) Fixed costs : Department fixed costs 6,22,500 6,84,750 Apportioned fixed costs 10,00,000 12,50,000 (Refer to working note 4) Nursing staff 6 2,88,000 3,24,000 (6 Nurse × (6 Nurse × Total fixed costs : (B) 19,10,500 22,58,750

Rs. 48,000 Rs. 54,000)

Profit (Loss) : { (A) – (B)} 2,28,000 (2,55,962)

Working notes :

1. Total number of bed days of occupancy = Total fees collected ÷ Fee per bed days = Rs. 34,95,625 ÷ Rs. 425 = 8,225 2. Variable cost per bed day Variable cost per bed das (Rs.) 165.00 (Rs. 13,57,125 / 8,225) Variable cost per bed day (Rs.) 181.50 in the year 2002 (Rs. 165 + 10% × Rs. 165) 3. Contribution per bed day Contribution per bed days 260.00 in the year 2001 (Rs.) (Rs. 425 -- Rs. 165) Contribution per bed days 243.50 In the year 2002 (Rs.) (Rs. 425 -- Rs. 181.50) 4. Departmental fixed costs Departmental fixed costs (Rs.) 6,22,500 for the year 2001 Department fixed cost (Rs.) 6,84,750 for the year 2002 (Rs. 6,22,500 + 10% × Rs. 6,22,500) (ii) Break even bed capacity for the year 2002 = Total fixed costs ÷ Contribution per bed day = Rs. 22,58,750 ÷ Rs. 243.50 = 9,276 bed days (approx.) (this is not a valid answer because for 9,276 bed days 8 nurses service will be

required)

7

Nursing staff required; 8 Remuneration of 8 nursing staff (Rs.) 4,32,000 8 nurses × Rs. 54,000 Department fixed costs (Rs.) 6,84,750 Apportioned fixed costs (Rs.) Total fixed costs 23,66,750

12,50,000

Break even point = Rs. 23,66,750 ÷ Rs. 243.50 = 9,720 bed days Increase in fee per day required to justify continuance of the Special Health Care

department Desired contribution (Rs.) 22,58,750 Bed days of occupancy 8,225 Contribution per bed days (Rs. ) ; (a) 274.62 (Rs. 22,58,750 / 8,225) Variable costs (Rs.) ; (B) Required fee per bed day; {(A) + (B) }

181.50 456.12

Increase in fee per bed day (Rs.) 31.12

(Rs. 456.12 – 425) Ans. 9 (Pg. 16): (i) Profit Statement of M/s Satish Enterprises for first and second year on monthly and

yearly basis.

First year Second Year Monthly

Rs. Yearly

Rs. Monthly

Rs. Yearly

Rs. Sales revenue: (A) 600 7,200 600 7,200 (3,000 units × Rs.200) Material cost 180 2,160 180 2,160 (3,000 units × Rs.60) Labour cost 75 900 75 900 (3,000 units × Rs.25) Variable overheads 60 720 60 720 (3,000 units × Rs.20) Primary packing cost 45 540 45 540 (3,000 units × Rs.15 Boxes cost 24 288 24 288

months 12units Rs.3,000 ×400

Total fixed overhead 108 1,296 110 1,320

8

(Refer to working note 1)

months 12Rs.1,296

month 12Rs.1,320

Total cost : (B) 492 5,904 494 5,928 Profit : C = [(A)-(B)] 108 1,296 106 1,272

Working Note : 1. (i)

Fixed overhead First year : (Rs.) Second year (Rs.) Depreciation 8,96,000 8,96,000

years 3duty 0Rs.2,88,00 24,00,000 Rs, +

Other fixed overheads 4,00,000 4,24,000 Total Fixed overheads 12,96,000 13,20,000

(ii) Statement of monthly break – even units of the first year.

Levels – No. of units (Refer to working note)

1351 – 1400

1401 – 1450

1451 – 1500

1501 – 1500

Rs. Rs. Rs. Rs. Fixed costs (A) Total fixed overheads per month (Refer to working note)

1,08,000 1,08,000 1,08,000 1,08,000

Semi – variable costs (Special boxes cost) – (B)

11,200 11,600 12,000 12,400

(28 boxes × Rs.400)

(29 boxes × Rs.400)

(30 boxes × Rs.400)

(31boxes × Rs.400

Total fixed and semi variable costs : (A+B)

1,19,200 1,19,600 1,20,000 1,20,000

Break-even level of units: 1490 1495 1500 1505

unit per onContributi

costs variable - semi and fised Total (Rs. 1,19,200 / Rs.80)

(Rs. 1,19,600 / Rs.80)

(Rs. 1,20,000 / Rs.80)

(Rs. 1,20,000 / Rs.80)

The first and second break-even level of unit viz. 1490 and 1495 units falls outside the range of 1351 – 1400 and 1401 – 1450 units respectively. Here a monthly break-even level of units is 1,500 units which lies in the range of 1451 – 1500 units.

Statement of yearly break-even points of the first year

Levels No. of units 17851-17900 17901-17950 17951-18000 18001-18050 Rs. Rs. Rs. Rs. Fixed Costs (A) 12,96,000 12,96,000 12,96,000 12,96,000 Semi-variable costs (Special boxes costs): (B)

1,43,200 1,43,600 1,44,000 1,44,000

9

(358 boxes × Rs.400)

(359 boxes × Rs.400)

(360 boxes × Rs.400)

(361 boxes × Rs.400)

Total fixed and semi-variable costs (A + B)

14,39,200 14,39,600 14,40,000 14,40,400

Break-even level units 17,990 17,995 18,000 18,005 (Rs.14,39,200

/ Rs.80) (Rs.14,32,600

/ Rs.80) (Rs.14,40,000

/ Rs.80) (Rs.14,40,400

/ Rs.80) Have a break-even level of units (on yearly basis) is 18,000 units which lies in the range of 17,951 – 18,000 units as well. The other first two figures do not lie in the respective ranges, so they are rejected. Working note:

Rs.

1. Fixed overhead in the first year 12,06,000 Fixed overhead per month 1,08,000 Contribution per unit (S.P. per unit – VC per unit) 80 Hence the break-even number of units will be above 1,350 units

Rs.80 0Rs.1,08,00

(iii) If the number of toys goes beyond the level of 1,500 numbers, one more box will be required to accommodate each 50 additional units of toys. In that case the additional cost of a box will be Rs.400/- this amount can be recovered by the additional contribution of 5 toys. Hence, the second break-even point in such a contingency is 1,505 toys. (Refer to 1(b) (ii) last column of first statement).

(iv) Comments: Yearly break-even point of 18,000 units of toys in the first instance is equal to 12 times the monthly break-even point of 1,500 units, because the monthly and yearly figures of break-even point fell on the upper limit of the respective range.

In the second instance, it is not so because the monthly and early break-even point fell within the range of 50 toys.

Ans. 10 (Pg. 16): (a) Statement showing total costs indicating each item of cost

No. of students 60 120 180 240 300 Rs. Rs. Rs. Rs. Rs. Variable costs: Break fast 420 840 1,260 1,680 2,100 Lunch 1,800 3,600 5,400 7,200 9,000 Tea 180 360 540 720 900 Entrance fee for Zoo & Aquarium

300 600 900 1,200 1,500

10

Total (A) 2,700 5,400 8,100 10,800 13,500 Rent of buses 1,400 2,100 2,800 3,500 4,200 (Refer to working note 1) Special permit fee 100 150 200 250 300 (Refer to working note 2) Daily allowance paid to teacher (Refer to working table)

400 600 800 1,000 1,200

Block entrance fee 200 300 300 450 450 (Refer to given table) Cost of prizes 1,050 1,050 1,300 1,400 1,500 (Refer to given table) Total (B) 3,150 4,200 5,400 6,600 7,650 Grand Total (A) + (B) 5,850 9,600 13,500 17,400 21,150

(b) Average cost per student at each of the above levels

No. of students: (A) 60 120 180 240 300 Total Costs (Rs.) : (B) 5,850 9,600 13,500 17,400 21,150 [Refer to (a) Part] Average cost (Rs.): (B)/(A) 97.50 80 75 72.50 70.50

(c) Statement showing number of students to break-even

No. of students in the trip

51-100 101-125 126-150 151-200 201-250 251-300

No. of buses 2 3 3 4 5 6 Semi variable costs

Bus Rent (Rs.) 1,400 2,100 2,100 2,800 3,500 4,200 Permit fee (Rs.) 100 150 150 200 250 300 Block entrance fee (Rs.)

200 300 300 300 450 450

Daily allowance paid to teachers (Rs.)

400 600 600 800 1,000 1,200

Cost of prizes 1,050 1,050 1,200 1,300 1,400 1,500 Total cost (Rs.) 3,150 4,200 4,350 5,400 6,600 7,650 No. of students to break even:

105 140 145 180 220 255

(Total semi (Rs.3,150 Rs.4,200/ Rs.4,350/ Rs.5,400/ Rs.6,600/ Rs.7,650

11

variable cost/contribution per student)

/ Rs.30 Rs.30 Rs.30 Rs.30 Rs.30 / Rs.30

As the figure of 105 and 140 student fall outside the limits (No. of students in the trip), therefore there are four break-even points in this case viz., 145,180, 220 and 255 students. The college authorities should keep these figures in mind while hiring 3, 4, 5 and 6 buses respectively to avoid losses. The college incurred loss during the previous year s they hired 5 buses and 72% of total students (216 out of 300 students) joined the trip. The break-even in case college authorities hire 5 buses for the trip comes to 220 students. Working Notes: 1. No. of buses required and Rent of buses @ Rs.700/- per bus

No. of students 60 120 180 240 300 Bo. of buses 2 3 4 5 6 Rent of buses (Rs.) 1,400 2,100 2,800 3,500 4,200 (No. of buses × Rs.700)

2. Special permit fee:

No. of buses × Rs.50) 100 150 200 250 300

3. Allowance paid to Teachers (Rs.)

No. of buses × Rs.200) 400 600 800 1,000 1,200

4. Contribution per student towards semi-variable costs Rs. Collection from each student 65 Subsidy provided by the college 75

10

Less: Variable cost per student Contribution per student

45

30

12

Activity Based Costing Ans. 9

The total production overheads are `26,00,000:

Product A: 10,000 × `30 = `3,00,000

Product B: 20,000 × `40 = `8,00,000

Product C: 30,000 × ` 50 = `15,00,000

On the basis of ABC analysis this amount will be apportioned as follows:

Statement of Activity Based Production Cost

Activity Cost Pool

Cost Driver Ratio Total Amount (`)

A (`)

B (`)

C

Stores Receiving Inspection

Dispatch

Machine Setups

Total Activity Cost

Quantity Sold

Unit Cost

Add: Conversion Cost Total

Purchase requisition Production Runs

Orders Executed Set ups

6:9:10

5:7:8

6:9:10

12:13:15

2,96,000

8,94,000

2,10,000

12,00,000

71,040

2,23,500

50,400

3,60,000

7,04,940

10,000

70.49

80

150.49

1,06,560

3,12,900

75,600

3,90,000

8,85,060

20,000

44.25

80

124.25

1,18,400

3,57,600

84,000

4,50,000

10,10,000

30,000

33.67

90

123.67

(i) Traditional Method Ans 10:

`, Cost per Unit P Q R Direct Method 90 80 120 Direct Labour 80 240 160 Overhead @ `6/Hr on Machine Hour 60

(10 x6) 108 (18 x 6)

84 (14 x 6)

230 428 364

Workings under ABC Product No. of Units M Hrs/Unit M Hrs Batches Inspection Purchase Order

P 3000 10 30000 20 (3000/150)

100 (20 x 5)

60 (20 x 3)

Q 5000 18 90000 10 (5000/500)

40 (10 x 4)

100 (10 x 10)

R 20000 14 280000 20 (20000/1000)

60 (20 x 3)

160 (20 x 8)

400000 50 200 320 Overhead @ `6/Hr =4L x 6`24L

[`In ooo’s] (ii) Activities % Cost Pool C Driver CDQ CDQ Rate(`)

13

MC Setup 20 480 Batches 50 Batches 9600 Mc Operation 30 720 M Hrs 4L 1.80 Inspection 40 960 Inspection 200 4800 Mat 10 240 Purchase Order 320 750

100 2400

(iii) Link of overheads Product Set up cost Machine

Operation Cost Inspection Cost Purchase

Order Cost Total Rate

P 192000 (20 x 9600)

54000 [30000x1.8]

480000 [100x4800]

45000 [60x750]

771000 257

Q 96000 [10x9600]

162000 [90000x1.8]

192000 [40x4800]

75000 [100x750]

525000 105

R 192000 [20x9600]

504000 [280000x1.8]

288000 [60x4800]

120000 [160x750]

1104000 55.2

Cost sheet under ABC

P Q R Direct Material 90 80 120.00 Direct Labour 80 240 160.00 Overhead 257 105 55.20

427 425 335.20 Ans. 11:

(i) Computation of the activity based overheads Step 1: Compute cost per unit of cost driver = Cost pool / cost driver volume

Activity Cost Driver Cost Pool (a)

Cost driver volume/yr (b)

Cost/Unit of cost driver (a)/(b)

Purchasing Setting Materials handling Inspection Machining

Purchase orders Batches produced Material movements

Batches produced Machine hours

`75,000 `112,000

`96,000 `70,000

`150 000

1,500 2,800

8,000 2,800

50,000

`50/pruchse order `40/batch

`12/movement

`25/batch

`3/machine hour

Step 2: Compute the volume of cost drivers consumed by Product Nova Shaft

Purchase orders (given) = 25 Batches = 15,000/100 = 150

Materials movement = 150 batches × 6 = 900 Machine hours = 15,000 units × 0.1 = 1,500 Step 3: Compute the Activity Based Overheads Cost for Product Nova Shaft

Activity Cost Driver Costing Rate /

Cost Driver Unit `

14

Purchasing

Setting

Material handling

Inspection

Machining

Purchase orders

Batches produced

Material movements

Batches produced

Machine hours

50

40

12

25

3

25 order × `50

150 batches × `40

900 movement × `12

150 batches × `25

1,500 hours × `3

`1,250

`6,000

`10,800

`3,750

`4,500

`26,300 (ii) Computation of budgeted overheads costs for Product Nova Shaft using absorption

costing

Budgeted overheads = (`75,000 + `96,000 + `112,000 + `70,000 + `150,000) = `503,000

Budgeted absorption cost/machine hour = `503,000 / 50,000 = `10.06

Budgeted machining hours for Product Nova Shaft = 1,500

Budgeted absorbed overhead = 1,500 × `10.06 = `15,090

(iii) Ways in which the company can reduce the ABC for product Nova Shaft:

Reduce the number of batches by increasing the batch size which will then reduce the setting up overhead, materials handling and inspection costs.

Reduce the number of purchase orders

Innovate ways of speeding up production so that the machining hours are reduced.

(a) Ans. 12:

Sales A B C Total (i) Units ` 25,000 56,000 27,000 1,08,000 Selling price/unit 18 14 12 (ii) Sales Value (`) 4,50,000 7,84,000 3,24,000 15,58,000 (iii) Prime Cost Overhead 12 9 8 (iv) No. of units/run 2,520 2,810 3,010 (v) Prime Cost ` 3,02,400 5,05,800 2,16,720 (vi) Gross Margin (ii − v) 1,47,600 2,78,200 1,07,280 5,33,080

15

Workings:

A B C Total Gross Production/unit /run (1) 2,520 2,810 3,010 Defectives/run (2) 20 10 10 Good units / run (3) 2,500 2,800 3,000 Sales (Goods units)(4) 25,000 56,000 27,000 No. of runs (5) 10 20 9 Gross Production (6) = (1) × (5) 25,200 56,200 27,090 Prime Cost / unit (7) 12 9 8 Prime Cost (8) ` 3,02,400 5,05,800 2,16,720 10,24,920 Inspection hours/run (9) 3 4 4 Inspection hours (10) = (9) × (5) 30 80 36 146 M/c hours / run (11) 20 12 30 M/c hours (12) = (1) × (5) 200 240 270 710 Dye Cost/run (13) 200 300 250 Dye cost (14) (13) × (5) 2,000 6,000 2,250 10,250

Conventional Accounting System Total A B C

Sales – units / Production (good units) 1,08,000 25,000 56,000 27,000 Gross Margin (`) 5,33,080 1,47,600 2,78,200 1,07,280 Production overheads (`) 2,25,250 52,141 1,16,797 56,313 Selling Overhead (`) 1,62,000 37,500 84,000 40,500 Sub-Total Overhead (`) 3,87,250 89,641 2,00,797 96,813 Net profit (`) 1,45,830 57,959 77,403 10,467

16

Ranking II I III Activity Based System

Sub-Total Overhead (`) 62,787 2,16,963 1,07,500 Net profit (`) 84,813 61,237 (220) Ranking I II III

Ans. 13:Total Machine hours = Volume × Machine hour required for each period

(i) Factory overhead applicable to machine oriented activity = `37424

= (500 × ¼) + (5000 × ¼) + (600×1) + (7000 ×3/2) = 12475 hours Machine overhead charges = `37424/12475 hours = `3 per hour Setup Costs = `4355/17 i.e., total number of setups = `256.18 Material ordering cost = `1920/10 operations = `192 Material handling cost = `7580/27 operations = `280.74 Spare parts = `8600/12 parts = `716.67

Products Overheads Items A B C D Machine Overhead

1/4×`3 = 0.75 1/4×`3 = 0.75 1× `3 = 3.00 3/2×`3 = 4.50

Setup cost 1×256.18/500 = .51 6×256.18/5000=.31 2×256.18/600=.85 8×256.18/7000=.29 Material ordering cost

1×192/500=.38 4×192/5000=.15 1×192/600=.32 4×192/7000=.29

Material handling cost

2×280.74/500=1.12 10×280.74/5000=.56 3×280.74/600=1.40 12×280.74/7000=.48

Spare parts cost 2×716.67/500=2.87 5×716.67/5000=.72 12×716.67/600=1/19 4×716.67/7000=.41 (ii) Competition of overhead per unit based on two system and their difference Products Machine

overhead `

Setup `

Material ordering

`

Material handling

`

Spare parts

`

Total (ABC

system)

Old system

`

Difference

A 0.75 0.51 0.38 1.12 2.87 5.63 1.20 +4.43 B 0.75 0.31 0.15 0.56 0.72 2.49 1.20 +1.29 C 3.00 0.85 0.32 1.40 1.19 6.76 4.80 +1.96 D 4.50 0.29 0.11 0.48 0.41 5.79 7.20 -1.41

The traditional system does not make correct assumptions that all overheads are related to volume and machine time. Under traditional system products A and C are under costed because it misallocates costs for small volume products. The activity based costing system recognizes the amount of input to each cost unit. Product B previously avoided its full share of overheads because of its low machine time and may still do so if part of `37425 of machine oriented overhead should be apportioned on some other basis. Product D is overcosted because the additional system loaded it with overhead attributable to activities concerned with products A, B & C as a result of using a volume-based and machine oriented rate which failed to pay proper attention to activity costing. Ans.: 14 (i) Statement of Operating income and Operating income as a

percentage of revenues for each product line

17

(When support costs are allocated to product lines on the basis of cost of goods sold of each product) Soft

Drinks Rs.

Fresh Produce

Rs.

Packaged Foods Rs.

Total Rs.

Revenues: (A) 7,93,500 21,00,600 12,09,900 41,04,000 Cost of Goods sold (COGS): (B)

6,00,000 15,00,000 9,00,000 30,00,000

Support cost (30% of COGS): (C)

1,80,000 4,50,000 2,70,000 9,00,000

Total cost: (D) = {(B) + (C)} 7,80,000 19,50,000 11,70,000 39,00,000 Operating income: E= {(A)-(D)}

13,500 1,50,600 39,900 2,04,000

Operating income as a percentage of revenues: (E/A) x 100)

1.70% 7.17% 3.30% 4.97%

Working notes: 1. Total support cost: Rs. Bottles returns 12,000 Ordering 1,56,000 Delivery 2,52,000 Shelf stocking 1,72,800 Customer support Total support cost

3,07,200

2. Percentage of support cost to cost of goods sold (COGS):

9,00,000

= 100 sold goods ofcost Total

costsupport Total×

100000,00,30.Rs000,00,9.Rs

×= = 30%

3. Cost for each activity cost driver: Activity (1)

Total cost Rs. (2)

Cost allocation base (3)

Cost driver rate (4)=[(2)÷(3)]

Ordering 1,56,000 1,560 purchase orders

100 per purchase order

Delivery 2,52,000 3,150 deliveries 80 per delivery Shelf-stocking 1,72,800 8,640 hours 20 per stocking

hour Customer support 3,07,200 15,36,000 items

sold 0.20 per item sold

(ii) Statement of Operating income and Operating income as a percentage of revenues for each product line

18

(When support costs are allocated to product lines using an activity-based costing system) Soft drinks

Rs.

Fresh Produce

Rs.

Packaged Food

Rs.

Total

Rs. Revenues: (A) 7,93,500 21,00,600 12,09,900 41,04,000 Cost & Goods sold 6,00,000 15,00,000 9,00,000 30,00,000 Bottle return costs 12,000 0 0 12,000 Ordering cost* (360:840:360)

36,000 84,000 36,000 1,56,000

Delivery cost* (300:2,190:660)

24,000 1,75,200 52,800 2,52,000

Shelf stocking cost* (540:5,400:2,700)

10,800 1,08,000 54,000 1,72,800

Customer Support cost* (1,26,000:11,04,000:3,06,000)

25,200 2,20,800 61,200

Total cost: (B)

3,07,200

7,08,000 20,88,000 11,04,000 39,00,000 Operating income C:{(A)- (B)}

85,500 12,600 1,05,900

Operating income as a % of revenues

2,04,000

10.78% 0.60% 8.75% 4.97%

* Refer to working note 3 (iii) Comment: Managers believe that activity based costing (ABC) system is more credible

than the traditional costing system. The ABC system distinguishes with different type of activities at family store more precisely. It also tracks more precisely how individual product lines use resources. Soft drinks consume less resources than either fresh produce or packaged food. Soft drinks have fewer deliveries and require less shelf stocking time. Family store managers can use ABC information to guide their decisions, such as how to allocate a planned increase in floor space. Pricing decision can also be made in a more informed way with ABC information.

Ans. 15

(a) Statement showing total cost of different products, assuming absorption of overhead on a machine hour basis

Product A Product B Product C Product D Direct material 40 50 30 60 Direct labour* 28 21 14 21 Overhead 80 60 40 60 Cost of production per unit

148 131 84 141

Output in units 120 100 80 120 Total Costs (`) 17760 13100 6720 16920 * Rate per machine hour = `26000/1300 hours = `20 Machine Hours = 480 + 300 + 160 + 360 = 1300 hours (b) Cost ` Drivers No. Cost/unit of driver Setups 5250 Production runs 21* `250 Stores/receiving 3600 Requisitions 80@ 45 Inspection/quality 2100 Production runs 21 100

19

Handling/dispatch 4620 Orders 42 110 * Production runs = (120/20) + (100/20) + (80/20) + (120/20) @ Requisitions = 20 for each product or 80 in total. It may be pointed out that machine department cost of `10430 will continue to be absorbed on a machine hour basis as before. The relevant absorption rate will be = `10430/1300 = `8.02 per machine hour. Total cost (`) A B C S Direct material 4800 5000 2400 7200 Direct labour 3360 2100 1120 2520 Set-ups 1500 1250 1000 1500 Stores/receiving 900 900 900 900 Inspection/quality 600 500 400 600 Handling/dispatch 1320 1100 880 1320 Machine dept. costs

3851 2407 1284 2888

16331 13257 7984 16928 Cost per unit 136.09 132.57 99.80 141.07 (c) A B C D Cost per unit (a) 148 131 84 141 Cost per unit (b) 136.09 132.57 99.80 141.07 Difference (11.91) 1.57 15.80 0.07 The total overheads which are spread over the four products have been apportioned on different bases, causing the product cost to differ substantially in respect of products A and C. A change from traditional machine hour rate to an activity based system may have effect on:

(a) pricing and profits tot the extent that pricing is based on a ‘cost plus’ approach. (b) Reported profits to the extent that stock levels fluctuate between reporting periods.

(a) Total cost of different products (overhead absorption on Machine hour basis) Ans. 16

A `

B `

C `

D `

Direct material 42 45 40 48 Direct labour 10 09 07 08 Overhead 72 54 36 18 Cost of production per unit 124 108 83 74 Out put in unit 720 600 480 504 Total cost 89,280 64,800 39,840 37,296

Machine hours (720 × 4 + 600 × 3 + 480 × 2 + 504 × 1) = 6,144 hours.

Rate per hour = hours 6,144

1,10,592 Rs = `18 per hour.

(b) Activity based costing system

Set up Store receiving

Inspection

Machine operation and maintenance cost of ` 63,000 to be distributed in the ratio of 4: 3: 2.

28,000 21,000 14,000

20

Cost ` Drivers No Cost per unit of driver (`)

Set up 48,000 Production runs 96 500 Store receiving 36,000 Requisitions raised 200 180 Inspection 24,000 Production runs 96 250 Material handling and disp

2,592

Orders 192 13.50

Production Run for A (720/24) = 30 ; B (600/24) = 25 ; C (480/24) = 20 ; D (504/24) = 21. A (`) B(`) C(`) D(`)

Direct material 30,240 27,000 19,200 24,192 Direct labour 7,200 5,400 3,360 4,032 Setup 15,000 12,500 10,000 10,500 Store receiving 9,000 9,000 9,000 9,000 Inspection 7,500 6,250 5,000 5,250 Material handling and dispatch 810 675 540 567 Total cost 69,750 60,825 47,100 53,541 Per unit cost 96.875 101.375 98.125 106.23

(c)

A B C D Cost per unit (a) 124 108 83 74 Cost per unit (b) 96.88 101.38 98.13 106.23 Difference (27.12) (6.62) 15.13 32.23 The total overheads which are spread over the four products have been apportioned on different bases, causing the product cost to differ substantially: in respect of product A and D a change from traditional machine hour rate to an activity system may have effect on price and profits to the extent that pricing is based on cost plus approach.

(a) Budget Cost Statement Ans. 17:

Activity Activity Cost (`)

(Budgeted)

Activity Driver No. of Units of Activity Driver

(Budget)

Activity Rate (`)

Deposits Loans Credit Cards

1.ATM Services 2. Computer Processing 3. Issuing Statements 4. Customer Inquiries Budgeted Cost

8,00,000

10,00,000

20,00,000

3,60,000

41,60,000

ATM Transaction Computer Transaction No. of Statements Telephone Minutes

2,00,000

20,00,000

5,00,000

7,20,000

4

0.50

4.00

0.50

6,00,000

7,50,000 14,00,000

1,80,000

- 1,00,000

2,00,000

90,000

2,00,000

1,50,000

4,00,000

90,000

29,30,000 3,90,000 8,40,000

21

Units of product as estimated in the budget period Budgeted Cost per unit of the product

58,600 50

13,000 30

14,000 60

Working Notes: (i) ATM 4,00,000 + 2,00,000 + 2 × 1,00,000 = 8,00,000 (ii) Computer 5,00,000 (Fixed = 2,50,000) Variable= 10,00,000

2,50,000 increase to 3 times = 7,50,000

(iii) Issuing Statements 2,00,000 + 80% × 2,00,000 = 2 + 1.6 = 3,60,000

(a) Working: Ans. 18:

Calculation of Direct Labour hours: ` Total Indirect Costs (`)* 23,85,000 Total Direct labour hours (30,000 + 9,750)

39,750

Overhead absorption rate hour per 60 Rs. hours 39,750

23,85,000 Rs.=

(i) Statement showing total manufacturing costs and profits Product A

(60,000 units)

Product B (15,000 units)

Total (`)

Per unit Amount (`) Per unit Amount (`) Direct materials 18.75 11,25,000 45.00 6,75,000 18,00,000 Direct labour 10.00 6,00,000 13.00 1,95,000 7,95,000 Prime cost 28.75 17,25,000 58.00 8,70,000 25,95,000 Indirect costs (absorbed on the basis of direct labour hours)

30.00 (18,00,000/

60,000 units)

18,00,000 (30,000 hours

@ `60 per hour)

39.00 (5,85,000/

15,000 units)

5,85,000 (9,750 hours

@ `60 per hour)

23,85,000

Total cost 58.75 35,25,000 97.00 14,55,000 49,80,000 Sales 63.00 37,80,000 137.00 20,55,000 58,35,000 Profit (Sales – Total cost)

4.25 2,55,000 40.00 6,00,000 8,55,000

* Calculation of total Indirect Cost:

` Cleaning and maintenance wages 2,70,000 Designing costs 4,50,000 Set-up costs 3,00,000 Manufacturing operations cost 6,37,500 Shipment costs 81,000 Distribution costs 3,91,500 Factory Administration Costs 2,55,000 23,85,000

Indirect cost allocation to products A and B:

22

Product A Product B Direct labour hours 30,000 9,750 Direct labour hour rate: `

60 60

Indirect costs `18,00,000 5,85,000 Output (units) 60,000 15,000 Cost per unit of output `

30 39

Statement showing the total manufacturing costs and profits using direct labour hour basis of absorption and treating cleaning and maintenance cost as indirect cost:

Product A Product B Total `/unit Amount `/unit Amount Output (units) 60,000 15,000 ` ` ` Sales 63.00 37,80,000 137.00 20,55,000 58,35,000 Direct Materials

18.75 11,25,000 45.00 6,75,000 18,00,000

Direct Labour 10.00 6,00,000 13.00 1,95,000 7,95,000 Prime Cost 28.75 17,25,000 58.00 8,70,000 25,95,000 Indirect costs 30.00 18,00,000 39.00 5,85,000 23,85,000 Total costs 58.75 35,25,000 97.00 14,55,000 49,80,000 Profit 4.25 2,55,000 40.00 6,00,000 8,55,000

(ii) Calculation of Setup hours

Product A Product B Total Output (in units) 60,000 15,000 No. of quantity produced per batch

240 50

Setup time per batch 2 hours 5 hours Setup hours (Total) (No. of batches × set up time per batch)

×2

24060,000 = 500

×5

5015,000 = 1,500

Calculation of Cost Driver, Rates and summary of indirect cost relating to Product A & B:

Activity and Cost Drivers Amount (`)

Cost Drivers for Product Activity Cost Rates Indirect Costs

A B (Amount / total of cost driver)

Product A Product B

Cleaning & Maintenance (Direct Labour hours)

2,70,000 30,000 9,750 39,750 6.7925 per Direct labour hour

2,03,775 66,227

Designing costs (square feet) 4,50,000 30 sq. feet 70 sq. feet 100 4,500 per sq. feet 1,35,000 3,15,000

23

Setup costs (setup hours) 3,00,000 500 hours 1,500 hours 2,000 150 per setup hour 75,000 2,25,000

Manufacturing operations costs (molding machine hours)

6,37,500 9,000 3,750 12,750 50 per molding hours 4,50,000 1,87,500

Shipment costs (No. of shipments)

81,000 100 100 200 405 per shipment 40,500 40,500

Distribution costs (area in cubic feet)

3,91,500 45,000

cubic feet

22,500 cubic feet

67,500 5.80 per cubic feet 2,61,000 1,30,500

Factory administration costs (direct labour hours)

2,55,000 30,000 9,750 39,750 6.4151 per labour hour

1,92,453 62,547

Production (units) 13,57,728 10,27,274

60,000 15,000

22.63 68.48

Cost Sheet based on activity based costing system:

Description Product A Product B Total cost Per unit Total cost Per unit ` ` ` ` Sales 37,80,000 63.00 20,55,000 137.00 Direct Cost Direct Materials

11,25,000 18.75 6,75,000 45.00

Direct Labour

6,00,000 10.00 1,95,000 13.00

Total 17,25,000 28.75 8,70,000 58.00 Indirect costs 13,57,728 22.63 10,27,274 68.48 Total costs 30,82,728 51.38 18,97,274 126.48 Profit 6,97,272 11.62 1,57,726 10.52

(iii) Comparison of results:

Description Product A Product B Traditional

Costing System

Activity Based System

Traditional Costing System

Activity Based System

` ` ` ` Selling Price 63.00 63.00 137.00 137.00 Direct costs 28.75 28.75 58.00 58.00 Indirect costs 30.00 22.63 39.00 68.48 Total cost per unit

58.75 51.38 97.00 126.48

Profit per unit

4.25 11.62 40.00 10.52

Opinion: In the traditional costing system, Product B appears to be more profitable than Product A whereas under the activity based costing system, Product A appears to be more profitable than product B. The activities

24

like designing, set up, manufacturing operation cost, shipment and distribution are support service activities and the consumption of resources relating to these activities are not dependent on direct labour hours. The quantum of consumption of resource of each support service activity is different in respect of the two products manufactured and hence activity based costing presents a true view of cost of production. Moreover, the suggestion to treat cleaning and maintenance activity as a direct cost pool is commendable because costs should be charged direct wherever possible. The results reveal that the company should concentrate upon product B.

Alternative Solution: Cleaning and maintenance activity will not find a place in the statement of calculation of cost driver rates. However, other cost driver rates will be unchanged. Statement showing total cost and profits on the basis of Activity Based Costing

Product A Product B Total (`) Per

unit Amount (`) Per unit Amount

(`)

Direct materials 18.75 11,25,000 45.00 6,75,000 18,00,000 Direct labour 10.00 6,00,000 13.00 1,95,000 7,95,000 Cleaning & maintenance expenses

2.00 1,20,000* 10.00 1,50,000* 2,70,000

Prime cost 30.75 18,45,000 68.00 10,20,000 28,65,000 Indirect costs: Designing 2.25 1,35,000 21.00 3,15,000 4,50,000 Setup 1.25 75,000 15.00 2,25,000 3,00,000 Manufacturing operation

7.50 4,50,000 12.50 1,87,500 6,37,500

Shipments 0.67 40,500 2.70 40,500 81,000 Distribution 4.35 2,61,000 8.70 1,30,500 3,91,500 Factory administration

3.21 1,92,453 4.17 62,547 2,55,000

Total indirect costs 19.23 11,53,953 64.07 9,61,047 21,15,000 Total costs 49.98 29,98,953 132.07 19,81,047 49,80,000

Sales 63.00 37,80,000 137.00 20,55,000 58,35,000 Profits (Sales – total costs)

13.23

7,81,047

4.93

74,953

8,55,000

* The Cost Accountant identified `1,20,000 for Product A and balance

`1,50,000 of cleaning and maintenance wages for Product B. (iii) Comparison of results:

Product A Product B Allocation basis Direct

Labour Activity

Based Direct

Labour Activity

Based

25

Hour Costing Hour Costing Selling Price 63 63 137.00 137.00 Prime cost 28.75 30.75 58.00 68.00 Total Indirect costs 30.00 19.23 39.00 64.07 Total costs (Prime cost + Total indirect costs)

58.75

49.98

97.00

132.07

Profit per unit 4.25 13.02 40.00 4.93

Comments: It is evident from the comparison of results that under single cost pool system the product A is overcost and product B is undercost. This is due to allocation of indirect cost on the basis of blanket rate based on direct labour hour and considering one of the significant cost as an indirect one. Cost Accountant’s decision for allocation of indirect costs on the basis of ABC methods and identifying be cleaning and maintenance cost as direct element of cost appears to be a good decision. Result show that the firm enjoys competitive advantage with regards to product A.

Ans. 19

(1) Single factory direct labour hour overhead rate =2,0003,10,000 Rs = ` 155 per direct labour hour

Computation of unit cost ( existing system)

R (`) S(`) T(`) Direct labour cost @ ` 12 per hour 300 5,760 600 Direct material 1,200 2,900 1,800 Overheads(direct labour hours × ` 155 per hour 3,875 74,400 7,750 5,375 83,060 10,150 Quantity Produced (No) 560 12,800 2,400 Cost per unit 9.60 6.49 4.23

(2) ABC system involves the following stages, 1. Identifying the major activities that take place in an organisation. 2. Creating a cost pool /cost centre for each activity 3. Determining the cost driver for each activity 4. Assigning the cost of activities to cost objects (e.g. products, components, customers etc)

The most significant activities have been identified e.g. receiving components consignments from suppliers, setting up equipment for production runs, quality inspections, and despatching orders to customers. The following shows the assignment of the costs to these activities,

(` ,000)

Receiving supplies

Set ups Quality inspection

Despatch Total

Equipment operation expenses 18.75 87.50 18.75 125.00 Maintenance 3.75 17.50 3.75 25.00 Technicians wages initially 3.83 17.85 3.82 25.50

26

allocated to Maintenance(30% of ` 85,000= ` 25,500 and then reallocated on same basis on maintenance) Balance of technicians wages allocated to set ups and quality inspections

34.00 25.50 59.50

Stores wages - Receiving 35.00 35.00 Despatch wages - Despatch 40.00 40.00 61.33 156.85 25.50 66.32 310.00

Note : Equipment operation expenses and Maintenance allocated on the basis 15%,70% and 15% as specified in the question.

The next stage is to identify the cost drivers for each activity and establish cost driver rates by dividing the activity costs by a measure of cost driver usage for the period. The calculations are as follows :-

Receiving supplies (98061,330 Rs ) = ` 62.58 per component.

Performing set ups (1,020

1,56,850 ) = ` 153.77 per set up

Despatching goods ( 420

320,66 ) = ` 157.93 per despatch

Quality inspection (640

500,25 ) = ` 39.84 per quality inspection

Finally, costs are assigned to components based on their cost driver usage. The assignments are as follows,

R (`) S(`) T(`) Direct labour 300 5,760 600 Direct materials 1,200 2,900 1,800 Receiving supplies 2,628.36 1,501.92 1,752.24 Performing set ups 2,460.32 2,767.86 1,845.24 Quality inspections 398.40 318.72 717.12 Despatching goods 3,474.46 13,424.05 7,264.78 Total costs 10,461.54 26,672.55 13,979.38 No of units produced 560 12,800 2,400 Cost per unit 18.682 2.08 5.82

For components, the overhead costs have been assigned as follows, (Component R) Receiving supplies (42 receipts at ` 62.58) Performing set ups (16 production runs at ` 153.77) Quality inspections (10 at ` 39.84)

27

Despatching goods ( 22 at ` 157.93). Ans 20: Overhead rate per labour hour = Overhead incurred in first half year = `21,00,000 = `52.50 per labour hour Direct labour hours worked 40,000 hours Apportionment of technical staff salaries Machine maintenance = 6,37,500 X 31/100 = ` 1,91,250 Set up = 6,37,500 X 40/100 = ` 2,55,000 Quality Inspection = 6,37,500 X 30/100 = ` 1,91,250 Statement showing apportionment of ‘Machine operation’ and ‘Machine maintenance’ between stares and production activity (set up) in ratio 20:80

Particulars Total Expenses

Stores / Receiving

Set up/ Production run

Machine operation Machine maintenance (`1,87,500 + `1,91,250)

10,12,500 3,78,750

2,02,500 75,750

8,10,000 3,03,000

Particulars Total

Expenses Stores / Receiving

Set up / Production run

Wages and salaries of stores staff Component of set- up cost Total

2,62,500 2,55,000

2,62,500 -

- 2,55,000

19,08,750 5,40,750 13,68,000

Rate per activity cost driver Particulars Stores /

Receiving Set up/ Production run

Quality inspection

Total overheads (`) Units of activities carries out Rate per activity cost driver (`)

5,40,750 1,960 275.89

13,68,000 2,040 670.59

1,91,250 1,280 149.41

Statement showing computation of cost of products P and Q (Based on the existing system of single overhead recovery rate) Particulars Product

P Q Direct Labour hours Unit made Direct materials cost Direct labour cost (@ `6 per D.L.H.) Overheads ( @ `52.50 per D.L.H.) Total cost of products Cost per unit

960 15,000 6,000 5,760 50,400 62,160

100 5,000 4,000 600 5,250 9,850

4.144

1.97

Statement showing computation af cost of products P and Q (Using activity based costing system)

28

Particulars Product

P Q Units Direct materials cost Receiving/ Stores cost Receiving Stores cost (48 X 275.89) (52 X 275.89) Production runs / Set ups cost (36 X 670.59) (24 X 670.59) Inspection cost (30 X 149.41) (10 X 149.41) Total Cost products Coat per unit

15,000 6,000 5,760 13,243 24,141 4,482

5,000 4,000 600 14,346 16,094 1,494

53,626 36,534 3.58 7.31

Computation of sales value per quarter of component K (Using activity based costing system)

Units of component K To be delivered per quarter

3,000

Component of initial design cost per quarter ( `60,0000/8 quarters) Direct material costs Direct labour cost (600 hours X `6) Receiving cost (50 X `275.89) Production runs cost (6 X `670.59) Inspection cost (24 X `149.41) Total cost Add: Mark up (25% of cost) Sales value Selling price per unit of K (`43,035/3,000 units)

` 7,500 12,000 1,800 5,518 4,024 3,586 34,428 8,607

43,035 16.34

Ans 21

(i) Job cost sheet for Host Restaurant and Pizza Hut (using a simplified costing system)

Host Restaurant

(`)

Pizza Hut

(`) Professional labour cost: 25 hours @ `60 per hour 1,500 40 hours @ `60 per hour 2,400 (Refer to working note 1) Professional Support staff 25 hours @ `120per hour 3,000 40 hours @ `120 per hour 4,800 (Refer to working note 2) Total 4,500 7,200

(ii) Job cost sheet using an Activity based costing

Host Restaurant Pizza Hut (`) (`)

Professional labour cost 500

29

5 hours @ `100 per hour 3,000 30 hours @ `100 per hour (Refer to working note 3) Associate labour cost 800 20 hours @ `40 400 10 hours @ `40 (Refer to working note 4) Design support 1,690 `1.30 × `1,300 4,420 `1.30 × `3,400 (Refer to working note 5) Staff support 1,056 25 hours @ `42.22 1,689 40 hours @ `42.22 (Refer to working note 6)

4,046 9,509 (iii) Determining the amount by which each job was under or overcosted using a simplified costing

system.

Host Restaurant

(`)

Pizza Hut

(`) Cost using simplified system 4,500 7,200 Cost using Activity Based system 4,046 9,509 Difference 454 (2,309)

The simplified costing system overcosted Host Restaurant job by `454 and undercosted Pizza Hut job by `2,309.

30

31

Ans. 22: (i) Comparison of manufacturing cost per unit.

Audio Player Model

‘AB 100’ ‘AB 200’

` `

Direct material cost 1,000.00 800.00 Direct manufacturing labour cost 200.00 180.00 Machining costs 200.00 160.00 Testing costs 250.00 200.00 Rework costs 150.00 75.00 Ordering costs 2.00 1.25 Engineering costs 198.00 198.00 Total manufacturing cost per unit 2,000.00 1,614.25

Working notes for audio player model ‘AB 200’ (i) Machining hours and cost: Machining hours = (1 hour–0.20 hours) or 0.80 hours) Machining cost is 0.80 hours × `200 or `160

(ii) Testing hours and cost: Testing hours = 2 hours × (1 hour – 0.20) or 1.60 hours. Testing cost is 1.60 hours × `125 or `200

(iii) Rework cost per unit: Rework units = 5% × 10,000 units or 500 units. Rework cost = 500 units × `1,500 or `7,50,000. Rework cost per unit `7,50,000 / 10,000 units or `75 per unit.

(iv) Ordering cost: No. of orders per month 50 components × 2 orders = 100 Ordering cost per month 100 orders × `125 per order = `12,500 Ordering cost per unit = `12,500 / 10,000 units = `1.25 per unit.

(v) It is assumed that total available engineering hours will be used for manufacturing ‘AB 200’ model of audio player.

(ii) Effect of design change and pricing decision on operating income of ABC. (`Lakhs)

Revenue loss on 10,000 units (40) (`10,000 units × `400) Saving in cost: Direct material costs 20.00 (`200 × 10,000 units) Direct manufacturing labour costs 2.00 (`20 × 10,000 units) Rework costs 7.50 29.50

32

(5% × 10,000 units × `1,500) Net effect on operating income (10.50)

Conclusion: Operating income per month will be reduced by `10.50 Lakhs. Effects of reduction in components, machining time, and testing time will not have any immediate effect, because it is difficult to adjust the available facilities in ordering department, machining department and testing department.

33

Target Costing, Value Chain Analysis

Maximum capacity 80,000 units Ans. 7:

Presented sales 20,000 units @ `100 p.u. Selling price/unit Demand

100 20,000 90 40,000

80 80,000 = Full capacity

∴Target cost/unit = 80 –25% of sales = 80- 20 = 60 p.u.

(b) At present Variable cost/unit = 40% of cost i.e. 75 = `30

∴Fixed cost/unit = 100 –25% = 75 COS 75 Less: Variable cost/unit

Fixed cost 45 p.u. Total fixed

cost 45×80,000 = 36 lakhs

30

∴Add full capacity target cost = `60/unit ×80,000 units = `48 lakhs

Total estimate cost Fixed cost 36 lakhs Variable cost (80,000×40)

60 lakhs 24 lakhs

∴Required. Cost reduction following value engineering is `12 lakhs.

(e) Rate of return 15% Profit p.u. 25% of 80 = 20/unit

Profit before tax = 20×80,000 = 16 lakhs ROCE = (PBI/Investment) ∴Investment = (PBI/ROCE) = 16 lakhs/15% = `10666667.

Ans. 8

: Target profit 25,000 Add: Fixed cost 1,40,000 Add: Additional Advertisement (a) Total contribution

28,500 1,93,500

(b) Required. Sales volume 12,000 contribution/unit (a¸b) 16.125 Target Selling price/unit 32 Less: Contribution/unit Target variable cost p.u.

16.125 15.875

Less: material cost p.u. Labour + Variable overhead

8.000 7.875

34

Labour: x hr. @ 4 Variable overhead x hr. @ 0.5

∴4.5x = 7.875 x (hr.) 1.75 Time/unit 1.75 Present _ 2.00 Time reduced 0.25 hr.

(i) Cost of product as per Target Costing Ans. 9

Coco Stawberry Vanilla Selling Price per unit 23.00 18.00 13.00 Less: Markup (25% of cost or 20% of selling Price)

4.60 3.60 2.60

Target Cost per unit (`) 18.40 14.40 10.40 (ii) Cost of product as per Traditional Costing Coco Stawberry Vanilla Maximum Volume (units) 60,500 24,200 72,600 ` ` ` Material 8.00 6.00 5.00 Labour 5.00 4.00 3.00 Prime Cost 13.00 10.00 8.00 Store Support (30% of Prime Cost) 3.90 3.00 2.40 Total Cost per unit 16.90 13.00 10.40 Total Cost 10,22,450 3,14,600 7,55,040 (iii) Cost of product as per Activity Based Costing Coco Stawberry Vanilla Maximum Volume (units) 60,500 24,200 72,600 ` ` ` Material 8.00 6.00 5.00 Labour 5.00 4.00 3.00 Prime Cost 13.00 10.00 8.00 Overheads (Working Note-2) 3.29 5.23 2.17 Total Cost per unit 16.29 15.23 10.17 Total Cost 9,85,320 3,68,670 7,38,100 (iv) Comparision in Cost of each product under each method Coco Stawberry Vanilla As per Target Costing 18.40 14.40 10.40 As per Traditional Costing 16.90 13.00 10.40 As per Activity based Costing 16.29 15.23 10.17 Comment: Since cost of Strawberry is high in ABC costing in comparison to target costing and traditional methods, it is indicating that actual profit under target costing is less than targeted. Working Note-1 : Coco Stawberry Vanilla Current Selling Price per unit (`) 25.00 20.00 15.00 Current Sales (units) 50,000 20,000 60,000 Selling Price (`) 24.00 19.00 14.00 Revised Sales (units) 55,000 22,000 66,000 Selling Price (`) 23.00 18.00 13.00 Revised Sales (units) (upto production capacity) 60,500 24,200 72,600

35

Working Note-2 : Coco Stawberry Vanilla Ordering Cost (35/30/15 @ 800) 28,000 24,000 12,000 Delivery Cost (112/66/48 @ 700) 78,400 46,200 33,600 Shelf Stocking (130/150/160 @ 199) 25,870 29,850 31,840 Customer Support (60,500/24,200/72,600 @ 1.1)

66,550 26,620 79,860

TOTAL COST 1,98,820 1,26,670 1,57,300 No. of units 60,500 24,200 72,600 Cost per unit 3.29 5.23 2.17 Note: On calculation of total overhead costs under traditional & ABC system, costs are same i.e. `4,82,790, hence we will ignore the line “In ABC these costs are coming under customer support and assistance.” written in question.

(a) (i) The target cost of each product after reduction is computed as follows: Ans. 10:

Product Present Price (`)

Proposed Price (`)

Target Cost (`) (with 25% Margin)

A B C D

180 175 130 180

175 170 125 175

140 136 100 140

(ii) Statement showing cost/unit of Driver as per ABC

Cost Amount Driver No. Cost/unit of Driver

Set-ups 26,250 Production runs 105* `250.00 Stores receiving 18,000 Requisition 400** `45.00 Inspection/Quality 10,500 Production runs 105 `100.00 Handling/Dispatch 23,100 Orders 210 `110.00 Machine Department 52,130 Machine Hrs. 6,500 `8.02

* Production runs = (600/20) + (500/20) + (400/20) + (600/20) = 105

** Requisitions = 100 for each product or 400 total

Machine hours = 2,400 + 1,500 + 800 + 1,800 = 6,500 hours.

Statement showing Total Cost and Cost Per Unit as per ABC

Item A B C D ` ` ` ` Direct Material 24,000 25,000 12,000 36,000 Direct Labour 16,800 10,500 5,600 12,600 Set-up 7,500 6,250 5,000 7,500 Stores receiving 4,500 4,500 4,500 4,500 Inspection/Quality 3,000 2,500 2,000 3,000 Handling/Dispatch 6,600 5,500 4,400 6,600

36

Machine Dept. Cost 19,248 12,030 6,416 14,436 Total Cost 81,648 66,280 39,916 84,636 Output (Units) 600 500 400 600 Cost per unit 136.08 132.56 99.79 141.06

(iii) Comparison of Actual Cost and Target Cost

Cost A B C D ` ` ` `

Actual 136.08 132.56 99.79 141.06 Target 140.00 136.00 100.00 140.00 Difference (-) 3.92 (-) 3.44 (-) 0.21 (+) 1.06

Comment:

The total actual cost of A, B and C product is less than the target cost so there is no problem in reducing the cost of these product by `5 from the present price. It will increase the profitability of the company but the cost of D is slightly more than the target cost, it is therefore, suggested that the company should either control it or redesign it.

Ans. 11

: Working Notes: Particulars P Q

(a) Production/Sales Quantity (units) 1,00,000 50,000 (b) Batch Size (units) 1000 500 (c) No. of batches 100 100 (d) Set up time per batch (hours) 30 36 (e) Total set up hours (c d) (hours) 3,000 3,600 (f) Machine set up cost (`) 4,62,000 (g) Cost driver per machine set up hour

4,62,000 = `70 6,600

(h) Testing time per unit 5 hours 9 hours (i) Total testing time (a h) (hours) 5,00,000 4,50,000 (j) Testing cost

`23,75,000 (k) Cost driver per testing hour

23,75,000 = `2.50 9,50,000

(a) Computation of full cost per unit using Activity Based Costing:

Particulars Basis P Q Direct material Direct 42,00,000 30,00,000 Direct labour Direct 15,00,000 10,00,000 Direct machine cost Direct 7,00,000 5,50,000 Machine set up cost 3,000 hours @ `70 2,10,000

3,600 hours @ `70 2,52,000

37

Testing cost 5,00,000 hours @ `2.50 12,50,000 4,50,000 hours @ `2.50 11,25,000

Engineering cost Allocated 8,40,000 14,10,000 Total cost (`) 87,00,000 73,37,000 Cost per unit (`) 87.00 146.74

(b) Mark up on full cost basis for Product P: Particulars Per unit Selling price 100.05 Less: Full cost 87.00 Mark up 13.05

Percentage of mark up on full cost = 13.05 /87 = 15 % (c) Target cost of Product P after new design is implemented

Target price (given) 86.25

Mark-up 86.25 ×15 11.25 115

Target cost per unit (`) 75.00

(d) Statement of cost for new design of P

Particulars Basis Cost P.U. Total Cost

Direct Material Decreased by `5 p.u. 37.00 37,00,000 Direct Labour Decreased by `2 p.u. 13.00 13,00,000 Direct Machining cost No change as machine is 7.00 7,00,000

dedicated Machine set up cost 100 set up 28 hours `70 1.96 1,96,000 Testing cost 1,00,000 units `2.5 4 hours 10.00 10,00,000 Engineering cost No change 8.40 8,40,000 Total cost 77.36 77,36,000

The target cost is `75 p.u. and estimated cost of new design is `77.36 p.u. The new design does not achieve the target cost set by Computo Ltd. Hence the target mark up shall not be achieved.

(e) Possible Management Action: Value engineering and value analysis to reduce the direct material costs.

Time and motion study in order to redefine the direct labour time and related costs. Exploring possibility of cost reduction in direct machining cost by using appropriate techniques.

Identification of non-value added activities and eliminating them in order to reduce overheads.

The expected selling price based on estimated cost of `77.36 per unit is (`77.36 + 15%) `88.96. Introduce sensitivity analysis after implementation of new design to study the sales quantity changes in the price range of ` 86.25 to `88.96.

Ans. 12:

38

P1 P2 `/unit `/unit

Material 407.5 292.1 Overhead-Material handling 85×1.2 = 102 46×1.2 = 55.2 Assembly Management 40×3.2 = 128 40×1.9 = 76 Machine insertion 48×0.7 = 33.6 31×0.7 = 21.7 Manual insertion 36×2.1 = 75.6 25×2.1= 31.5 Quality testing 1.4×2 1.1×25 5 = 35 Present cost

= 27.5 781.70 504.00

Target cost 680.00 390.00

Revised P1

Revised P2 `/unit `/unit

Direct material 381.20 263.10 Overhead: Material handling (71×1.2) = 85.2 (39×1.2) = 46.8 Assembly hour (21×40) = 84.0 (1.6×40) = 64.0

Machine inspection (59×0.7) = 41.3 (29×0.7) = 20.30

Manual inspection (12×2.10) = 25.2 (10×2.10) = 21.00

Electronics (1.2×25) = 30.00 (0.9×25) = 22.50

Estimated cost 646.90 437.70

Target cost 680.00 390.00

Achieved not achieved Ans. 2

4: Machine X-Life 12 years Year Cost Discount Discounted

` Factor Cost ` Purchase price 0 19,000 1.00 19,000 Overhead cost 8 4,000 0.47 1,880 Trade-in-value 12 (3,000) 0.32 (960) Annual repair cost 1-12 2,000 6.81 13,620 33,540

Annualized equivalent =`33,540 / 6.81=`4,925 Machine W-Life 6 years

Year Cost Discount Discounted ` Factor Cost ` Purchase price 0 13,000 1.00 13,000 Overhead cost 4 2,000 0.68 1,360 Trade-in –value 6 (3,000) 0.56 (1,680) Annual repair cost 1-6 2,600 4.36 11,336 24,016

Annualized equivalent `24,601 / 4.36=`5,508 Recommendation : Purchase machine ‘X’ Assumptions:

a. Same performance, capacity and speed. b. No. inflation. c. 12 year-estimates are as accurate as 6 – year estimates.

39

d. Cash flow at the year end. Ans. 25Product design = `250 per design hour (`2m/8000 hours)

: The cost driver rates are as follows:

Purchasing = `50 per purchase order (`200000/4000 orders) Production (excluding depreciation) = `100 per machine hour ((`1 500000-`300000)/ 12000 hours) Packing =`20 per cubic meter (`400000/ 20000) Distribution =`5 per kg (`600000/ 120000) The activity –based overhead cost per unit is as follows:

Product design (400 design hours at `250 per hour=`100000 (`)

Divided by life –cycle output of 5000 units) 20.00 Purchasing (5 purchase orders at 50 units per order costing A total of `250 per output of 250 units) 1.00 Production (0.75 machine hours at `100 per machine hour) 75.00 Depreciation (Asset cost over life cycle of 4 years= 16 quarters Depreciation at `8000 per quarter divided by life cycle Output of 5000 units) 25.60 Packing (0.4 cubic meters at `20) 8.00 Distribution (3 kg at `5) Total costs

15.00

144.60

Ans. 26(i) So total cost for Electric immersion heater =`160 + 200X5 =`1160

: The total cost consists of the installation cost plus electrical charges for 5 years.

(ii) Total cost for a gas boiler =`760 + `80X5 =`1160 Hence, on the total cost basis, both the equipments have equal preference, and the housewife can choose any one. Let us now calculate the present value of money for each of the two possibilities. Year PV factor @

9% p.a Electric Immersion heater Gas Boiler

Operating Cost ` Discounted Cost ` Operating Cost `

Discounted Cost `

0 1.0000 160 160.00 760 760.00 1 0.9174 200 183.48 80 73.39 2 0.8417 200 168.34 80 67.33 3 0.7722 200 154.44 80 61.78 4 0.7084 200 141.68 80 56.67 5 0.6499 200 129.98 80 51.99 Total Cost=937.92

(`938,say) Total Cost

=1071.16 (`1071 say)

On the basis of present value @ 9% p.a over a period of five years, the total cost of Electric immersion heater is `938 and that of a Gas boiler is `1071. Hence, the housewife is advised to purchase an electric immersion heater. If the equipment are to be considered for a period of 8 years, then Total cost for electrical immersion heater =`160+200X8 =`1760 Total cost for gas boiler =`760+`80X8 =`1400 Hence, the housewife will be advised to purchase a gas boiler. Year PV factor @

9% p.a Electric Immersion heater Gas Boiler

Operating Cost ` Discounted Cost ` Operating Cost `

Discounted Cost `

6 0.5963 200 119.26 80 47.70 7 0.5470 200 109.40 80 43.76 8 0.5019 200 100.38 80 40.15 329.04 (329,say) 131.61 (`132

say)

40

Present value in case of electric immersion heater = P.V. over five years + P.V. over next three years =`938+`329 =`1267 Present value in case of gas boiler =`1071+`132 =`1203 Hence, over a 8 years period, the present value of a gas boiler is less. On the basis of total cost as well as present value of money, gas boiler is cheaper over 8 years period, hence the housewife is advised to purchase a gas boiler.

Ans. 2Purchase Cost (Cash outflow) (a)

7: Relevant Operating Cash outflow p.a. if part X 248 is outsourced 50000

Relevant Cash inflow from outsourcing: Direct materials 22000 Direct Labour 11000 Variable Overhead 7000 Product and Process engineering 4000 Rent Total Cash Savings (b)

1000

Net Cash Outflow (a) - (b) 45000 (5000)

Net Present Value of cash inflow if part is outsourced Particulars Year Amount ` P.V. factor @ 12% P.V ` Disposal value of machine 0 15000 1000 15000 Cash Outflow due to outsourcing 1 5000 0.893 (4465) 2 5000 0.797 (3985) 3 5000 0.712 (3560) 4 5000 0.636 (3180) 5 5000 0.567 NPV

(2835)

Analysis : Since the NPV is negative , it is desirable to manufacture the part internally. (3025)

Notes: (1) Equipment depreciation is a non- cash cost item. Therefore, it is not relevant. (2) Product and process engineering cost being avoidable hence relevant for the entire period of

outsourcing i.e. for 5 years. (3) Allocated rent is irrelevant but rent saved (i.e, `1000) is relevant. (4) Allocated general plant overhead is irrelevant.

(ii) Sensitivity analysis with respect to quantity is desirable:

If demand for the part decreases vendor is willing to supply a lower quantity at the same price (` 50/-).

If the part is continued to be made internally, the costs would not decrease quite fast with lower quantities because of fixed costs.

Net cash outflows of outsourcing will be smaller if lower quantities of the part are demanded. But if the demand increase, it would be preferable to make the part – in – house.

Non – financial factors:

Will the units of part required be delivered on schedule? Will quality be maintained? Can suggested modifications be really accommodated? Will the subcontractor remain in business for next five years?

(iii) As the outsourcing of part X – 248 will start from July ‘1998, the bonus of Gemini enterprises based on the accounting income, which Mr. Sen wishes to maximise will remain unchanged for the year 1997 - 98 Ans. 28Alternative I :Repairs to existing machine: (`)

: Evaluation of Alternative proposals

Cost of Repairs 19000 X 50 / 100 =`9500 Equivalent annual cost for 5 years (9500 / 3.791) 2506 Add: Running and Maintenance cost p.a net of tax (20000 X 50 / 100) Present value of cash outflows p.a

10000 12506

41

Alternative II : Replace the old machine Purchase cost of new machine 49000 Less: sale proceeds of old machine Net: Cash Outflow

5000

Equivalent annual cost for 10 years (44000 / 6.145) 44000 7160

Add: Running and maintenance cost p.a. net of tax (14000 X 50 / 100)

7000 14160

Less : Tax Saving on depreciation (49000 / 10 ) X 50 / 100 Present value of cash outflow p.a.

2450

Analysis : From the above analysis it is observed that alternative II i.e., replacement of old machine with a new machine is more profitable, since the cash outflow p.a. will decrease by `796 (i.e. `12506 – `11710 ) if old machine is replaced with new machine.

11710

42

Costing in Service Sector Ans. 8. Total Room days = No of rooms x Days in a year = 300 rooms x 365 days = 10,95,000 Rooms days = Rs. 50-Rs.10 = Rs.40

Dally contribution required per room (Rs.) Desired profit after tax Add Income Tax (Rs.6,00,000X40/60)

600000 400000

Desired profit before tax Add: Fixed cost

10,00,000 7,50,000

Total Revenue to be earned 17,50,000 No. of room days to be rented = Rs.17,50,000 / Rs.40 = 43.750 Room days No. of rooms to be rented to attain break- even = Rs.7,50,000 / Rs.40 = 18.750 Room days Ans 9: Room Occupancy days per annum Single rooms (180 rooms X 365days X85/100) 55845 Double rooms (60 rooms X 365 days X 85/100) 18615 Variable and Fixed cost p.a. Particulars Single rooms Double rooms Total Room occupancy days 55845 18615 Variable cost per day 300 500 Total Variable cost 16753500 9307500 26061000 Fixed cost per room day 500 780 Total Fixed cost 27922500 14519700 42442200 Margin of Safety desired at 20% of total revenue. Therefore, Break even should be at 80% of total revenue. Revenue at break even level = Variable cost + Fixed cost = 26061000+42442200 = Rs. 68503200 Desired total revenue to be = Rs. 68503200 X 100/80 = Rs. 85629000 (i) Computation of tariff per room day Single room days occupancy 55845 Double room days occupancy equivalent to single room day (18615X160/100) 29784 Total single room days 85629 Rent per single room day = Rs. 85620000/85629 room days = Rs. 1000 Rent per double room day = Rs. 1000 X 160/100 = Rs. 1600 Tariff per room for single room = Rs. 1000 X 100/80 = Rs. 1250 Tariff per room for double room = Rs. 1600 X 100/80 = Rs. 2000 (ii) Computation of increase in occupancy of the remaining single rooms days required to compensate the loss arising from the discount. Number of single rooms intends to reserve for corporate customers = 12 Occupancy days for reserved rooms = 12 rooms X 365 days X 85/100 = 3723 Discount given on room rent per day = Rs. 1000 X 10/100 = Rs. 100 Amount of revenue lost due to discounting = 3723 room days X 100 = Rs.372300 Contribution per day on a single room = Rs. 1000- Rs. 300 = Rs. 700 Increase in occupancy days required in single rooms = Rs. 372300/Rs. 700 = 532 days Ans. 10 Working Name: Calculation of occupancy (a) Single room occupancy p. a. ( 100 rooms X 365 days X 75/100) 27,375

43

(b) Double room occupancy p. a. ( 20 rooms X 365 X 75/1000) = 5475 Conversion of double room to single room occupancy ( 5,475 X 1.20)

6,570

Total 33,945 Statement of Rent chargeable to single room and double room per day Particulars Single Room Double room No. of occupancy days (a) 27,375 5,475 Costs per day Variable cost Fixed cost

Rs. 400 200

Rs. 500 250

(b) 600 750 Total (Rs.) (a) X (b) 1,64,25,000 41,06,250 (Rs.) Total Cost (Rs.1,64,25,000 + Rs.41,06,250) Add: 20% Margin safety on hire of room (Rs.25% 0n cost)

2,05,31,250 51,32,812

Total rental charges to be received 2,56,64,062 Room rent per day to be collected (Rs.) (a) Single Room (Rs.2,56,64,062 / 33,945) 756 (b) Double Room (Rs.756 X 1.20) 907 Profitability statement of restaurant (Rs.) Sales Revenue (Rs.1,00,000 X 365 days) 3,65,00,000 Contribution (30% of Rs.365 Lakhs) Less: Fixed cost p. a.

1,09,50,000 10,00,000

Profit 99,50,000 Profitability statement of sports centre (Rs.) Contribution p. a. (50 persons X Rs.50X 365 days) Less: Fixed Cost p. a.

9,12,500 5,00,000

Profit 4,12,500 Profitability statement of shopping arcade (Rs.) Contribution p. a. (Rs.50,000 X 12 months) Less: Fixed Cost p. a.

6,00,000 6,00,000

Profit Nil Ans. 11 (i) Income Statement of Kangan Resort for the next year

Rs.

Sales Revenue Lodging house room receipts (40 Rooms × 200 days Rs. 200 × 85%)

13,60,000

Shopping Arcade (40 Rooms × 2 persons × 200 days × Rs. 50 ×85%)

6,80,000

Restaurant (40 Rooms × 2 persons × 200 days) × Rs. 80 × 85%)

10,88,000

44

Total Sales Revenue 31,28,000 Less: Variable Cost Lodging house rooms (40 Rooms × 200 days × Rs. 30 × 85%)

2,04,000

Shopping Arcade (50% of Rs. 6,80,000) 3,40,000

Restaurant (60% of Rs. 10,88 ,000) 6,52,800 Total Variable Cost 11,96,800 Contribution (Total Sales Revenue – Total Variable Cost) 19,31,200 Less: Fixed Cost 10,00,000 Profit (Estimated) 9,31,200

(ii) Income Statement on the basis of reduced room rent

Rs.

Sales Revenue Lodging house room receipts (40 Rooms × 200 days Rs. 150 × 95%)

11,40,000

Shopping Arcade (40 Rooms × 2 persons × 200 days × Rs. 50 ×95%)

7,60,000

Restaurant (40 Rooms × 2 persons × 200 days) × Rs. 80 × 95%)

12,16,000

Total Sales Revenue 31,16,000 Less: Variable Cost Lodging house rooms (40 Rooms × 200 days × Rs. 30 × 85%)

2,28,000

Shopping Arcade (50% of Rs. 7,60,000) 3,80,000

Restaurant (60% of Rs. 12,16 ,000) 7,29,600 Total Variable Cost 13,37,600 Contribution (Total Sales Revenue – Total Variable Cost) 17,78,400 Less: Fixed Cost 10,00,000 Profit 7,78,400 The profitability decreases by 9,31,200 – 7,78,400 = Rs. 1,52,800. Hence reducing room rent proposal may not be accepted. Ans. 12 Estimated Income Statement for the coming year (Rs.) Revenue Hotel Room Rent (100 rooms X 250 days X Rs.150 X 75/100) Receipts from shop (100 rooms X 2 persons X 250 days X Rs.30 X 75/100) Receipts from Restaurant (100 rooms X 2 persons X 250 days X Rs.60 X 75/100)

28,12,500 11,25,000 22,50,000

(a) 61,87,500 Variable Cost Hotel Rooms (100 rooms X 250 days X Rs.25 X 75/100) Shops (Rs.11,25,000 X 50/100) Restaurant (Rs.22,50,000 X 55/100)

4,68,750 5,62,500

12,37,500 (b) 22,68,750

45

Contribution (a) - (b) Less: Fixed Costs

39,18,750 19,50,000

Estimated Profit 19,68,750 (a) Revised estimated income statement or the coming year ( if room rent reduced to Rs.125 per day to enhance occupancy to 90%) (Rs.) Revenue Hotel Room Rent (100 rooms X 250 days X Rs.125 X 90/100) Receipts from shop (100 rooms X 2 persons X 250 days X Rs.30 X 90/100) Receipts from Restaurant (100 rooms X 2 persons X 250 days X Rs.60 X 90/100)

28,12,500 13,50,000 27,00,000

(a) 68,62,500 Variable Cost Hotel Rooms (100 rooms X 250 days X Rs.25 X 90/100) Shops (Rs.13,50,000 X 50/100) Restaurant (Rs.27,00,000 X 55/100)

5,62,500 6,75,000

14,85,000 (b) 27,22,500 Contribution (a) - (b) Less: Fixed Costs

41,40,000 19,50,000

Estimated Profit 21,90,000 (b) Analysis: With the reduction in room rent from Rs.150 per day to Rs.125 the occupancy will increase to 90% which will result in increase of profit by Rs.2,21,250 (i.e, Rs.21,90,000- Rs.19,68,750). Ans. 13

(i) Occupancy: Single rooms 100 X 365 X 80/100=29,200 Double rooms 20 X 365 X 80/100 = 5,840

Variable costs: Single rooms (29,200 X 220) Double rooms (5,840 X 350)

64,24,000 20,44,000

84,68,000 Fixed Costs: Single rooms (29,200 X 120) Double rooms (5,840 X 250)

35,04,000 14,60,000

49,64,000 Total costs: 1,34,32,000

Margin of safety 20%, Break- even point 80% Sales at BEP = Total Costs =Rs.1,34,32,000 Total revenue = 1,34,32,000 X 100

80 =Rs.1,67,90,000 (Rs.)

Single rooms (29,200 X 1) Double rooms (5,840 X 1.25)

29,200 7,300

National single rooms/days 36,500 Rent per day per Single room = 1,67,90,000

36,500 = Rs.460

Rent per day per Double room =Rs.460 X 1.25 = Rs.575

(ii) Restaurant (a) Sales /day Rs.25,000 Contribution 30% Total contribution 25,000 X 30/100 = Rs.7,500 per day (Rs.)

Contribution p. a. (7,500 X 365) Fixed cost p. a.

27,37,500 8,00,000

46

Profit 19,37,500 (b) Sports centre (Rs.)

No. of persons /days Average contribution per person / day

50 15

Total contribution/day (50X 15) 750 (Rs.)

Total contribution/p. a. (750X 365) Fixed Overheads

2,73,750 4,00,000

Loss 1,26,250 (c) Shopping arcade Average contribution p.m. Rs.35,000 (Rs.)

Average contribution p. a. (Rs.35,000 X 12) Fixed expenses

4,20,000 4,00,000

Profit 20,000 Profit Statement (Rs.)

Hotel accommodation Rentals 1,67,90,000 Less: Costs 1,34,32,00 Restaurant Sports centre Shopping arcade

33,58,000 19,37,500 (1,26,250)

20,000 Total 51,89,250 (III) Reservation = 10 rooms X 365 X 80 /100 = 2,920 Rent = 2,920 X 460 =Rs.13,43,200 Discount 10% =Rs. 1,34,320 Total contribution of remaining rooms (Rs.) Single 90 X 365 X 80/100 X (460-220) Double 20 X 365 X 80/100 X (575-350)

63,07,200 13,14,000

Total 76,21,200 Increase in contribution required 76,21,200 + 1,34,320 = Rs.77,55,520

% occupancy = 7755520 80 81.417621200

(i.e. Current Occupancy level) × =

= Say 81.5% Alternatively,

% Increase in contribution required = 134320 100 1.76%7621200

× =

Current occupancy level = 80 Revised occupancy level = 101.76% of 80 = 81.41% = Say 81.5% (IV) Total profit per annum = Rs.51, 89,250 Capital recovery factor 3.79 Discounted income for 5 years Rs.1, 96, 67,257 Lease rent Rs.1, 75, 00,000 Hence lease not acceptable Ans 14: Calculation of variable cost Distance Distance X Y

47

One side distance 24 km 16 km Round trip 48 km 32 km Variable cost @ 0.80 per km Rs. 38.40 Rs. 25.60

Calculation of fixed cost Distance Distance X Y Actual running time for round trip distance at the Speed of 24 km per hour 120 Min 80 Min Filling time 40 Min 30 Min Empty time 40 Min 40 Min Total time 200 Min 150 Min Fixed cost @ Rs. 7.50 per hour Rs. 25 Rs. 18.75 Calculation of ton km Capacity 8 tones 8 tones Full load 24 km 16 km Tons km 192 128

Cost per ton km 192

2540.38 + = Rs. 0.33 128

75.1860.25 + = Rs. 0.347

Ans.15 Working notes:

(1) Total distance travelled (in 25 days) = 60 km.(two sides ) X 6 trips per day X 25 days = 9,000 km. (2) Total passenger km. = 9,000 km. X 20 seats = 1,80,000 passenger km. (3) Depreciation p.a. = Purchase price – Scrap value = (Rs.4,00,000-Rs.10,000) =Rs.78,000

5 Years 5 Years Statement suggesting fare per passenger – km (Rs.) Fixed Expenses Cost per annum Cost per annum Insurance Garage rent Road Tax Administrative charges Depreciation Interest on Loan Running Expenses Repair and maintenance Replacement of tyre-tube Diesel and oil cost (9,000 km. X Rs.5 Driver and conductor’s salary Total cost (per month) Add: Profit (20% of total revenue or 25% of total cost

15,000 9,000 3,000 5,000

78,000 10,000

1,20,000

10,000

1,250 300

45,000 5,000

61,550.00 15,387.50

Total Revenue 76,937.50 Rate per passenger – km =Rs.76,937.50/1,80,000 passenger km. =0.4274305 or 0.43 Paise

48

Ans.16 (i) Comparative cost sheet Particulars 10 Tonne Capacity

Trucks 8 Tonne Capacity Trucks

Total trips per day No. of days per month Total trips per month Tonnes carried per truck Capacity to be handed p.m. tones No .of trucks required No. of drivers (including relievers) Total km. run per truck per month (120 X 12) Total km. run by all trucks per month Km. per litre of diesel Diesel required ( Litres)

5 24

120 1,200

24,000 20 22

1,440 28,800

3 9,600

5 24

120 960

24,000 25 27

1,440 36,000

4 9,000

Monthly Sheet No. of Trucks 10 Tonne Capacity 20 10 Tonne Capacity

25 (a) Variable with km run Diesel @ Rs.10 per litre Oil and sundries Rs.10 per 100 km. Total (b) Variable with No. of trucks run Repairs & Maintenance Road Tax Drivers Salary Depreciation Total © Fixed Supervisor Mechanic Fitter Miscellaneous Expenses Total Grand Total Tonnage hauled Cost / Tonne

96,000

2,880 98,880

78,500 4,000

35,200 1,16,000 2,33,700

3,200 2,000 1,600 3,000 9,800

3,42,380 24,000

14.27

90,000

3,600 93,600

80,000 5,000

43,200 1,50,000 2,78,200

3,200 2,000 1,600 3,000 9,800

3,81,600 24,000

15.90 Cost/Tonne: 10 Tonne Trucks Rs.14.27 8 Tonne Trucks Rs.15.90 Hire charges Rs.18.00 Hence buy 10 tonne trucks.

(iii) Before taking final decision on purchase of trucks, on factor that may have to be given weight age is that we have assumed consistent operation of all the 20 trucks for 24 days in a month, transporting 24,000 tonnes without default for a period of five years. This aspect must be considered on the basis of past recorded of hiring trucks on day to day basis over a three y3ear period so that optimum calculations on saving get properly weighed down. Second issue that an immediate investment of Rs.86 lakhs in purchase of 20 tracks has to be made. This could be totally from own resources or totally out to borrowings or could be partly either way. For own investment technique of discounted cash flow is to be applied while is case of borrowings, recurrent interest cost as also initial cost of procuring the same has to be provided out of saving from year to year apart from meeting normal schedule of loan repayment. Net

49

saving works out to Rs.10.74 lakhs per annum on hauling of 24,000 tonnes for 12 months in comparison to hiring of trucks. Third issue is to compare return on investment of own funds made for procurement of trucks either fully or in part vis-à-vis return in alternate outlets. This is opportunity cost of capital will have to be given consideration. Decision will be made after considering all the above factors.

Ans. 17: Costs specific to booking operations:

Direct person’s salary 20,000

Mobile expenses 3,000 Conveyance 4,000 27,000

Share of other overheads:

Office space 4,000 General Telephone 2,400 Security/Maintenance 1,600 Miscellaneous Expenses 1,000 9,000

Total Cost allocated to the service 36,000

Average demand per month= 2500×3+1000×2+700×7

12=1200

Total cost per booking= Total cost per month

average booking per month=

360001200

=`30

Revenue per ticket = Rs. 30

Total revenue less total cost = 30 - 30 = 0

Assuming that other overheads will anyway exist even of the service is not provided, the manager can hope to achieve a profit of Rs. 30x 1,200 - 27,000 is Rs. 9,000 for the full year. Minimum average volume to set up the service will be the amount needed to recover the specific costs of this service, is 27,000 per month.

Minimum average bookings = 27,000 = 900 bookings 30

Ans.18 Working Notes:

(1) Calculation of requirement of trucks: No. of Trips X No. of working days in a month X No. of tones 10 tonne = 5 X 24 X 10 = 1,200 tonnes 8 tonne = 5 X 24 x 8 = 960 tonnes No. of trucks required to handle 24,000 tonnes 10 tonne trucks =24,000 tonnes/1200 tonnes = 20 trucks 8 tonne trucks =24,000 tonnes/960 tonnes =25 trucks (2) No. of drivers required: 10 tonne =20 trucks X 2 drivers =40 Drivers

50

8 tonne =25 trucks X 2drivers =50 Drivers (3) Total monthly depreciation: 10 tonne = 20 trucks X Rs.10,00,000 X 1 =Rs.3,33,333 5 years 12

8 tonne = 25 trucks X Rs.8,50,000 X 1 =Rs.3,54,167 5 years 12

(4) Diesel Required: (No. of km. X No. of trips X No. of days in month X No. of trucks) Diesel required =(6 km. X 10 trips X 24 days x 20 trucks )/No. km. per litre of diesel 10 tonne =(6 km. X 10 trips X 24 days x 20 trucks )/3. km. per litre =9,600 litres 8 tonne =(6 km. X 10 trips X 24 days x 25 trucks )/4. km. per litre =9,000 litres Comparative Cost Sheet (Rs.) Particulars 10 tonne 8 tonne Fixed charges (p.m.) Drivers salary(@ Rs.3,000 p.m) Staff Expenses Other fixed expenses (i) Operating and Maintenance charges Depreciation Diesel Cost Lubricants & Sundries Repairs & Maintenance (ii) Total Operating Cost (i) + (ii) Tonnage carried (tonnes) Cost per tonne

1,20,000

9,000 5,000

1,34,000

3,33,333 1,44,000

5,760 1,00,000 5,83,093 7,17,093

24,000 Rs.29.88

1,50,000

9,000 3,000

1,62,000

3,54,167 1,35,000

7,200 1,00,000 5,96,367 7,58,367

24,000 Rs.31.60

Analysis : From the above analysis it is observed that cost per tonne is lowest if 10 tonne trucks are used, and the cost of Rs.50 per tonne presently incurring is highest and it can be reduced to Rs.29.88 by using 10 tonne trucks. Ans.19 (a) Statement of operating income of Modern Airways operating between EXETOWN and WYETOWN (on each one way flight) Rs. Fare received (per flight): (A) 10,00,000 200 passenger × Rs. 5,000 Variable costs (per flight) Commission paid 80,000 Rs. 10,00,000 × 8% Food services 200 passengers × Rs. 200 40,000 Fuel costs 1,40,000 Total variable costs: (B) 2,60,000 Contribution (per flight): (C): {(A) – (B)} 7,40,000 Fixed costs (per flight): Fixed annual lease costs 5,30,000 Baggage handling (Fixed ground services) costs 70,000 Fixed salaries of flight crew ___40,000

51

Total fixed costs: (D) 6,40,000 Operating income (per flight): {(C) – (D)} 1,00,000 Rs. (b) Fare received (per flight): (X) 10,17,600 212 passenger × Rs. 4,800 Variable costs: Commission paid 81,408 Rs. 10,17,600 × 8% Food services 212 passenger × Rs. 200 42,400 Fuel costs 1,40,000 Total variable cost: (Y) 2,63,808 Contribution per flight: (Z): {(X) – (Y)} 7,53,792 Excess contribution due to lowering of fare: {(Z) – (C)} 13,792 [Refer to (a) part] (Rs. 7,53,792 – Rs. 7,40,000)

Modern Airways should lower its fare as it would increase it contribution towards profit by Rs. 13,792 per flight.

(C) Financial consideration of Modern Airways to Charter its plane to Zed Tours and Travel should use

option (b) and not (a). Rs. Under option (b) Modern Airways Receives contribution (per flight): 7,53,792 Modern Airways would get (per flight) 7,50,000 If it charters the plane A comparison of the above data clearly shows that the Modern Airways would be financially better off

by not chartering the plane. Other consideration with regard to chartering a plane to Zed Tours and Travels 1. The loss of contribution involved in chartering a plane is Rs. 3,792 (per flight). This loss is on a

lower side as compared with uncertainties about the number of passengers on scheduled fights.

2. modern Airways passengers may be inconvenienced when a plane is chartered to zed Tour

and Travel. They may go other airlines. 3. The relationship between the two parties is important. If it is not a long term arrangement.

Modern Airways may lose. Ans.20 Working Notes: Calculation operating capacity of a single aircraft =160 seats X 60/100 =96 passengers per flight (i) Calculation of net operating income per flight (Rs.) Fare collection (96 X 7000) Variable costs: Fuel Food (96 X 130) Commission @ 5% Total Variable costs Contribution per flight Fixed Costs: Lease 3,50,000

6,72,000

95,000 12,480 33,600

1,41,080 5,30,920

52

Crew 72,000 Net Income per flight

4,22,000 1,08,920

(ii) Evaluation of proposal if Occupancy increases to 108 passengers per flight and the fare reduced to Rs.6,720 (Rs.) Fare collection (108 X 6720) Variable costs: Fuel Food (108 X 130) Commission @ 5% Contribution

7,25,760

95,000 14,040 36,288

1,45,328 5,80,432

Analysis: The contribution will increase by Rs.49,512 (i.e Rs.5,80,432-Rs.5,30,920). Hence, it is suggested to accept the proposal (iii) Evaluation of proposal to charter the aircraft Current contribution Less: Fixed charge Loss:

5,30,920 5,00,000

30,920 Analysis: if the aircraft is given on charter, it will cause loss of contribution by Rs.30,920. Hence the proposal is not suggested. Ans. 21:

(i) With respect to the passenger, the only variable costs are : 10% Commission on fare Rs. 500 Food Rs. 300 Total variable cost/passenger Rs. 800

Revenue per passenger = gross fare = 5000

Contribution = 5000 – 800 = Rs. 4200

Total Contribution 4200 x 240 10,08,000 Less: Costs/flight

Fuel 90,000 Lease 2,00,000 Baggage 40,000 Flight Crew 48,000 3,78,000 Profit per flight 6,30,000

(ii) Cost per flight Rs. 3,78,000 are fixed in relation to the number of passengers.

B.E.= 3780004200

=90 passengers

Effect of Mid Air’s offer Rs

A to D Fare 2000 Less: Comm. 200

1800

53

Less:Snacks 300

Contribution per passenger 1500

Additional Cost ( Rs)

Additional Revenue

(Rs) 50 seats x 2500 ( D to B ) 1,25,000 Fuel 45,000 Baggage 19,000 Snacks @ Rs 200 for passenger ( 240 -25+ 50): 200 x [ 240 – 25 + 50 ] 53,000 Additional Contribution (A to D) 60 x 1500 90,000

Contribution lost (A to B) : 25 x 4200 ( opportunity cost) 1,05,000 2,22,000 2,15,000

Aero will loose Rs. 7,000 per flight if it accepts Mid Air’s offer.

Decision : Reject Mid Air’s offer. Ans.22 Calculation of variable cost per student of last year (Rs.lakhs) Revenue 1. Students tuition-75% (Rs.3,600 X 12,000 students) 2. Endowment & contribution-25% (Rs.432 lakhs X 25/75) Total revenue Less: Fixed cost Variable cost

432 144 576 300 276

Variable cost per student =Rs.2,76,00,000 12,000 students =Rs.2,300 per student (i) Calculation of amount available in the first year for capital improvements and building (Rs.lalhs) Revenue 1. Tuition Fee (Rs.4,200 X 11,200 students) 2. Endowment & contribution 3. Grant Total revenue Less: Variable cost (2,300 X 1.10 X 11200 students) Contribution Less: Fixed cost (Rs.300 lakhs + Rs.30 lakhs) Balance available for capital improvements and building

470.40 144.00

50.00 664.40 283.36 381.04 330.00

51.04 Calculation of break-even if the grant is received and costs increases as predicted for the coming year (Rs.lakhs) Variable cost (Rs.2,300 X 1.10 X 12,000 students) Fixed Cost (Rs.300 lakhs + Rs. 30 lakhs) Capital improvement Total cost Less: Endowment and contribution 144.00

303.60 330.00

40.40 674.00

54

Grant 50.00 Balance amount to be collected as tuition fee

194.00 480.00

Tuition fee to be collected per student = Rs.4,80,00,000 12,000 students =Rs.4,000 per student Ans.23 Working Notes: (i) Expected Variable cost this year (Re.per ride) Variable cost last year Add: Expected increase this year (25% of Re.0.80) Expected variable cost this year

0.80 0.20 1.00

(ii) Expected fixed costs this year (Rs.) Fixed cost last year Add: Expected increase this year (10% of Rs.32,00,000) Expected variable cost this year

32,00,000 3,20,000

35,20,000

(1) Rides which DD Amusement park sell last year (No. of rides DD sell last year) = Total Sales of rides last year =Rs.48,00,000 =12,00,000 rides Charges per ride last year Rs.4 (2) Expected net income for the year if price increase if not implemented (Rs.) Charges per ride Less: Expected Variable cost per ride Contribution per ride No. of rides Total expected contribution Less: Expected fixed costs Expected net income

4 1 3

12,00,000 36,00,000 35,20,000

80,000

(3)Price indifference point for the new ride Price indifference point is a point at which the expected profits remains the same irrespective of sales price and costs. (Rs.)

New ride price Less: Variable cost Contribution per ride Fixed Costs of this year Net Income of last year Contribution require

5.00 1.00 4.00

35,20,000 6,40,000

41,60,000

Price- Indifference point = Rs.41,60,000 =10,40,000 rides Rs.4

(4) Break –even point for this year using the old price and the new price Break-even point = Fixed costs

Contribution per ride At old price = Rs.35,20,000 =11,73,334 rides Rs.4-Re.1 At New price = Rs.35,20,000 =8,80,000 rides

55

Rs.5-Re.1 (5) Expected net income if the price increase will reduce ride volume by 10% from the last year’s levels (Rs.)

Charges per ride Less: Variable cost Contribution per ride: (a) No. of rides (12,00,000-1,20,000): (b) Total contribution for all rides: (a) X (b) Less: fixed costs Expected net income

5.00 1.00 4.00

10,80,000 43,20,000 35,20,000

80,000 Justification: Since the increase in price of a ride will increase the net income by Rs.1,60,000(Rs.8,00,000-Rs.6,40,000) the management should raise the price of a ride. Ans 24: (1) Total number of patients attended

Number of patients attended per day by a physician: 20 Number of physicians employed 6 Number of days in week 6 Number of weeks in a year 52 Total number of patients attended = 20×6 ×6×52 = 37,440. (2) Patient Mix: Adults (50%) 37,440 ×50/100 = 18,720 Children (40%) 37,440 ×40/100 = 14,976 Senior Citizens (10%) 37,440 ×10/100 = __3,744 37,440 (3) Patient Appointments: No treatment required (70%) 37,440 ×70/100 = 26,208 Minor treatment (20%) 37,440×20/100 = 7,488 Major treatment (10%) 37,440 ×10/100 = ___3,744 37,440 (4) Income from Insurance Companies: Number of Rs. Rs. patients (A) (B) (A×B) No treatment patients 26,208 60 15,72,480 Minor treatment patients 7,488 250 18,72,000 Major treatment patients 3,744 500 18,72,000 Total 53,16,480 (5) Co-payment from adult patients: Number of Payment Total Patients Rs. Payment (Rs.) Total number of adult patients 18,720 No treatment patients (70%) 13,104 60 7,86,240 Minor treatment (20%) 3,744 250 9,36,000 Major treatment (10%) 1,872 500 9,36,000 Total 26,58,240

56

(6) Net income: Rs. Rs. Payment from Insurance companies 53,16,480 Co-payment from adult patients 26,58,240 Total 79,74,720 Other Income (fixed) 2,25,280 Total Income (A) 82,00,000 Less: Expenditure Variable expenses: Material and consumables 22,32,000 Fixed expenses: Physician’s salary (6 ×4,50,000) 27,00,000 Assistants salary (7 ×1,50,000) 10,50,000 Administrative staff’s salary (2 ×90,000) 1,80,000 Establishment and other operating costs 16,00,000 55,30,000 Total Expenditure (B) 77,62,000 Net Income (A – B) __4,38,000

(ii) 1. Contribution Analysis: (Rs.) Total Fees from Insurance Companies and adult patients 79,74,720 Less: Variable costs 22,32,000 Contribution 57,42,720 Average contribution per patient (57,42,720÷37,440) 153.38 2. Break-even patients: (Rs.) Fixed costs 55,30,000 Less: Fixed income 2,25,280 Net Fixed costs 53,04,720 Break-even patients = (Net fixed costs÷ Contribution per patient) = (53,04,720÷ 34,585) 153.38 3. Percentage of maximum capacity required to be utilized in order to break-even

Present utilization = patientspatients

2420

= 83.33% = 37,440

100% patient capacity is 37,440 ÷0.8333 =44,930 patients Percentage of maximum capacity required to be utilized in order to break-even

Break Even patients ÷100% patients capacity ×100 = {(34,585÷ 44,930)×100 } = 76.98% say 77%. Assumption: Patient mix and mix of patient appointments will be same in the next year.

57

Ans 25

(a) Statement of Total Cost

Total cost Amount (Rs)

Salary of Supervisor , Nurses, Ward boys

4,25,000

Repairs and Maintenance 90,000 Salary of doctors 13,50,000 Food supplied to patients 40,000 Laundry charges for their bed linens 80,500 Medicines supplied 74,000 Cost of oxygen, X ray etc, other than directly borne for treatment of patients

49,500

General administration charges 63,000 Rs 21,72,000 Building rent (10 ×

12,000) Rs 1,20,000

Additional building rent on takings 5% on Total Taking Hire charges extra beds Rs 12,000 Fees to heart specialists (3 × 15,000) Rs 45,000 Total cost Rs 23,49,000 + 5% on

Total Taking Profit 20% on Total Taking Total takings Rs 23,49,000 + 25% of

Total Taking Total taking(assuming X to be the rent per day)

1,05,000 × X

Rent to be charged 1,05,000 × X = 23,49,000 +25% (1,05,000 × X) = 78750 X = 23,49,000 or X = 29.83(Rounded Off)

No of beds with Equivalent Rent

Nature of wards Occupancy Weight of rent

Ward Days

General ward 100 × 360 × 100%

36,000 × 1 36,000

Additional general ward

20000,12

600 × 1 600

Cottage ward 50 × 360 × 80% 14,400 × 2.5 36,000 Deluxe ward 50 × 360 × 60% 6,480 × 5 32,400 Total 1,05,000 Rent to be charged

Particulars Basic Service tax Total General ward 29.83 2.39 32.22

58

Cottage ward 74.58 5.97 80.55 Deluxe ward 149.15 11.93 161.08 Note : You may assume Total Taking to include Service Tax also.

Rent = 23,49,000 + 25% × (1,05,000 X × 1.08) + 0.08 × (1,05,000X ) = 1,05,000X × 1.08

= 23,49,000 + 28350X + 8400X = 1,13,400X

Therefore X = Rs 30.65

Rent to be charged

Particulars Basic Service tax Total General ward 30.65 2.45 33.10 Cottage ward 76.63 6.13 82.76 Deluxe ward 153.25 12.26 165.51

59

Standard Costing

Working Notes Ans.2

(1) For actual (standard) output of 85 kgs. Std. Input is 100 kgs.

For actual output of 1,700 kgs. the Std. input = 100 1700

85kgs kgs

kgs×

=2,000 kgs.

(2) 2,000 kgs of standard input for an actual output of 1,700 kgs. Contains the Materials A and B in the proportion of (40:60) i.e., 800 kgs. of A and 1,200 kgs. of Material B. (3) Actual Material consumption for 1,700 kgs. of actual output (Kgs.) Particulars Materials A B Stock on 1-9-2004 Add: Purchase during Sept. 2004 Less: Stock on 30-09-2004 Material consumed during Sept.2004

35 800 835

5 830

40 1,200 1,240

50 1,190

(4) Calculation actual purchase price per kg. of material

A = .3400 .4.25

800Rs Rs

kgs= B =

.3000 .2.501200Rs Rs

kgs=

Statement shoeing Standard and Actual Cost of Actual output Material Standard Actual Quantity

Kg. Rate Rs.

Amount Rs.

Quantity Kg.

Rate Rs.

Amount Rs.

A B Loss Output

800 1,200 2,000 300 1,700

4 3

3,200 3,600 6,800

35830

795

401190

1150

2,020 320 1,700

4.004.25

3.002.50

140.00 3,378.75 120.00 2,875.00 6,513.75

Calculation of Material Variances (a) Material price variance Actual quantity (Std. price – Actual Price) A = [35 (4 – 4)] + [ 795 ( 4 – 4.25)] =Rs.198.75 (A) B = [40 ( 3 – 3)] +[1,150 ( 3 – 2.50 )] =Rs. 575 (F)

=Rs.376.25 (F)

(b) Material Usage variance Std. rate (Std. quantity – Actual Quantity) A = 4 (800 – 830) =Rs.120 (A) B = 3 (1,200 – 1,190) =Rs. 30 (F) =Rs.90 (A) (c) Material Yield Variance Std. rate of output (Actual yield – Std. Yield) =[Rs.6,800 1,700

x ( 1,700 kg. – 1,717 kg.)] =Rs.68 (A)

* Std. Yield = Actual std Output Actual inputStd. Input

× = 85 2020 1717100

kgs kgs kgskgs

× =

(d) Material Mix Variance Actual Quantity ( Std. cost of Std. mix per kg. – Std. cost of actual mix per kg. )

60

= Rs. 6800 Rs. 6890*2020 kgs 2000 kgs 2020 kgs

−

=Rs.22(A)

*[(830 kgs. x Rs.4)] + [(1,190 kgs x Rs.3 )] =Rs.6,890 (e) Total Materials Cost Variance Std. Cost – Actual Cost =Rs.6,800 – Rs.6,513.75 =Rs.286.25 (F) Summary of Material variance (Rs.) Price variance Usage variance 1. Yield variance 68 (A) 2. Mix variance Total Material cost variance

22 (A)

376.25 (F)

90 (A) 286.25 (A)

Ans. 3:

Working Note:

Standard cost Actual cost Revised std.quantity Component Qty. Rate Amount

Kg. Rs. Rs. Qty. Rate Amount Kg. Rs. Rs.

Oty. Kg.

A B

48 10 480

112 30 224

72 12 864 (B.F.) 108 8 864

54 126

Total Input (-) Loss

160 704 16(10%)

180 1728 36

180

Total output 144 144 5,360 — Solution

(i) Mix variance = Std. price (Revised Std. quantity – Actual quantity) A: 10 × (54-72) = 180 (A) B: 2 × (126-108) =

36 (F) 144 (A)

(ii) Yield variance = Std. price of yield (Actual yield – Std. yield for actual mix)

= Rs. 880180

× (144 –180×90%) = Rs. 88 (A)

(iii) Price variance =Actual qty. (Std. price – Actual price.) A: 72 × (10-12) = 144 (A) B: 108 × (2-8) =

648 (A) 792 (A)

(iv) Total usage variance = Std. price (Std. qty. – Actual qty.)

A: 10 × (48-72) = 240 (A) B: 2 × (112-108) =

8 (F)

232 (A)

Ans. 4: Take the good output of 182 kgs. The standard quantity of material required for 182 kg. of output

61

is 182 100 202.2290

× =

Statement showing the standard and actual costs and standard cost of actual mix

Standard cost Actual cost Revised std.quantity Component Qty. Rate Amount

Kg. Rs. Rs. Qty. Rate Amount Kg. Rs. Rs.

Oty. Kg.

A (40% of 202.22 kg.) B (60% of 202.22 kg.)

80.89 60 4,853.40

121.33 30 3,639.90

90 18 1,620 110 34 3,740

80 120

Total Input (-) Loss

202.22 8,493.30 20.22

200 5,360 18

200

Total output 182.00 182 5,360 — Standard yield in actual input is 90 % of 200 kg. i.e. 180 kg.

Variances :

(i) Price variance =Actual qty. (Std. price – Actual price.) A: 90 × (60-18) = 3780 (F) B: 110 × (30-34) =

440 (A) 3340 (F)

(ii) Total usage variance = Std. price (Std. qty. – Actual qty.)

A: 60 × (80.89-90) = 546.60 (A) B: 30 × (121.33-110) =

339.90 (A) 206.70 (A)

(iii) Mix variance = Std. price (Revised Std. quantity – Actual quantity)

A: 60 × (80-90) = 600 (A) B: 30 × (120-110) =

300 (F) 300 (A)

(iv) Yield variance = Std. price of yield (Actual yield – Std. yield for actual mix)

= Rs. 8493 30182

. × (182 – 182 200202 22.

× ) = Rs. 93.30 (F)

(v) Total variance = Std. cost – Actual cost = Rs. 8,493.30 – Rs. 5,360 = Rs. 3133.30 (F)

Note : (iii) and (iv) above are subparts of total usage variance Proof : Price variance + Mix variance + Yield variance = Total variance

Rs. 3340 (F) + Rs.300 (A) + Rs. 93.30 (F) = Rs. 3133.30 (F) Ans. 5: (i) Since the actual output is 1,000 units, the standard quantity of materials required for the actual

output is 1,000 units × 4 kgs. = 4,000 kgs.

Working Notes :

(ii) Statement showing computation of standard cost, standard cost of actual quantity and actual cost.

62

Material Std. cost per Kg.

Rs.

Actual cost per Kg.

Rs.

Std. qty in Kgs.

Actual qty in Kgs.

Std. cost (Std. qty × Std. price) Rs.

Std. cost of actual qty. (Actual qty. × Std. price) Rs.

Actual cost (Actual qty. × Actual price) Rs.

a b c d e = a×c f = a×d g = b×d

A B C D

1.25 1.50 3.50 3.00

1.30 1.80 3.40 3.00

1,200 1,600

800 400

1,180 1,580

830 440

1,500 2,400 2,800 1,200

1,475 2,370 2,905 1,320

1,534 2,844 2,822 1,320

4,000 4,030 7,900 8,070 8,520

(iii) Standard cost per unit of the standard mix Rs. 7,900

= 4,000 Kgs. = Rs.1.975

(iv) Standard cost per unit of the actual mix = .8070 .2.002

4030Rs Rs

kgs=

Variances:

(i) Price variance = Actual qty. (Std. price – Actual price) = Rs.8,070 – Rs. 8,520 = Rs. 450 (A) (ii) Mix variance = Total actual qty. (Std. cost per unit of

std.mix – Std. cost per unit of actual mix) = 4,030 Kgs. (Rs. 1.975 – Rs. 2.002) = Rs. 110 (A) (iii) Sub usage variance = Std. price per unit of std. mix (Total std. qty –

Total actual qty.) = Rs. 1.975 (4,000 – 4,030) = Rs. 60.00 (A)

(iv) Total material cost variance = Std. cost – Actual cost = Rs. 7,900 – Rs.8,520 = Rs. 620 (A)

Proof : Price variance + Mix variance + Sub-usage variance = Total variance Rs. 450 (A) + Rs. 110 (A) + Rs. 60 (A) = Rs. 620 (A)

Note : ‘Mix variance’ and sub usage variance are sub-part of total usage variance which may be calculated as below:

Usage variance = Std. price (Std. qty. – Actual qty.) = Standard cost – Standard cost of actual quantity = Rs. 7,900 – Rs. 8,070 = Rs. 170 (A)

Basic data for calculation of Labour variances Ans.6

Category of Workmen Standard Actual Weeks Rate

Rs. Amount Rs.

Weeks Rate Rs.

Amount Rs.

Skilled Semi – Skilled Unskilled

3,000 1,200 1,800

60 36 24

1,80,000 43,200 43,200

2,560 1,600 2,240

65 40 20

1,66,400 64,000 44,800

Total 6,000 2,66,400 6,400 2,75,200

63

Calculation of Labour variances (1) Direct Labour Cost Variance Std. cost for actual output – Actual Cost

=2,75,200 – 2,66,400 =Rs.8,800 (A)

(2) Direct Labour Rate Variance Actual time (Std. rate – Actual rate)

Skilled = 2,560 (60 – 65) =Rs.12,800 (A) Semi – Skilled =1,600 (36 – 40) =Rs. 6,400 (A) Unskilled =2,240 (24 – 20) =Rs. 8,960 (F)

=Rs.10,240(A)

(3) Direct Labour Efficiency Variance Std. rate ( Std. time for actual output – Actual time)

Skilled =60(3,000 -2,560 ) =Rs.26,400 (F) Semi – Skilled =36 (1,200 -1,600) =Rs.14,400 (A) Unskilled =24 (1,800 – 2,240) =Rs.10,560(A)

Direct Material efficiency Variance can be further analysed into: =Rs.1,440(F)

(a) Direct Labour Mix Variance Std. rate ( Revised Std. time – Actual time)

Skilled =60(3,200 -2,560 ) =Rs.38,400 (F) Semi – Skilled =36 (1,280 -1,600) =Rs.11,520 (A) Unskilled =24 (1,920 – 2,240) =Rs. 7,680 (A)* Revised Std. time

=Rs.19,200 (F)

Skilled =6,400 6,000

x 3,000 =3,200

Semi- skilled =6,400 6,000

x 1,200 =1,280

Unskilled =6,400 6,000

x 1,800 =1,920

(b) Direct Labour Revised Efficiency variance Std. rate ( Std. time for actual output –Revised Std. time)

Skilled =60(3,000 -3,200 ) =Rs.12,000 (A) Semi – Skilled =36 (1,200 -1,280) =Rs. 2,880 (A) Unskilled =24 (1,800 – 1,920) =Rs. 2,880 (A)

Summary of Labour variances (Rs.) =Rs.17,760(A)

Rate variance Efficiency variance (a) Mix variance 19,200 (F) (b) Revised efficiency variance 17,760 (A) Direct Material cost variance

10,240 (A)

1,440 (F) 8,800 (A)

Ans. 7:

Gang: -

In a 40 hour week, the standard gang should have produced 1,000 std. hours as shown below:

Skilled 16 No. of workers × 40 hrs. 640 Semi - skilled 6 No. of workers × 40 hrs. 240 Unskilled 3 No. of workers × 40 hrs. 120

64

1,000 hours

However, the actual output is 900 standard hours. Hence to find out the total labour cost variance, the standard cost (or cost charged to production) is to be computed with reference to 900 standard hours. This is done in the following statement:

Statement showing the Standard cost, Actual cost and Standard cost of Actual time for Actual output, i.e. 900

Standard hours.

Gang Standard cost

Hours Rate Amount Rs. Rs.

Actual cost

Hours Rate Amount Rs. Rs.

Standard cost of Actual time Hours Rate Amount

Rs Rs. Skilled

600 9001000

× 576 3 1,728

Semi-skilled 240 900

1000 × 216 2 432

Unskilled 120 900

1000 × 108 1 108

14×40 = 560 4 2,240

9 × 40 = 360 3 1,080

2 × 40 = 80 2 160

560 3 1,680

360 2 720

80 1 80

900 2.52 2,268 1,000 3.48 3,480 1,000 2.48 2,480

Variances:

(i) Rate variance = Actual time (Std. rate – Actual rate) = (Standard cost of actual time – Actual cost) = Rs. 2,480 – Rs.3,480 = Rs. 1,000 (A) (ii) Gang variance = Total actual time ( Std. rate of std. gang–

Std. rate of actual gang)

= 1,000 (Rs. 2.52 – Rs. 2.48) = Rs. 40(F) (iii) Sub-efficiency variance = Std. rate (Total std. time – Total actual time)

= Rs. 2.52 (900 hours – 1,000) = Rs. 252 (A) (iv) Total labour cost variance = Std. labour cost – Actual labour cost

= Rs. 2,268 – Rs. 3,480 = Rs. 1,212 (A) The gang composition variance may also be known as labour mix variance and is part of efficiency variance which may be computed as under:

Efficiency variance = Std. rate (Std. time – Actual time) = Standard cost – Std. cost of actual time = Rs. 2,268 – Rs. 2,480 = Rs.212 (A)

Ans. 8:

(1,000 units× 2.5 hours × Rs.2) Standard cost charged to production Rs. 5,000

Actual wages paid Rs. 4,500 Actual wage rate per hour (Rs. 4500÷2000) Rs. 2.25 Std. wage rate per hour Rs. 2.00 Abnormal idle time (25% of 2,000 hours) 500 hrs. Variances :

(i) Wage rate variance = Actual time (Std.rate – Actual rate)

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= 2,000 hours (Rs.2 – Rs.2.25) = Rs.500 (A) (ii) Efficiency variance = Std. rate (Std.time – Actual time*)

Rs.2 (2,500 hrs. –1500 hrs.) = Rs. 2,000 (F) (iii) Idle time variance = Idle time × Std.rate

= 500 hrs. × Rs. 2 = Rs. 1,000 (A) (iv) Total variance = Std.labour cost – Actual labour cost

Rs. 5,000 – Rs. 4,500 = Rs. 500 (F) *Actual time less idle time.

Basic data for Standard and actual labour cost of producing 1,000 articles of ‘A’ and standard cost of actual labour hours

Ans.9

Standard Cost Actual Cost Labour Hours Rate

Rs. Amount Rs.

Hours Rate Rs.

Amount Rs.

Std. cost of actual labour hours ( Actual hours x Std. rate)Rs

Skilled Semi – Skilled Unskilled

10,000 8,000 16,000

3.00 1.50 1.00

30,000 12,000 16,000

9,000 8,400 20,000

4.00 1.50 0.90

36,000 12,600 18,000

27,000 12,600 20,000

Total 34,000 58,000 37,400 66,600 59,600 Calculation of Labour variances (1) Labour Cost Variance Std. cost – Actual Cost

=Rs.58,000 – Rs.66,600 =Rs.8,600 (A) (2) Labour Rate Variance

Actual Hours (Standard rate – Actual rate) OR Std. cost of actual hours – Actual Cost =Rs.59,600 – Rs.66,600 =Rs.7,000 (A)

(3) Labour Efficiency Variance Std. rate of Std. mix (Total Std. hours for actual output – Total Actual hours)

= ( )Rs. 58000 34000 3740034000

− =Rs.5,800(A)

(4) Labour Mix Variance Total actual hours ( Std. rate of standard mix – Std. rate of actual mix)

= 58000 596003400034000 37400

−

=Rs.4,200(F)

Summary of Labour variances (Rs.) Rate variance Efficiency variance Mix variance Labour Cost variance

7,000 (A) 5,800 (A) 4,200 (F) 8,600 (A)

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Ans. 10: = (Standard variable overhead – Actual variable overhead)

(i) Variable overhead variance:

= (Rs. 2,40,000 – Rs. 2,00,000) = Rs. 40,000 (Favourable) (Refer to Working note 1)

(ii) Variable overhead budget variance: = (Budgeted variable overhead for actual hours – Actual variable overhead) = Rs. 2,24,000 – Rs. 2,00,000 = Rs. 24,000 (Favourable) (Refer to Working note 2)

(iii) Variable overhead efficiency variance:

= Standard variable overhead rate per hour [Std. hours for actual output – Actual hours] = Rs. 2 [1,20,000 hours – 1,12,000 hours] = Rs.2 × 8,000 hours = Rs. 16,000 (Favourable)

Working notes: (1) Standard variable overhead = Standard cost of actual output = 20,000 units × 6 hours × Rs. 2

= Rs. 2,40,000

(2) Budgeted variable overhead (for actual hours)

= 1,12,000 hours × Rs.2 = Rs.2,24,000 Ans. 11:

Actual output = 9,000 units Idle time = 5,000 hours

Production time (Actual) = 1,05,000 hours Standard hours for actual production = 10 hours / unit × 9,000 units = 90,000 hours.

Labour efficiency variance = 3,75,000 (A)

i.e. Standard rate × (Standard Production time – Actual production time) = 3,75,000(A).

SR (90,000 – 1,05,000) = – 3,75,000

SR = − 3,75,000 = Rs. 25

− 15,000

(i) Idle time variance = 5,000 hours × 25 Rs. / hour = 1,25,000. (A) (ii) Standard Variable Overhead = Rs. 150 / unit

Standard hours = 10 hours / unit

Standard Variable Overhead rate / hour = 150 / 10 = Rs. 15 / hour

Total Variable Overhead variance = Standard Variable Overhead – Actual Variable Overhead = Standard Rate × Standard hours – Actual rate × Actual hours = (15) × (10 × 9,000) – 16,00,000

= 13,50,000 – 16,00,000

Total Variable Overhead Variance = 2,50,000 (A)

(iii) Variable Overhead Expenditure Variance = (Standard Rate × Actual Hours) – (Actual Rate × Actual Hours) = (15 × 1,05,000) – 16,00,000

= 15,75,000 – 16,00,000

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= 25,000 (A) (iv) Variable Overhead Efficiency Variance = Standard Rate × (Standard Hours for actual output – Actual hours for Actual output)

= 15 (90,000 – 1,05,000) = 15 (–15,000) = 2,25,000 (A)

(b) Alternative Solution

Actual Output = 9,000 Units Idle time = 5,000 hrs Direct Wages Paid = 1,10,000 hours @ Rs. 22 out of which 5,000 hours being idle, were not recorded in production. Standard hours = 10 per unit. Labour efficiency variance = Rs. 3,75,000 (A) or

Standard Rate (Standard Time – Actual Time) = – 3,75,000

Or Standard Rate = Rs 25/- (i) Idle time variance = Standard Rate × Idle time 25 × 5,000 = Rs 1,25,000 (A)

(ii) Standard Variable Overhead / unit = 150

Standard Rate = 150 = Rs.15/hour

10 Standard Quantity = 10 hours Actual Variable Overhead = 16,00,000 Standard Variable Overhead = 150 × 9,000 = 13,50,000

Actual Variable Overhead = 16,00,000 Total Variable Overhead Variance = 2,50,000 (A) (iii) Variable Overhead expenditure

= Standard Variable Overhead for

actual hours – Actual Variable Overhead = (150 × 1,05,000) – 16,00,000

= 15,75,000 – 16,00,000

= 25,000 (A)

(iv) Variable overhead efficiency variance = Standard Variable Overhead for actual output – Standard Variable Overhead for Actual hours)

= 15 (10 hours × 90,000 units – 1,05,000)

= 15 (90,000 – 1,05,000)

= 15 (–15,000) = 2,25,000 (A)

Standard Cost

Ans.12: Computation of standard cost and actual cost

Direct Materials (6,000 x Rs.12) Direct Labour (6,000 x Rs.4.40) Variable Overheads (6,000 x Rs.3) Total standard Costs (a) Actual Costs Direct Materials (12,670meters x Rs.5.70)

72,000 26,400 18,000

1,16,400

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Direct Wages Variable Overheads Total Actual Costs (b) Total Variance (a)-(b)

72,219 27,950 20,475

1,20,644 4,244,(A)

Computation of Missing figures

(1) Actual Labour hours Standard variable overhead rate hour (Standard hours – Actual hours) = Rs.1,500 (A) Rs.1,500 A =Rs.3 (6,000 x 1 hour – Actual hours) Rs.1,500 A =Rs.18,000 –(Rs.3 x actual hours) (Rs.3 x Actual hours) =Rs.18,000 + Rs.1,500 Actual hours =Rs.19,500 / 3 = 6,500 hours (2) Actual Wage rate hour = Actual wages paid =Rs.27,950 Total Actual hours 6,500 hours

=Rs.4.3

Computation of Material Labour and Variable Overhead Variances 1. Material variances

(1) Material Cost Variance Standard Cost- Actual Cost =(Rs.72,000 – Rs.72,219) =Rs.219 (A)

(2) Material Price Variance Actual Quantity of Material consumed (Std, price- Actual Price) =12,670 meters (Rs.6- Rs.5.70) =Rs.3,801 (F)

(3) Material Usage Variance Standard price (Standard Quantity –Actual Quantity) =Rs.6 (12,000 metres -12,670 metres) =Rs.4,020 (A) 2. Labour Variances

(1) Labour Cost Variance Standard Cost- Actual Cost =(Rs.26,400 – Rs.27,950) =Rs.1,550 (A)

(3) Labour Rate Variance Actual hours (Std. wage rate per hour- Actual wage rate per hour) =6,500 hours (Rs.4.40- Rs.4.30) =Rs.650 (F)

(3) Labour Efficiency Variance Standard rate per hour (Standard hours –Actual hours) =Rs.4.40 (6,000 hours- 6,500 hours) =Rs.2,200 (A) 3. Variable Overhead Variances

(1) Total Variable overhead Variance Standard Variable Overhead- Actual Variable Overhead =Rs.18,000 – Rs.20,475 =Rs.2,475 (A)

(4) Variable overhead Efficiency Variance Standard Variable overhead rate per hour (Std. hours for actual output-Actual hours) =Rs.3 ( 6,000 – 6,500) =Rs.1,500 (A)

(3) Variable overhead Budget Variance Budgeted variable overhead –Actual variable overhead) =(Actual hours worked x Std. variable overhead per hour) – Actual variable overhead =(6,500 x Rs.3 ) – Rs.20,475 =Rs.975 (A) Note: (F) denoted Favourable Variance; (A) denoted Adverse Variance

Working Notes : Ans 13:

1. Standard cost of raw-material consumed : Rs. Rs. Total standard cost of ZED (1,000 units × Rs.21) 21,000 Less: Standard cost : Labour 8,000

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Ov er h ead s 1,600 9,600 Standard cost of raw materials used 11,400

2. Standard cost of raw–material per finished unit.

3. Standard quantity of raw - material per finished unit and total quantity of raw material required:

Total quantity – 3.8 kg. × 1,000 units = 3,800 kgs.

4. Total material cost variance : Actual cost of raw material Rs.10,000 Standard cost of raw material Rs.11,400 Total material cost variance Rs. 1,400 (F)

5. Actual quantity (A Q) of raw–material (in kgs): Material usage variance = Standard rate (Standard quantity – Actual quantity). or, Rs. 600 (A) = Rs. 3 (3,800 Kgs. – AQ) or, 3AQ = 12,000 kgs. or, AQ = 4,000 kgs.

(Material usage variance is as given in the question and standard quantity is as per (3) above )

6. Actual rate of raw material per kg

7. Standard direct labour rate Standard direct labour hours = 1,600 (given) Standard direct labour cost = Rs. 8,000 (given)

8. Actual labour cost and actual labour rate per hour:

Actual total cost of 1,000 units Rs. 21,070 1,000 units (Rs. 21 + Re. 0.07)

Less : Actual cost of material Rs. 10,000 Actual variable overheads Rs. 1Rs. 1,62 Actual direct labour cost

1,620 Rs. 9,450

9. Standard labour hours to produce one unit:

10. Standard labour cost per unit:

Standard labour cost per unit = 1.6 hours × Rs. 5 = Rs.8

11. Actual hourly rate of variable overheads

: (a) Standard qu antity of raw material per unit of ZED : 3.8 kg. (Refer to working note 3). (b) Standard direct labour rate per hour Rs. 5 (Refer to working note 7).

70

(c) Standard direct material cost per unit of ZED : Rs. 11.40 (Refer to working note 2 ) . (d) Standard direct labour cost per unit of ZED: Rs. 8 (Refer to working note 10). (e) Standard total material cost for the output: Rs. 11,400 (Refer to working note 1). (f) Actual total direct labour cost for the output: Rs. 9,450 (Refer to working note 8). (g) Material price variance = Total material cost variance – Material usage variance.

= Rs. 1,400 (favourable)* – Rs. 600 (Adverse) (*Refer to working note 4)

= Rs. 2000 (Favourable) Alternatively,

= Actual quantity (Standard rate – Actual rate)

= 4,000 units (Rs. 3 – Rs. 2.50)* (* Refer to working note 6)

= Rs. 2,000 (Favourable)

(h) Labour rate variance: = Actual hours (Standard rate – Actual rate) = 1,800 hours (Rs. 5 – Rs. 5.25) = Rs. 450 (Adverse)

(i) Labour efficiency variance: Standard rate (Standard hours – Actual hours) = Rs. 5 per hour (1,600 hours – 1,800 hours) = Rs. 1,000 (Adverse)

(j) Variable overhead expenditure variance : = Actual hours (Standard rate – Actual rate) = 1,800 hours (Re. 1 – Re. 0.90)* = Rs. 180 (Favourable) (*Refer to working note)

(k) Variable overhead efficiency variance = Standard rate (Standard hours – Actual hours) = Re. 1 per hour (1,600 hours – 1,800 hours) = Rs. 200 (Adverse)

Ans. 14:12000 500 /

24hrs hrs day

days= Budgeted daily hours per day of June =

Actual available hours for June = 500 hours × 25 days = 12,500 hours

Calendar Variance = Std. fixed overhead rate per hr (No. of hrs. in actual period – No. of hrs. in budgeted period)

= Re.0.50 (12,500 hours – 12,000 hours) = Rs. 250 (F)

Alternatively, this variance can be calculated by using number of days instead of hours. In that case, overhead rate will be on per day basis.

Ans. 15:

Standard output per man hour: 1 Actual output : 8,400 hours × 22days × 1.2 units per hour = 2,21,760 units.

Standard hours produced or std. hrs. for actual production :2,21,760 units×1 hr. = 2,21,760 hrs. Budgeted hrs. in budgeted days: 8,000 hours × 20 days = 1,60,000 hours Budgeted hours (capacity) in actual working days: 8,000 hrs. × 22 days = 1,76,000 hours Actual hours worked: 8,400 hours × 22 days = 1,84,800 hours Overheads as per budget: 8,000 hours × 20 days × Rs. 2 per hour = Rs.3,20,000

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Rs.

(a) Standard cost charged to production : 2,21,760 hours × Rs.2 4,43,520 (b) Actual hours worked × Standard rate : 1,84,800 hours × Rs.2 3,69,600 (c) Budgeted hours in actual days × Std. rate: 1,76,000 × Rs.2 3,52,000 (d) Overheads as per budget 3,20,000 (e) Actual overheads 3,25,000 Efficiency variance = Std.fixed overhead rate per hour (Std. hrs. for

production – Actual hrs.) = Rs.2 (2,21,760 hours – 1,84,800 hours) = Rs.73,920 (F) Capacity variance = Standard fixed overhead rate per hour (Actual capacity –

Budgeted capacity) = Rs.2 (1,84,800 hours – 1,76,000 hours) = Rs.17,600 (F) Calendar variance = Standard fixed overhead rate per hour (Budgeted hrs. in

actual days – Budgeted hrs. in budgeted days) = Rs.2 (1,76,000 hours – 1,60,000 hours) = Rs.32,000 (F) Volume variance = Standard fixed overhead rate per hour

(Actual volume in hrs. – Budgeted volume in hrs.) = Rs.2 (2,21,760 hours – 1,60,000 hours) = Rs. 1,23,520(F) Expenses variance = Budgeted expenses – Actual expenses

= Rs.3,20,000 – Rs.3,25,000 = Rs.5,000 (A) Total variance = Overheads charged to production – Actual overheads

= Rs. 4,43,520 – Rs.3,25,000 = Rs. 1,18,520 (F) OR

Rs.

Efficiency variance : (a – b) 73,920 (F) Capacity variance : (b – c) 17,600 (F) Calendar variance : (c – d) 32,000 (F) Volume variance : (a – d) 1,23,520 (F) Expense variance : (d – e) 5,000 (A) Total variance : (a – e) 1,18,520 (F)

Ans. 16:

(a)Total fixed overhead variance = Absorbed fixed overheads – Actual fixed overheads = (5,200units× Rs. 2) – Rs. 10,200 = Rs.200 (F) (b) Expenditure variance = Budgeted overheads–Actual overheads

= Rs. 10,000 – Rs. 10,200 = Rs. 200(A) (c) Volume variance = Standard rate of absorption per unit ×

(Actual production – Budgeted production = Rs.2 (5,200 units —5,000 units)=Rs. 400 (F)

This can be divided into capacity variance and efficiency variance as shown below :

Capacity variance = Standard rate of absorption per hour (Actual hours capacity – Budgeted hours capacity)

= Re. 0.50 (20,100 hours – 20,000 hours) = Rs 50(F) Efficiency variance = Standard rate of absorption per hour (Standard hours required – Actual hours)

= Re.0.50 (20,800 hours – 20,100 hours) = Rs.350 (F)

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Working Notes :

Std. fixed overhead rate of absorption per unit = .10000 .2

5000Rs Rs

units=

Std. fixed overhead rate of absorption per hour: .10000 Re.0.50

5000 4 .Rsunits hrs

=×

Std. hours required for actual production: 5,200 units × 4 hours = 20,800 hours

Ans. 17:

Working Notes:

1) Budgeted output in units 40,000 man hours X 3.2 units per man hours = 1,28,000 units. 2) Standards variable overhead rate per unit Rs, 1,02,400/1,28,000 units = Rs. 0.80 per unit 3) Standard variable overhead rate per man hour Rs. 1,02,400/40,000 man hours = Rs. 2.56 per man hour 4) Standard fixed overhead rate per unit Rs 32,000/1,28,000 units = Rs. 0.25 per unit 5) Actual Production units 43,000 man hours X 3 units per man hour = 1,29,000 units Computation of variable Overhead variances: i) Total Variable Overhead Variances = Variable overhead recovered on actual output – Actual variable overhead = (1,29,000 units X 0.80 P – Rs. 1,14,000) = Rs. 11,200 (A) ii) Variable Overhead Expenditure Variance = Budgeted variable overhead for actual hours – Actual Variable overhead = (43,000 X 2.56 – Rs. 1,14,400) = Rs. 4,320 (A) iii) Variable Overhead Efficiency Variance = Standard variable overhead rate per hour (Standard hours for actual output- Actual hours) = Rs. 2.56 (40,312.5 hours – 43,000 Hours) = Rs. 6,880 (A) Computation on Fixed Overhead Variances: i) Total Fixed Overhead Cost Variance = Fixed overhead recovered on actual output – Actual fixed overhead = (1,29,000 units – 0.25 P – Rs. 31,500) = Rs. 750 (F) ii) Fixed Overhead Expenditure Variance = Budgeted fixed overhead – Actual fixed overhead = (Rs. 32,000 – Rs. 31,500) = Rs. 500 (F) iii) Fixed Overhead Volume Variance = Standard fixed overhead per unit (Actual output units – Budgeted output units) = 0.25 P (1,29,000 – 1,28,000) = Rs. 250 (F) iv) Fixed Overhead Efficiency Variance = Standard fixed overhead rate per unit (Actual Quantity – Standard Quantity)

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= 0.25 P (43,000 hours X 3.2 units – 1,29,000 units) = Rs. 2,150 (A) v) Fixed Overhead Capacity Variance = Standard fixed overhead rate per hour (Actual capacity hours – Budgeted capacity hours in actual days) = (Rs. 32,000/40,000 hours) (43,000 – 21 days X 2,000 hours) = Rs. 800 (F) vi) Calendar Variance = (Budgeted Days – Actual Days) Standard fixed overhead per day = (20 days – 21 days) (Rs. 32,000/20 days) = Rs. 1,600 (F) Computation of Total Overhead Variances = Total variable overhead variances + Total fixed overhead variances = Rs. 11,200 (A) + Rs. 750 (F) = Rs. 10,450

Ans. 18:

Basic calculation:

Product Budgeted price

Actual price

Budgeted quantity

Actual quantity

Budgeted sales

Actual quantity at budgeted

sales Price

Actual sales

a b c d (e)=a × c f=(a × d) g=(b × d)

A B C D

Rs. 2.50 5.00 7.50

10.00

Rs. 3.00 4.50 7.00

10.50

2,000 1,500 1,000

500

2,400 1,400 1,200

400

Rs. 5,000 7,500 7,500 5,000

Rs. 6,000 7,000 9,000 4,000

Rs. 7,200 6,300 8,400 4,200

5,000 5,400 25,000 26,000 26,100

Computation of Variances :

Sales price variance = Actual quantity (Actual price – Budgeted price) = Actual sales – Standard sales = Rs.26,100 – Rs. 26,000 = Rs.100(F)

Sales volume variance = Budgeted price (Actual quantity – Budgeted quantity) = Std. sales – Budgeted sales = Rs.26,000 – Rs.25,000 = Rs.1,000 (F)

Total variance = Actual sales – Budgeted sales = Rs.26,100 – Rs.25,000 = Rs.1,100 (F)

Average budgeted price per unit of budgeted mix:

Average budgeted price per unit of actual mix: Hence, Sales mix variance = Actual total qty. (Budgeted price per unit of actual mix –

Budgeted price per unit of budgeted mix)

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= =

5,400 units (Rs.4.815—Rs.5.00) Rs. 1,000 (A)

Sales quantity variance = Budgeted price per unit of budgeted mix = (Actual total qty. – Budgeted total qty.) = Rs.5 (5,400 – 5,000) = Rs. 2,000 (F) Note: Instead of computing average price, one may use total figures to do away with the effect of

rounding off.

For example, in case of sales mix variance figures may be as under:

= Rs. 26,000 – Rs 27,000 = Rs.1,000 (A)

A. (a) Analysis of variances to show the effects on turnover : Ans. 19:

B. Working Notes : ( 1 ) Budgeted sales :

Budgeted sales units at budgeted (or standard) prices. Units Price Amount

Rs. Rs. Bravo 5,000 100 5,00,000 Champion 4,000 200 8,00,000 Super 6,000 180 10,80,000

15,000 23,80,000 (2) Actual sales :

Actual sales units at actual prices

(3) Standard sales:

Actual sales units at Budgeted (or Standard) prices.

Units Price Amount Rs. Rs.

Bravo 5,750 100 5,75,000 Champion 4,850 200 9,70,000 Super 5,000 180 9,00,000

15,600 24,45,000 Computation of Variances : (i) Sales price variance = Actual quantity (Actual price – Budgeted price)

or Actual sales – Standard sales

Units Price Rs.

Amount Rs.

Bravo 5,750 120 6,90,000 Champion 4,850 180 8,73,000 Super 5,000 165 8,25,000

15,600 23,88,000

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= Rs.23,88,000 – Rs.24,45,000 = Rs.57,000 (A)

(ii) Sales mix variance = Total actual quantity (Budgeted price of actual mix – Budgeted price of budgeted mix

.2445000 .23800001560015600 15000

Rs Rsunits = −

=Rs. 2475200 – Rs. 2380000 = Rs. 95200F = Rs. 24,45,000 – Rs. 24,75,200 = Rs. 30,200 (A)

(iii) Sales quantity variance = Budgeted price of budgeted mix × (Total actual quantity – Total budgeted quantity)

Rs. 23,80,000

= 15,000 units ( 15,600 units – 15,000 units)

= Rs. 24,75,200 – Rs. 23,80,000 = Rs. 95,200 (F) (iv) Total sales value variance = Actual sales – Budgeted sales

= Rs.23,88,000 – Rs.23,80,000 = Rs. 8,000 (F) (b) Analysis of variances to show the effects on profit : Working Notes :

(1) Budgeted margin per unit

Sales price Rs.

Cost Rs.

Margin Rs.

Bravo 100 90 10 Champion 200 170 30 Super 180 130 50

(2) Actual margin per unit

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Computation

of variances:

(i) Sale margin price variance Actual quantity (Actual margin – Budgeted margin)

or Actual profit – Standard profit

Rs. 3,96,000 – Rs. 4,53,000 = Rs. 57,000 (A) (ii) Sales margin mix variance = Total actual quantity (Budgeted margin on actual mix – Budgeted Margin on budgeted mix

= Rs. 4,53,000 – Rs. 4,88,800 = Rs. 35,800 (A)

(iii) Sales quantity variance = Budgeted margin on budgeted mix (Total actual qty. – Total budgeted qty.)

= Rs. 4,88,800 – Rs. 4,70,000 = Rs. 18,800 (F) (iv) Total sales margin variance = Actual profit – Budgeted profit

= Rs. 3,96,000 – Rs. 4,70,000 = Rs. 74,000 (A) Ans. 20:1. Statement of budgeted average contribution margin per unit for the year 1995:

Working Notes:

Product different PC models

Budgeted contribution margin per unit of each

product

Budgeted sales volume

Total budgeted contribution

margin (Rs.) (Units) (Rs.) PC 10,000 7,000 7,00,00,000 Portable PC 6,000 1,000 60,00,000 Super PC 40,000 2,000 8,00,00,000 10,000 15,60,00,000

Budgeted average contribution margin per unit = units 10,0000,000Rs.15,60,0

= Rs.15,600

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2. Actual market share percentage = salesindustry Actual

models PC 3 - of sales Actual × 100

= units 68,750units 11,000 × 100

= 16

3. Actual sales mix percentage of product = models PC 3 of sale ActualTotal

Product of sales Actual × 100

Actual sales mix percentage of product PC = units 11,000units 8,250 × 100 = 75

Actual sales mix %age of product Portable PC = units 11,000

units 1,650 × 100 = 15

Actual sales mix %age of product Super PC = units 11,000

units 1,100 × 100 = 10

(i) Computation of individual product and total sales volume variance

Sales =

unit

per margin

oncontributi

Budgeted

units inVolumeSalesBudgeted

units inVolumeSalesActual

×−

Individual product sales volume variance: PC = (8,250 units – 7,000 units) × Rs.10,000 = Rs.1,25,00,000 (Fav.) Portable PC = (1,650 units – 1,000 units) × Rs.6,000 = Rs.39,00,000 (Fav.) Super PC = (1,100 units – 2,000 units) × Rs.40,000 = Rs.2,60,00,000 (Adv.) Total Sales Volume Variance = Rs.1,96,00,000 (Adv.) (ii) Computation of total sales quantity variance:

Total sales quantity variance = unit per

margin oncontributiaverage Budgeted

units SalesBudgeted Total

Unit sales actual Total ×−

= (11,000 units – 10,000 units) × Rs.15,600 = Rs.1,56,00,000 (Fav.) (iii) Computation of the market size and market share variance 1. Market size variance:

Budgeted market Share %age =

unit per

margin oncontributi

average Budgeted

units in SalesIndustry Budgeted

units in SalesIndustry Actual

×−

= 0.20 (68,750 units – 50,000 units) × Rs.15,600 = Rs.5,85,00,000 (Fav.) 2. Market share variance:

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=

×−

unit permargin onContributi

average Budgeted

units inVolume SalesTotal Actual

percentage sharemarket Budgeted

percentage sharemarket Actual

= (0.16 – 0.20) × 68,750 units × Rs.15,600 = Rs.4,29,00,000 (Adv.) (iv) Computation of individual product and total sales mix variances 1. Individual product and total sales mix variance:

Sales mix variance:

−××−margin

oncontributiaverage Budgeted

margin onContributi

IndividualBudgeted

units inVolume SalesTotal Actual

productof %age mixsales Budgeted

product of %age mix

sales Actual

PC*** = (0.75 – 0.70) × 11,000 units × (Rs.10,000 – Rs.15,600) = Rs.30,80,000 (Adv.) Super PC****= (0.10 – 0.20) × 11,000 units × (Rs.40,000 – Rs.15,600) = Rs.2,68,40,000 (Adv.) 2. Total sales mix variance = rs.3,52,00,000 (Adv.) * Refer to working note 1. **Refer to working note 2. ***Refer to working note 3.

Note: Sales variances can also be calculated by using sales value approach. (v) Comment on above results:

1. Favourable sales quantity variance of Rs.1.56 crores was because of growth in industry as a whole. However the firm could not retain the budgeted market share of 20%. As a result the benefit of increased market size i.e. Rs.5.85 crores is partly offset by loss due to fall in market share i.e. Rs.4.29 crores.

2. Increase in the percentage sale of computers below-average budgeted margins and a decrease in the percentage sale of computers above-average budgeted margins had resulted in the reduction of operating profit by Rs.3.52 crores.

3. As a result of above, the operating profit of ‘Super Computers’ had been adversely affected by Rs.1.96 crores due to sales variances.

Ans 21:1. Material data

Working Notes

Standard data for actual output Actual output 6,400 units Actual data for actual output

Quantity Kgs.

Price Per Kg.

Amount Rs.

Quantity Kgs.

Price Per Kg.

Amount Rs.

32,000 8 2,56,000 36,000 7.50 2,70,000 2. Labour data

Standard data for actual output Actual output 6,400 units Actual data for actual output

Labour Rate/hour Amount Labour Rate/hour Amount

79

hours Rs. Rs. hours Rs. Rs. 32,000 8 2,56,000 36,000 7.50 2,70,000

3. Variable overheads data

Standard/Budgeted data Actual data Budgeted variable overheads for actual hours

6,50,000 Actual variable overheads (Rs.)

6,48,000

Actual Units 6,400 Actual Hours 65,000 Standard variable overhead Rate/hour

Rs. 10

Standard variable overhead rate/ unit

Rs. 100

4. Sales data

Budgeted data Actual data

Sales Units

Budgeted Margin p.u.

Rs.

Amount Rs.

Sales Units

Actual Margin p.u.

Rs.

Amount Rs.

6,000 50 (Rs. 250 – Rs. 200) 3,00,000 6,400 65

(Rs. 265 – Rs. 200) 4,16,000

1. Market Size Variance = Budgeted market share percentage [Actual industry sales in units – Budgeted industry sales in units] Budgeted contribution margin per unit = 0.12 [60,000 units – 6,000 units/12%] Rs. 50 = 0.12 [60,000 units – 50,000 units] Rs. 50 = Rs. 60,000 (F) 2. Market Share Variance

= [ =[0.106666 – 0.12] 60,000 units X 50 = (6,400 units – 7,200 units) Rs. 50 = Rs. 40,000 (A)

3. Gross Margin Sales Volume Variance = (Actual quantity – Budgeted quantity) Budgeted margin per unit = (6,400 units – 6,000 units) Rs. 50 = Rs. 20,000 (F) 4. Gross Margin Sales Price Variance = (Actual margin per unit – Budgeted margin per unit) Actual quantity of units sold = [(Rs. 65 – Rs. 50) 6,400] 6,400 units = Rs. 96,000 (F) 5. Direct Material Usage Variance

= (Standard quantity – Actual Quantity) Standard Price per kg. = (32,000 kgs – 36,000 kgs.) Rs. 8 = Rs. 32,000 (A) Direct Material Price Variance = (Standard price/kg. – Actual price/kg.) Actual quantity of material used = (Rs. 8 – Rs. 7.50) 3,600 kgs. = Rs. 18,000 (F)

6. Direct Labour Efficiency Variance = (Standard labour hours – Actual labour hours) Standard rate per hour = (64,000 hours – 65,000 hours) Rs. 6 = Rs. 6,000 (A) Direct Labour Rate Variance = (Standard labour rate per hour – Actual labour rate per hour) Actual time taken in hours

80

= (Rs. 6 – Rs. 6.40) 65,000 hours = Rs. 26,000 (A) 7. Variable Overhead Efficiency Variance = (Standard hours for actual output – Actual Hours) Standard variable overhead per hour = (64,000 hours – 65,000 hours) Rs. 10 = Rs. 10,000 (A) Variable Overhead Expense Variance = Budgeted Variable Overhead – Actual Variable Overhead = Rs. 6,50,000 – Rs. 6,48,000 = Rs. 2,000 (F)

Operating Statement (Reconciling the budgeted contribution with actual contribution

Rs. Rs. Rs. Budgeted Contribution 3,00,000 Gross margin sales volume variance 20,000 - Gross margin sales price variance 96,000 - 1,16,000 4,16,000 Cost Variances Material usage - 32,000 Material price 18,000 - Labour efficiency - 6,000 Labour rate - 26,000 Variable overhead efficiency - 10,000 Variable overhead expense 2,000 - 20,000 74,000 54,000 Total Actual Contribution 3,62,000

Verification: Actual Contribution = Actual sales revenue – Actual variable costs = Rs. 16,96,000 – [ RS. 2,70,000 (actual material cost) + Rs. 4,16,000 (actual labour cost) + Rs. 6,48,000 (actual variable

overheads)] = Rs. 16,96,000 – Rs. 13,34,000 = Rs. 3,62,000

Ans.22:(i) Normal / Budgeted hours =60,000 Direct Labour hours.

Working

(ii) Budgeted output =60,000/ 12 =5,000 units (iii) Budgeted fixed overhead rate =9,00,000 / 60,000 =Rs.15 per hour or 9,00,000 / 5,000 =Rs.180 per unit (iv) standard cost and profit per unit (Rs.) Direct materials (20kg X 10) Direct labour (12 hrs. X 5.50) Variable overheads (12 hrs. X 10) Fixed Overheads (12 hrs. X 15) Total Selling price Standard profit

200 66

120 180 566 600 34

(v) Actual profit (Rs.) Sales Less: cost of sales; Direct Material 10,50,000 Direct wages 3,10,000 Overheads Actual profit

15,26,000

28,32,000 28,86,000 (54,000)

Direct Material variances

81

DMCV = Standard Cost for actual output – Actual cost =(4,800 X 200 )-10,50,000 =9,60,000-10,50,000 =Rs.90,000 (A) DMPV = Actual qty. X ( standard rate – Actual rate) =1,00,000 X (10-10.5) =Rs.50,000 (A) DMUV = Std. rate X (std. qty. for actual output- actual qty.) =10 x ( 4,800 X 20)-1,00,000 ) =10 X (96,000-1,00,000) =Rs.40,000 (A) Direct Labour variances DLCV = Standard Cost of actual output – Actual cost =(4,800 X 12 X 5.50 )-3,10,000 =3,16,800-3,10,000 =Rs.6,800 (F) DLRV = Actual Time X ( Standard rate – Actual rate) =62,000 X (5.50-5) =Rs.31,000 (F) DLEV = Std. Rate X (Std. Time. for actual output- actual Time) =5.50 x ( 4,800 X 12)-62,000 ) =5.50 x (57,600-62,000) =Rs.24,200 (A) Overhead variances VOCV = Recovered variable Overheads – Actual variable Overheads =(4,800 X 120 ) – 5,86,000 = 5,76,000 – 5,86,000 =Rs.10,000 (A) FOCV = Recovered fixed overheads – Actual fixed overheads =(4,800 X 180 ) – 9,40,000 =8,64,000 – 9,40,000 =Rs.76,000 (A) FOEXPV = Budgeted fixed overheads – Actual fixed overheads =9,00,000 – 9,40,000 =Rs.40,000 (A) FOVV = Recovered fixed overheads – Budgeted fixed overheads =8,64,000 – 9,00,000 =Rs.36,000 (A) FOCAPV = Std. rate per hour (Actual time – budgeted time) =15 X (62,000 – 60,000 ) =Rs.30,000 (F) FOEFEV =Std. Rate per hour X (Std. time for actual output – Actual time) =15 X (4,800 X 12) – 62,0000 =15 X (57,600 – 62,0000=15 X 4400 =Rs.66,000(A) Sales Variances Sales Value = Budgeted Sales – Actual Sales Variance =( 5,000 X 600 ) -28,32,000 = Rs.30,00,000 – Rs.28,32,000 =1,68,000(A) Sales Price = Actual qty. (Std. Price – Actual price) Variance = 4,800 X ( 600 – 590) =Rs.48,000 (A) Sales Volume = Std. Price X (Budgeted qty. – Actual qty.) Variance =600 X ( 5,000 – 4,800) =Rs.1,20,000(A) Loss of profit due to loss of sales volume = 200 X 34 =Rs.6,800 (A)

Ans. 23:

Rs. Working Notes :

( a ) Actual sales 2,22,750

Less : Price variance (Favourable) 6,750 Standard sales 2,16,000 Units sold 4,800

82

( d ) Standard direct wage rate is Rs.4.50 per hour.

Hence standard time per unit: Rs. 9 ÷ 4.50 hour = 2 hours (e) Variable overheads :

Standard rate Rs.7.50 per hour Variable overhead per unit: 2 hrs. × Rs.7.50 = Rs. 15

(Note : Alternatively, this may be calculated by adjusting variances as in other cases).

(f) Fixed overhead spent Rs.39,000 Less : Fixed overhead expense

variance (Adverse) Rs.1,500

Budgeted overheads Rs. 37,500

(g) Fixed overhead recovered: 4,800 units × Rs.7.50 = Rs.36,000 (h) Fixed overhead volume variance

Rs.36,000 – Rs.37,500 = Rs.1,500 (Adverse) (i) Budgeted sales: 5,000 units × Rs.45 = Rs.2,25,000 (j) Standard sales: 4,800 units × Rs.45 = Rs.2,16,000 (k) Actual sales = Rs.2,22,750 (1) Sales volume variance: = Rs.9,000 (Adverse)

Rs. 2,16,000 – Rs.2,25,000 (m) Sales price variance:

Rs.2,22,750 – Rs.2,16,000 = Rs. 6,750 (Favourable)

(i) Original budget: Rs. Budgeted sales : (A) (5,000 units × Rs.45) 2,25,000

83

Budgeted costs Direct material (5,000 units × Rs.6) 30,000 Direct wages (5,000 units × Rs.9) 45,000 Variable overheads (5,000 units × Rs.15) 75,000 Fixed overheads (5,000 units × Rs.7.50) 37,500 Total budgeted costs : (B) 1,87,500 Profit : (A) – (B) 37,500

(ii) Standard product cost sheet per unit

Rs. Direct materials 6.00 Direct wages 9.00 Prime cost 15.00 Variable overheads 15.00 Fixed overheads 7.50 Total cost 37.50 Profit 7.50 Selling price 45.00

(iii) Statement showing Reconciliation of the original Budgeted Profit and the Actual Profit.

Rs. Rs. Budgeted profit 37,500 Less: Sales margin volume variance (Adverse)*

or loss of profit on sales volume variance

= Rs. 9000 × 16 2 %3

**

Standard profit 36,000

1500

*Sales margin volume variance (Adverse) (200 units × Rs.7.50 = Rs.1,500)

**Profit as % of selling price : Rs. 7.50 × %

Add: Sales price variance (Favourable) 6,750 42,750

Add: Favourable cost variances: Wage rate 750 Variable overhead expenses 3,000 3,750

Less : Adverse cost variances 46,500 Material price 300 Material usage 600 Labour efficiency 2,250 Variable overhead efficiency 3,750 Fixed overhead expense 1,500 8,400

38,100 Less: Fixed overhead volume variance (Adverse) 1,500

[See working note (h)] 36,600

84

Ans. 24

:Details of original and revised standards and actual achieved

Original standards Revised standards Actual

Fruit 400 Kgs × Rs16 Rs6,400 400 Kgs × Rs 19 Rs7,600 428 Kgs× Rs 18 Rs7,704

Glucose 700 Kgs × Rs10 Rs7,000 700 Kgs × Rs12 Rs 8,400 742 Kgs × Rs 12 Rs 8,904

Pectin 99 Kgs × Rs 33.2 Rs 3286.8 99 Kgs × Rs 33.2 Rs 3286.8 125Kgs× Rs 32.8 Rs 4,100

Citric acid 1 Kg× Rs 200 Rs 200 1 Kg× Rs 200 Rs 200 1 Kg× Rs 95 Rs 95

1,200 kgs Rs16,886.8 1,200 kgs Rs19,486.8 1,296 kgs Rs20,803

Labour Rs 585.0 Rs 585.0 Rs 600

1,200 kgs 17,471.8 1,200 kgs 20,071.8 1,296 kgs 21,403

Loss 36 kgs 36kgs 132

1,164kgs Rs 17,471.8 1,164kgs Rs 20,071.8 1,164 Kgs Rs 21,403

(i) Planning variances * Fruit extract (6,400 less 7,600) Rs 1,200(Adverse) Glucose syrup (7,000 less 8,400) Rs1,400(Adverse) Total Rs 2,600(Adverse) * (Std qty × Std price less Std qty × Revised Std price)

(ii) Ingredients operating variances Total (19,486.8 less 20,803) = Rs 1,316.2(Adverse)

Ingredients Price variance (Revised Material Price – Actual Material Price)× ( Actual Qty Consumed)

Variance in Rs Fruit extract (19 – 18) × 428 428(F) Glucose syrup Nil Pectin (33.2 – 32.8) × 125 50(F) Citric acid (200 – 95) × 1 105(F) 583(F)

Usage variance (Std Qty on Actual Production less Actual Qty on Actual Production) × Revised Std Price/Unit

Rs Variance in Rs Fruit extract (400 – 428) × 19 532(A) Glucose syrup (700 – 742) ×12 504(A) Pectin (99 – 125) ×33.2 863.2(A) Citric acid Nil

1,899.2(A) (iii) Mix Variance

(Actual usage in std mix less Actual usage in actual mix ) ×std price

Variance in Rs Fruit extract (432 – 428) ×19 76(F)

85

Glucose syrup (756 – 742) × 12 168 (F) Pectin (106.92 – 125) ×33.2 600.3(A) Citric acid (1.08 – 1) ×200 16(F) 340.3 (A)

Yield variance (Actual yield – Std yield from actual output) × Std cost per unit of output

= (1,164 – 1,296 × 0.97) × 1164

8.19486 = 1,558.9(A)

Labour operating variance 585 – 600 = 15(A) (iv) Total variance = Planning variance + Usage Variance + Price Variance + labour operating Variance. Or Total Variance = (2,600) + ( 1,899.2 ) + 583 + (15) = 3931.2 (A). Ans.26: Product X Product Y Total

Standard hours produced

Out put (units) 1,200 800 Hours per unit 8 12 Standard hours 9,600 9,600 19,200 Actual hours worked 100 workers ×8 hours × 22 days = 17,600 Budgeted hours per month

1,86,000/12 = 15,500

Capacity Ratio = 500,15600,17100

hours Budgetedhours actual

=× = 113.55 %

Efficiency Ratio = 100600,17200,19100

hours ActualProduced Hours Standard

×=× 109.09%

Activity Ratio = 100500,15200,19100

hoursBudget Produced Hours Standard

×=× 123.87%

Relationship : Activity Ratio = Efficiency Ratio × Capacity Ratio

or 123.87 =100

55.11309.109 ×

Ans: 27:

(1) Capacity Ratio

= Budgeted working hours x 100

Actual working Hours

86

= 25 days x 8 hours x 50 workers 8,500 hours (i.e.,1,02,000/12)

x 100 =117.65%

(2) Activity Ratio =Actual production in standard hours Budgeted hours

x 100

=(1,000 units x 5 hours) + (600 units x 10 hours) 8,5000 hours

x 100 =129.41%

(3) Efficiency Ratio =Standard hours for actual production Actual hours

x 100

=(1,000 units x 5 hours ) + (600 units x 10 hours) 10,000 hours

x 100 =110%

Inter – relationship Capacity Ratio x Efficiency Ratio =Activity Ratio 117.65% x 110% =129.41% Ans. 28: (a)

Report to the Departmental Manager showing the cost ratios: Standard hours produced 2112Efficiency Ratio = 100 110%

Actual hours worked 1920= × =

(b) Standard hours produced 2112Activity Ratio = 100 82.50%Budgeted Std. Hours 2560

= × =

(c) Budgeted Std. Hours 2560Standard Capacity usage Ratio = 100 80%Maximum Possible Hours 3200

= × =

(d) Actual hours worked 1920Actual Capacity utilisation Ratio = 100 75%Budgeted hours 2560

= × =

(e) 24Calendar Ratio = 100 96%25

× =

(ii) Report to the Departmental Manager Setting out the analysis of variances Standard fixed overhead rate per hour = 15360 .6

2560Rs=

A. Fixed Overheads Rs.

(a) Charged to production (2112 × 6) 12672 (b) Actual hours × Std. rate (1920 × 6) 11520

(c) Revised budgeted hours × Std. rate (24×8×16× 80100

×6) 14746

(d) Original budgeted overheads 15360 (e) Actual overheads 16500

Variances: Efficiency variance (a-b) 1152(F) Capacity variance (b-c) 3226(A)

87

Calendar variance (c-d) 614(A) Volume variance (a-d) 2688(A) Expenditure variance (d-e) 1140(A) Total variance 3828(A) B. Variable overheads:

Standard variable overhead rate per hour = 208402560

=Rs.8

(a) Charged to production (2112 × 8) 16896 (b) Actual hours × Std. rate (1920 × 8) 15360 (c) Actual overheads 14500

Variances: Efficiency variance (a-b) 1536(F) Expenditure variance (b-c) 860(F) Total variance (a-c) 2396(F) Working note: Maximum possible hours (25×8×16) 3200 Budgeted hours: 3200 less 20% downtime 2560 Actual hours 1920 Budgeted standard hours 2560 Standard hours produced 5112 Budgeted working days 25 Actual working days 24

Ans. 29:Maximum capacity in a budget period

= 50 employees × 8 hrs.×5 days×4 weeks = 8,000 hrs. Budgeted hours 40 employees ×8 hrs.×5 days×4 weeks = 6,400 hrs. Actual hrs. = 6,000 hrs. (from the sum) Standard hrs. for actual output = 7,000 hrs. Budget no. of days = 20 days = 20 days (4 weeks ´5 days) Actual no. of days = 20-1 = 19 days

100 {(7000 6000) 100} 116.67%Standard Hrs1. Efficiency ratio = Actual Hrs

× = ÷ × =

2. Activity ratio = {(7,000÷6,400)×100} = 109.375% 3. Calendar Ratio = (Available working days ÷ budgeted working days) × 100

88

= {(19÷20)×100} = 95% 4. Standard Capacity Usage Ratio =

(Budgeted hours ÷ Max. possible hours in the budgeted period) × 100 = {(6,400÷8,000)×100} = 80%

5. Actual Capacity Usage Ratio = (Actual hours worked ÷ Maximum possible working hours in a period) × 100 = {(6,000÷8,000)×100} = 75%

6. Actual Usage of Budgeted Capacity Ratio = (Actual working hours ÷ Budgeted hours) × 100 = {(6,000÷6,400)×100} = 93.75%

(i)

Ans.30:

Dr. Material Control A/c Dr. or Cr. Material Price Variance A/c Cr. Creditors A/c (Being price variance during purchase of

materials)

(ii) Dr. WIP Control A/c Dr. or Cr. Material Usage Variance A/c Cr. Material Control A/c (Being recording of usage variance at

Standard cost of excess/under utilized quantity)

(iii) Dr. Wages Control A/c Dr. or Cr. Labour Rate Variance A/c Cr. Cash (Being entry to record wages at standard rate)

Ans. 31:

(A) The cost sheet for 900 units will appear as under :

Cost Std. qty. Std. rate Std.cost Rs. Direct material 9,000 1.00 9,000 Direct labour 2,250 3.00 6,750 Overheads 2,250 6.00 13,500

29,250 (B) Calculation of variances:

Material price variance = 9,500 Pcs. (Re. 1.00 – Rs.1.10) = Rs. 950 (A) Material usage variance = Re. 1.00 (9,000 pcs. – 9,500 pcs.) = Rs. 500 (A) Labour rate variance = 2,475 hrs. (Rs. 3.00 – Rs. 3.50)

= Rs. 1,237.50 (A) Labour efficiency variance = Rs. 3.00 (2,250 hrs. – 2,475 hrs.) = Rs. 675(A)

Overhead variances : (a) Charged to production as per cost sheet Rs. 13,500 (b) Actual

89

Work-in-Progress A/c Dr. 17,000 To Overhead Expense Control A/c 17,000

(Being the actual overhead expenses incurred) Finished Stock Control A/c Dr. 29,250

To Work-in-Progess A/c 29,250

hours × Std. rate: 2,475 hrs. × Rs. 6 Rs. 14,850 (c) Overheads as per budget Rs. 16,500 (d) Actual overheads Rs. 17,000

Efficiency variance : (a – b) Rs. 1,350 (A) Capacity variance : (b – c) Rs.1,650 (A) (idle time) Expense variance : (c – d) Rs. 500 (A) Total variance : (a – d) Rs. 3,500 (A)

(C) The. journal entries for recording these transactions are as under Dr. Cr. Rs. Rs. (i) Material Control A/c

To General Ledger Adjustment A/c (Being the purchase value of 10,000 pieces of materials at Rs. 1.10 each)

Dr. 11,000

11,000

(ii) Work-in-Progress A/c Dr. 10,450 To Material Control A/c 10,450 (Being the cost of 9,500 pieces of materials actually issued to production

at the actual price of Rs. 1.10 each) (iii) Work-in-Progress A/c Dr. 8,662.50

To Wages Control A/c 8,662.50

(Being the actual amount of direct wages paid for 2,475 hours at Rs. 3.50 per hour

(iv)

(v)

(Being the standard cost of production transferred to finished goods account)

(vi) Cost of Sales A/c Dr. 29,250 To Finished Stock Control A/c 29,250

(Being the standard cost of goods sold transferred to Cost of Sales A/c)

After the basic transactions are posted, the materials control account will show the actual value of stock of material in hand and the work-in-progress account will show a balance representing the cumulative variances on all the accounts and closing balance of work-in- progress at standard cost. The variances have already been analysed in Para (B) above and they will be carried to the respective accounts pending investigation before being finally disposed off. In this problem we have assumed that there is no closing balance of work-in- progress.

(D) The journal entries for transferring the variances to their respective

90

accounts are as under

Rs. Rs. Material price variance A/c Dr. 950.00 Material usage variance A/c Dr. 500.00 Labour rate variance A/c Dr. 1,237.50 Labour efficiency variance A/c Dr. 675.00

Overhead efficiency variance A/c Dr. 1,350.00

Overhead capacity variance A/c Dr. 1,650.00

Overhead expense variance A/c Dr. 500.00

To work-in-progress A/c 6,862.5 (E) The ledger accounts will appear as under:

Dr. Material Control A/c Cr.

Rs. Rs.

To Opening balance - By Work-in-Progress A/c 10,450 To General Ledger By Balance c/d 550 Adjustment A/c 11,000

11,000 11,000 Work-in-Progress Control A/c

Rs. Rs. To Opening balance – By Finished stock control A/c 29,250.00 To Material control A/c 10,450.00 By material price variance A/c 950.00 To Wages control A/c 8,662.50 By material usage variance A/c 500.00 To Overheads control A/c 17,000.00 By labour rate variance A/c 1,237.50

By labour efficiency variance A/c 675.00 By overhead efficiency A/c Variance A/c 1,350.00 By overhead capacity Variance A/c . 1,650.00 By overhead expense Variance A/c 500.00

36,112.50 36,112.50 Ans. 32:

(i) Material price variance: 8,600 pcs. (Rs. 2.15 – Rs. 2.50) = Rs. 3,010 (A) (ii) Material usage variance: Rs. 2.15 (8,400 Pcs. – 8,600 Pcs.) = Rs. 430 (A)

(A)Computation of variance:

[Standard requirement of materials = 2,800 units produced × 3 pcs. per unit = 8,400 pcs.] (iii) Labour efficiency variance: Dept. A: Standard time required = 2,800 pcs. × 2 hrs. = 5,600 hours. Dept. B: Standard time required = 2,800 pcs. × 4 hrs. = 11,200 hours.

Variances : Dept. A: 1.75 (5,600 – 5,200) = Rs. 700 (F) Dept. B: 1.50 (11,200 – 12,000) = Rs. 1,200 (A) (iv) Overheads variances:

91

(i) Material Control A/c Dr. 18,490

Material price variance A/c Dr. 3,010 To Creditors A/c 21,500 (ii) Work-in-Progress Dept. A. A/c Dr. 18,060

Material usage variance A/c Dr. 430 To Material Control A/c 18,490 (iii) Work-in-progress Dept. A. A/c Dr. 9,800

To wages control A/c 9,800 (iv) Wages Control A/c Dr. 700

To Labour Efficiency Variance Dept A A/c 700 (v) Work-in-Progress Dept. B A/c. Dr. 16,800

Labour Efficiency Variance Dept. B A/c Dr. 1,200 To Wages Control A/c 18,000 (vi) Work-in-Progress Dept. A A/c Dr. 2,800

Overhead Capacity Variance Dept. A. A/c Dr. 400 To Overhead Efficiency Variance Dept. A. A/c 200 To Overhead Expense Control Dept. A A/c 3,000 (vii) Work-in-Progress Dept. B A/c Dr. 11,200

Overhead Efficiency Variance A/c Dr. 800 Overhead Expenses Variance A/c Dr. 500 To Overhead Control Dept. B A/c 12,500 (viii) Work-in-Progress Dept. B A/c Dr. 30,660

To Work-in-Progress Dept. A A/c 30,660 (Being the transfer at standard cost of finished Production of Department A to Department B for processing in Department B) (ix) Finished Stock control A/c Dr. 58,660

92

To Work-in-Progress Dept. B A/c 58,660

93

94

Ans.33:

All figures of Ans. 31are 5 times of Ans. 32

Ans. 34: = Rs24, 000 – Rs21, 600 = Rs2, 400 (F)

Material – 1 Rate Variance = Standard cost of material purchased – Actual cost

Material – 2 Quantity Variance = SR × SQ – SR × AQ = Rs900 × 80 units – Rs75, 600 = Rs3, 600 (A) Labour Spending Variance = SR × AH – AR × AH = Rs24/per hour × 2300 hours – Rs51, 750 = Rs3, 450 (A) Labour Efficiency Variance = SR × (SH – AH) – 7200 = 24 (SH – 2300) SH = 2000 Hrs.

Rs Total Cost of material purchased 1,27,200 Less Purchase Value of Material – 2 1,05,600 Cost of material –1 21,600

Working Notes: (1) Standard Cost of Material – 2 actually consumed in production = Rs72, 000 (Given) Standard cost of Material – 2 per unit: 5 litres × Rs180 = Rs900 ∴No of units produced = Rs72, 000 / Rs900 = 80 units Total material – 1 used in production = Rs18, 000 (Given) Add Closing Inventory = Rs6, 000 (Given) Less Opening Inventory = 0 Hence Standard Cost of Material – 1 purchased = Rs24, 000

95

(2) Standard Rate of Material -1 = Rs24, 000 / 1,000kg = Rs24 per kg

Standard Cost of Material – 1 = Rs18, 000 Add favourable Quantity Variance = Rs1, 200 Material – 1 allowed = Rs19, 200 Standard quantity of Material – 1 allowed = Rs19, 200/Rs24= 800 Kg. Standard quantity per unit = 800kg/80units = 10 kg Standard purchase price for Material – 2 = (550liters × Rs180)= Rs99, 000 Add unfavourable Rate Variance = Rs6, 600 Actual cost Price of Material – 2 = Rs1, 05, 600 (3) Opening balance of Material – 2 = Rs18, 000 Add Standard Cost of Purchase (550 litres × Rs180) = Rs99, 000 Less Closing Balance = Rs41, 400 Material-2 Consumed at Standard cost = Rs75, 600 Ans. 35:

We know that: (i) Budgeted Machine Hours:

Volume variance =

−

output actual for hours machined Budgeted

output actual for hours machine Std.

hour per rateoverhead fixed Std.

or Rs.80,000 (Fav.) = Rs.100 (11,300 – Y) or 800 = 11,300 – Y or Y = (11,300 – 800) hours or Y = 10,500 hours Hence budgeted machine hours for actual output are 10,500 hours.

(ii) Actual machine Hours: We know that:

Efficiency variance =

−

output actual for hours Actual

output actual for hours Std.

hour per rateoverhead variable Std.

or Rs.36,000 (Fav.) = Rs.60 (11,300 hours – X) or 600 = 11,300 hours – X or X = 10,700 hours. Hence Actual machine hours are 10,700 hours. (iii) Applied Manufacturing Overhead: Applied Manufacturing overhead Actual overhead incurred + Total Variance = Rs.16,50,000 + Rs.30,000 (Refer to working note) = Rs.16,80,000 Hence total applied manufacturing overhead are Rs.16,80,000.

96

(iv) Total Amount of Fixed Overhead Cost: We know that: Spending variance = (Flexible budget for actual hours – Actual factory overhead incurred) Rs.86,000 (Adv.) = 10,700 hours × Rs.60 + total amount of fixed overhead) – Rs.16,50,000) Rs.86,000 (Adv.) = (Rs.6,42,000 + Total amount of fixed overhead cost (budgeted) – Rs.16,50,000) Total amount of fixed overhead cost = Rs.10,08,000 – Rs.86,000 = Rs.9,22,000 Total amount of fixed overhead cost = Rs.9,22,000 Working note: Given that: Spending variance (Rs.) 86,000 (Adv.) Efficiency variance (Rs.) 36,000 (Fav.) Volume variance (Rs.) 80,000 (Fav.) Therefore, Total variance = Spending variance + Efficiency variance + Volume variance = Rs.86,000 (Adv.) + Rs.36,000 (Fav.) + Rs.80,000 (Fav.) = Rs.30,000 (Fav.) Alternative approach: Total factory overhead variance = {factory overhead applied - actual factory overhead incurred} = (Std. hours for actual output × Budget rate per hour – Actual cost incurred) = (11,300 hours × Rs.160 – Rs.16,50,000) = Rs.1,58,000 (Fav.)

Under alternative approach, Applied Manufacturing Overhead and Total Amount of Fixed Overhead Cost would come to Rs.18,08,000 and Rs.10,50,000. Budgeted and actual machine hours would come to 10,500 and 10,700. Spending, Efficiency and Volume Variances would come to Rs.42,000 (Fav.), Rs.36,000 (Fav.) and Rs.80,000 (Fav.) respectively. Ans. 36:

Material cost variance = Standard cost of material of actual output – Actual material cost incurred (1) Actual material cost incurred

Or Actual material cost incurred =

−

Standard variable of material Material cost varianceof actual output

= (10,000 units × 2 units× Rs.15 + Rs.50,000) = Rs.3,00,000 + Rs.50,000 (2) Standard cost of materials actually consumed

Material price variance = (Standard cost – Actual cost) Actual quantity consumed

Or Standard cost of materials actually consumed =

+

Actual material Material price cost incurred variance

= Rs.3,50,000 – Rs.70,000 = Rs.2,80,000 (3) Labour efficiency variance (Refer to working note 1)

97

= hour per

rate Standardworked

hours Actualoutput actual

for hours Standard

−

= (10,000 units × 3 hours – 35,000 hours) Rs.20 = (Rs.6,00,000 – Rs.7,00,000) = Rs.1,00,000 (Adv.) (4) Variable OH efficiency variance (Refer to working note 2)

=

−

hours Actual

hours Standard

hour per rateoverhead variable Standard

= Rs.5 (30,000 hours – 35,000 hours) – Rs.25,000 (Adv.) (5) Variable OH expenditure variance (Refer to working note 1)

=

−

overhead variable Actual

hours actual foroverhead variable Budgeted

= (Rs.5 × 35,000 hours – Rs.2,00,000) – Rs.25,000 (Adv.) (6) Fixed OH efficiency variance (Refer to working notes 1 & 2)

=

−−

hoursActual

ouput actualfor hour Standard

hour per rateoverhead fixed Standard

= Rs.5 (30,000 hours – 35,000 hours) = Rs.25,000 (Adv.) Fixed OH capacity variance (Refer to working notes 1 & 2)

=

−−

hourscapacity Budgeted

hourscapacity Actual

hour per rateoverhead variable Standard

= Rs.5 (35,000 hours – 50,000 hours) = Rs.75,000 (Adv.) (7) Fixed OH volume variance (Refer to working note 3)

=

−

output Budgeted

output Actual

hour per rateoverhead variable Standard

= Rs.15

−

hours 3hours 50,000units 10,000

= Rs.1,50,000 – Rs.2,50,000 = Rs.1,00,000 (Adv.) Working notes: 1. Labour rate variance: = (Standard rate per hour – Actual rate per hour) Actual hours (x) Or Rs.50,000 = 20x – Rs.6,50,000 Or x = 35,000 hours 2. Standard hours = 10,000 units × 2 hours = 30,000 hours

Budgeted hours =

×

60100 hours 30,000 = 50,000 hours

Budgeted fixed overhead = Actual fixed overhead + Expenditure variance = Rs.3,00,000 – Rs.50,000 = Rs.2,50,000

98

hour per raterecovery

overhead fixed Standard =

hours 50,0000Rs.2,50,00 = Rs.5 per hour

Total overhead rate per hour = Rs.10 Variable overhead rate per hour = Rs.5 (Rs.10 – Rs.5) 3. Standard fixed overhead per unit = Rs.15 (3 hours × Rs.5/-)

Ans. 37: 1. (a) Budgeted fixed overhead per unit:

Working notes:

= (Budgeted fixed overheads p.a / Budgeted output for the year) = Rs.4,80,000 p.a. / 1,20,000 units = Rs.4 per unit. (b) Budgeted fixed overhead hour: = Budgeted fixed overhead per unit / Standard labour hours per unit = Rs.4 / 2 hours = Rs.2 per hour 2. (a) Standard cost per unit: Rs. Direct material 20 (5 kg × Rs.4/- per kg) Direct labour 6 (2 hours × Rs.3/- per hour) Fixed overhead 4 (2 hours × Rs.2) Total standard cost (per unit) 30 (b) Budgeted selling price per unit Standard cost per unit 30 Standard profit per unit 10 (25% on slaes or 33 – 1/3% of standard cost) Budgeted selling price per unit 40 3 (a) Actual output units for April, 2001: Fixed overhead volume Variance = Efficiency variance + Capacity variance or (Budgeted output units – Actual output units) Budgeted fixed overhead p.u. Rs.2,400 (Favourable) + Rs.4,000 (Adverse) = Rs.1,600 (Adverse) or (10,000 units – x units) Rs.4 – Rs.1,600 (Adverse) or (10,000 units – 400 units) = x (Actual output units) or Actual output units = 9,600 units (b) Actual fixed overhead expenses: (budgeted fixed overhead – Actual fixed overhead) = Fixed overhead expenses variance or (Rs.40,000 – x) = Rs.1,400 (Favourable)

99

or x = Rs.40,000 – Rs.1,400 = Rs.38,600 4. (a) Actual sales quantity units: Sales volume variance

= Budgeted margin per unit

−

unitsquantity Budgeted

unitsquantity sales Actual

= Rs.4,000 (Adverse) = Rs.10 (x – 10,000 units) or 400 units = x – 10,000 units or x (Actual sales quantity) = 9,600 units (b) Actual selling price per units

Sales price variance = units Sales

Actualunit per price

selling Budgetedunit per price

Selling Actual

−

or Rs.9,600 (Fav.) = (x – Rs.40) × 9,600 units or Actual selling price per unit = Rs.41/- 5. (a) Actual quantity of material consumed:

Material usage variance = unit per

price Standardquantity

ActualquantityStandard

−

or 6,400 (Adv.) = (9,600 units × 5 kgs.) Rs.4 or x kgs. = 49,600 kgs. (actual quantity of material consumed) (b) Actual price per kg: Actual price per kg.: Material price variance = (Standard price per kg – Actual price per kg) Actual quantity of material

consumed -Rs.4,960 = (Rs.4 –Rs. y per kg.) 49,600 kg. -0.1 = (Rs.4 – Rs. y per kg) or y = Rs.4.10 per kg. 6. (a) Actual direct labour hour used: Labour efficiency variance = (Standard hours – Actual hours) Standard rate per hour Rs.3,600 (Favourable) = (9,600 units × 2 hours – p hours) Rs.3 Rs.3,600 (Favourable) = (19,200 hours – p hours) Rs.3 P hours = (19,200 hours – 1,200 hours) – 18,000 hours (Actual direct labour hours) (b) Actual direct labour hour rate:

Labour rate variance = hours labourDirect Actual

hour per rate Actual

hour per rateStandard

−

Rs.3,600 (Adverse) = (Rs.3 per hour – t per hour) 18,000 hours or t = Rs.3 + Rs.0.20 – Rs.3.20 per hour

100

(actual direct labour hour rate) 7. Actual fixed overheads: Fixed overhead expense variance = Budgeted fixed overhead – Actual fixed overhead

or Rs.1,400 (Favourable) = 10,000 units × Rs.4 p.u. – Actual fixed overhead or Actual fixed overhead = Rs.40,000 – Rs.1,400

or Actual fixed overhead = Rs.38,600 Annual financial Profit /Loss Statement

(for April, 2001)

Account Qty./ Hours Rate/Price Actual/ Value (a) (b) (c) (d)=(b)×(c) Sales: (A) 9,600 units 41 3,93,600 (Refer to working note 4) Direct Materials 49,600 kgs. 4.10 per kg. 2,03,360 (Refer to working note 5) Direct labour 18,000 hours 3,20 per hour 57,600 (Refer to working note 6) Fixed Overheads 18,000 hours 2.14444 per hour 38,600 (Refer to working note 6 (a) and 7) (Rs.38,600/18,000 hours) (absorbed on direct labour hour basis) Total costs: (B) 2,99,560 Profit : [(A) – (B)] 94,040

Working notes: Ans: 38.

1. Direct material units in actual output (Units) Output of units produced Add: Closing WIP units (200 units x 50% complete) Less: Opening WIP units (300 units x 100% complete) Total direct material units in actual output (work done)(i.e. units introduced)

7,620 100

(300) 7,420

2. Basic data of direct materials Standard Data

Actual output units 7,420 Actual Data

Standard quantity of material 11.130 (7,420 units x 1.5 kgs.)

S.P./ KG. Rs. 24

Amount Rs. 2,67,120

Actual qty. of material kgs. 11,224

A.P./KG. Rs. 23.75

Amount Rs. 2,66,570

3. Direct wages and overhead units in actual output (Units) Output of units produced Add: Closing WIP units (200 units x 40% complete) Less: Opening WIP units (300 units x 60% complete) Total direct wages and overhead units in actual output (work done)(i.e. units introduced)

7,620 80

(180) 7,520

4. Basic data of direct wages Standard Data

Actual output units 7,520 Actual Data

101

Standard Labour hours 22,560 (7,520 units x 3 hours)

S.W./ hour Rs. 400

Amount Rs. 90,240

Actual Labour hours 22,400

A.W./ hour Rs. 4.30

Amount Rs. 96,320

5. Budgeted variable overhead per unit = Difference in output

Difference in factory overhead

= (7,500 units – 6,000 units)

Rs.92,400 – Rs.81,600

=Rs.7.20 per unit 6 Budgeted fixed overheads (Rs.) Total overhead on 8,000 units (8,000 units x 12 0 Less: Variable overhead of 8,000 units @ Rs.7.20 per unit Budgeted fixed overheads

96,000 (57,600)

38,400 7. Basic data for variable overhead Budgeted data Actual data Budgeted variable overhead For actual hours (22,400 hours x Rs.2.40 Standard hours required per unit Standard variable overhead rate p.u Standard variable overhead rate p.u.

Rs.53,760

3 Rs.7.20

Rs.240

Actual variable overhead Actual output units Actual hours Actual variable overhead Recovery rate per hour

Rs.58,240 7,520

22,400 Rs.2.60

8. Basic data for fixed overhead Standard / Budgeted data Actual data Budgeted fixed overhead Budgeted output Budgeted hours Standard fixed overhead rate per hour Standard fixed overhead p.u Standard hours required p.u.

Rs.38,400

8,000 units 24,000

Rs.1.60 Rs.4.80

3

Actual fixed overhead (Rs.96,440 – Rs.58,240) Actual output Actual hours

Rs.38,200

7,520 units 22,400

Computation of Variances: Material variances 1. Material usage variance = (S.Q.-A.Q.) S.P. = (11,130 kgs.-11,224 kgs.) Rs.24 =Rs.2,256 (A) 2. Material price variance = (S.P.-A.P.) A.Q = (Rs.24-Rs.23.75) 11,224 kgs. =Rs.2,806 (F) 3. Material cost variance = (S.C.-A.C.) = (Rs.2,67,120-Rs.2,66,570) =Rs.550 (F) Labour variances 1. Labour efficiency variance = (S.H.-A.H.) S.R. = (22,500 hours- 22,400 hours) Rs.4 =Rs.640 (F) 2. Labour rate variance = (S.R.-A.R.) A.H = (Rs.4-Rs.4.3) 22,400 hours =Rs.6,720 (A) 3. Labour cost variance = (S.C.-A.C.) = (Rs.90,240 - Rs.96,320) =Rs.6,080 (A) Variable Overhead variances

102

1. Variable overhead ={ Budgeted variable overhead – Actual variable overhead} Expenditure variance = (Rs.53,760 – Rs.58,240) =Rs.4,480 (A) 2. Variable overhead =Standard variable {Standard hrs. – Actual hrs} Efficiency variance overhead rate per hour =Rs.2,40 (22,560 hrs – 22,400 hrs) =Rs.384 (F) 3. Total variable overhead cost variance = { Standard variable overhead –Actual variable overhead} = (7,520 units x Rs.7.20 – Rs.58,240) =Rs.4,096 (A) Fixed Overhead variances 1. Expenditure variance ={ Budgeted fixed overhead – Actual fixed overhead} = (Rs.38,400 – Rs.38,200) =Rs.200 (F) 2. Volume variance = { Budgeted volume – Actual volume} Standard fixed overhead rare per

unit =(8,000 units – 7,520 units) Rs.4.80 =Rs.2,304 (A) 3. Efficiency variance = { Standard hours for actual production –Actual hours} Standard fixed

overhead rate per hour = 22,560 hours – 22,400 hours) Rs.1.60 =Rs.256 (F) 4.Capacity variance ={Budgeted hours – Actual Hours } standard fixed overhead rate per hour = (24,000 hours – 22,400 hours ) Rs.1.60 =Rs.2,560 (A) 5.Total fixed overhead cost variance ={Fixed overhead recovered – Actual overhead} ={7,520 units x Rs.4.80 – Rs.38,200} =Rs.2,104 (A)

Statement of Equivalent Production in Units Ans. 39:

Particulars Materials Wages & Overhead % age Units %age Units

Units Completed 100% 9000 100% 9000 Closing W.I.P. 100% 900 50% 900 Equivalent Units 9900 9900

Material Variances

Standard qty for actual output ** x std price

Actual qty X actual price

Material A Material B

19,800 @ 3 9,900 @ 4

= 59,400 = 39,600

22,275@2.8* 10,889 @4.1*

= 62,370 = 44,649

29,700 99,000 33,165 1,07,019

*Actual Cost / Actual Quantity

** Standard Quantity for actual output = ( std qty/ budgeted prod) x actual output

MCV = TSC – TAC = 99,000 – 1,07,019 = 8,019 (A) MPV = AQ (SP – AP)

A = 22,275 (3 – 2.80) = 4,455 (F) B = 10,890 (4 – 4.10) = 1,089 (A)

103

3,366 (F) MUV = SP (SQ – AQ)

A = 3 (19,800 – 22,275) = 7,425 (A) B = 4 (9,900 – 10,890) = 3,960 (A)

11,385 (A) MMV = SP (RSQ – AQ)

A = 3 {19,800 ÷ 29,700 × 33,165 – 22,275} = 495 (A) B = 4 {9,900 ÷ 29,700 × 3,165 – 10,890} = 660 (F)

165 (F) MYV = S. C Per Unit (S. O. For Actual Mix – A. O.)

= 99,000 ÷ 9,900 {9,900 ÷ 29,700 × 33,165 – 9,900}

= 10 (11.055 – 9,900) = 11,550 (A)

Labour Variances:

LCV = TSC – TAC

= 2,40,000 ÷ 12,000 × 9,450 – 1,91,250 = 2,250 (A) LRV = AH (SR – AR)

= 48,000 {4 – (1,91,250 ÷ 48,000)} = 750 (F) LITV = No. of Idle hours × SR

= 48,000 – (47,500 ÷ 4) = 1,200 (A) LEV = SR (SH – AH)

= 4 {(60,000 ÷ 12,000) × 9,450 – 47,700} = 1,800 (A)

(ii) Variable Overhead Variances

VOC = Recovered Overheads – Actual Overheads

= 9,450 × 5 – 45,000 = 2,250 (F)

V.O (Exp.) V = Standard V.O. – Actual V.O.

= 47,700 × 1 – 45,000 = 2,700 (F)

V.O. (Eff.) V = Recovered Overheads – Standard Overheads

= 9,450 × 5 – 47,700 = 450 (A)

Fixed Overheads Variances

FOCV = Recovered Overheads – Actual Overheads

= (1,20,000 ÷ 12,000) × 9,450 – 1,20,900 = 94,500 – 1,20,900

= 26,400 (A)

F.O.(Exp.) V = Budgeted Overheads – Actual Overheads

= 1,20,000 – 1,20,900 = 900 (A)

FOVV = Recovered Overheads – Budgeted Overheads

= 95,500 – 1,20,000 = 25,500 (A)

Sales Variances

Sales Price Variance = Actual Unit Sold (SP – AP)

104

= 9,000 {50 – (4,57,500 ÷ 9,000)} = 7,500 (F) Sales Volume Variance (Contribution Loss)

= S. R. of Profit (Budgeted Qty. – Actual Qty.)

= (60,000 ÷ 12,000) (12,000 – 9,000) = 15,000 (A)

(a) sales Variance Ans 40:.

Present Market size =60,000 units. At 16% the share should have been = 60,000 x 16 100 =9,600 units.

Standard Gross Margin : SP Rs.53 – ( DM Rs.9 + DL Rs.24 + VO Rs.4 + FO Rs.12) = Rs.4 Budgeted Qty. Revised Budgeted

Qty Actual Qty. Booked Actual Qty.

Supplied Std. Gross Margin (Rs.)

8,000 9,600 8,200 7,500 4 (Rs.) Budgeted Qty. x Std. G.M.

Revised Budgeted Qty x Std. G.M.

Actual Qty. Booked x Std. G.M.

Actual Qty. Supplied x Std.G.M.

Actual G.M. Actual Qty. supplied x Actual G.M.

32,000 38,400 32,800 30,000 5 37,500 Market size variance 32,000 - 38,400 =6,400 F Market share variance 38,400 – 32,800 =5,600 A Sales volume variance 32,800 – 30,000 =2,800 A Sales price variance 30,000 – 37,500 =7,500 F Sales Margin Production Quantity Variance = (7500-8200)X4 = 2800 A [Note: Since actual order received ≠ actual sales quantity, Market share variance will be on the basis of actual order received and we will also calculate one further variance regarding inefficiency of production department about fulfilling order quantity, Sales Margin Production Quantity Variance = (Actual sales quantity – Sales order quantity) × Std. margin p.u. While calculating all other variance sales order quantity shall be ignored.] (b) Direct Material Variances (Units)

Std. requirement 7,200 units @ 1.5 kg. =10,800 kg.

Std. Qty.

Actual Qty. S.P. Rs.

Std. Qty. x SP Rs.

Actual Qty. x SP Rs.

AP Rs.

Actual Qty. x AP Rs.

10,800 12,000 6 64,800 72,000 6/50 78,000 Usage Variance Rs.64,800 – Rs.72,000 =Rs.7,200 A Price Variance Rs.72,000 – Rs.78,000 =Rs.6,000 A Total Variance Rs.64,800 – Rs.78,000 =Rs.13,200 A (c ) Direct Labour Variance

Std. hours produced 7,230 x 4 = 28,920

Production - Op. Stock + Cl. Stock Introduced

7,500 600 300

7200

Production Less: Op. Stock 600 x 100

75

Add: Cl. Stock 300 x 100

60

7,500

450

180 7,230

105

Std. Hours

Actual Hours S.R. Rs.

Std. Hrs. x SR Rs.

Actual Hrs. x SR Rs.

AR Rs.

Actual Hrs. x AR Rs.

28,920 29,000 6 1,73,520 1,74,000 6 / 25 1,81,250 Efficiency Variance (1,73,520 – 1,74,000) =480 A Rate Variance (1,74,000 – 1,81,250) =7,250 A Total variance =7,730 A (d) Variable Overheads Variance Rs. A =Charged to Production 28,920 Efficiency variance =Rs.80A 28,920 x 1 B =Std. Cost of Actual Hours 29,000 Expenditure variance =Rs.7,000 A 29,000 x 1 C =Actual Overheads 36,000 A – C Total V =Rs.7,080 A (e) Fixed Overhead Variance (Rs.) A = Charged to Production 28,920 x 3 86,760 B = Std. Cost of Act. Hrs. 29,000 x 3 87,000 C = Budget 96,000 D = Actual 94,000 Efficiency Variance (86,760 – 87,000) =Rs.240 (A) Volume Variance (86,760 – 94,000) =Rs.9,240 (A)

Ans. 41:

Rs. (1) Budgeted contribution = Budgeted Profit + Budgeted Fixed

Cost 15,000 + 15,000 = 30,000

Plus Contribution quantity variance 1,800 Total Standard contribution 31,800 Standard Contribution per unit 3 Actual Sales Volume 10,600 units (2) Actual Sales Volume 10,600 × 17 1,80,200 (3) Actual quantity of Raw Materials used Standard consumption 10,600 × 5 2,000 Kgs. Add: Material Usage Variance

.2400

2,000 kgs.

Actual consumption 55,000 Kgs. (4) Labour Efficiency variance Standard labour cost for Standard hours (63,000 + 600) 63,600 Standard labour cost for actual hours 61,950

106

Labour efficiency variance 1,650 F (5) Actual variable overhead Selling Overhead variance – Variable overhead Rs. 84,800 − Rs. 1,800 = Rs. 83,000 (6) Variable Overhead efficiency variance Actual hours (AH)

5.1950,61 41,300 hours

Standard hours (SH) 60,600 × 4 42,400 hours Standard rate per hour (SR)

4600,10600,63

× Rs. 1.5

Efficiency variance SR (SH – AH) = 2 (42,400 – 41,300) = 2,200F (7) Actual fixed overheads: Budgeted Overhead + Fixed Overhead

variance = 15,000 + 600 = Rs. 15,600.

(8) Operating profit variance If budgeted profit is considered (15,000 – 7,000) = Rs. 8,000 adverse If standard profit is considered (16,800 – 7,000) = Rs. 9,800 adverse

Ans. 42:

Where RSQ B = Revised Standard Quantity of ‘B’ = (Actual total qty of all DM used) × Standard Mix %age of ‘B’ and

SQ B = Standard quantity of DM ‘B’ for Actual Production = Standard quantity of all DM allowed for actual output × Standard Mix %age of ‘B’

Since Standard Mix %age is the same for both ‘A’ and ‘B’ (1: 1) we have, Total Yield variance for ‘A’ and ‘B’= T × (Std price of ‘A’ + Std price of ‘B’) Where T = (Std qty of all DM allowed for actual output - Actual total qty of all DM used)× 0.5

As Total Yield variance for ‘A’ and ‘B’ is given as – Rs 270, we have

- Rs 270 = T × Rs 24 + T × Rs 30

Or T = - 5

Hence Yield Variance for ‘A’ = - 5 × 24 = - Rs 120 and

107

Yield variance for ‘B’ = - 5 × 30 = - Rs 150. Also

Similarly

(SQ B - RSQ B ) × 30 = - 150 or SQ B - RSQ B = - 5

Alternative 1

Let total actual quantity consumed; X kg. Then, Quantity of A = X – 70

RSQ = X of A & X of B. (Since the Mix ratio is 1:1) 2 2

The Standard input for both ‘A’ and ‘B’ will be 0.5X – 5

Since Cost Variance for ‘A’ is given to be nil, we have, (SPA × SQA) − (AQA × APA) = 0 i.e. 24 × (0.5 X – 5) – (X − 70) × 30 = 0

or X = 110 Kgs

Therefore Actual Input for ‘A’ = 110 – 70 = 40 Kgs

Alternative 2

Let the standard input of ‘A’ = X kg. Therefore, the total standard input for ‘A’ + ‘B’= 2X Actual input = (2X

+ 10) Kgs. ∴ Actual input for ‘A’ = (2X +10 – 70)= (2X – 60)Kgs Forming the equation for nil cost variance of ‘A’. Rs. 24 × X – Rs. 30 × (2X – 60) = 0

Or X = 50 Kgs. Using this quantity in the Cost Variance of ‘B’, the actual price per kg. of ‘B’ (AP B) will be , 50 × 30 – 70 × APB = −1,300

Or APB = Rs. 40.

Alternative 3

Let the actual input of ‘A’ =X Then the total actual input = (X + 70). Therefore, RSQ of ‘A’ and ‘B’ each = 0.5X + 35 and Standard Input of ‘A’ and ‘B’ each = 0.5X +30.

Forming the equation for nil cost variance of ‘A’, we have,

24 × (0.5X + 30) – 30 × X = 0

Or X = 40 Kgs. ∴Standard Input will be 50 Kgs. Using this, quantity in the Cost Variance of ‘B’, the actual price per kg. of ‘B’ (AP B) will be, 50 × 30 – 70 × APB = −1,300

Or APB = Rs. 40.

Substituting various values for quantity and price, we get the following table.

(1) (2) (3) (4)

108

Std. Price × SQ

Std. Price × RSQ Std. Price × Actual Qty.

Actual Price × Actual Qty.

A 24 × 50 = 1200

24 × 55 = 1320 24 × 40 = 960 30 × 40 = 1200

B 30 × 50 = 1500

30 × 55 = 1650 30 × 70 = 2100 40 × 70 = 2800

2700 2970 3060 4000

(1) – (2) (2) – (3) (1) – (3) (3) – (4) (1) – (4) Yld variance Mix variance Usage variance Price variance Cost variance

A 1200 − 1320 = 120(A)

1320 − 960 = 360(F)

1200 − 960 = 240(F)

960 − 1200 = 240(A)

1200 − 1200 = 0

B 1500 − 1650 = 150(A)

1650 − 2100 = 450(A)

1500 − 2100 = 600(A)

2100 − 2800 = 700(A)

1500 − 2800 = 1300(A)

270A) 90A) 360A) 940A) 1300A) Actual Output = 90 Kgs.

(Actual output and standard o utput are always equal numerically in any material variance analysis) Standard output = Standard input – Standard loss or 100 – 10 = 90 Kgs.

Ans. 43:

Working Notes

a) Computation of Standard Price per kg of Material Let ‘x’ be the standard price per kg Direct material price variance = Rs. 15,750 (A) (given) A.Q. (S.P. – A.P.) = DMVP 63,000 kgs (x – 3.25) = -15,750 63,000 x – 2,04,750 = -15,750 63,000x = 1,89,000 x = 1,89,000 / 63,000 = 3 ∴ Standard price per kg of material is Rs. 3 b) Computation of Standard Quantity of material for actual output Let ‘x’ be the standard quantity Direct material usage variance = Rs. 27,000 (A) (given) S.P. (S.Q. – A.Q.) = DMUV 3(x – 63,000) = -27,000 3x – 1,89,000 = -27,000 3x = 1,62,000 x = 1,62,000/ 3 = 54,000 ∴ Standard Quantity for actual output is 54,000 kgs. c) Computation of Standard Labours hours per unit Let ‘x’ be the Standard labour hours per unit D.L. rate variance + D.L. efficiency variance =D.L. Cost Variance Rs. 6,840 (A) + Rs. 10,800 (F) = Rs. 3,960 (F) Direct labour cost variance = Rs. 3,960 (F) (given) Standard cost of Standard hours – Actual cost of actual hours = Rs. 3,960 (F) (x X Rs.6) – (Rs. 2,12,040 = Rs. 3,960 (F) 6x = Rs. 2,16,000 x = 2,16,000 / 6 = 36,000

109

∴ Standard hours for actual output is 36,000 hours Standard hours per unit = 36,000 hours/ 18,000 units = 2 hrs. d) Computation of Actual Hours per unit Let ‘x’ be actual hours Direct labour efficiency variance = Rs. 10,800 (F) (given) (Standard hours – Actual hours) Std. rate = DLEV [(18,000 units X 2) – x] Rs. 6 = Rs. 10,800 (F) 2,16,000 – 6x = 10,800 6x = 2,16,000 – 10,800 x = 34,200 ∴ Actual labour hours are 34,200 for actual output Actual labour hours per unit = 34,200 hrs / 18,000 units = 1.9 hrs. e) Computation of Standard variable overhead per hour Budgeted fixed overheads – Actual fixed overheads = Fixed overhead expense variance Let Budgeted fixed overheads be ‘x’ FOEV = Rs. 25,000 (A) (given) x – Rs. 3,25,000 = Rs. 25,000 (A) x = 3,25,000 – 25,000 = 3,00,000 ∴ Budgeted fixed overheads is Rs. 3,00,000 Standard fixed overhead rate per unit = Rs. 3,00,000/ 20,000 units = Rs. 15 per unit Standard fixed overhead rate per hour = Rs. 15 / 2 hours = Rs. 7.50 per hour f) Computation of Budgeted selling price per unit Let ‘x’ be the budgeted selling price per unit Sales price variance = Rs. 45,000 (F) (given) Actual quantity (Actual selling price – Budgeted selling price) = Sales price variance 18,000 units (Rs. 67.50 – y) = Rs. 45,000 (F) 12,15,000 – 18,000y = 45,000 18,000y = 12,15,000 – 45,000 y = 11,70,000 / 18,000 = 65 ∴ Budgeted selling price is Rs. 65 per unit.

Budgeted Sales Actual Sales Quantity (Units)

Price (Rs. p.u.)

Amount Rs.

Quantity (Units)

Price (Rs. p.u.)

Amount Rs.

20,000 65 13,00,000 18,000 67.50 12,15,000

Statement showing Standard Cost per unit and Budgeted Profit for 20,000 units. Particulars Per Unit For 20,000 Units Sales (a) 65 13,00,000 Costs: Direct Material 9 1,80,000 Direct Labour 12 2,40,000 Variable Overhead 16 3,20,000 Fixed Overhead 15 3,00,000 Total Cost (b) 52 10,40,000 Standard Gross Margin 13 2,60,000 (ii) Computation of sales gross margin volume and fixed overheads volume variances Sales Gross Margin Volume Variance = Standard Margin per unit (Actual Quantity – Budgeted Quantity) = Rs. 13 (18,000 units – 20,000 units) = Rs. 26,000 (A) Fixed Overhead Volume Variance = Standard fixed overhead rate per unit (Actual output – Budgeted output)

110

= Rs. 15 (18,000 units – 20,000 units) = Rs. 30,000 (A) Operating Statement Reconciling the Budgeted Profit with Actual Profit (Rs.) Budgeted Profit (20,000 units X Rs. 13 p.u.) 2,60,000 Sales Margin Volume Variance 26,000 (A) Standard Profit 2,34,000 Sales Price Variance 45,000 (F) 2,79,000 Cost Variances: Favourable Adverse Direct Material Price Variance - 15,750 Direct Material Usage Variance - 27,000 Direct Labour Rate Variance - 6,840 Direct Labour Efficiency Variance 10,800 - Variable Overheads Expense Variance - 3,420 Variable Overheads Efficiency Variance 14,400 - Fixed Overheads Expense Variance - 25,000 Fixed Overheads Volume Variance - 30,000 25,200 1,08,010 82,810 (A) Actual Profit 1,96,190

Ans: 44: Reconciliation Statement of Actual profit and Standard profit. (Rs)

Budgeted Profit (10,000 @ Rs.32) Less: Sales volume variance (Adverse) (Rs.32 (8,000-10,000) Standard profit (8,000 units @ Rs.32)

3,20,000 64,000

2,56,000 Cost Variances:

1. Direct Materials (i) Price variance 16,500(Rs.20-Rs.24) (ii) Usage Variance Rs.20 (16,000-16,500)

2. Direct labour (i) Labour rate variance 1,70,000(Rs.2.00-Rs.2.04) (ii) Labour efficiency variance Rs.2 (1,60,000-1,66,000) (iii) Idle time variance (Rs.2.00 x 4,0000

3. Variable Overheads (Rs.8 x 8,000) – Rs.60,000 4. Fixed Overheads (i) Expenses variance (Rs.20 x 10,000) –Rs.1,84,000

(ii) Efficiency variance Rs.20 (8,000 – 8,300) (iii) Capacity variance Rs.20 (8,300 – 10,000) Total

Less: Net Adverse variance Actual profit for the period

Adverse

66,000 10,000

6,800

12,000 8,000 4,000

16,000 6,000

34,000 1,42,800

Favourable

20,000

1,22,800 1,33,200

Ans. 45:

(b) Working notes:

Ravi Richard Rahim Roop Singh (i) Standard sales units : 1,875 2,250 2,875 1,500

Sales quota ÷ Rs. 400 (ii) Standard selling expenses per unit (Rs.) 120 110 100 150

(Std. selling expenses/Std. sales units) (iii) Actual sales units : 2,000 2,500 2,625 1,300

Actual sales÷Rs. 400

(iv) Actual selling costs Rs. Rs. Rs. Rs. Daily allowance 16,000 14,000 18,000 20,000

111

Conveyance allowances 30,000 27,000 27,000 45,000 Salaries 80,000 80,000 80,000 80,000 Free samples 9,000 7,500 5,375 8,000 Postage & stationery 8,000 9,000 10,000 6,000 Other expenses 9,000 5,000 4,000 10,000 Commission on sales 48,000 50,000 52,500 26,000 Corporate sales office expenses 60,000 75,000 1,05,000 52,000 Total actual selling cost 2,60,000 2,67,500 3,01,875 2,47,000 (v) Standard selling cost 2,40,000 2,75,000 2,62,500 1,95,000

(Actual units sold × Std. selling expenses per unit)

Since all the selling expenses have been related to sales units, only one variance can be calculated by comparing the standard and actual selling costs as is shown in the schedule below:

Schedule showing the selling cost variances by salesman Rs. Rs. Rs. Rs. Total (Rs.)

Standard Selling expenses (Refer to Working Note (v)) 2,40,000 2,75,000 2,62,500 1,95,000 9,72,500 Actual selling expenses (Refer to Working Note (iv)) 2,60,000 2,67,500 3,01,875 2,47,000 10,76,375 Selling cost variance (20,000) 7,500 (39,375) (52,000) (1,03,875) (A) (F) (A) (A) (A)

A = Adverse F = Favourable

Statement showing the computation of standard cost of production of shirts Ans 46:

Lot no. Units Cost per Total standard (Dozen) Dozen cost( Rs.) 45(UK) 1,700 531.00 9,02,700 46(US) 1,200 477.60 5,73,120 47(CAN) 1,000 531.00 Total

5,31,000

20,06,820

Cost per Dozen of 46 (US) lot. (Rs.) Material cost 100% 264.00 Conversion cost 80%(80%of Rs.267) Total

213.60

477.60

Statement of material used and its variance Lot no. Output Std. Qty Total Total Variation Dozen per Dozen Std. qty. Actual Qty. ( Mtrs.) ( Mtrs.) ( Mtrs.) 45(UK) 1,700 24 40,800 40,440 360(F) 46(US) 1,200 24 28,800 28,825 25(A) 47(CAN) 1,000 24 Total

24,000 24,100 100(A)

93,600 93,365 235(F)

Statement of labour hour worked and its variance Lot no. Output Std.labour Total labour Total actual Variation Dozen hour per hours labour hours (Hours) Dozen

112

45(UK) 1,700 3 5,100 5,130 30(A) 46(US) 960 3 2,880 2,980 10(A) (1200×0.8) 47(CAN) 1,000 3 Total

3,000 2,890 20(F)

10,980 11,000 20(A)

Calculation of variances (1) Material price variance actual quantity (standard rate –actual rate) = (95,000 metres *Rs. 11)-Rs.10,64,000 = Rs.10,45,000-Rs. 10,64,000 =Rs. 19,000(A) (2) Labour rate variance actual hour (Std. rate per hour – actual rate per hour ) = 11,000 (Rs. 49-Rs.50) = Rs.11,000(A) (3) Variable overhead efficiency variance Std. variable overhead rate per hour (Std.hour –actual hour) = Rs. 24(10980-11,000) = Rs. 480 (A) (4) Fixed overhead volume variance Std. fixed overhead rate per hour (Std.hour for actual output–Budgeted hour) = Rs. 16(10980-48000×3/12) = Rs. 16,320(A) Working Notes :

(1) standard variance overhead rate per hour = 40*60/100 = Rs.24

(2) standard fixed overhead rate per hour

= Rs. 40*40/100= Rs. 16

Ans: 47.

1. Sales variances (5) Sales Volume Margin Variance

(Std. Margin on actual Sales – Budgeted Margin) =(Rs.25,000 units x Rs.6) – (36,000 units x Rs.6) =(Rs.1,50,000 – Rs.2,16,000) =Rs.66,000 (A)

(6) Sales Price Variance (Actual Sales at actual price – Actual Sales at Std. Price) =(25,000 Units x Rs.51.50)-(25,000 units x Rs.50) =(Rs.12,87,500 – Rs.12,50,000) =Rs.37,500 (F)

2. Material variances (1) Material Price Variance

(Std Cost of Material Used- Actual Material Cost =(96,000 kgs x Rs.2) – (96,000 kg. x Rs.2.25) =(Rs.1,92,000 – Rs.2,16,000) =Rs.24,000(A)

(3) Material Usage Variance Std Material cost of Actual production- Std. Cost of Material used) =(1,00,000 kgs. x Rs.2) – (96,000 Kgs. x Rs.2) =(Rs.2,00,000 – Rs.1,92,000) =Rs.8,000 (F) 3. Labour Variances

(1) Labour Wages Rate Variance (Actual Labour hrs. at Std. rate- Actual Labour Wages) =(1,60,000 hrs x Rs.4) – (1,60,000 hrs. x Rs.4.10) =(Rs.6,40,00 – Rs.6,56,000) =Rs.16,000 (A)

113

(2) Labour Efficiency Variance Std. Labour Wages for actual production –Actual Labour hours worked at Std. rate) =(1,50,000 hrs. x Rs.4) –(1,54,000 hrs. xRs.4)

=(Rs.6,00,000 – Rs.6,16,000) =Rs.16,000 (A)

(3) Idle Time variance (6,000 hrs. x Rs.4 variance) =Rs.24,000 (A) 4. Variable Overhead Variances

(1) Total Variable overhead Variance (Allowed Expenditure for actual hours-Actual variable overheads) =Rs.(1,84,000 – Rs.1,82,000) =Rs.2,800 (F)

(2) Variable overhead Efficiency Variance ( Allowed Expenditure for Std. hours- Allowed Expenditure for actual hours) =(Rs.1,50,000 hrs. x Rs.1.20)- 1,54,000 hrs. x Rs.1.20) =(Rs.1,80,000 – Rs.1,84,800) =Rs.4,800 (A)

5. Fixed Overhead Variances (1) Fixed Overhead Expenditure variance (Budgeted Expenditure – Actual Expenditure) =(Rs.1,44,000 – Rs.1,50,000) =Rs.6,000 (A) (2) Fixed Overheads Efficiency variance (Std. hours of production x Std. fixed overhead recovery rate per hour)-(Actual hours worked x Fixed overhead recovery rate per hour) =(Rs.1,50,000 hrs. x Re.0.80)-(1,54,000 hrs. x Re.0.80) =(Rs.1,20,000 – Rs.1,23,200) =Rs.3,200(A) (3) Fixed Overhead Capacity variance (Actual hours worked x Fixed overhead recovery rate per hour)-(Std. Fixed overhead recovery r rate per hour x Budgeted capacity hours) =(1,54,000 hrs. x 0.80)-(Re.0.80 x 1,80,000 hrs.) =(Rs.1,23,200 – Rs.1,44,000) =Rs.20,800(A)

A. Std. Variable Overhead Rate per hour. = Total Std. hours

Std. Variable Overheads

=(30,000 units x Rs.12)-Rs.1,44,000 1,80,000 units

=Rs.1.20

B. Std Fixed Overheads rate per hour

= Budgeted hours

Budgeted Overheads

=Rs.1,44,000 / 1,80,000 hrs. =Rs.0.80 Statement of actual profit / loss for the second quarter of the year (Rs.) Direct Material (96,000 kgs.@Rs.2.25) Direct Wages (1,60,000 hrs. ‘ Rs.4.10) Overhead Total Cost Sales Revenue (25,000 units @ 51.50) Actual Profit

2,16,000 6,56,000 3,32,000

12,04,000 12,87,500

83,500

Operating Statement reconciling the budgeted profit with actual profit (Rs.) Particulars Reference to

working note Variance

Favourable Adverse

Actual

Budgeted profit (36,000 units x Rs.6) 1. Sales – Volume Margin Variance

Price Variance Profit before adjustment of Cost Variances

- (1) (2)

- -

37,500

- 66,000

-

2,16,000 - -

1,87,500

114

II Material - Price - Usage

III. Labour - Rate -Efficiency -Idle time

IV. V. Overheads -Expenditure -Efficiency V. F. Overheads -Expenditure - Efficiency -Capacity Actual Profit

(1) (2) (1) (2) (3) (1) (2) (1) (2) (3)

- 8,000

- - -

2,800 - - - -

10,800

24,000 -

16,000 16,000 24,000

- 4,800 6,000 3,200

20,800 1,14,800

1,04,000 83,500

Ans. 48:

Expenses

Overhead Expenses Schedule Budget: 120 Std. Hours Actual: 156 Hours

Rate per hour Rs.

Expenses R s .

Rate per hour Rs.

Expenses R s .

Indirect material Indirect labour Maintenance Power Sundries Total variable overheads Fixed overheads Total overheads

0.40 0.60 0.40 0.30 0.30

48 72 48 36 36

0.50 0.60 0.45 0.32 0.29

78 94 70 50 45

2.00

2.00

240

240

2.16 337

250 480 587

Actual output = 12,160 units. Hence standard hours produced or std. hours for actual production

=

Computation of variances:

A. Fixed expenses (a) Charged to production (152 hours × Rs. 2 per hours) Rs. 304 (b) Fixed expenses as per budget Rs. 240 (c) Actual fixed overheads Rs. 250

Volume variance = Fixed overhead recovery rate (Actual volume in std. hrs. – Budgeted volume in standard hrs.)

= Rs.2 (152 – 120) = Rs.64 (F) Expenses variance = (Budgeted expenses – Actual expenses)

= Rs.240 – Rs.250 = Rs. 10 (A) Total variance = (Fixed overheads absorbed – Actual fixed overheads)

= Rs.304 – Rs.250 = Rs.54 (F) Or Volume variance: (a – b) Rs.64 (F) Expenses variance: (b – c) Rs. 10 (A) Total variance : (a – c) Rs.54 (F)

B. Variable expenses (a) Charged to production: (152 hours × Rs.2) Rs.304

115

(b) Actual expenses Rs.337 Variable overhead cost variance (a – b) Rs.33 (A)

Ans. 49:(1) Statement showing standard and actual costs of material for 1,000 units of output and standard cost of actual

input

Basic Data:

Standard Cost Actual cost Standard cost of actual input = (Actual quantity × Standard

price)

Ma Qty. Price Amount Qty. Price Amount Actual Qty.

Standard Price/kg

Amount

Kg. Rs. Rs. Kg. Rs. Rs. Kg. Rs. Rs.

A 12,000 10 1,20,000 11,000 11 1,21,000 11,000 10 1,10,000

B 5,000 6 30,000 5,200 5.50 28,600 5,200 6 31,200

1,50,000 1,49,600 1,41,200

Standard yield (units) = Kg. 17,000

units 1,000 × 16,200 kg. = 952.941764 units approx.

(2) Statement showing standard and actual labour cost of 1,000 units produced and standard cost of actual labour hrs.

Hours Rate p.h.

Amount Hours Rate p.h.

Amount Hours Rate p.h.

Amount

Rs. Rs. Rs. Rs. Rs. Rs. 5,000 3 15,000 5,500 3.1818 17,500 5,500 3 17,500

(3) Overheads

Fixed overheads (Rs.) Budgeted Actual Hours 38,500 39,000 Output 5,500 5,500 Standard time p.u. (hrs.) 1,100 1,000 Standard fixed overheads p.u. (Rs.) 5 Standard fixed overhead rate p.h. (Rs.) 35 Computation of material variances (Refer to Basic data 1): 7 Computation of material variances (Refer to Basic data (1): Material cost variance = Standard cost – Actual cost

= Rs.1,50,000 – Rs.1,59,500 = Rs.9,500 (Adv.) Material price variance = Actual quantity (Std. price – Actual price)

= 12,000 kg (Rs.10 – Rs.11) + 5,000 kg (Rs.6 – Rs.5.50) = Rs.12,000 (Adv.) + Rs.2,500 (Fav.) = Rs.9,500 (Adv.)

Material usage variance = Standard price (Standard quantity – Actual quantity)

116

= Rs.10 (12,000 kg – 11,000 kg) + Rs.6(5,000 kg–5,200 kg) = Rs.10,000 (Fav.) + Rs.1,200 (Adv.) = Rs.8,800 (Fav.)

Material mix variance = Total actual quantity

−kg 16,200

of price Std.kg per mix Std.

of price Std.

= 16,200 kg

−kg 16,200

0Rs.1,41,20kg 17,000

0Rs.1,50,00

= Rs.1,741.18 (Fav.) Material yield variance = Std. Rate (Actual yield – Std. Yield

= Rs.150 (1,000 units – 952.9411764 units) = Rs.7058.82 Material purchase price variance: = Actual quantity of material purchased (Std. Price per kg. – Actual price per kg) = 12,000 kg (Rs.10 – Rs.11) + 5,000 kg (Rs.6 – Rs.5.50) = Rs.12,000 (Adv.) + Rs.2,500 (Fav.) = Rs.9,500 (Adv.)

Computation of labour variances (Refer to basic data 2): Labour cost variance = (Standard cost – Actual cost)

= Rs.15,000 – Rs.17,500 = Rs.2,500 (Adv.) Labour rate variance = Actual hrs. (Std. Rate – Actual rate)

= 5,500 (Rs.3 – Rs.3.1818) = Rs.1,000 (Adv.)

Labour efficiency variance = Std. rate p.h. (Std. Hours – Actual hours) = Rs.3 (5,000 hrs. – 5,500 hrs.) = Rs.1,500 (Adv.)

Computation of fixed overhead variance: Total fixed overhead variance: = Fixed overhead absorbed – Actual fixed overhead = 1,000 units × Rs.35 – Rs.39,000 = Rs.35,000 – Rs.39,000 = Rs.4,000 (Adv.) Fixed overhead expenditure variance: = Budgeted fixed overhead – Actual fixed overhead = Rs.38,500 – Rs.39,000 = Rs.500 (Adv.) Fixed overhead volume variance: = Std. Fixed overhead rate per unit (Actual output – Budgeted output) = Rs.35 (1,000 units – 1,000 units) = Rs.3,500 (Adv.) Efficiency variance: = Std. fixed overhead rate per unit (Actual output – Budgeted output)

117

= Rs.35 (1,000 units – 1,000 units) = Rs.3,500 (Adv.) Ans. 50:

1. Standard quantity and cost of raw material required for actual output (i) Working Notes:

Actual output of EXE (units) Standard output per kg. of raw material (units) Standard quantity of raw material required for actual output (kgs.) (4,680 units / 12 units) Standard cost of 390 kgs. of raw material at Rs.60 per kg. (Rs.) 2. Basic data for the computation of labour variances:

Standard labour data for actual output

Actual data

Std. Time hours Rate p.h.

Amount Standard cost of actual hours

Actual cost

hours

Rate p.h.

Amount

2,340 5 11,700 12,000 240 4.80 1,152 (4,680 units ×½ hr.) 320 5.20 1,664 5.00 1,840 9,200

2,340 11,700 12,000 2,400 3. Basic data for the computation of fixed overhead variances:

12,016

Budgeted / Std. data Actual data

Budgeted fixed overhead (Rs.) (for 1 week)

24,400 Actual fixed overhead (Rs.) 19,800

Budgeted hours 2,400 Actual labour hours 2,400

(60 workers×40 hrs. per week) Actual output (units) 4,680

Budgeted output (units) 4,800

Std. rate p.h. (Rs.) 8.50

Std. rate p.u. (Rs.) 4.25 (i) Computation of labour and overhead (variances): Labour cost variance: (Refer to working Note 2) = (Std. cost of labour – Actual cost of labour) = Rs.11,700 – Rs.12,016 = Rs.316 (Adverse) Labour rate variance: = Actual hours (Std. rate – Actual rate) = Rs.12,000 – Rs.12,016 = Rs.16 (Adv.) Labour efficiency variance:

118

= Standard rate per hr. (Std. hours – Actual hours paid) = (Rs.11,700 – Rs.12,000) = Rs.300 (Adv.) = Total fixed overhead cost variance: = (Fixed overhead absorbed – Actual fixed overhead) = [(4,680 units × Rs.4.25) – Rs.19,800] = Rs.19,890 – Rs.19,800 = Rs.90 (Fav.) Fixed overhead volume variance: = Std. fixed overhead rate per unit [Actual output – Budgeted output] = Rs.4.25 (4,680 units – 4,800units) = Rs.510 (Adv.) Fixed overhead expenditure variance: = [Budgeted fixed overhead – Actual fixed overhead] = [Rs.20,400 – Rs.19,800] – Rs.600 (Fav.) (ii) Statement showing total standard cost, standard profit and actual profit for the week.

Sales Rs. Rs. 4,680 units × Rs.15 70,200 Less: Standard cost of : Direct material 23,400 Direct labour 11,700 Overheads 19,890 54,990 (4,680 × Rs.4.25) (Refer to working notes 1 to 3) Standard Profit 15,210 Less: Adjustment for variance: Raw Material: Price variance : 800 (A) Usage variance : 600 (A) 1,400 (A) Labour: Rate Variance : 16 (A) Efficiency variance : 300 (A) 316 (A) Overhead: Expenditure variance: 600 (F) Volume variance: 510 (F) 90 (F) 1,626 Actual Profit 13,584

Sales variances (Sales Value Method) Ans.51:

Budgeted Calculations: Budgeted Sales Actual Sales

119

Product Qty. Units

Rate Rs.

Amount Rs.

Qty. Units

Rate Rs.

Amount Rs.

Actual quantity×

Budgeted price Rs.

A 10,000 12 1,20,000 11,000 11.50 1,26,500 1,32,000 B 6,000 15 90,000 5,000 15.10 75,500 75,000 C 8,000 9 72,000 9,000 8.55 76,950 81,000 24,000 2,82,000 25,000 2,78,950 2,88,000 Computation of sales variances :

(1) Sales value variance = Actual sales – Budgeted sales = Rs. 2,78,950 – Rs. 2,82,000 = Rs. 3,050 (A) (2) Sales price variance = Actual quantity (Actual price – Budgeted price) = Rs. 2,78,950 – Rs. 2,88,000

= Rs. 9,050 (A) (3) Sales volume variance = Budgeted price (Actual Qty. –Budgeted Qty.)

= Rs. 2,88,000 – Rs. 2,82,000 = Rs. 6,000 (F) (4) Sales mix variance = Total actual qty. (Budgeted price of actual mix –

Budgeted price of budgeted mix)

= = 25,000 units (Rs. 11.52 – Rs. 11.75)

Rs. 5,750 (A) (5) Sales quantity variance = Budgeted price of budgeted mix (Total actual

quantity – Total budgeted qty.)

Check

=

= Rs. 11.75 (25,000 – 24,000) Rs. 11,750 (F)

Sales value variance = Sales price variance + Sales volume variance Rs. 3,050 (A) = Rs. 9,050 (A) + Rs. 6,000 (F) Sales volume variance = Sales mix variance + Sales quantity variance Rs. 6,000 (F) = Rs. 5,750 (A) + Rs. 11,750 (F)

Alternative solution (sales margin method)

Basic calculations : Budgeted margin Actual margin

Actual quantity ×

Budgeted margin

Product Qty. Rate Amount Qty. Rate Amount

Units Rs. Rs. Units Rs. Rs. Rs. A 10,000 5 50,000 11,000 4.50 49,500 55,000 B 6,000 6 36,000 5,000 6.10 30,500 30,000

120

C 8,000 3 24,000 9,000 2.55 22,950 27,000 24,000 1,10,000 25,000 1,02,950 1,12,000 Computation of variances:

Sales margin variance = Actual margin – Budgeted margin = Rs. 1,02,950 – Rs. 1,10,000

= Rs. 7,050 (A) Sales price margin variance = Actual quantity (Actual margin – Budgeted margin)

= Rs. 1,02,950 – Rs. 1,12,000 = Rs. 9,050 (A) Sales margin mix variance = Total actual quantity (Budgeted margin of actual mix –Budgeted

margin of budgeted mix

Material Variances: Basic Calculations

Standard and actual costs of material for actual output i.e. 11,000 units of A, 5,000 units of B and 9,000 units of C and standard cost of actual input material.

Material Standard cost Actual cost Actual quantity × standard price

Q t y Units

Rate Rs.

Amount Rs.

Qty. Units

Rs.

Rate Amount Rs.

X 51,000* 2 1,02,000 54,000 1,09,620 1,08,000 Y 74,000** 1 74,000 72,000 73,000 72,000 1,25,000 1,76,000 1,26,000 1,82,620 1,80,000 * 11,000 × 2 + 5,000 × 4 + 9,000 × 1 = 51,000 **11,000 × 3 + 5,000 × 1 + 9,000 × 4 = 74,000.

Computation of variances : Material cost variance = Standard cost – Actual cost

= Rs. 1,76,000 – 1,82,620 = Rs. 6,620 (A) Material price variance = Actual quantity (Standard price – Actual price)

= Rs. 1,80,000 – Rs. 1,82,620 = Rs. 2,620 (A) Material mix variance = Total quantity (Standard price of standard mix – Standard price of actual mix

121

Check: Material cost variance = Material price variance + Material mix variance

+ Material yield variance

Rs. 6,620(A) = Rs. 2,620(A) + Rs. 2,592(A) + Rs. 1,408(A)

(i) Reconciliation statement showing which factor has contributed change in profit Ans. 52

(Rs. in lacs)

Favourable Adverse Increase in contribution due to increase in volume (Rs.280 lacs – Rs.240 lacs) 40 — (Refer to working note 3) Sales price variance 140 (Refer to working note 3) Material usage variance 52 (Refer to working note 4) Material price variance — 0 (Refer to working note 4) Direct labour rate variance — 28 (Refer to working note 4)

Direct labour efficiency variance 36 — (Refer to working note 4) Fixed overhead expenditure variance (Refer to working note 3) — 140

268 168 Total change in profit 100

= 160 lakhs = Rs. 800 lakhsRs. 240 lakhs 100Rs. 1200 lakhs

×

Break-even sales (Year 2)

122

(Refer to working note 3) = 300 lakhs = Rs. 962.50 lakhsRs. 480 lakhs 100Rs. 1540 lakhs

×

(iii) Percentage increase in selling price needed over the sales value of year 2 to earn a margin of safety of 45% in year 2 P/V ratio = (Rs. 480 lacs/Rs. 1,540 lacs) × 100 = 31.169%

If Margin of safety to be earned is 45% then Break-even point should be 55% Revised contribution = 1,540 lacs × 35.4193% = 545.45 lacs Present contribution = Rs. 480 lacs Increase in selling price required = Rs. 65.45 lacs (Rs. 545.45 lacs – Rs. 480 lacs)

Working notes: 1 . Budgeted sales in year 2 If actual sales in year 2 is Rs. 110 then budgeted sales is Rs. 100.

3 . Statement of figures extracted from working results of a company

(Figure in lacs of Rs.)

Year 1 Year 2 Year 2 Total Actual (Budgeted) Actual Variance

(a) (b) (c) d = (c) – (b)

Sales : (A) 1,200 1,400 1,540 140 (Fav.)

123

(Refer to working note 1)

Variable costs : Direct material 600 700 648 52 (Fav.) (Refer to working note 2) Direct wages and variable overhead 360 420 412 8 (Fav.) (Refer to working note 2) Total variable costs : (B) 960 1,120 1,060 60(Fav.) Contribution (C) = {(A) – (B)} 240 280 480 200 (Fav.) Less : Fixed cost 160 160 300 140 (Adv.)

Profit 80 120 180 60(Fav)

Total variable costs : (B) 960 1,120 1,060 60(Fav.) Contribution (C) = {(A) – (B)} 240 280 480 200 (Fav.) Less : Fixed cost 160 160 300 140 (Adv.) Total variable costs : (B) 960 1,120 1,060 60(Fav.) Contribution (C) = {(A) – (B)} 240 280 480 200 (Fav.) Less : Fixed cost 160 160 300 140 (Adv.)

Profit 80 120 180 60(Fav)

(4) (i) Data for Material variances :

Standard data for actual output Actual data

Quantity Rate per Amount Quantity Rate per Amount of material m/t of material m/t

m/t m/t Rs. Rs. Rs. Rs.

5,83,333 120 700 lacs 5,40,000 120 648 lacs Material price variance = (Standard rate – Actual rate ) Actual quantity = Nil

Material usage variance = (Standard quantity - Actual quantity) Standard rate per m/t

= (5,83,333 – 5,40,000) Rs.120 = Rs. 52 lacs (Fav.)

(ii) Data for labour variances overhead variances

Standard data for actual output Actual data

Labour Rate per Amount Labour Rate per Amount hours hour hours hour

Rs. Rs. Rs. Rs.

87,50,000 4.80 4.20 lacs 80,00,000 5.15 412 lacs Labour rate variance = (Standard rate – Actual rate) Actual labour hours

= (Rs.4.80 – Rs.5.15) 80,00,000 = Rs. 28 lacs (Adv.)

Labour and variable overhead efficiency variance :

= {Standard labour hours – Actual labour hours} × Standard rate per hour

= {87,50,000 – 80,00,000} Rs. 4.80 = Rs. 36 lacs (Adv.)

124

Ans. 53:Equivalent Production in Units

Basic Calculations

Particulars Direct Material Labour & Overhead Units completed 100 % 6,000 100 % 6,000 Work-in-progress 100 % 600 50 % 300 Total Equivalent Units 6,600 6,300 (a) Direct Material Variances

Material Standard output 6,600 units Actual

output 6,600 units

Qty. Rate (Rs.) Amount (Rs.) Qty. (kg) Rate (Rs.) Amount (Rs.) A 13,200 3 39,600 14,850 2.90* 43,065 B 6,600 4 26,400 7,260 4.098* 29,750

19,800 66,000 22,110 72,815 *(Actual Cost/ Actual Quantity) DMCV = Standard Cost for actual output – Actual Cost = 66,000 – 72, 815 = Rs. 6,815 (A) DMPV = Actual Qty. (Std, Rate – Actual Rate) A = 14,850 (3 – 2.90) = 1,485 (F) B = 7,260 (4 - 4.098) = 710 (A) 775 DMUV = Std. Rate (Std. Qty. for actual output – Actual Qty.)

(F)

A = 3 (13,200 – 14,850) = 4,950 (A) B = 4 (6,600 – 7,260) = 2,640 (A) 7,590DMMV = Std. Rate (Revised Std. Qty. – Actual Qty.)

(A)

A = 3 = 3 (14,740 – 14,850) = 330 (A) B = 4 = 4 (7,370 – 7,260) = 440

(F) 110

(F)

DMYV = Std. Cost per Unit (Std. output for actual mix – Actual output) = 66,000 = 10 (7,370 -6,600) = Rs. 7,700 (A) (b) Direct Labour Variances DLCV = Std. Cost for Actual Output – Actual Cost = (6,300 X 20) – 1,27,500 = Rs. 1,500 (A) DLRV = Actual Time (Std. Rate – Actual Rate) = 32,000 [ = Rs. 500 (F) ITV = Std. Rate X Idle Hours = 4 X 200 = Rs. 800 (A) DLEV = Std. Rate (Std. Time for actual production – Actual time worked) = 4 [(6,300 X5) – 31,800] = 4 (31,500 – 31,800) = Rs. 1,200 (A) (c) Variable Overhead Variances VOC = Recovered Overheads – Actual Overheads

125

= 6,300 X 5 – 30,000 = 31,500 – 30,000 = Rs. 1,500 (A) VOEXPV = Std. Variable Overheads – Actual Variable Overheads. = (31,800 X 1) – 30,000 = 31,800 – 30,000 = Rs. 1,800 (F) VOEEFV = Recovered Overheads – Standard Overheads = 1 X (31,500 -31,800) = Rs. 300 (A) (d) Fixed Overhead Variances FOCV = Recovered Fixed Overheads – Actual Fixed Overheads = (6,300 X 10) – 80,600 = 63,000 – 80,600 = Rs. 17,600 (A) FOEXPV = Budgeted Fixed Overheads – Actual Fixed Overheads = (8,000 X 10) – 80,600 = Rs. 600 (A) FOVV = Recovered Fixed Overhead – Budgeted Fixed Overhead = 63,000 – 80,000 = Rs. 17,000 (A) Fixed Overhead Volume Variances may be segregated into the following: FOEFFV = Std. Rate (Std. time for actual production – Actual time booked) = 2 (31,500 – 31,800) = Rs. 600 (A) FOITV = Std. Rate per hour X Idle hours = 2 X 200 = Rs. 400 (A) FOCAPV = Std. Rate per hour (Actual time – Budgeted time) = 2 (32,000 – 40,000) = Rs. 16,000 (A) (e) Sales Variances SPV = Actual Qty. (Std. Price – Actual Price) = 6,000 = Rs. 5,000 (F) Sales Volume Variance (Contribution loss) : = Std. Rate of profit (Budgeted Qty. – Actual Qty.) = 5 (8,000 – 6,000) = Rs. 10,000 (A) Operating Statement showing the Reconciliation between Budgeted and Actual Profit for the Month (Rs.) Budgeted Profit (8,000 X Rs. 5) Rs. Price 40,000 Sales Variances 5,000 (F) Volume 10,000 (A) Total 5,000 (A) 5,000 (A) Cost Variances: Direct Materials Price 775 (F) Yield 7,700 (A) Mix 110 (F) Direct Wages Rate 500 (F) Efficiency 1,200 (A) Idle Time 800 (A)

126

Variable Overheads Expense 1,800 (F) Efficiency 300 (A) Fixed Overheads Expense 600 (A) Efficiency 600 (A) Idle Time 400 (A) Capacity 16,000 (A) Total Cost Variances 24,415 (A) 24,415 (A) Actual Profit 10,585 Ans:54:(a) Material Price variance

Computation of Variances

Material (1)

Qty. Purchase Kg. (2)

Std. Price Rs. (3)

Actual Price Rs.(4)

Std. cost Rs. (2x3)=5

Actual Cost Rs. (2x4)=(6)

Price Variance Rs. (5-6)=(7)

A B

9,000 5,000

10.00 3.00

10.25 2.75

90,000 15,000

1,05,000

92,250 13,750

1,06,000

2,250 (A) 1,250 (F) 1,000 (A)

(b) Material Usage Variance

Material (1)

Std. Qty. for actual output (2)

Actual Qty. (3)

Std. Price (4)

Std. Cost of Std. Qty. (2x4)=5

Std. Cost of Actual (4x5)=6

Usage Variance (5-6)=(7)

A B

8,000 4,000

7,800 4,300

10 3

80,000 12,000 92,000

78,000 12,900 90,900

2,000 (F) 900 (A) 1,100 (F)

(C ) Labour Rate Variance

Actual Hours (1)

Std. Rate (2) Rs.

Actual Rate (3) Rs.

Std. Wage (4)=(1x2) Rs.

Actual Wages (5)=(1x3) Rs.

Rate Variance (6)=(4-5) Rs.

4200 3 2,875 12,600 12,075 525 (F) (d) Labour Efficiency Variance

Std. Hours for actual output (1)

Actual Hours (2)

Std. Rate (3) Rs.

Std. Cost of Std. Hours (4)=(1x3) Rs.

Std. Cost. Of Actual Hours (5)=(2x3) Rs.

Efficiency Variance (6)=(5-6) Rs.

4,000 4,200 3 12,000 12,600 600 (A) Overhead Variances Basic calculations (a) Budgeted overheads for November = 10,800 X 25

12 =Rs.22,500

(b) Std. hours produced for November = 800 units X 5 hrs per unit=4,000 (c ) Fixed production overheads per hour = 25/5=5 (d) Recovered overhead = 4,000 X 5 =Rs.20,000 (e) Actual overheads = Rs.23,500 (f) Standard overheads = 4,200 X 5 =Rs.21,000 Variances Overhead Cost variance =Recovered Overheads- Actual Overheads =20,000-23,5000 =Rs.3,500 (A) Overhead Expenditure Variance =Budgeted Overheads-Actual overheads =22,500-23,500 =Rs.1,000 (A)

127

Overheads Volume variance =Recovered Overheads-Budgeted Overheads =20,000-22,500 =Rs.2,500 (A) Overhead Volume Variance may be segregated into: (a) Overhead Capacity Variance =( Std. Overhead rate per hour) X (Actual hours-Budgeted hours) = Standard Overheads-Budgeted Overheads =21,000-22,500 =Rs.1,500 (A) (b) Overhead Revised Capacity variance = ( Std. rate per hour ) X (Std. hrs. produced – Actual hours) Or = Recovered overheads- Std. overheads =20,000-21,000 =Rs.1,000 (A) (ii) Operating Statement (Rs.) (a) Sales (800 X Rs.200) 1,60,000 Less: std. Cost of Sales (800 X Rs.155) 1,24,000 Standard profit (b) Variances Favourable Adverse Materials Price - 1,000 Usage 1,100 - Direct Labour Rate 525 - Efficiency - 600 Fixed Overheads Expenditure - 1,000 Capacity 1,500 (A) Efficiency 1,000 (A) - 2,500 ( c) Actual Profit

1,625 5,100

36,000 3,475 (A) 32,525

(iii) In the solution given the price variance has been calculated at the point of purchase. In case it is calculated at the point of issue the variance will be as follows: (Rs.) A 7,800 X (10-10.25) B 4,300 X ( 3-2.75) Present variance Hence difference Actual profit as in (ii) above Price variance difference Actual profit as per question

1,950 (A) 1,075 (F) 875 (A) 1,000 (A) 125 32,525 125 32,650

Statement showing the computation of standard cost per unit (Rs.) Ans: 55:

Particulars Actual 960 units Variance (-) Adv. (+) Fav.

Standard 960 units

Standard cost per unit

Direct Material Direct Wages Variable overhead Fixed overhead Total Cost Profit

792 1,192 1,940 1,040 4,964 976

5,940

(-)24 (-) 40 (-) 20 (-) 40 (-)124 (+)56

(+)180

768 1,152 1,920 1,000 4,840 920

5,760

0.80 1.20 2.00 1.04 5.04 0.96 6.00

Balancing figure

128

Original Budget and Flexible budget for sales achieved (Rs.) Particulars Standard Cost

(per unit) Original budget (1,000 units)

Flexible budget (960 units)

Direct Material Direct Wages Variable overhead Fixed overhead Cost of Sales Profit Sales

0.80 1.20 2.00 1.04 5.04 0.96 6.00

800 1,200 2,000 1,040 5,040 960

6,000

768 1,152 1,920 1,040 4,880 880

5,760

(i) Flexible budget for May 2004 Ans: 56:

Units Original Budget 20,000

Flexible Budget for May 2004

18,000

Actuals may 2004

18,000

Variance

1 2 3 4 5 Sales Variable costs Direct Materials Direct Labour Factory Overheads Selling overheads Total Contribution (A) Fixed Cost Factory overheads Selling overheads Total (B) Profit (A-B) Volume variance Net Loss

24,00,000 6,00,000 8,00,000 2,00,000 3,00,000

19,00,000 5,00,000

1,00,000 2,00,000 3,00,000 2,00,000 2,00,000

-1,50,000

21,60,000 5,40,000 7,20,000 1,80,000 2,70,000

17,10,000 4,50,000

1,00,000 2,00,000 3,00,000 1,50,000

-

22,00,000 5,20,000 7,56,000 1,84,000 2,88,000

17,48,000 4,52,000

1,16,000 1,84,000 3,00,000 1,52,000

40,000 F 20,000 F 36,000 A 4,000 A

18,000 A 38,000 A

2,000 F

16,000 A 16,000 F

- 2,000 F

50,000 A (48,000)

(ii) Variance Analysis

(1) Sales Std. Price =Rs.24 lakhs /20,000 =Rs.120

Std. profit =Rs.2 lakhs / 20,000 =Rs.10 Actual quantity =18,000 and standard price =Rs.120 Turnover on Std. Price =18,000 X 120 =Rs.21,60,000 Actual turnover is given at Rs.22 lakhs. : Price Variance =40,000 (F) Std. Qty X Std. Profit =20,000 X 10 =Rs.2 lakhs Actual Qty .X Std. Profit =18000 X 10 =Rs.180 lakhs Quantity Variance =Rs.20,000 A

(2) Direct Materials Std. Cost =Rs.6,00,000/20,000 =Rs.30 Actual Qty.=18,000 AQ X SC =18,000 X 30 =Rs.5,40,000 Total Actual Cost =Rs.5,20,000 Material Price Variance =Rs.20,000 (F) (3) Direct Wages Std. Time per unit =1,00,000/20,000 =5 hours Std. hourly rate =8,00,000/1,00,000 =Rs.8/hr. Std. Hours produced =18,000 units X 5 hrs. =90,000 hrs. Std. Hours=90,000 Actual Hours=95,000 Std. Rate Rs.8 (a) Std. Hrs. X Std. rate =90,000 X 8. =Rs.7,20,000

(b) Actual Hrs. X Actual Rate =Rs.7,56,000 © Actual Hrs. X Std. Rate =95,000 X 8 =Rs.7,60,000 Efficiency variance =(a)-( c)=Rs.40,000 (A)

129

Rate Variance =( c) –(b)=Rs.4,000 (F) (4) Factory Variable overheads: Std. Rate =Rs.2,00,000/1,00,000 =Rs.2/hr. (a) Charged to production =90,000 X2 =Rs.1,80,000 (b) Std. cost of actual hours =95,000 X 2 =Rs.1,90,000 (c ) Actual overheads =Rs.1,84,000 (a) – (b) =Rs.10,000 (A) Being efficiency variance (b) – (c ) =Rs.6,000 (F) Being expense variance (5) Selling variable overheads: Std. Rate =Rs.3,00,000/20,000 =Rs.15 / unit (a) Std. cost of output =18,000 X 15 =Rs.2,70,00 (b) Actual overheads =2,88,000 Adverse Variance =18,000 (6) Factory overheads- Fixed: Std. Rate = Rs.1,00,000/1,00,000 =Re.1/hr. (a) Std. cost of output of 90,000 =Rs.90,000 (b) Std. cost of actual hours. (95,000) =Rs.95,000 (c ) Budgeted =Rs.1,00,000 (d) actual Efficiency variance : (a) – ( b) =Rs.5,000 (A) Capacity variance : (b) – ( c) =Rs.5,000 (A) Expenses variance : (c )- (d) =Rs.16,000 (A) (7) Selling overheads : Fixed: Standard =Rs.2 lakhs / 20,000 =Rs.10 per unit (a) Std. cost of output =18,000 x 10 =Rs.1,80,000 (b) Budget =Rs.2,00,000 (c )Actual =Rs.1,84,000 Volume variance = (a) – (b) =Rs.20,000 (A) Expense variance = (b)-( c) =Rs.16,000 (F) Ans: 57:

1. Sales Variances Working Notes:

(1) Sales Volume Margin Variance (Actual Sales Volume – Budgeted Volume ) x Standard Margin =(22,000 units – 20,000 units) x Re.1 =Rs.2,000 (F)

(2) Sales Margin Price Variance Actual Sales Volume x (Actual Selling Price – Budgeted Selling Price) =(14,000 units (Rs.5 – Rs.5) + ( 8,000 units x (Rs.4.75 – Rs.5) =Rs.2,000 (A)

2. Material Variances (1) Material Price Variance

(Std. Price – Actual Price) x Actual Quantity A : (0.30 – 0.20) x 16,000 kg. =Rs.1,600 (F) B : (0.70 – 0.80) x 10,000 kg. =Rs.1,000 (A)

=Rs.600 (F)

(2) Material Mix Variance Total Actual Quantity (S.C. of Std. mix per kg. – S.C. of actual mix per kg.)

=.10000 .1180026000

20000 26000Rs Rskg

kg kg

−

=Rs.1,200 (F) (3) Material Yield Variance Std. rate per kg. of output (Actual Yield – Std. Yield ) = 0.50 ( 24,000 kg. – 26,000 kg.) =Rs.1,000 (A)

(3) Labour Variance (1) Labour Rate Variance

(Std. rate p.h. – Actual rate p.h. ) x Actual hours Skilled Labour : (Rs.3 – Rs.2.95 ) x 13,000 hrs. =Rs.650(F)

130

Unskilled Labour : (Rs.2.50 – Rs.2.60 ) x 6,300 hrs. =Rs.630(A)(2) Labour Efficiency Variance

=Rs.20(F)

(Std. hrs. for Actual output – Actual hours ) x Std. rate p.h. Skilled Labour : (Rs.10,800 hrs-12,000 hrs.) x Rs.3 =Rs.3,600 (A)

Unskilled Labour : (6,240 hrs. – 6,300 hrs.) x Rs.2.50 =Rs.150 (A) (3) Idle Time Variance

=Rs.3,750 (A)

(Idle hours x Standard Wage rate p.h) Skilled Labour : 1,000 hours x Rs.3 =Rs.3,000 (A)

(4) Variable Overhead Variance (1) Variable Overhead Expenditure Variance

(Variable Overhead recovered on actual output – Actual Variable Overhead) = (24,000 units x Re.0.50) – Rs.15,000 =Rs.3,000 (A)

(5) Fixed Overhead Variances (1) Fixed Overhead Expenditure Variance

(Budgeted Expenditure – Actual Expenditure) = (Rs.20,000 – Rs.18,020) =Rs.1,980 (F)

(2) Fixed Overhead Volume Variance (Budgeted Volume – Actual Volume ) x Std. rate per unit = (20,000 units – 24,000 units ) x Re.1 =Rs.4,000 (F)

Statement reconciling Actual Profit and Budgeted Profit Particulars Reference to

working note Variance

Favourable Adverse

Actual

Budgeted profit (as per Budgeted income statement) 1.Sales Variances Sales Volume Margin Variance Sales Volume Margin Variance Profit before adjustment of Cost Variances II Material - Price - Mix - Yield III. Labour Variance - Rate

-Efficiency -Idle time

IV. V. Overheads -Expenditure V. F. Overheads -Expenditure -Volume Actual Profit

-

(1) (2)

(1) (2) (3)

(1) (2) (3) (1)

(1) (2)

2,000 -

600 1,200

-

20 - - -

1,980 4,000 7,800

2,000 - -

1,000 -

3,750 3,000 3,000

- -

10,750

20,000

20,000

2,950 17,050

Ans. 58:

Zonal Sales Officers

(1) Statement showing the amount of sales target fixed and the actual amount of contribution earned. (Rs.’000)

A B C D

Commission earned 29.9 23.5 24.5 25.8 Actual sales: (Commission earned / 5%) 598 470 490 516 Sales price variance 4 (F) 6 (A) 5 (A) 2 (A) Sales volume variance 6 (A) 26 (F) 15 (F) 8 (F)

131

Sales target / Budgeted sales 600 450 480 510 Standard cost of sales target 500 375 400 Standard margin/ Budgeted margin

425 100 75 80 85

Sales margin mix variance 14 (A) 8 (F) 17 (F) 3 (A) Sales price variance 4 (F) 6 (A) 5 (A) Actual margin

2 (A) 90 77 92 80

Note: As there is no information about sales margin quantity variances, therefore for calculating actual contribution the same has been assumed to be zero.

(2) Statement to evaluate the performance of zonal sales officers

Zonal Sales Officers S. No. Base factor to

evaluate performance A B C D

Efficiency towards the target sales:

1. (a) Whether target achieved

No Yes Yes Yes

(b) Actual sales to Target sales ratio (Actual / target) (%)

99.67

×

600100598

104.44

×

450100470

102.98

×

480100490

101.18

×

510100516

(c) Ranking IV I II III 2. (a) Contribution

earned (in Rs.’000) 90 77 92 80

(b) Ranking II IV I III 3.. (a) Standard margin/

sales target ratio 16.67 16.67 16.67 16.67

(b) Actual margin / Actual sales ratio (%)

15.05 16.38 18.78 15.50

(c) Ranking IV II I III

Recommendation: A review of performance of four officers based on three based factors, shows that the performance of officer C is the best. Ans. 69:

Financial Prospective – Increase in operating income by charging higher margins on Maharaja.

Kitchen King’s Score card should describe its product differentiation strategy. The key points that should be included in its balance score card are

Customer Prospective – Market share in high-end kitchen range market and customer satisfaction. Internal business perspectives: Manufacturing quality, order delivery time, on time delivery and new

product feature added. Learning and Growth prospective: Development time for designing new end product and improvement

in manufacturing process. Operative Income:

(Amount in 000

Rs.) 2003 2004 Revenue (40000×1000: 42000×1100) 40000 46200

132

Direct Material 12000 13530 Conversion cost 10000 11000 Selling and Customer service 7200 7250 Total cost 29200 31780 Operative Income 10800 14420

Change in operating Income 36, 20,000 (F) A. Growth Component

(a) Revenue effect = Output Price in 2003{Actual units sold in 04 – Actual units sold in 03} = Rs.1, 000 (42,000 units – 40,000 units) = Rs.20, 00,000 (F) (b) The cost effect = Input price in 2003{Actual units of input to produce 2003 output less Actual units of input which would have been used to produce year 2004 output on the basis of 2003}

(i) Direct Material = Rs.100 [1, 20,000sqft – 1, 20,000sqft ×

= Rs.6, 00,000 (A) (ii) Conversion cost and selling and customer service will not change since adequate capacity exists in 2003 to support 2004 output and customers. Hence variance Conversion cost = 200(50000 – 50000) = 0 S & Customer Service = 25000(300 – 300) = 0 Increase in operating effect of Growth component is Rs14, 00,000 (F)

B. Price recovery Component: (i) Revenue effect = Actual output in 2004 [Selling price per unit in 2004 less Selling price per unit in 2003]

= 42,000units (Rs.1, 100 – Rs1, 000) = Rs.42, 00,000 (F) (ii) Cost effect = Unit of input based on 2003 actual that would have been used to produce 2004 output {Input prices per unit in 2003 less Input prices per unit in 2004}

(a) Direct material = 1, 26,000sqft (Rs.100/sqft – Rs.110/sqft) = Rs.12, 60,000 (A)

(b) Conversion Cost = 50,000 units (Rs.200/unit –Rs.220/unit) = Rs.10, 00,000 (A)

(c) S & Custr Service = 300 customers (Rs.24, 000 –Rs.25,000) = Rs.3,00,000 (A) = Rs.25, 60,000 (A)

Increase in Operating income due to Price Recovery is Rs.16, 40,000 (F) {Rs.42, 00,000 – Rs.25, 60,000} (C) Productivity Component

Productivity component = Input Prices in 04 {Actual units of input which would have been used to produce year 2004 output on the basis of 2003 actual less Actual Input} (i) Direct Material: Rs.110/sqft (1, 26,000 units – 1, 23,000 units) = Rs.3, 30,000(F) (ii) Conversion Cost: Rs.200/unit (50,000 units – 50,000 units) = 0 (iii) Selling & Customer = Rs.25, 000 (300 customers – 290 customers)

= Rs.2,50,000 (F) = Rs. 5,80,000 (F)

The change in operating income from 2003 to 2004 is analyzed as follows: (Amount in 000 Rs.) 2003 Growth component Price recovery Cost effect of productivity component 2004 Revenue 40000 2000 (F) 4200 (F) ------------ 46200 Cost 29200 600 (A) 2560 (A) 580 (F) 31780 Operating Income 10800 1400(F) 1640 (F) 580 (F) 14420

40000 units 42000 units]

133

Ans.1: Statement showing ranking Key Factor, Throughput Accounting & Budgeting

Products Particulars P Q R Selling Price/unit (Rs.) 25.00 30.00 35.00 Variable cost/unit (Rs.) Direct material 11.00 16.25 21.00 Direct labour 2.50 2.50 2.50 Other variable costs 1.50 2.25 3.50 Contribution per unit (Rs.) 10.00 9.00 8.00 Machine hours/unit 0.67 0.33 0.4167 Contribution/machine hour 15 27 19.2 Ranking III I II Ans: 2 Working Note The limiting factor in the company is the No. of labour hours in department II. Hence, contribution per labour hour of department II has to be found and products ranked on that basis. A B C Selling price / unit Less: Variable cost: Direct materials Direct Labour: Department I Department II Department III Variable overhead Contribution per unit Time taken in department II Contribution per labour hour of Department II 20/0.5 = Ranking for allotment of department II labour hour

100 40 10 6 12 12

20 80

0.5 hr.

40

II

130 50 12 12 15 11

30 100

1 hr.

30

III

175 64 15 12 18 16 125

50

1 hr.

50 I

Solution

(a) Current mix profit and total labour hour in dept. IIs Product No. of units Contribution

/ unit Total contribution

Labour time in department II per unit

Total labour time in department II

A 30,000 Rs.20 Rs.6 lakhs 0.5 hr. 15,000 hr. B 40,000 Rs.30 12 lakhs 1.0 hr. 40,000 hr. C 25,000 Rs.50 12.50 lakhs 1.0 hr. 25,000 hr. Total

FOH 30.50 25.00

80,000 hr.

134

Profit 5.50 The suggested product mix is the optimum one because the first ranked product C is proposed to be produced & sold to the maximum of 30,000 units. Similarly, the second ranked product A can be produced and sold up to 50,000 units. The balance hours can be utilized to produce B to the extent of 25,000 units only. This will be optimum mix as indicated below:

Product Ranking No. of Units No. of hours in Dept. II C A B

I II III

30,000 (Maximum) 50,000 (Maximum)

25,000 (Balance)

30,000 25,000 25,000 (Balance)

Total 80,000 (b) Statement of increase in profit

Product No. of Units Contribution per unit Amounts (Rs.lakhs) C A B

Less: FOH Profit Profit under proposed plan in question Increase in profit

30,000 50,000 25,000

50 20 30

Total

15.00 10.00 7.50 32.50 25.00 7.50

5.50 2.00

If the suggestion for optimum product mix is implemented, the increase in profit would be Rs.2.00 lakhs. Ans: 3 Working Notes

Statement of contribution per machine hour (Limiting factor ) and ranking Particulars PIE SIGMA Selling price Less: Variable cost Contribution per unit Contribution per machine hour =

20 11 9

9/1 =Rs.9.00

30 16 14

14/2 Rs.7.00

Ranking I II Solution (a) Best combination: Pie should be produced fully one lakh units. Then , sigma should be produced within the balance machine hours. This combination will give optimum contribution as follows: Product Ranking No. of Units No. of

Machine Hours

CPU Total contribution(Rs.)

135

Pie Sigma Less: Fixed Profit

I II Total

1,00,000 1,50,000 (300000 /2 )

1,00,000 3,00,000

4,00,000 (Balance)

9.00 14.00

9,00,000 21,00,000 30,00,000 (Optimum) 26,00,000 4,00,000

(b) There is market for Sigma for one lakh units (i.e., 2,50,000 – 1,50,000 units). Two machine

hours are required per unit of production of Sigma. That is 1,00,000 units at 2 hours = 2,00,000 machine hours required. For this purpose, 7 machines are to be taken on rental basis. Then, the profit will improve as follows:

(Rs.lakhs) Pie 1 lakh units at Rs.9 9.00 Sigma 2.5 lakh units at Rs.14 Total contribution 44.00

35.00

Less: Fixed cost 26.00 Rent 7 X 1.5 = 10.50 Profit

36.50

7.50

(c) There is no change in number of machines required on rental basis. Total rental charges will come down and profit will improve further as follows: (Rs.lakhs) Total contribution (as calculated above) 44.00 Less: Fixed cost 26.00 Rent 7 X 1.25 = 8.75 Profit

34.75

9.25

Ans. 4: Working Notes Products Particulars X Y Z Selling Price/unit (Rs.) 1900 2400 4000 Variable cost/unit (Rs.) 700 1200 2800 Contribution per unit 1200 1200 1200 Machine hours/unit 3 2 1 Contribution/machine hour 400 600 1200 Ranking III II I (b) Machine hours available will be only 20000 hours

Product Ranking No. of units DLH CPU Total contribution Z I 1000 1000 1200 1200000 Y II 2000 4000 1200 2400000 X III 5000 (15000/3) 15000 (B.F.) 1200 6000000

Total 20000 Rs. 9600000 Ans. 5: Statement of Ranking Working Notes Products

136

Particulars X Y Z Selling Price/unit (Rs.) 30 40 50 Variable cost/unit (Rs.) Direct material(@Rs. 8 p.kg) 5.6 3.2 12 Direct labour(@Rs. 8 p.h.) 8 16 12 Variable overheads(@Rs. 5.6 p.h.) 5.6 11.2 8.4 Sellling commission (10% of SP) 3 4 5 22.2 34.4 37.4 Contribution/unit 7.8 5.6 12.6 Raw material per unit (kg) 0.7 0.4 1.5 Contribution per kg (Rs.) 11.14 14 8.4 Ranking II I III Statement of Ranking (if additional 4500kg are made of RM is available) Products Particulars X Y Z Selling Price/unit (Rs.) 30 40 50 Variable cost/unit (Rs.) Direct material(@Rs. 8 p.kg) 5.6 3.2 12 Direct labour(@Rs. 10 p.h.) 10 20 15 Variable overheads(@Rs. 7 p.h.) 7 14 10.5 Sellling commission (10% of SP) 3 4 5 25.6 41.2 42.5 Contribution/unit 4.4 (1.2) 7.5 Raw material per unit (kg) 0.7 0.4 1.5 Contribution per kg (Rs.) 6.28 (3) 5 Ranking I - II (a) Raw material available will be only 10400 kg

Product Ranking No. of units RM (kgs) CPU Total contribution Y I 6000 2400 5.6 33600 X II 8000 5600 7.8 62400 Z III 1600 (2400/1.5) 2400 (B.F.) 12.6 20160

Total 10400 Rs. 116160 Less: Fixed overheads 50000 Profit 66160 (b) Raw material available will be only 14900(10400+4500) kg

Product Ranking No. of units RM (kgs) CPU Total contribution X I 8000 5600 4.4 35200 Z II 5000 7500 7.5 37500

Balance 1800 - Total 14900 Rs. 72700 Less: Fixed overheads 75000

137

Profit (2300) Hence firm should not go into further production Ans. 6: Statement of Ranking Working Notes Products Particulars A B C Selling Price/unit (Rs.) 20 16 10 Variable cost/unit (Rs.) Direct material 6 4 2.00 Direct labour 3 3 1.50 Variable overheads 2 1 1.00 11 8 4.50 Contribution/unit 9 8 5.50 Units 10000 12000 20000 Total contribution 90000 96000 110000 Ranking III II I Raw material per unit (kg) 0.6 0.4 0.10 Contribution per kg (Rs.) 15 20 27.50 Ranking III II I DLH required per unit 0.20 0.20 0.10 Contribution per DLH Rs. 45 Rs. 40 Rs. 55 Ranking II III I Solution (a) Raw material available will be only 12100 kg

Product Ranking No. of units RM (kgs) CPU Total contribution C I 20000 4000 5.50 110000 B II 12000 4800 8 96000 A III 5500 (3300/0.6) 3300 (B.F.) 9 49500

Total 12100 Rs. 255500 Less: Fixed overheads 138000 Profit 117500 (b) Direct labour hours available will be only 5000 hours

Product Ranking No. of units DLH CPU Total contribution C I 20000 2000 5.50 110000 A II 10000 2000 9 90000 B III 5000 (1000/0.2) 1000 (B.F.) 8 40000

Total 5500 Rs. 240000 Less: Fixed overheads 138000 Profit 102000 (c) No shortage of materials and labour: Ranking as per total contribution is to be considered.

Product Ranking No. of units CPU Total contribution

138

C I 25000 (20000 + 25%) 5.50 137500 B II 12000 9 96000 A III 10000 8 90000

Total Rs. 323500 Less: Advertisement cost 20000 Net contribution 303500 Less: Fixed overheads 138000 Profit 165500 Ans 7:

Working Notes Statement of comparative contribution and Ranking (Direct labour Hour (DLH) is key

factor) Particulars A B C

Selling Less: Variable cost Contribution per unit (CPU) DLH per unit 10/10 = Contribution per DLH =CPU/DLH

28 23 5 1

5/1 =5.00

60 45 15 2

15/2 =7.50

125 95 30 5

30/5 =6.00

Ranking III I II

Solution (a) Profit according to current plan

Product No. of Units DLH CPU Total

amount(Rs.) A B C D Less :Fixed overheads Profit

500 (Minimum) 500 (Minimum) 500 (Minimum) 1,400(from surplus DLH) Total

500 1,000 2,500 7,000

11,000 (Balance)

5 15 30 30

2,500 7,500 15,000 42,000

67,000 25,000 42,000

(b) Alternative plan for maximum profit

Product B is a Rank No. 1. Hence, instead of C Product. B should be manufactured by using surplus labour hours. This will maximize the profit as follows:

Product No. of Units DLH CPU Total

amount(Rs.) A 500 (Minimum) 500 5 2,500

139

B C D Less :Fixed overheads Profit

500 (Minimum) 500 (Minimum) 3,500(from surplus DLH) Total

1,000 2,500 7,000

11,000 (Balance)

15 30 15

7,500 15,000 52,500

77,500 25,000 52,500

Note: This profit of Rs.52,500 is higher than current plan.

( C ) BEP (units and value) At BEP, contribution is equal to fixed overheads, i.e., and C=F. In such case, the company

has to earn the contribution of Rs.25,000 in order to get BEP as follows:

Rank

Product No. of Units CPU Total amount(Rs.)

I II II

Total contribution Less: Fixed overheads Profit

B C A

500 (Minimum) 500 (Minimum) 500 (Minimum)

15 30 5

7,500 15,000 2,500 25,000

25,000 Nil

BEP (Units and Value)

Product No. of Units Selling Price Per unit

Sales Value at BEP (Rs.)

B C A Total

500 500 500 1500

60 125 28

30,000 62,500 14,000

1,06,500 BEP in terms of units: 1,500 units BEP in terms of Sales Value : Rs.1,06,500 (d) Profit after tax (PAT) 24% on 1,00,0000 Rs.24,000 Tax Rate 50% Hence, Profit Before tax 24,000 x 100 50

Rs.48,000

Less: Tax at 50% Rs. PAT

24,000

24,000

Note: By production and selling minimum quantities of A,B and C, BEP is achieved. Hence, in order to earn profit before tax of 48,000, Rank No.1, Product B should be sold to the extent of 3,2000 units (48,000 / CUP rs.15).

Then, the position will be as follows: Product No. of Units DLH CPU Total

140

amount(Rs.) A B C B Less: Fixed overheads Profit

500 500 500 3,200 Total

500 1,000 2,500 6,400 10,400

5 15 30

15

2,500 7,500 15,000 25,000 48,000 73,000

25,000

48,000 No. of Units and Sales value:

Product No. of Units Selling Price Per

unit Sales Value (Rs.)

A B C Total

500 3,700 500

4,700

28 60 125

14,000 2,22,000 62,500

2,98,500

The sales value of Rs.2,98,500 will earn the profit of Rs.48,000 (Profit Before Tax) as worked out in the previous statement. PBT 48,000 Less: Tax at 50% 24,000 PAT 24,000 (24% on capital employed of Rs.1,00,000) Ans: 8 Working Notes

Statement of contributions per unit of raw material (Key factor)

A B C Contribution per

unit= Contribution per unit of Materials

2,00,000/20,000=Rs.10

10/4 = Rs.2.50

4,00,000/40,000=Rs.10

10/5 = Rs.2.00

3,00,000/20,000=Rs.15

15/6 = Rs.2.50

Ranking I II I Solution

(i) Production / Sales mix. Product Units Materials (Units) CPU Total Amount(Rs.)

A C B

20,000 20,000 20,000

20,000 X 4 = 80,000 20,000 X 6 = 1,20,000 Balance 1,00,000

10 15 10

2,00,000 3,00,000 2,00,000

Total Less: Fixed Cost Loss

60,000 3,00,000 (-)

7,00,000 7,50,000

141

50,000

(ii) Product No. of Units CPU Total Amount(Rs.) A C B B

20,000 20,000 20,000 40,000

10 15 10 6.25(Notes)

2,00,000 3,00,000 2,00,000 2,50,000

Total Less: fixed Cost 7,50,000 + 50,000 = Profit

1,00,000 9,50,000 8,00,000 1,50,000

Yes, The company can optimize production of 1,00,000 units with local substitute materials. Note 1. Imported Raw material cost Rs.3.00 per unit x 5 units = Rs.15.00 Local substitute materials 3.75 per unit x 5 unit = Extra cost of materials

18.75 0.75 per unit

Contribution = 10.00-3.75= Rs.6.25 per unit 3.75

(iii) Product No. of Units CPU Total Amount(Rs.) A C B

20,000 20,000 10,000

10 15 10

2,00,000 3,00,000 1,00,000

Total Add: Lease amount Less: Fixed cost Profit

50,000 6,00,000 2,75,000 8,75,000 7,50,000 1,25,000

60,000-50,000 = 10,000 The company cannot enhance profits by leasing out a part of the plant. Conclusion – The proposal at (ii) will maximize the profit at Rs.1,50,000. Ans:9

Working Notes Product A (Rs.per unit) Product B (Rs. per unit) Sales Less: Variable cost Contribution P/V ratio = C x 100 = S

2,500 1,500 1,000

2,500 1,000

=40%

5,000

1,750 3,250

1,7505,000

x 100

=35% Solution (i) When total sales in value is limited: Product A is more profitable as its P/v ratio is 40% which is higher than that of B. (ii) When raw material is in short supply: Product A B Raw material required per unit Rs.500/50=

10 kg.

25 kg. (Rs.1,250/50)

142

Contribution per kg of material =Contribution per unit /kg

1,000/10 kg.

=Rs.100

1,750/25

Rs.70

In this case also, product A is more profitable as its contribution per kg of raw material is Rs.100 which is higher than that of B. (iii) When Production capacity is the limiting factor:

Product A B Direct Labour hours (DLH) Required per unit = Rs.750/30 Contribution per DLH =Contribution per unit/No. of DLH

25 hours

1,000 / 25 hours =Rs.40

1,500 / 30 = 50 hours

1,750 /50 hours =Rs.35

In this case also, Product A is more profitable as its contribution per DLH is Rs.40 which is higher than that of B (iv) Statement of Product Mix and Maximum profit:

Product Raw Material (kg)

No. of Units. Contribution per Unit (Rs.)

Amount (Rs.)

A B Total Less: Fixed Overheads Profit (Maximum)

10,000 10,000 (Balance) 20,000

1,000 400 (10,000/25)

1,000 1,750

10,00,000 7,00,000 17,00,000 10,00,000 7,00,000

Ans:10 To maximize Profit. (a) Statement of current profit (Rs.lakhs)

Products A B C Total Direct Materials : 10,000 x 20 Direct labour : 10,000 x 12 Variable overheads : 10,000 x 8

2.00 1.20 0.80

0.80 0.70 0.50

1.44 0.96 0.48

4.24 2.86 1.78

Marginal cost Sales 10,000 x 64

4.00 6.40

2.00 3.00

2.88 4.16

8.88 13.56

Contribution Less: Fixed overheads 10,000 x 6

2.40 0.60

1.00 0.30

1.28 0.32

4.68 1.22

Profit 10,000 x 18 1.80 0.70 0.96 3.46 Ranking according to profitability P/v Ratio = C x 100 S

I 2.40 6.40

x 100

=37.5%

III 1.003.00

x 100

1 33 -- % 3

II 1.28 x 100 4.16 30.77%

143

( b) Though the contribution per unit of C is lowest, it should not be discontinued. Instead, B should be discontinued. Total contribution from C is more than that of B. Analysis:

Product A B C Selling price Less: Variable cost

64 40

60 40

52 36

CPU 24 20 16 If C is discontinued, Sales of A and B will increase by 50%. Rs.lakhs

Contribution A 10,000 + 50% = 15,000 units at 24= 3.60 B 5,000 + 50% = 7,500 units at 20=

5.10 1.50

Less: Fixed overheads Profit

1.22 3.88

If B is discontinued, sales of A and C will increase by 50%

Contribution

A 3.60 C 8,000 + 50% = 12,000 units at 16 = 5.52

1.92

Less: Fixed overheads Profit

1.22

4.30

Hence, C should not be discontinued. Product B should be discontinued. Then , the profit will improve to Rs. 4,30,000. Present profit 3,46,000 Proposed profit Increase in profit

4,30,000

84,000

C. Product D: Selling Price 48 Less: Marginal cost Contribution per unit Rs.

25 23

Total contribution Rs.5,52,000 less contribution from a & C 3,68,000 = 1,84,000 Minimum sales = Rs.1,84,000/23 = 8,000 units are to be sold in order to ensure maximum profit as per (b) above, i.e., Rs.4,30,000.

Statement of Profitability Contribution from A (original level) Contribution from C (original level) Contribution from D ( proposed ) 8,000 x 23

Rs.lakhs 2.40 1.28 1.84

Total 5.52

144

Less: Fixed overheads 1.22 Profit 4.30

Ans:12 Working Note

Statement of contribution per labour hour (limiting Factor) P Q R

Selling price / unit (Rs.) Variable cost / unit (Rs.) Contribution (Rs.) Labour hrs/unit 20/10= Contribution /labour hr(Rs.) 18/2= Current sales (Units)

80 62

2 18

9 15,000

60 49

1.5 11

7.33 20,000

50 36

1 14

14 10,000

Solution (a) Current Profit

Contribution: P : 15,000 x Rs.18 = Rs.2,70,000 Q : 20,000 x Rs.11 = Rs.2,20,000 R : 10,000 x Rs.14 = Rs. Total contribution Rs.6,30,000

1,40,000

Less: Fixed overheads Rs. Profit as per estimate Rs

5,50,000

. 80,000

(b) Labour is the limiting factor Total Labour Hours utilized for the above production units : (Production and sales same). P = 30,000 hrs.(15,000 x 2) Q = 30,000 hrs.(20,000 x 1.5) R = 10,000

hrs.(10,000 x 1) 70,000

Available hrs. 75,000 hrs. hrs

Since contribution per labour hour is Maximum for R, and since labour hour is the limiting Factor, normally this excess 5,000 hrs have to be allocated to R. But, increase in production / sales is limited to 25% of current sales of any one of the products:

Product (i)

Labour hours available (ii)

Production/sales possible (iii)

25% of current sales (iv)

Lower of the (iii) & (iv)

Contribution per unit (Rs.)

Total contribution Rs.

P Q R

5,000 5,000 5,000

2,500 3,333 5,000

3,750 5,000 2,500

2,500 3,333 2,500

18 11 14

45,000 36,663 35,000

Contribution is highest for P.P should be chosen and after deduction of Rs. 30,000 for advertisement, profit is Rs.15,000. © If selling price is reduced by 5% the position will be as follows:

145

Product Reduced

Selling price Rs.

Variable cost Rs.

Contribution per unit Rs.

Labour hrs reqd per unit

Contribution per labour hour

Ranking for production Rs.

P Q R

80-5%=76 60-5%=57 50-5% 47.50

62 49 36

14 8

11.50

2 1.5

1

7 5.33 11.50

II III

I

Since labour hours are limited to 75000 hours only,product mix will be as follows: Product No of units with

increase Labour hrs. reqd. Total contribution

R P Q

15,000 22,500

10,000 (15,000/1.5)

15,000 45,000

15,00075,000

(Bal.Fig)

@ Rs.11.5=1,72,500 @ Rs.14 =3,15,000 @ Rs. 8 = 5,67,500

80,000

Less: Fixed overheads Profit

5,50,000 17,500

This proposal is not recommended because of lower profit.

Ans. 13:

146

147

148

Contribution per unit 120 125 121 -

Option 1: Units - 115 100 215

Contribution (Rs.) - 14,375 12,100 26,475 26,780 (305)

Option 2: Units 100 115 - 215

Contribution (Rs.) 12,000 14,375 - 26,375 22,000 4,375

Option 3: Units 80 - 135 215

Contribution (Rs.) 9,600 - 16,335 25,935 24,780 1,155

Best strategy is to produce 100 units of product A and 115 units of product B during off - season.

Maximum profit = Rs. 4,375.

(i) Best strategy for peak-season is to produce 202 units of A. (ii) Maximum profit for off-season Rs. 4,375.

Ans:14

(a) Profit for the current year (Rs.) Products A B C D Total

Sale Value Per acre 10 x 1000= Variable cost per acre Contribution per acre Area occupied (acres) Total contribution 25 x 5,300= Less: Fixed overheads Profit

10,000

4,700 5,300

25

1,32,500

10,000

5,100 4,900

20

98,000

13,500

5,950 7,550

30

2,26,500

16,200

6,600 9,600

25

2,40,000

100

6,97,000 5,40,000 1,57,000

(b) profit for the product mix The land which is being used for A and B can be used for either items. A gives higher

contribution per acre. Hence, b should be produced to the minimum of 40 tonnes and in balance land A should be produced.

Similarly, the land which is being used for C and D can be used for either items. D gives higher contribution per acre. Hence, C should be produced to the minimum of 36 tonnes and in balance land , D should be produced. Then, the position will be as follows:

A + B Area occupied = 25 + 20 = 45 acres. B : Minimum production : 40 tonnes i.e., 40

8 = 5

Acres required.

149

A : Balance 40 acres : A should be produced C + D : Area occupied = 30 + 25 = 55 acres C : Minimum production = 36 tonnes, i.e., 36

= 4 acres required.

D : Balance 51 acres : D should be produced. Then, the profitability will improve as follows:

Products A B C D Total No of acres Contribution per acre Total Contribution Less: Fixed Overheads Profit

40 5,300

2,12,000

5 4,900 24,500

4 7,550 30,200

51 9,600

4,89,600

100 Rs.

7,56,300 5,40,000 2,16,300

The profit will improve from Rs.1,57,000 to Rs.2,16,300 Ans. 15: Calculation of area to be cultivated in respect of each crop to achieve the largest total profit Available information: Land available for all four vegetables 340 hectares Land available for peas and carrots Total land available

140

Min. requirement of each variety 500 boxes 480

Max. requirement of each variety 113750 boxes Potato Peas Carrots Tomatoes Boxes per hectare 350 100 70 180 (a) Market price Rs. 30.76 Rs. 31.74 Rs. 36.80 Rs. 44.55 (b) Variable costs: Direct material 2.72* 4.32 5.49 3.47 Labour – Growing 5.12* 12.16 10.63 5.87 - Harvesting & Packing 7.20 6.56 8.80 10.40 Transport per box 10.40 10.40 8.00 Total variable costs

19.20 25.44 33.44 32.92

(c) Contribution per box (a)-(b) 38.94

5.32 (1.70) 3.88 5.61 Contribution per hectare × Boxes per hectare (c)

1862 (170) 271.60 1009.80

150

Ranking I IV III II *Cost per hectare ÷Boxes per hectare Best cultivation plan: From 140 hectares for peas and carrots: Peas: Minimum 5000 boxes = 5000÷100 = 50 hectares Carrots: Balance land 140 hectares – 50 hectares = 90 hectares From 340 hectares all four vegetables: Tomatoes: Minimum 5000 boxes = 5000÷180 = 28 hectares (in terms of complete hectares) Potatoes: Balance of land i.e. 340 -28 = 312 hectares Area to be cultivated for each variety and total contribution Potatoes Peas Carrots Tomatoes Hectares 312 50 90 28 Contribution per hectares

Rs. 1862 (170) 271.60 1009.80

Contribution Rs. 580944 (8500) 24444 Total contribution

28274.40 Rs. 625162.40

Less: Fixed expenses Profit

424000.00

201162.40

(ii) Analysis to show whether land development should be undertaken Carrot yield a lower contribution per hectare than Potatoes and Tomatoes, but it is grown in excess of the requirement of 5000 boxes or 72 hectares i.e. 5000 boxes ÷700. Therefore, 18 hectares i.e., 90 hectares – 72 hectares can be made available for Potatoes and Tomatoes by land improvement. After land improvement the contribution per hectare of Tomatoes will be foloows: Present contribution per hectare Rs. 1009.80 Saving per hectare after land improvement Rs. 2.60 ×180 boxes

460.00

Allocation of 18 hectares available 1477.80

Crop Maximum Sales (Boxes)

Present Production (Boxes)

Addl. Reqt. (Boxes)

Yield per hectare (Boxes)

Additional hectares to be allotted

Potatoes 113750 109200* 4550 350 13 Tomatoes 113750 5000 900 180 5(B.F.) * 312 hectares X 350 boxes = 109200

151

Profit by revised Cultivation plan Potatoes Peas Carrots Tomatoes Total Hectares 325 50 72 33 480 Contribution per hectare Rs. 1862 (170) 271.60 1477.80 Total contribution Rs. 605150 (8500) 19555.20 48767.40 664972.60 Less: Fixed cost (revised)* 440200.00 Profit 2224772.60 *Capital expenditure = 18 hectares X 6000 = 108000 Interest ( 108000 X 0.15) = Rs. 16200 Existing fixed expenses 424000 440200 Conclusion: Since the profit after land development is greater, the company should implement the proposal to develop 18 hectares of land. Question 16: (i) Statement of Cost break-up

Sambalpur Bilaspur Total cost (Rs.

Lacs) Cost per M.T. of

output (Rs.) Total cost (Rs.

Lacs) Cost per M.T. output (Rs.)

Material cost 198 1,650 240 1,600 (Refer to working note)

(6,000 M. T. × Rs.1,800 +

3,600 M. T. × Rs.2,500)

(Rs.198 lacs/ 12,000 M. T.)

(12,000 M. T. × Rs.12,000)

(Rs. 240 lacs/ 15,000 M. T.)

Other variables 156 1,300 192 1,280 (156 lacs/

12,000 M. T.) (192 lacs/

15,000 M. T.) Fixed Cost 108 900 120 800 (108 lacs/

12,000 M. T.) (120 lacs/

15,000 M. T.) Total Cost 462 3,850 552 3,680

Working Note: Sambalpur Bilaspur

Annual output (M. T.) 12,000 15,000 Maximum possible output (M. T.) 15,000 25,000 (12,000/80%) (15,000/60%) Basic raw material requirement (M. T.) 9,600 12,000 (12,000 × 80%) (15,000 × 80%)

152

Material available locally (M. T.) 6,000 16,000 Possible output from local material (M. T.) 7,500 20,000 (6,000 / 80%) (16,000 / 80%)

(ii) Quantity of production at each unit from the availability of local supplies of basic raw material: Sambalpur Bilaspur

Maximum output/ possible (M. T.) 15,000 25,000 (Refer to above working note) Material cost/ M. T. of output from locals (Rs.) 1,440 (6,000 ×

Rs.1,800) / 7,500 M T.

1,600

Other variables / M. T. of output from locals (Rs.) 1,300 [Refer to part (i)]

1,280

Total variable cost / M. T. of output 2,740 Possible output (M. T.) from local supplies of basic raw material

2,880 7,500 19,500

(Balancing Figure) (iii) Cost saving as per revised schedule of production :

Sambalpur Bilaspur Total (Rs. lacs) (Rs. lacs) (Rs. lacs) Total variable cost of output 205.5 561.6 767.1 (Refer to part ii) (7,500 M. T. ×

Rs.2,740) (19,500 M. T. ×

Rs.2,880)

Fixed Cost 108.0 120.0 Total cost: (A)

228.0 313.5 681.6 995.1

Previous total cost: (B) 462.0 552.0 [as per (i) above]

1014.0

Cost savings: {(B) – (A)} 148.5 (129.6)

18.9

Statement of cost per tonne and net profit earned in respect of each factory Ans. 17

Lucknow Pune Present production tonnes: (A) 7,200 10,800 Rs. Rs. Cost of raw material (Rs. in lacs) 59.04 87.48 (Refer to working note 1) Other variable costs (Rs. in lacs) 22.32 32.94 Fixed cost (Rs. in lacs) 18.00 Total cost (Rs. in lacs): (B)

24.84 99.36 145.26

Cost per tonne (Rs) : (C) = [(B) / (A)] 1,380 1,345

153

Selling price (Rs. Per tonne: (D) 1,450 1,460 Net profit per tonne (Rs.) : [(D) – (C)] 70 115 Total net profit (Rs. in lacs) 5.04 12.42 (Rs.70 ×7,200 tonnes) (Rs.115×10,800 tonnes) Total profit of the company = Rs.15.46 lacs (Rs.5.04 lacs + Rs.12.42 lacs)

Alternative production plan to earn optimum

Lucknow Pune Maximum production capacity (tonnes) 9,000 11,880 Present production (tonnes) 7,200 10,800 Rs. Rs. Cost per tonne of output: 800 810 Cost per tonne of output manufactured from locally purchased raw material: (A)

(Refer to working note 2) Cost per tonne of output manufactured from material purchased from Bhopal : (B)

880 880

(Return to working note 3) Other variable cost (Rs.) : (C) 310 305

tonnes 7,200Lacs Rs.22.32

tonnes 10,800Lacs Rs.32.94

Selling price per tonne (Rs.) : (D) 1,450 1,460 Contribution per tonne of Output : [(D)–{(A)+(C)}] 340 345 Contribution per tonne of Output : [(D) – {(B)+(C)}] 260 275 (When material was purchased from Bhopal) The priority to produce 18,000 tonnes of total output is as below as apparent from the above data: Priority

Pune factory (Local purchase of raw material) 1st

Lucknow factory (local) purchase of raw material) 2

nd

Pune factory (raw material purchased from Bhopal) 3

rd

Lucknow factory (raw material purchased from Bhopal) 4

th

Suggested alternative production plan :

Production priority Raw Material Output (in tonnes) Input(in tonnes) Lucknow Pune Total I 11,700 tonnes 13,000 -- 11,700 11,700 II 5,400 tonnes 6,000 5,400 -- 5,400 III (11,880 – 11,700) = 180 tonnes 200 -- 180 180 IV 720 tonnes balancing figure 800 720 -- 720

154

(18,000 – 17,280 tonnes) 20,000 6,120 11,880 18,000 Working Notes:

Lucknow Pune 1. Present production output (tonnes) 7,200 10,800 Total raw material required for present

production (tonnes) 8,000 12,000

×

90100

200,7

×

90100

800,10

Raw material produced locally (tonnes) 6,000 12,000 Raw material product from Bhopal 2,000 -- Cost of raw material purchased locally 59.04 87.48 and from Bhopal (Rs. in lacs) (Rs.720×6,000+

Rs.792 × 2,000) (12,000 × Rs.729)

2. Cost per tone of output manufactured from locally purchased raw material

800 810

(in Rs.)

×

90100

720

×

90100

729

3. Cost per tonne of output manufactured from material purchased from Bhopal

880 880

(in Rs.)

×

90100

792

Ans.: 20:

Throughout Accounting ratio is highest for ‘Machine 2’. ∴ ‘Machine 2’ is the bottleneck

Contribution per unit of bottleneck machine hour : A B C Total ‘Machine 2’ hours available = 6,000

A. Contribution per unit (Rs.) 30 25 15

B. ‘Machine 2’ hours 15 3 6

C. Contribution per ‘Machine 2’ hours (A / B) 2 8.33 2.50

D. Ranking 3 1 2

E. Maximum Demand 500 500 500

‘Machine 2’ hours required (B × E) 7,500 1,500 3,000

‘Machine 2’ hours available 1,500 1,500 3,000

Units 100 500 500 Ans. 21:

155

Production

A B C Total Mach TA Capacity ratio

Demand (units) 200 200 200 Hrs. required in Dept. Machine 1 2,400 800 400 3,600 3,200 112.5%

2 3,600 1,200 600 5,400 3,200 168.75% 3 1,200 400 200 1,800 3,200 56.25%

∴Machine 2 is the bottleneck Note-2:

Through put contribution & rank

A B C (a) Throughput Contribution 24 20 12 (b) MR/unit in Machine 2 18 6 3 (c) Contribution/hr. Machine –2 1.33 3.33 4

Rank III II I Identification of product mix.

Hrs. in machine 2 units Available 3,200 Less: Rank I C _ 200 600

2,600 Less: Rank II B 200 1,200 Less: Rank III A 18 77.77

i.e. 77 units

(a) Ans. 22:

Machine Time required for products Total Time

Time Available

Machine utilization A B C D

1 2 3

2000 2000 2000

1200 1800 600

400 600 200

200 300 100

3800 4700 2900

3000 3000 3000

126.67% 156.67% 96.67%

Since Machine 2 has the highest machine Utilization it represents the bottleneck activity hence product, ranking & resource allocation should be based on contribution/machine hour of Machine 2.

Allocation of Resources

A B C D Machine Utilization

Spare Capacity

156

Contribution per unit (Rs.) Time required in Machine 2 Contribution per Machine – hour (Rs.) Rank as per contribution / mach. Hour Allocation of Machine 2 time Production Quantity Allocation Machine 1 time Allocation of Machine 3 time

1500

10

150

3rd

200×10 =

2000

200 2000

2000

1200

9

133.33

4th

100 (balan

cing figure)

100/9=11.11

11.11×6 = 66.66

11.11×3 =

33.33

1000

3

333.33

2nd

200×3 =

600

200 400

200

600

1.5

400

1st

200×1.5 = 300

200 200

100

3000

2666.66

2333.33

333.34

666.67

Ans. 23: Rs. p. u Rs. p. u.

W. Note 1

A B

Material 2 40

Variable production overhead cost 28 4

TVC 30 44

Selling price 60 70

(a) Contribution 30 26 (b) Limiting factor (hr./u) 0.25 0.15 (c) Contribution/hr. (a/b) Rs. 120 173.33 (d) Rank II II (e) Budgeted production & sales 1,20,000 45,000 (f) Maximum demand 1,44,000 54,000

Total Fixed cost Rs 14,70,000 W. Note-2:

Fixed overhead recovery rate =(Amount÷Budgeted hours) = 14,70,000 ÷36,750 = Rs. 40/hr.

Budgeted hours A 1,20,000 units @ Rs. 0.25 = 30,000 hrs.

B 45,000 units @ Rs. 0.15 = 6,750 hrs.

36,750 hrs. (a) A B

Contribution per unit Rs. 30 26

157

Less: Fixed overhead per unit Rs. 10 6

(a) Profit per unit Rs.

20 20 (b) Units 1,20,000 45,000 Total (a×b) 24 lakhs + 9 lakhs = 33 lakhs

Management is indifferent on the basis of profit per unit however this is wrong concept on selecting the product mix.

(b) A B (a) Contribution per unit Rs.

30 26 (b) Limiting time/unit 0.02 0.015 Contribution /hr. (a/b) Rs. 1,500 Rs. 1,733 Rank II II

Statement of product mix & profit

Hrs. units Contribution/u Total Available 3,075 Less: for Rank I 810 54,000 26 14,04,000 For Rank II

2,265/0.02 1,13,250 30 33,97,500 Product A 48,01,500

Less: Fixed cost 14,70,000

Profit 33,31,500 (c) Return per bottleneck hour = (selling price – material cost)/ (Time on bottleneck resource)

Product A = Rs. 2,900 [(Rs. 60 – Rs. 2)/ Rs. 0.02 hours]

Product B = Rs. 2,000 [(Rs. 70 – Rs. 40)/ 0.015 hours] Product A should be sold up to its maximum capacity of utilizing 2,880 bottleneck hours (1,44,000 units × 0.02 hours). This will leave 195 hours for product B thus enabling 13,000 units (195/0.015) to be produced.

The maximum profit is calculated as follows:

Rs.

Throughput return from product A (1,44,000 × Rs. 58)

83,52,000 Contribution from product B (13,000 × Rs. 30) 3,90,000

87,42,000 Less: Variable overheads 35,40,000 Fixed overhead cost 14,70,000

Net profit

37,32,000 Note: It is assumed that the variable overheads (e.g. direct labour) are fixed in the short term. They are derived from part (a) – [(120,000 × Rs. 28) + (45,000 × Rs. 4)]

Ans. 30:

Installed Capacity for the machine = 365 * 8 *3 * 500 = 43.8 lakh units

158

Practical Capacity = ( 365 – 52 - 13 ) * ( 8 - 1) * 3 * 500 = 31.5 lakh units Out of the past five years, normal capacity is average of 3 normal years. Normal Capacity = ( 30.1 + 29.7 + 30.2 ) / 3 = 30.0 lakh units Actual Capacity Utilization = 30.1 lakh units = 68.7 % Idle Capacity = ( 43.8 – 30.1) = 13.7 lakh unit = 31.3 % Abnormal idle capacity = 31.5 – 30.1 = 1.4 lakh units

Ans. 31:

Capacity Details of Computation Machine hours Production units @ 10

units per hour 1. Maximum capacity ( 365 days × 8 hours per day) 2,920 29,200 2. Practical capacity Maximum capacity (in hours) 2,920 Less: Idle capacity Sundays: (52 days × 8 hours) 416 Holidays (10 days × 8 hours) 80 Plant maintenance 2,224 200 22,240 3. Normal capacity 2,000 20,000 4. Expected capacity 1,900 19,000 Determination of Factory overhead application rate (a) Total Budgeted overheads Fixed overhead costs Rs. 6,00,000 Variable overhead costs (2,000 hours × Rs. 100) 2,00,000 8,00,000 (b) Normal Capacity (machine-hours) 2000 (c) (i) Factory overhead application rate (Rs. 8,00,000÷2,000) per hour 400 (ii) Factory overhead application rate (Rs. 8,00,000÷2,0000) per unit 40 Ans. 32

Working Notes:

(Amount in Rupees) X Y Z

Selling price per unit (A) 135.00 140.00 200.00 Variable costs per unit Direct material 32.00 76.00 58.50 Direct labour Department 1 45.00 25.00 50.00 Department 2 15.00 12.00 21.00 Department 3 20.00 10.00 40.00 Variable overheads 8.00 4.50 10.50 Total variable costs (B) 120.00 127.50 180.00 Contribution per unit (A−B) 15.00 12.50 20.00

159

(i) Statement of budgeted profitability

X Y Z Budgeted quantity (units) 19,500 15,600 15,600 Contribution per unit (Rs.) 15.00 12.50 20.00 Total contribution (Rs.) 2,92,500 1,95,000 3,12,000

Contribution fund (Rs.) Fixed overheads (Rs.) Profit (Rs.) 3,99,500

(ii) Contribution per direct labour hour for Department 2

X Y Z Contribution per unit (Rs.) 15.00 12.50 20 Direct labour hours per unit 5 4 7 Contribution per labour hour 3.00 3.125 2.857 Rank II I III

(iii) Total hours available in department 2

X 19,500 units × 5 = 97,500 hours Y 15,600 units × 4 = 62,400 hours Z 15,600 units × 7 = 1,09,200 hours Total = 2,69,100 hours

Y 19,500 2,69,100 4 19,500 78,000 1,91,100 X 23,400 1,91,100 5 23,400 1,17,000 74,100 Z 19,500 74,100 7 10,585 74,095 5

Optimal profit (Rs.) Contribution (Rs.) Y 19,500 × Rs. 12.50 = Rs. 2,43,750

X 23,400 × Rs. 15 = Rs. 3,51,000 Z 10,585 × Rs. 20 = Rs. 2,11,700 Total Contribution = Rs. 8,06,450 Less fixed cost = Rs. 4,00,000

160

Profit = Rs. 4,06,450

Ans 33:

(a) Flexible Budget

Output level (units) 50,000 (Rs. in lakhs)

80,000 (Rs. in lakhs)

1,00,000 (Rs. in lakhs)

Sales Direct Material 12.5 per unit (reduction for 1,00,000 units by Rs.0.50) Direct wages (5.00 per unit) Semi variable cost (variable) Factory overhead (V) Rs.5 per unit) Selling and Adm. (25% variable) Total variable cost Contribution Fixed factory overheads (5×60,000) Selling and adm. (6 × 60,000) Semi variable fixed part Increase due to expansion Interest Depreciation Special Advertisement exp. Total fixed costs

20.00 6.25

2.50 0.25 2.50

1.00 12.50 7.50

3.00 3.60

.30

. 6.90 0.60

32.00 10.00

4.00 0.40 4.00

1.60 20.00 12.00

3.00 3.60

.30 2.00

.60

.50 .50 10.50 1.50

36.00 12.00

5.00 0.50 5.00

2.08 24.58 11.42 3.00 3.60

.30 2.80

.60

.50 . 10.80 0.62

Therefore activity level 80,000 units is most profitable level. Calculation of

Break even point P/V ratio

7.5/20.00 × 100 = 37.5%, 12.00/32.00 × 100 = 37.5%, 11.42/36.00 × 100 = 31.72%BEP (value) = 6.90/37.5% = Rs.18,40,000, 10.50/37.5% = Rs.28,00,000, 10.80/31.72% = 34,04,792

BEP (Units) 6.90

.15lakhs

Rs

10.50.15lakhs

Rs

10.80.15lakhs

Rs

= 46,000 units = 70,000 units = 94,571 units Alternative Solution (BEP in Sales)

Break Even Point in value of sales: (F x S) / (S – V)

At 50000 units’ level : (6,90,000 x 20,00,000)/7,50,000 = Rs. 18,40,000 At 80000 units’ level : (10,50,000 x 32,00,000)/12,00,000 = Rs. 28,00,000 At 100000 units’ level : (10,80,000 x 36,00,000)/11,42,000 = Rs. 34,04,553

161

Ans. 34Overheads

: Budget statement for April Budget Actual Variance

Fixed Variable Total Adverse Favourable Management Rs.30,000 - 30,000 30,000 - - Shift premium - 3,600 3,600 4,000 400 - ESI 6,000 7,920 13,920 15,000 1,080 - Inspection 20,000 9,000 29,000 28,000 - 1,000 Supplies 6,000 6,480 12,480 12,700 220 - Power - 7,200 7,200 7,800 600 - Lighting and heating 4,000 - 4,000 4,200 200 - Rates 9,000 - 9,000 9,000 - - Repairs 8,000 5,400 13,400 15,100 1,700 - Materials handling 10,000 10,800 20,800 21,400 600 - Depreciation 15,000 - 15,000 15,000 - - Administration 12,000 - 12,000 11,500 - 500 Idle time - - - 1,600 1,600 - 1,20,000 50,400 1,70,400 1,75,300 6,400 1,500 Rs.4,900 (A) (b) E.S.I. This variance may be due to increase of E.S.I. rates. If this assumption is correct, then the variance will be beyond the control of management. It should be noted that actual activity is less than budgeted activity. It is , therefore, unlikely that increase is due to increase in the number of labour hours worked. Another possibility is that E.S.I. Payment might have got increased due to increase in E.S.I. rates. Inspection: There is a possibility that standard inspection has been lowered, thus resulting in a saving in costs. If this is not due to management policy, then the variance requires immediate investigation. Another possibility is that a number of staff members have resigned and consequently actual inspection is less than the budget. Repairs and Maintenance: This increase may be due to unexpected repair, which might not have been envisaged. The variance for this item over a period of several months should be studied to form an opinion. Idle Time: No Idle time has been included in the budget. Consequently this idle time must be of an abnormal nature. Possible uncontrollable causes include a power failure or machine breakdown. Controllable causes may include poor scheduling or lack of material. (c ) (i) Calling for comments on variances in excess of a specific figure may not be satisfactory for control purpose. For decision on whether to investigate or not, Cost of investigation should be compared with benefits of investigation. Statistical tests may also be applied. (ii) The statement could be improved by analyzing the expense items into their controllable and non- controllable elements. Variances should be analysed according to whether they are due to price and quantity changes. Analysis should include non- financial measures such as a comparison of actual hours worked with standard hours produced. (d) (i) Overhead absorbed = Rs.1,58,400, i.e.,36,000 hrs x Rs.4.40 (ii) Over spending = Rs.4,900 (iii) Actual production was 4,000 standard hours less than budgeted production and this decline

in output has resulted in a failure to recover Rs.12,000 fixed overheads. This under recovery of Rs.12,000 is also known as the volume variance.

162

Ans. 35:Analysis of the information required for preparation of cash budget (Rs.’000) A.Z. Limited

April May June July August Sales receipts - 401.70 450.28 425.88 - Variable cost of sales (60%) 240.00 270.00 312.00 252.00 288.00 Variable production costs: In the month of sales (60%) 144.00 162.00 187.20 151.20 - In prior month (40%) 108.00 124.80 100.80 115.20 - 252.00 286.80 288.00 266.40 Material costs 60% of production cost 151.20 172.08 172.80 159.84 Purchases: In the month of production (50%) 75.60 86.04 86.40 79.92 In prior month (50%) 86.04 86.40 79.92 Payment to supplier 161.64 172.44 166.32 Labour costs (Variable production cost x 0.3) 75.60 86.04 86.40 79.92 Variable overhead 25.20 28.68 28.80 26.64 (Variable production cost x 0.1) Variable cost was paid as follows: Paid in the month of incurrence (40%) 10.08 11.47 11.52 10.66 Paid in the following month (60%) 15.12 17.21 17.28 Variable overhead expenditure 26.59 28.73 27.94

Cash budget for the month of May to July 1997

May June July Receipts from sales 401.70 450.28 Payments:

425.88

Materials 161.64 172.44 166.32 Labour 86.04 86.40 79.92 Variable overhead 26.59 28.73 27.94 Fixed costs (12,00,000-3,00,000)/12 75.00 75.00 75.00 Capital expenditure Total expenditure 349.27 552.57 349.18 Net inflow (outflow) 52.43 (102.29) 76.70 Balance b/f 40.00 92.43 (9.86) Balance c/f 92.43 (9.86) 66.84 Note. In this question language should be given particular attention:

(a) Variable production cost 60% in the same month 40% in the prior month. Production cost relevant for cash budget for each month should be found.

(b) 60% of production cost is material 50% in the same month and 50% in the prior month. 30% of production cost is labour which is paid the same month. 10% of production cost is variable overhead, 40% is paid the same month. 60% is paid in the following months.

(c) This question illustrates the interaction of sales, purchase and manufacturing process and requires the reader to think clearly about these relationships

Ans. 36

Note: Since question has not clearly specified that whether labour efficiency is lower by

163

ANOTHER 1% or by 1%, also it is unclear that efficiency is to reduced based on BUDGETED EFFICIENCY OR ACTUAL EFFICIENCY, hence this question can be solved in following 3 ways (after giving prompt assumption)

Solution – Way 1

Production Cost Budget (for 6 months ending 30th September, 2009) 30,000 units Cost per unit Total Rs. Rs. Material cost 180 54,00,000 Labour cost 115.47 34,64,208 Variable overhead 23.65 7,09,500 Fixed overhead 23.2

6,96,000 342.34

1,02,69,708

Assumption : Here, difference in actual and standard time is also considered for calculating the lower efficiency i.e. 3.74% + 1% = 4.74% based on budgeted efficiency Working Notes: I. Material cost Material consumption per unit = 1,600MT ÷16,000 = 0.10 MT Consumption for 30,000 units = 3,000 MT. Cost of 3,000 MT @ Rs. 1,800 per MT = Rs. 54,00,000. II. Labour cost can be calculated as follows: 2008 – Total Budgeted Hour = 16,00,000 ÷40 = 40,000 hours Labour hour budget for each unit = 40,000÷ 16,000 = 2.5 Actual time paid = 15,99,840÷ 44 = 36,360 hours Less: Standard labour hours for 14,000 units (i.e. 14,000×2.5)= 35,000 hours Difference in actual and standard hours = 1,360 3.74% = Difference in actual and standard hours ÷ Actual hours ×100 = 1,360 hours÷ 36,360 hours Budget unit (2008) for each labour hour = 16,000÷40000 = 0.4 units Less: (3.74% + 1%) = 4.74% for lower efficiency Budget unit (2009) for each labour hour = 0.38104 units

= 0.01896 units

Time required for 30,000 units (30,000 ÷ 0.38104) = 78,732 hours

Labour cost = 78,732 hours× 44 per hour = Rs. 34,64,208. III. Variable overhead Actual rate = Rs.2,76,000 ÷14,000 units = 19.71 per unit Add: 20 % = 3.94 New rate 23.65

164

Total variable overhead = 30,000 ×23.65 = Rs. 7,09,500 IV. Fixed overhead Actual = Rs. 5,80,000 Add: 20%

= Rs. 1,16,000

= Rs. 6,96,000

According to above the production cost budget will be as follows:

Production Cost Budget Solution – Way 2

(for 6 months ending 30th September, 2009) 30,000 units Cost per unit Total Rs. Rs.

Material cost 180 54,00,000 Labour cost 111.11 33,33,352

Variable overhead 23.65 7,09,500 Fixed overhead 23.2 6,96,000

337.96 1,01,38,652 Assumption : Here, lower efficiency of 1% is based on budgeted efficiency Working Notes: I. Material cost Material consumption per unit = 1,600MT ÷ 16,000 = 0.10 MT Consumption for 30,000 units = 3,000 MT. Cost of 3,000 MT @ Rs. 1,800 per MT = Rs. 54,00,000. II. Labour Cost: 2008 – Total Budgeted Hour = 16,00,000 ÷40 = 40,000 hours Budget unit (2008) for each labour hour = 16,000÷40000 = 0.4 units Less: 1% for lower efficiency Budget unit (2009) for each labour hour = 0.396 units

= 0.004units

Time required for 30,000 units (30,000 ÷ 0.396) = 75,758 hours Labour cost = 75,758 hours × 44 per hour = Rs. 33,33,352 III. Variable overhead Actual rate = Rs.2,76,000÷14,000 units = 19.71 per unit Add: 20 % New rate

= 3.94

Total variable overhead = 30,000 × 23.65 = Rs. 7,09,500 23.65

IV. Fixed overhead Actual = Rs. 5,80,000 Add: 20%

= Rs. 1,16,000

= Rs. 6,96,000

165

Production Cost Budget Solution – Way 3

(for 6 months ending 30th September, 2009) 30,000 units Cost per unit Total Rs. Rs.

Material cost 180 54,00,000 Labour cost 115.44 34,63,196

Variable overhead 23.65 7,09,500 Fixed overhead 23.2 6,96,000

342.29 1,02,68,696 Assumption : Here, lower efficiency of 1% is based on actual efficiency Working Notes: I. Material cost Material consumption per unit = 1,600MT ÷ 16,000 = 0.10 MT Consumption for 30,000 units = 3,000 MT. Cost of 3,000 MT @ Rs. 1,800 per MT = Rs. 54,00,000. II. Labour Cost: 2008 – Total Actual Hour = 15,99,840 ÷44 = 36,360 hours Actual unit (2008) for each labour hour = 14000÷36360 = 0.385 units Less: 1% for lower efficiency Budget unit (2009) for each labour hour = 0.38115 units

= 0.00385units

Time required for 30,000 units (30,000 ÷ 0.38115) = 78,709 hours Labour cost = 78,709 hours × 44 per hour = Rs. 34,63,196 III. Variable overhead Actual rate = Rs.2,76,000÷14,000 units = 19.71 per unit Add: 20 % New rate

= 3.94

Total variable overhead = 30,000 ×23.65 = Rs. 7,09,500 23.65

IV. Fixed overhead Actual = Rs. 5,80,000 Add: 20%

= Rs. 1,16,000

= Rs. 6,96,000

Ans. 37: (a) Cash Budget for October, November and December 1990 Opening balance of bank (overdraft) Cash inflows – Sales: From cash sales of current month From credit sales of previous month Total Receipts (A) Cash outflows:

October Rs.35,000

5,000

15,000 55,000

November Rs.(9,100)

- 6,000

18,000 14,900

December Rs.(12,600)

8,000

20,000 15,400

166

Creditors for purchases of the preceding month Equipment Wages Administration Rent Dividend Total payment (B) Closing balance (Overdraft) (A-B)

40,000 16,000

3,000 1,500 3,600

- 64,100 (9,100)

23,000

- 3,000 1,500

- -

27,500 (12,600)

27,000 -

3,000 1,500

- 15,000 46,500

(31,100) (b) Budgeted Income Statement for three months ending 31st

Sales December 1990

Less: Cost of Goods Sold: Material- Opening Stock Add: Purchases (23,000 + 27,000 + 26,000) Less: Closing stock Cost of material consumed Wages (3,000 x 3) Gross profit Less: Rent [ 3,600 x (3 / 12 ) ] Administration (1,500 x 3) Depreciation [3,000 x (3 / 12)] Loss on sale of asset ( Rs.15,000 – Rs.14,000) Net profit

Rs.20,000 76,000 96,000 43,500 52,500

9,000

900 4,500

750 1,000

Rs.82,000

61,500 20,500

7,150 13,350

Working Notes: (i) Total Sales Credit Sales Cash Sales Total October 1990 Rs.18,000 Rs.5,000 Rs.23,000 November 1990 20,000 6,000 26,000 December 1990 25,000 8,000

33,000 63,000 19,000

82,000

For Cost of Sales: (ii) Sales for the quarter Rs.82,000 Less: Gross Profit 25% of Sales Cost of sales

20,500

(iii) For Material consumed: 61,500

Cash of sales for three months Rs.61,500 Less: Wages (3,000 x 3) Cost of material consumed

9,000 52,500

(iv) For closing stock of material

Opening stock of material Rs.20,000 Add: Purchases (23,000 + 27,000 + 26,000) 76,000 96,000

Less: Material consumed Closing stock of material 43,500

52,500

167

Ans. 38:

Shirt Short Nov Dec Jan Feb Nov Dec Jan Feb Cl. Stock( 40% 6120 6242 6367 - 8160 8320 8490 - Of next month) Sales 15000 15300 15919 15606 20000 20400 21224 20800 Total 21120 21542 21973 28160 28720 29290 Op. Stock 6000 6120 6242 8000 8160 8320 Production 15120 15422 15731 20160 20560 20970

Shirts Shorts Opening stock 6000 8000 Sales November 6000 = 15,000

40% 8000 = 20,000 40%

December 1.02 x 15,000 = 15,300 1.02 X 20,000 = 20400 January 1.02 x 15,300 = 15,606 1.02 X 20,400 = 20,808 February 1.02 X 15, 606 = 15, 919 1.02 X 20,808 = 21,224

Alternative:

Opening Stock Shirts = 6000 = 40% of November Sales

Opening Stock of Shorts = 8000 =40% of November Sales

November sales 6000 = l5,000 40%

8000 = 20,000 40%

Dec. Sales l.02 x l5,000 = l5,300 l.02 x 20,000 = 20400 Closing Stock November 40% x l5, 300 = 6,l20 40% x 20,400 = 8l60 November Production = Closing Stock + sales – Opening stock

l5, l20 20,l60

December Production l.02 X l5, l20 = l5422 l.02 X 20,l60 = 20, 560 January Production l.02 Xl5422 = l5, 73l l.02 X 20,560 = 20, 970

(a) Production Budget for product A and B Ans39:

A units B units Inventory at the end of the year 1,000 2,000 Sales forecast 8,000 15,000

168

Total requirements 9,000 17,000 Less: Beginning inventory 3,000 5,000 Production 6,000 12,000

Budgeted requirements of components P, Q and R

Components P Q R For Product A: Production 6,000 units P: 6,000 × 1 per unit 6,000 Q: 6,000 × 2 per unit 12,000 For Product B: Production 12,000 units P: 12,000 × 2 per unit 24,000 Q: 12,000 × 1 per unit 12,000 R: 12,000 × 2 per unit 24,000 For comp R: Production 24,000 comp Q: 24,000 × 1 per component R 24,000 Total requirements 30,000 48,000 24,000

(b) The company is advised to adopt EOQ system. P Q

2 30,000 15EOQ 2 20%

× ××

2 48,000 150.8 20%× ×

×

= 1,500 components = 3,000 components (c) Calculation of savings arising from switching over to the new ordering system.

Existing situation:

P Q

Present order quantity (units)

(equivalent to 3 months consumption)

30,000 × ¼ 7,500 48,000 × ¼ 12,000

Average stock (units) 7,500 × ½ 3,750 12,000 × ½ 6,000

Investment in inventory of P & Q 3,750 × Rs. 2 7,500 6,000 × Re. 0.80 4,800

Total investment Rs. 7,500 + Rs. 4, 800 =Rs. 12,300

Carrying cost @ 20% p.a. of average inventory investment

Rs. 12,300 × 20% Rs. 2,460

Ordering cost: P = 4×Rs. 15 = Rs. 60

Total cost

Rs. 120

Rs. 2,580

After switching over:

P Q

Economic order quantity (units) 1,500 3,000

169

Average stock (units) 1,500 × ½ 750 3,000 × ½ 1,500

Investment in inventory of P & Q 750 × Rs. 2 1,500 1,500 × Re. 0.80 1,200

Total investment Rs. 1,500 + Rs. 1,200 =Rs. 2,700

Carrying cost @ 20% p.a. of average inventory investment

Rs. 2,700 × 20% Rs. 540

Ordering cost: P = 20×Rs. 15 = Rs. 300

Q = 16×Rs. 15 = Rs. 240

Total cost

Rs. 540

Rs. 1,080

Saving in costs: Rs. 2,580 – Rs. 1,080 = Rs. 1,500 Reduction in working capital: Rs. 12,300 – Rs.2,700 = Rs. 9600

Ans. 42: (showing quantities to be manufactured)

Production Budget

Chairs Tables Benches Units to be sold (Note 1) Add: Closing inventory as per budget Less: Opening inventory as per budget

4,200 200

4,400 400

4,000

800 300

1,100 100

1,000

500 50

550 50

500 (b) Material Purchase Budget (in quantities) Timber Upholstery (cu. ft.) (Sq. yards) Material required for production (Note 1) 4,450 1,000 Add: Closing stock as per budget 650 5,100 1,260

260

Less: Opening stock as per budget 600 Raw materials to b purchased

400 4,500

800

Materials Purchase (in rupees) Quantities to be purchased Rate Amount Timber (c.ft.) 4,500 50 Rs.2,25,000 Upholstery (sq. yds.) 860 20

17,200

2,42,200

(c) Direct wage Cost Budget Total hrs. Rate p.h. Amount Carpenter’s time and wages 4,625 6.00 Rs.27,750 Fixer’s and finisher’s time and wages 1,500 4.80 7,200

34,950

(d) Statement showing the variable cost of manufacture per unit of all three products. Chairs Tables Benches

170

Raw materials – Timer Upholstery Fixing and finishing materials cost (Note 2) Wages Carpenters Fixer’s and finisher’s

Rs.25.00 (0.5 x Rs.50)

5.00 (0.25 x 20)

1.50

4.50 (45/60) x Rs.6

1.20 (15/60) x 4.80

37.20

60.00 (1.2 x Rs.50)

-

3.00

6.00 (60/60) x Rs.6

1.20 (15/60) x 4.80

70.20

125.00 (2.5 x Rs.50)

-

6.25

7.50 (75/60) x Rs.6

2.40 (30/60) x 4.80

141.15 (e) Budgeted Net Income Statement (For the quarter) Selling price (per unit) Less: Variable cost Contribution per unit (A) Units to be sold (B) Total contribution Fixed cost for the quarter (Rs.8,000 x 30 Budgeted net income

Chairs Rs.50.00

37.20 12.80 4,200

53,760

Tables Rs.85.00

70.20 14.80

800 11,840

Benches Rs.158.00

141.15 16.85

500 8,425

Total Rs.

74,025

24,000 50,025

Working Notes:

1. Raw Materials, Carpenter’s Time and Fixer’s and finisher’s Time Units to be manufactured Timber (c. ft.) Upholstery (sq. yards) Carpenter’s time (hrs.) Fixer’s and Finisher’s time(hrs.)

Chairs 4,000 2,000

(4,000 x 0.5) 1,000

(4,000 x 0.25) 3,000

(4,000 x(45 /60) 1,000

4,000 x(15/60)

Tables 1,000 1,200

(1,000 x 1.2) -

1,000 1,000 x (60/60)

250 1,000 x (15/60)

Benches 500

1,250 (500 x 2.5)

-

625 500 x (75/60)

250 500 x (30/60)

Total

4,450

1,000

4,625

1,500

2. Per unit cost of materials of fixing and finishing

Chairs Tables Benches Total cost of Timber and Upholstery Rs.30 Rs.60 Rs.125 Fixing and Finishing Material will cost 5% Of total cost of timber and upholstery 1.5 3 6.25 (5% of 30) (5% of Rs.60) (5% of Rs.125) Ans. 43:Necessary Calculations

171

Statement showing total cost and selling price and sales in units for each product (Working Note 1) Working A Working B Working C Materials Rs. Rs. Rs. M1

(Rs.2x5 units) 10 - 2x12 24

M2

- (4x10) 40 (4x9) 36

M3 15 45 60

(Rs.1x5 units) 5 (1x5) 5

Labour Department I (Rs.2.5x4) 10 (2.5x2) 5 (2.5x2) 5 Department II (Rs.2.0x6) 12 (2x2) 4 (2x3) 6 Department 1II (Rs.1.5x2) 3 (1.5x4) 6 (1.5x6) 9 Variable overhead 10 20 15 Fixed Cost(Working Note 2) Department I (Rs.5x4 hrs.) 20 (5x2) 10 (5x2) 10 Department II (Rs.3x6 hrs) 18 (3x2) 6 (3x3) 9 Department 1II (Rs.6x2 hrs.) 12 (6x4) 24 (6x6) Total production cost 100 120 150

36

Adm.(Based on 20% of production cost) 20 24 30 Selling and Distb. Cost (40% of prod. Cost) 40 48 Total cost 160 192 240

60

Profit (25% of total cost) 40 (12 ½ % of 24 (16 2/3% of 40

Selling price per unit

total cost) total cost

200 216 280Sales in rupees 15,00,000 10,80,000 16,80,000

Sales in units 7,500 5,000 6,000 Sales in rupees / Selling price (per unit) (a) Production Budget for July 1986 A

(Units) B (units)

C (Units)

Sales Less: Closing stock (given) Add: Closing stock : 20% reduction (working Note 3) Production

7,500 3,000

4,500

2,400

5,000

6,900

2,000

3,000

1,600

4,600

6,000 2,500

3,500

2,000 5,500

(b) Material Usage budget for July 1986 Product Units of

product Qty. per unit of product

M1 Qty. per unit of product

total Qty reqd.

M2 M Total Qty reqd.

3 Total Qty. reqd.

Qty per units of product

A B C Total usage in unit

6,900 4,600 5,500

5 - 12

34,500 -

66,000 1,00,500

- 10

9

- 46,000 49,500 95,500

5 5 -

34,500 23,000

- 57,500

172

(c ) Material Purchase Budget M M1 M2 3 Units Rs. Units Rs. Units Rs. Usage 1,00,000 2,01,000 95,500 3,82,000 57,500 57,500 (price is given Less: O/stock

24,500

49,000

20,500

82,000

17,500

17,500

76,000 1,52,000 75,000 3,00,000 40,000 40,000 (Add: C/stock) (10% reduction)

22,050

44,100

18,450

73,800

15,750

15,750

98,050 1,96,100 93,450 3,73,800 55,750 55,750 (d) Budgeted profit and loss account for each product and in total A B C Total Sales Rs.15,00,000 Rs.10,80,000 Rs.16,80,000 Rs.42,60,000 Less: cost (Working Notes) 12,00,000 9,60,000 14,40,000 36,00,000 Profit 3,00,000 1,20,000 2,40,000 6,60,000 Working Notes Note: 1. Price per unit of material and material units required for each product should be multiplied. Note:2. Fixed overhead rate Deptt. I = Rs.2,39,000 47,800

or Rs.5 per hour

Deptt. II = Rs.2,01,300 67,100

or Rs.3 per hour

Deptt. II = Rs.3,91,200 65,200

or Rs.6 per hour

Note:3. A = 3,000 x 80 or 2,400 , B = 2,000 x 80 or 1,600, C = 2,500 x 80 100 100 100

or 2,000

Note:4. A -7,500 x 160 =Rs. 12,00,000; B - 5,000 x 192 Rs.9,60,000; C – 6,000 x 240 =Rs.14,40,000 Ans. 44:

For the production manager Responsibility Accounting Reports

Cutting Department Budgeted Rs. Actual Rs. Variance Rs.

Cloth 31,000 36,000 5,000 (A) Cutting Labour 6,000 6,600 600 (A)

173

Cutting utilises 800 700 Total cutting Deptt. (A)

100 (A) 37,800 43,300

Sewing Department: 5,700 (A)

Thread 500 450 50 (F) Sewing Labour 17,000 18,400 1,400 (A) Sewing utilities 900 950 Total Sewing Dept. (B)

50 (F) 18,400 19,800

Total (A + B) 1,400 (A)

56,200 63,100 6,900 (A) For the director-Manufacturing

Production Department * 56,200 63,100 6,900 (A) Production engineering expenses 13,000 12,200 800 (F) Production manager-office expenses 18,000 17,000 Total

1,000 (F) 87,200 92,300

(* As per responsibility accounting report for the production manager) 5,100 (A)

For the Direct-Marketing Sales representative:

Travelling expenses 9,000 10,200 1,200 (A) Sales commission 7,000 7,000 Total (A)

-- 16,000 17,200

Sales Management: 1,200 (A)

Office expenses 16,000 15,700 300 (F) Advertising 4,000 4,000 Total (B)

— 20,000 19,700

Credit Department: 300 (F)

Salaries 8,000 8,000 Credit reports 1,200 1,050 150 (F) Bad debt Losses 5,000 3,000 Total

2,000 (F) 14,200 12,050

Total (A + B + C) 2,150 (F)

50,200 48,950 1,250 (F) Note: ‘F’ denotes favourable variance while ‘A’ denotes adverse variance.

Performance Budget Ans. 45:

Original Revised Actual Variance Plan Rs. Budgeted Rs. Result Rs. Rs.

Revenue (5,000×10) 50,000 (4,000×10) 40,000 (4,000×11) 44,000 4,000 (F)

Variable (5,000×4) 20,000 Costs (4,000×4) 16,000

(4,000×4.5) 18,000 2,000 (A)

174

Contribution (5,000×4) 30,000 (4,000×6) 24,000 (4,000×6.5) 26,000 2,000 (F)

Fixed costs 20,000 20,000 21,000 1,000 (A) Net Profit 10,000 4,000 5,000 1,000 (F)

Summary Report on Profit Plan Planned Income (from Project plan) Rs. 10,000 Activity variance (lost contribution margin due

to shortage of materials) (6,000) Selling price variance (increased Selling price of Re. 1/- per unit) 4,000 Variance cost variance (increased production Costs at 0.50 per unit) (2,000) Fixed cost variance (new research programme to Develop raw materials and processes) (1,000) Actual income (from income statement) 5,000

175

TRANSFER PRICING

Ans 9 (i) In this case there are two options available –

(a) Sell at the sub assembly stage (after completion of Div. A) @ Rs. 2000/-

Incremental cost in Div. A Rs 1,200/- Contribution Rs 800/- (b) Sell at the final product stage Rs. 3,000 Cost at Div. A and Div. B Rs(1200+1500) Rs 2,700 Contribution Rs 300 Therefore it is profitable to sell at the subassembly stage because of higher contribution, provided there is a market. Hence, if there is market at intermediate stage, first priority is to sell intermediary (sub assembly).Therefore, 800 units should be sold as sale of intermediary. The balance capacity available of (1000 – 800) = 200 units should be transferred to B and B should complete the assembly and sell as final product, since the company can earn Rs. 300 per unit for each unit of such sale.

(ii) If B Div. receives the subassembly at market price of Rs. 2,000, plus its own incremental cost of Rs. 1,500 will give total cost of Rs. 3,500, thereby yielding a loss of Rs. 3500 – Rs. 3000 = Rs. 500 per unit, whereas the company makes a profit of Rs. 300 per unit.

In order to keep the manager of Div. B motivated, the profit earned of Rs. 300 per unit should be shared between A and B. Hence transfer price will be variable cost of Div. A + 50% of profit earned in the final product = 1200 + 150 = Rs. 1,350

(iii) Both Div. A and the Company make higher contribution by selling to intermediate market. If the market demand increases to 1,000 units, the full quantity should be sold outside as intermediary and nothing should be transferred to Div. B

Ans.10: Transfer Price is Rs. 4,500 for each consulting day. Profit mark-up = 150% Let cost = x

Profit = x × 100150

= 1.5x

Cost + profit = Transfer price x + 1.5x = 4,500 2.5x = 4,500 x = 1,800 ∴Cost = Rs. 1,800 and profit = 1.5x = 1.5×1,800 = Rs. 2,700 Variable cost (80%) = Rs. 1,800× 80% = Rs. 1,440 Fixed cost (20%) = Rs. 1,800 ×20% = Rs. 360. Scenario (i): Every consultancy team is fully engaged. There is no idle time or spare capacity. Hence, transfer price = Marginal cost plus opportunity cost Marginal cost = Rs. 1,440 Saving for internal work = Rs. 200 Net Marginal Cost = Rs. 1,240

176

Opportunity cost is the lost contribution. Lost contribution = Contribution from external client = Fee charged from external client – Variable cost = Rs. (4,500 – 1,440) = Rs. 3,060. ∴Transfer price = Rs. 1,240 + 3,060 = Rs. 4,300 per consulting day per team. Scenario (ii): One team is idle. Idle time has no opportunity cost. Variable cost for internal work is Rs. 1,240 per consulting day. Second team is busy. Hence opportunity cost is relevant in case of second team. Hence charge of second team is Rs. 4,300 per consulting day per team. Average of charge of two teams = Rs. (1,240 + 4,300) / 2 = Rs. 2,770 per consulting day per team. Scenario (iii): New client offers a fee of Rs. 15,84,000 Duration: 5 days of 48 weeks ×2 teams = 480 days Fee per day 15,84,000 / 480 = Rs. 3,300 Variable cost = Rs. 1,440 Contribution Rs. (3,300 – 1,440) = Rs. 1,860 Fee for consulting day for internal work: Variable cost = Rs. 1,240 Contribution lost = Rs. 1,860 Fee to be charged = Rs. 3,100 per consulting day per team. Ans.11: 100% capacity 4,000 tones (Maximum) Distribution market Processing unit

2,000 Tones 2,000 Tones

80% capacity 3,200 tones Market 2,000 Tones Processing unit 12,00 Tones (a) 80% capacity – price Rs. 400 per ton (Rs.) Particulars Basic unit Particulars Processing unit Sales (3,200 * 400) 12,80,000 (24,000 * 40) 9,60,000 Raw materials (3,200 * 70) Variable cost (3,200 * 140) Fixed overhead

2,24,000 4,48,000

9,72,000 3,00,000

Tr. Price (1,200 * 400) (1,200 * 170)

4,80,000 2,04,000

8,04,000 1,20,000

Profit 3,08000 1,56,000 Total profit of the company = Rs. 4, 64,000 (b) 100% capacity – price Rs. 400 per ton (Rs.) Particulars Basic unit Particulars Processing

unit Sales (4,000 X 400) Raw materials (4,000 X 70) Variable cost (4,000 X 140) Fixed overheads

16,00,000 2,80,000 5,60,000 3,00,000

14,00,000

(4000 X 320) Tr. Price (2,000 X 400) (2,000 X 170)

12,80,000 8,00,000 3,40,000 1,20,000

12,60,000 Profit 4,60,000 20,000 Total Profit of the Company = Rs. 4,80,000

177

(c ) 80% capacity- Market price @ Rs.360 & Transfer price to processing @ Rs. 400 per tonne (Rs) Particulars Basic unit Particulars Processing unit Sales (2,000 X 360) + (1,200 X 400) Raw materials (3,200 X 70) Variable Cost (3,200 X 140) Fixed overheads

2,24,000 12,00,000

4,48,000

9,72,000 3,00,000

(24,000 X 40) Tr. Price (1,200 X 400) (1,200 X 170)

4,80,000

9,60,000

2,04,000

8,04,000

1,20,000

Profit 2,28,000 1,56,000 Total Profit of the Company = Rs. 3,84,000 (d) 100% capacity- Price Rs. 360 per tonne (Rs.) Particulars Basic unit Particulars Processing units Sales (4,000 X 360) Raw material (4,0000 X 70) Variable overheads (4,000 X 140) Fixed overheads

2,80,000 14,40,000

5,60,000

11,40,000 3,00,000

Tr Price (2,000 X 360) (2,000 X 170)

7,20,000

12,80,000

3,40,000

11,80,000

1,20,000

Profit 3,00,000 1,00,000 Total profit o the Company = 4,00,000 Comments : At Rs. 400 per tonne, the processing unit will not be interested in buying more than 1,200 tonnes because the profitability of the processing unit will be reduce from Rs. 1,56,000 to Rs. 2,000. When the market price reduce to Rs. 360 per tonne the processing unit will not be interested in purchasing more than 1,200 tonnes because at this level it can maintain the same level of profit. Even if the price is reduced to Rs.360 for the processing unit, it may not be interested in buying more than 1,200 tonnes as its profitability will be reduced from Rs.1,56,000 to Rs.1,00,000. When the market price reduced to Rs.360 per tonne and the transfer price is maintained at Rs.400, the processing unit may get its suppliers of 1,200 tonnes via open market at the price less than Rs.400 per tonne. This will increase the profitability of the processing unit but reduced the profitability of the basic unit. Thus the present policy market price for transfer pricing does not offer incentive to the processing unit. Hence cost plus method should be restored to. Ans. 12

(i) (a) At 80% level (in Rs)

-Textile unit -Process house Sales (4,00,000 × 6) 24,00,000 Sales(1,50,000/100) × 825 12,37,500 Less Less Raw material (4,00,000 × 3) 12,00,000 Transfer Price (1,50,000 × 6) 9,00,000 Variable cost (4,00,000 ×1.2) 4,80,000 Variable cost (1,500 × 80) 1,20,000 Fixed cost 4,12,000 Fixed cost 1,00,000 Profit 3,08,000 Profit 1,17,500

Overall profit = 3,08,000 + 1,17,500 = Rs 4,25,500

At 100% level

Sales (5,00,000 × 6) 30,00,000 Sales (2,50,000/100) × 725 18,12,500

Less Less

Raw material (5,00,000 × 3) 15,00,000 Transfer Price (2,50,000 × 6)

15,00,000

Variable cost (5,00,000 × 1.2)

6,00,000 Variable cost 2,00,000

Fixed cost 4,12,000 Fixed cost 1,00,000 Profit 4,88,000 Profit 12,500

Overall profit = 4,88,000+12,500 = Rs 5,00,500

(b) At 80% level (market price 5.60 and transfer price 6/-) (in Rs)

Textile unit Process house

Sale (2,50,000 × 5.6) 1400000

178

(1,50,000 ×6.0) 900000

23,00,000 Less

Raw material (4,00,000 × 3) 12,00,000

Variable cost (4,00,000 × 1.2) 4,80,000

Fixed cost 4,12,000 Profit 2,08,000 Profit 1,17,500

Overall profit = 2,08,000+1,17,500 =Rs 3,25,500

(c) Sales 100% level at (5.60) (in Rs)

Sale (5,00,000 × 5.6) 28,00,000 Sales(2,50,000 × 725) 18,12,500

Less Less

Raw material (5,00,000 ×3) 15,00,000 Transfer Profit (2,50,000 × 5.6)

14,00,000

Variable cost (5,00,000 ×1.20) 6,00,000 Variable cost (2,500 × 80)

2,00,000

Fixed cost 4,12,000 Fixed cost 1,00,000 Profit 2,88,000 Profit 1,12,500

Overall profit = 2,88,000 + 1,12,500 =4,00,500

(ii) Comments on the profitability of processing units:-

Transfer price (Rs) Profit (Rs) (a) 80% capacity 6.00 1,17,500 100% capacity 6.00 12,500 (b) 80% capacity 6.00 1,17,500 (c) 100% capacity 5.60 1,12,500

Processing house will not be interested to buy more than 1,50,000 meters from textile units.

Ans.: 13 (Rs.) Particulars BRITE LITE TITE Selling Price Variable costs Contribution

300 150

60 40

700 590

150 20 110 Alternative I Division AD (Rs) Contribution (15,000 units of BRITE X Rs.150) (40,000 units of LITE X Rs.20) Total Contribution Fixed Expenses Profit (a)

22,50,000

8,00,000 30,50,000 20,00,000 10,50,000

Division CD (Rs) Contribution (5,000 units of TITE X Rs.110) Fixed Expenses Profit (b)

5,50,000 4,00,000 1,50,000

Overall profit of the company (a + b) Rs.12,00,000 Alternative II Division AD (Rs)

179

Contribution (15,000 units BRITE outside customer @ Rs.150) (5,000 units of BRITE Division CD @ 150) (20,000 units of LITE (limited capacity) @ Rs.20) Total contribution Fixed expenses Profit (a)

22,50,000

7,50,000 4,00,000

34,00,000 20,00,000 14,00,000

Division CD Extra cost of labour Rs.50 and variable cost Rs.640 Hence contribution Rs.700 - Rs.640 = Rs.60 (Rs) Contribution (5,000 units @ Rs.60) Fixed Expenses Loss (b) Overall profit of the company (a-b)

300,000 400,000 100,000

13,00,000 Alternative III Division AD Price of BRITE to CD reduced by Rs.50 Hence Contribution/unit Rs.250 – Rs.150 = Rs.100 (Rs) Contribution (15,000 units of BRITE outside party @ Rs150) (5,000 units of BRITE to CD @ Rs100) (20,000 units of LITE to capacity @ Rs20) Total contribution Fixed expenses Profit (a)

22,50,000

5,00,000 4,00,000

31,50,000 20,00,000 11,50,000

Division CD BRITE from AD Rs.250 contribution Rs.700-Rs.590 = Rs.110 per unit Lobour and overhead Rs.340, Variable costs Rs.590 (Rs.) Contribution (5,000 units @ Rs.110) Fixed expenses Loss (b) Overall profit of the company (a+b)

5,50,000 4,00,000 1,50,000

Rs.13,00,000 Alternative 1V Division AD (Rs.) Contribution (15,000 units BRITE outside customer @ Rs.150) (10,000 units of BRITE to CD @ Rs.250 i.e., contribution @ Rs.100) Total contribution Fixed expenses Profit (a)

22,50,000 10,00,000 32,50,000 20,00,000 12,50,000

Division CD (Rs.) Contribution (10,000 units with BRITE of AD @ Rs.110) (2,000 units with imported component @ Rs.110) Total contribution Fixed expenses Profit (b)

11,00,000

2,20,000 13,20,000 11,70,000

1,50,000 Overall profit of the company (a+b) Rs.14,00,000 Recommendation on best alternative Alternative (iv) seems to be the best because it leads to the maximum profit of Rs. 1400000 for the company. But management should consider whether stopping the production of Lite altogether will, in any way, be detrimental to company’s interests. Negotiated price of Rs. 240 per unit. The price of Rs. 240 per unit will be acceptable to AD because it will lead to a contribution of Rs. 22.50 per hour i.e. (Rs. 240-Rs.150)÷4 hours. If this proposal is not accepted AD will have to produce Lite which will yield a contribution of only Rs. 20 per hour, i.e. (Rs. 60-Rs.40)÷1 hour.

180

AJ Ans.: 14: Alternative I

Rs. DJ Rs. Sales : outside (18,000x15) DJ (2,000x10) Total Less V. Costs( 20,000x8.50) Net Contribution

2,70,000 20,000

2,90,000 1,70,000 1,20,000

Sales (2,000 x 105) Variable Costs (2,000 x 99) Contribution Interest Net Contribution

2,10,000 1,98,000

12,000 1,000

11,000 Total Group contribution =Rs.1,31,000

Alternative II Sales : (20,000x15) Variable costs(20,000x8.50) Contribution

3,00,000 1,70,000 1,30,000

Sales (2,000 x 105) Variable Costs (2,000 x104) Contribution Interest Net Contribution

2,10,000 2,08,000

2,000 1,000 1,000

Total Group contribution = Rs.1,31,000 Alternative III Sales : (20,000x15) Variable costs(20,000x8.50) Contribution

3,00,000 1,70,000 1,30,000

Sales (2,000 x 105) Variable Costs (2,000x 104) Contribution Interest Net Contribution

2,10,000 2,08,000

2,000 1,000 1,000

Total Group contribution = Rs.1,31,000 Alternative IV Sales : (22,000x15) Variable costs 1,87,000 Over time Contribution

4,000

3,30,000

1,91,000 1,39,000

Sales (2,000 x 105) Variable Costs(2,000 x 104) Contribution Interest Net Contribution

2,10,000 2,08,000

2,000 1,000 1,000

Total Group contribution = Rs.1,40,000

Comments: Alternative 1: AJ can supply part 35 to DJ at Rs.10 because the variable cost is Rs.8.50 only and by this transaction a contribution of Rs.1.50 is available. But the overall contribution which would have been Rs.13,000 if the part has been sold to outside buyers, would come down to Rs.1,20,000. DJ however, will earn a net contribution of Rs.11,000. Thus the divisional performance of AJ will go down and that of DJ will boost up at the cost of AJ. Alternative 2: AJ will maintain its performance but DJ’s performance will be reduced to a contribution of Rs.1,000 only. Alternative 3: AJ will maintain its performance but DJ’s performance will be reduced to a contribution of Rs.1,000 only. In these three cases the group income will not change but the performance of the individual divisions will vary. Alternative 4: AJ’s performance will boost up but DJ’s performance will remain at the low level .DJ cannot show better performance except at the cost of AJ. Hence AJ should not reduce the price particularly when it has an assured market for part 35 at Rs.15 each. Ans.: 15:

Statement showing profitability of two divisions at two different levels of output using different transfer prices

181

No. of bottles 8,00,000 12,00,000 Rs. Rs.

Sales value (Packed Product) : (A) 91,20,000 1,27,80,000 Less : Costs Product Manufacturing Division 64,80,000 96,80,000 Bottle Manufacturing Division 10,40,000 14,40,000 Total costs : (B) 75,20,000 1,11,20,000 Profit :{(A) – (B)} 16,00,000 16,60,000 Profit pro-rated to Bottle Mfg. Division and Product Mfg. Division.

Share of Bottle Manufacturing Division: 16,00,000 × 10,40,000/75,20,000 2,21,276 16,60,000 × 14,40,000/1,11,20,000 2,14,964 Balance profit relates to Product Mfg. Division 13,78,724 14,45,036

16,00,000 16,60,000 Rs. Rs. Transfer prices of bottles Costs 10,40,000 14,40,000 Profit as computed above 2,21,276 2,14,964 Total price 12,61,276 16,54,964 Transfer price per bottle Rs. 1.577 Rs. 1.379

From the above computations, it is observed that shared profit relative to the cost involved is Rs. 2,21,276 (Re. 0.2766 per bottle) at 8,00,000 production level and Rs. 2,14,964 (Re. 0.179 per bottle) at 12,00,000 production level. The profit of Product Mfg. Division is Rs.13,78,724 (Rs.1.723 per bottle) at 8,00,000 production level and Rs. 14,45,036 (Rs. 1.2042 per bottle) at 12,00,000 production level.

Profitability based on market price

No. of bottles 8,00,000 12,00,000

Bottle Mfg. Division Rs. Rs. Market price 14,00,000 20,00,000 Less: Cost 10,40,000 14,40,000 Profit (i) 3,60,000 5,60,000 Product Mfg. Division Sales 91,20,000 1,27,80,000 Less: Bottle cost 14,00,000 20,00,000

Product cost 64,80,000 96,80,000 Profit (ii) 12,40,000 11,00,000 Total profit : (i) + (ii) 16,00,000 16,60,000

Profit based on Profit based on cost (Rs.Lakhs) Market price (Rs.Lakhs)

Production level Bottle Product Bottle Product Mfg. Div. Mfg. Div. Mfg. Div. Mfg. Div. 8,00,000 bottles 2.21 13.79 3.60 12.40 12,00,000 bottles 2.15 14.45 5.60 11.00

Observations: 1. Market price methods gives a better profitability to Bottle Mfg. Division at both the

production levels. 2. Market price method gives a lower profitability to Product Mfg. Division as compared to Bottle

182

Mfg. Division. 3. Under Cost-based method, there is a better profit at lower level of production in Bottle

Mfg. Division. However in Product Mfg. Division 12,00,000 production level gives a higher profit. But in Market price method, the position is quite reverse.

Ans. 16(a) When component is purchased by Division B from outside (Rs.)

(i) Statement of contribution

Division A Division B Sales (2000x 400) Less: Cost of Purchase (2000x 200) 400000 Variable costs (200x 150) Company’s total contribution

300000

8,00,000

3,80,000

Nil

1,00,000 1,00,000

(b) When component is purchased from Division A by Division B (Rs.) Division A Sales (2000x 220) Less: Variable costs (2000x 190) Division B Sales (2000x 400) Less: Variable Costs: Purchase cost in Division A (2000x 220) 440000 Variable cost in Division B (2000x 150) Company’s total contribution

300000

4,40,000 7,00,000

8,00,000

7,40,000

60,000

60,000 1,20,000

Thus, it will be beneficial for the company as a whole to ask Division B to buy the component from Division A. (ii) Statement of total contribution if Division A could be put to alternative use: Division A: Contribution from alternative use of facilities Division B: Sales (2000x 400) Less: Variable costs: Cost of purchase (2000x 400) 400000 Division B (2000x 150) Company’s total contribution

300000

8,00,000

7,00,000

30,000

1,00,000 1,30,000

Since, the company’s contribution when component is purchased from outside, shows as increase of Rs.30,000 as compared to when there is inter departmental transfer. Hence, it will be beneficial to purchase the component from outside. (iii) Statement of total contribution when component is available from outside at Rs. 185 Division A: Division B: Sales (2000x 400) Less: Variable costs: Cost of purchase (2000x 185) 370000 Division B (2000x 150) Company’s total contribution

300000

8,00,000

6,70,000

Nil

1,30,000 1,30,000

If the component is purchased by Division B from Division A, the contribution is only Rs.1,20,000 as calculated under above. Hence it will be beneficial to buy the component from outside.

183

(iv) Fixations of transfer price (a) When there are no alternative uses of production facilities of Dept. A: In such a case the variable cost i.e. Rs.190 per component will be charged. (b) If facilities of Division A can be put to alternative uses: (Rs.)

Variable cost Opportunity cost Transfer price

190 15

205

(c) If market price gets reduced to Rs.185 and there is no alternative use of facilities of Division A. the variable cost of Rs.190 per component should be charged. Ans.17

Total overheads

For the budgeted level of activities and expenses of LD the various costs and prices can be worked out as follows: (Rs.)

Less: Variable overheads Fixed overheads per year

7,56,000 4,20,000 3,36,000

LX Variable overheads 4,20,000 x

LY 90,000 4,20,000 x

2,10,000 2,10,000 1,20,000

1,80,000 2,40,000 Fixed overheads per year 3,36,000 x 90,000 3,36,000 x 1,20,000At the budgeted level of activities 2,10,000 2,10,000

1,44,000 1,92,000 The costs and selling prices of the products of LD for normal sale to outside parties will be as under: (Rs.per kg.) Particulars LX LY Direct material Direct wages Variable overheads Total Variable cost: Fixed costs Total costs Add: Mark-up 50% Selling price

36 30 60

126 48

174 87

261

28 20 40 88 32

120 60

180 Labour hours calculated as under: Particulars LX LY Direct wages Wages rate (Rs./hr.) Direct labour hr.

30 5 6

20 5 4

Committed production of LY of 6,000 kg. would involve labour of 6000 x 4 = 24,000 Balance labour available for: Production of LX = 42,000-24,000 = 18,000 Hrs. Production of LY = 18,000 hrs. / 6 DLH = 3,000 Kg.

184

Cost estimate of KX it KD purchase Lx from LD at normal prices (Rs.) Cost of LX Processing materials & Wage costs Variable Overheads Total Variable Cost

261 30 4

295

Profit Statement of LD & KD (1) Transfer price based on total cost

LD Rs. KD Rs. Sales LX (3000 x 261) LY (6000 x 180) Total Sales Variable cost LX (2000 x 122) (1000 x 126) LY (6000 x 88) Total variable cost Fixed costs Total costs Profit

7,83,000 10,80,000 18,63,000

2,44,000 1,26,000 5,28,000 8,98,000 3,36,000

12,34,000 6,29,000

Sales KX (2000 x 300)

Variable cost (2000 x 295)

Fixed cost Total cost

Loss

6,00,000

5,90,000

1,00,000 6,90,000 (-)90,000

Total profit for the company = 6,29,000 – 90,000 =Rs.5,39,000 (ii) Transfer price based on total Cost after adjustment for selling expenses

LD Rs. KD Rs. Sales LX (2000 x 257) (1000 x 261) LY (6000 x 180) Total Sales Less: Costs as above Profit

5,14,000 2,61,000

10,80,000 18,55,000 12,34,000 6,21,000

Sales (2000 x 300)

Total costs (690000-4 x 2000) Less

6,00,000

6,82,000 (-)82,000

(iii) Total profit to the company =6,21,000-82,000 =Rs.5,39,000

LD Rs. KD Rs. Sales LX (2000 x 122) (1000 x 261) LY (6000 x 180) Total Sales Less: Total Costs as above Profit

2,44,000 2,61,000

10,80,000

15,85,000 12,34,000 3,51,000

Sales KX (2000 x 300)

Variable cost (2000 x 156) Fixed costs Total costs Profit

6,00,000

3,12,000 1,00,000 4,12,000

1,88,000

(iv) Total profit for the Company =3,51,000 + 1,88,000 =Rs.5,39,000 LD Rs. KD Rs.

Sales LX (3000 x 152) (a) (Including Rs.30 oT) (3000 x261) LY (6000 x 180) Total Sales

3,04,000

7,83,000 10,80,000

Sales KX (2000 x 300)(a)

Variable cost (2000 x 186)

6,00,000

3,72,000 1,00,000

185

Variable cost LX (2000 x 152) (3000 x 126) LY (6000 x 88) Total variable cost Fixed costs Total costs (b) Profit (a-b)

21,67,000

3,04,000 3,78,000 5,28,000

12,10,000 3,36,000

15,46,000 6,21,000

Total costs (b) Profit (a-b)

4,72,000 1,28,000

Total profit for the company =6,21,000 + 1,28,000 Rs.7,49,000 Ans.18 (i) Department ‘A’ By product BYEA Production 3000 Tonnes Sales Income (30% of 3000 Tonnes @ Rs.200) (70% of 3000 Tonnes @ Rs.1200) Total

(Rs.) 1,80,000

25,20,000 27,00,000

(ii) Department ‘B’ Production of RESP (3000 x 200,i.e.,600000 litres) Sales (600000 litres @ Rs.15) (a) Costs: Opportunity Cost of BYEA Variable Costs (600000 @ Rs.4) Fixed Costs Total (b) Profit (a-b)

(Rs.) 90,00,000 27,00,000 24,00,000 12,00,000 63,00,000 27,00,000

(iii) Department ‘C’ (ltrs.) Production of POTS (600000 x 1.6) 5% wastage

9,60,000 48,000

9,12,000 (a) Sales Pack (ML) % Litres No.of packs Price/Pack

Rs. Sales Value Rs

200 300 Total

75 25

6,84,000 2,28,000 9,12,000

34,20,000 7,60,000

2.50 3.50

85,50,000 26,60,000

1,12,10,000 (b) Costs (Rs.) RESP (600000 x 15) Mfg. Cost (912000 x 1.50) Total

90,00,000 13,68,000

1,03,68,000 Profit (a-b) 8,42,000 (iv) Total Profit under the existing arrangement A-27,00,000 + B-27,00,000 + C-8,42,000 =Rs.62,42,000 Under the new proposal (Ltrs.) Total quantity of RESP purchased (3000 x 120) Production of POTs (360000 x 1.60)

3,60,000 5,76,000

186

Amount of Saleable POTs (576000 x 95/100) 5,47,200 (a) Sales Pack (ML) % Litres No.of packs Price/Pack

Rs. Sales Value Rs

200 300 Total

75 25

4,10,400 1,36,800 5,47,200

2,05,200 4,56,000

2.50 3.50

51,30,000 15,96,000 67,26,000

(b) Costs (Rs.) RESP (360000 x 6.25) 22,50,000 Mfg. Cost (547200 x 1.50) 8,20,000 Fixed Overhead of Dept. B 12,00,000

42,70,800 Profit (a)- (b) 24,55,200 Analysis : Since under the new proposal profit gets lowered from Rs.62,42,000 to Rs.24,55,200 the proposal is not acceptable. Ans.19. The transfer price will be notional revenue to S and notional cost to T.

(a) S will continue to produce more output until the costs of further production exceed the transfer price revenue.

(b) T will continue to want to receive more output from S until its net revenue from further processing is not sufficient to cover the incremental transfer price costs.

Output Units Division S Incremental Cost

Rs. Division T Incremental Costs Rs.

600 700 800 900 1000 1100 1200

- 100 140 160 200 250 350

- 300 280 250 220 200 150

Since S will continue to produce more output if the transfer price exceeds the incremental costs of production, a price of at least Rs.200 per 100 units (Rs. 2 per unit ) is required to ‘persuade’ the manager of S of produce as many as 1,000 units, but a price in excess of Rs.250 per 100 units would motivate the manager of S to produce 1,100 units (or more). By a similar argument, T will continue to want more output from S if the incremental revenue exceed the transfer costs from S. If T wants 1,000 units the transfer price must be less than Rs.220 per 100 units. How ever, if the transfer price is lower than Rs.200 per 100 units, T will ask for 1100 units from S in order to improve its divisional profit further.

In summary (a) The total company profit I maximised at 1,000 units of output. (b) Division S will, want to produce 1,000 units, no more and no less, if the transfer price is

between Rs.2 and Rs.2.50(Rs.200 to Rs.250 per 100 units). (c) Division T will want to receive and process 1,000 units, no more and no less, if the

transfer price is between Rs.2 and Rs.2.20 (d) A transfer price must therefore be selected in the range Rs.2.00 to Rs.2.20 per

unit(exclusive).

187

Thus, if a price of Rs.2.10 per unit is selected, profits at 1,000 units of output would be; (Rs.)

Particulars Division S Division T Total Sales/Net revenue Costs Profit

2,100 1,200

900

4,000 2,100 1,900

4,000 1,200 2,800

At a transfer price of Rs.2.10 any increase in output above 1,000 units, or shortfall in output below this amount, would reduce the profits of company as a whole, but also the divisional profits of S and T.

Ans.20. (a)The problem The overall company interest is obviously to produce 1,400 units which will given the maximum profit. The problem is to fix the transfer price (TP) with which both X and Y will find 1,400 units to be the optimum output for them severally. Let us analyse and examine the incremental costs at X and the incremental revenue at Y Level of output Incremental Cost for

X Incremental Net revenue for Y Rs.

Company profit

1,000 1,100 1,200 1,300 1,400 1,500 1,600

- 100 120 130 150 180 220

- 300 240 190 170 130 80

3,100 3,300 3,420 3,480 3,500 3,450 3,310

A price of at least Rs. 150 per 100 units (Rs.1.50 per unit) is required to induce the manager of X to produce as many as 1,400 units; but the price must not exceed Rs.180 per 100 units, for in that event X would like to produce 1,500 units (or more) Similarly, Y will keep producing so long as the incremental revenues exceed the transfer cost from X. in order that Y wants 1,400 units, the TP must be lower than Rs.170 per 100units; but it shall not be lower than Rs.130,for Y will then ask for 1,500 units from X to increase his (Y’s) divisional profit further. If the TP is selected at Rs.1.60 per unit, profits at 1,400 units of output would be (Rs.) Particulars X Y Company Sales / Net revenue Costs Profit

2,240 1,400 840

4,900 2,240 2,660

4,900 1,400 3,500

At a TP of Rs.1.60 any increase in output above 1,400 units or shortfall in output below this level would reduce the profits of the company as a whole and also the divisional profits of X and y. With Rs.1.60 as TP, neither X or Y will like to deviate from 1,400 units, which incidentally is also wanted y the corporate Management. Ans. 21. (i) Calculation of transfer price to be quoted by Alfa to Beta based on residual income (Rs.) Fixed Costs Return on capital employed (Rs.750 lakhs x 12/100) Residual income desired Total

80 90

100 270

188

Desired contribution per unit =Selling price p.u.-Variable cost p.u. =Rs.180- Rs.60 =Rs.20 p.u. Total desired contribution =12,00,000 units x Rs.20 p.u =Rs.240 lakhs Minimum contribution to be earned from sale of additional 3 lakh units. Rs.270 lakhs-Rs.240 lakhs =Rs30 lakhs. Contribution p.u. on additional 3,00,000 units =Rs.30,00,000/3,00,000 units = 10 p.u. Variable cost of modification per unit =Rs.5 Hence, the minimum transfer price per unit to be quoted will be =Rs.160 + 10 + 5 =Rs.175 (ii) If Beta can buy from outside at less than the variable cost of manufacture, Rs.165, than only the decision to transfer at the price of Rs.175 will become sub-optimal for the group as a whole. Ans.22. Working Notes: (i) Computation of Sales revenue from Foam Division (Rs.) Sales of Foam Division to outside customers (Rs.1,600-Rs.200) Less: Variable Mfg. Costs (Rs.1,200-Rs.200) Mark-up on outside Sale (Rs.400/Rs.1000)x 100=40% Transfer Price of Foam to Upholstery Division Sales of Foam Division to outside Customers Total

1,400 1,000

400

280 1,400 1,680

(ii) Variable Mfg. Cost of Upholstery Division (Rs.’000) =(Rs.680-Rs.200 + Rs.280) =Rs.760 (iii) Computation of Traceable Administration Expenses ( Rs.’000) Divisions Foam Carpets Upholstery Total Given Administration expenses Less: Common expenses (10% of Gross Profit) Traceable Administration Expenses

134

40

94

116

40

76

172

50

122

422

130

292 (iv) Computation of Traceable Selling Expenses ( Rs.’000) Divisions Foam Carpets Upholstery Total Given Selling expenses Less: Common expenses (2.5% of Sales) Traceable Selling Expenses

202

40 162

210

30 180

232

30 202

644

100 544

(a) Revised operating statement (using Contribution approach) (Rs.000) Divisions Foam Carpets Upholstery Total Sales Revenue Less: Variable Mfg. Costs Contribution (i) Traceable Costs: Fixed Mfg. Costs Admn. Expenses

1,680 1,200 480

-

1,200 700 500

100 76

1,200 760 440

20 122

4,080 2,660 1,420

120

292

189

Selling Expenses Total (ii) Operating Income (i)-(ii) Less: Common expenses Net Income of the Company

94 162 256 224

180 356 144

202 344 96

544 956 464 230 234

(b) (i) Computation of contribution Margin (Rs.’000) Contribution Margin Ratio % = Sales

Contribution X 100

(Ranks)

Foam Carpets Upholstery

(Rs.480/Rs.1680) x100 (Rs.500/Rs.1200) x 100 (Rs.440/Rs.1200) x 100

28.57% 41.67% 36.67%

III I II

(ii) Computation of Net Contribution Ratio (Rs.’000) Net Contribution Ratio (%) =

Sales Net Contribution X 100

Foam Carpets Upholstery

(Rs.224/Rs.1680) x100 (Rs.144/Rs.1200) x 100 (Rs.96/Rs.1200) x 100

13.33% 12% 8%

III I II

It is observed from the above analysis that foam Division’s Manager argument I correct when we look at the calculation given above which shows that even though contribution margin ratio of Foam Division is lower, the divisions ranking is higher based on the Net Contribution Ration. The use of contribution approach for reporting is more realistic for assessing the performance of various divisions as it considers variable and traceable costs only and avoids common costs while finding out profitability. This approach enables the management to rightly interpret the information. Further, pricing of internal transfers at market price will give due credit to specific profits centre i.e. transferor.

The desired rate of return is 28% on investments. Investments include: (i) Fixed assets after depreciation

Ans. 23

(ii) Net working capital. In the question, current assets and debtors are given but current liabilities and creditors are not indicated. Therefore, these are assumed to have nil value. Investments

Fixed assets 5,00,000 Net working capital Rs. Current assets 3,00,000

Debtors 2,00,000 5,00,000 Total investments 10,00,000

The desired rate of return is 28% The profit margin will be Rs. 280000 Budgeted volume 400000unit Rs. Profit margin per unit (Rs. 280000 ÷ 400000 units) 0.70 Fixed cost per unit 2.00 Variable cost per unit 10.00

190

Transfer price per unit 12.70 Ans.24 (i) Profit =20% return on average assets employed Average assets (Rs.Lakhs) Sundry Debtors Inventories Plant & equipment Total

2 5 5

12 Profit =Rs.12,00,000 x 20 /100 =Rs.2,40,000 (2) Budgeted sales revenue (2,00,000 units of component X) (Rs.Lakhs) Fixed cost Variable cost (2,00,000 units @ Rs.1) Profit Total Sales

5.00 2.00 2.40 9.40

Selling price per unit of component X =Rs.9,40,000/2,00,000 units =Rs.4.70 per unit Options in hand with Division A Option 1 -Sell 1,50,000 units in market and transfer 50,000 units to Division B Option 11 -Sell only 1,50,000 units in market. Statement of profitability of Division A under two options (Rs.) Particulars Option-I Option-II Sales (1,50,000 units @ Rs.4.70) Transfer to Division-B (50,000 units @ Rs.2) Total Sales revenue Less: variable overhead Contribution Less: Fixed Cost Profit (a) Capital employed (b) Return on capital employed (a)/(b)X100

7,05,000 1,00,000 8,05,000 2,00,000 6,05,000 5,00,000 1,05,000

12,00,000 8.75%

7,05,000 -

7,05,000 1,50,000 5,55,000 4,75,000

80,000 10,00,000

8% Analysis : From the analysis of the above it is observed that under Option-I, Division A’s, Profit and ROCE is increased by Rs.25,000 and 0.75% respectively. Hence Option-I is suggested for Division-A. Ans. 25 (i) The company as a whole will not benefit if Division C bought the component from an outside supplier at

Rs.135/- per unit. Rs. Purchase cost from outside supplier 1,35,000 (1,000 units × Rs.135 per unit) Less: Saving in variable cost of division A by reducing Division’s output 1,20,000 (1,000 units × Rs.120 per unit) Net cost (benefit) to the company as a whole 15,000

The company as a while will not benefit, as it will be required to incur an additional cost of Rs.15,000 if Division C bought the component from outside supplier.

191

(ii) The company will be benefited if C purchased the component from an outside supplier and Division A uses the facilities for other activities. Rs. Rs. Purchase cost from outside supplier 1,35,000 (1,000 units × Rs.135) Less: Saving in variable cost of Division A for the units purchased by Division C from outside

1,20,000

(1,000 units × Rs.120 per unit) Cash operating saving of Division A for the use of facilities for other activities

18,000

Net cost (benefit) to the company as a whole

1,38,000

It is advisable that Division C should purchase the component from outside sources as this decision will

benefit the company by Rs.3,000.

(3,000)

(iii) The company will be benefited if C purchase the component from an outside supplier and there is no alternative use of Division A’s facilities. Rs. Purchase cost from outside supplier 1,15,000 (1,000 units × Rs.115) Less: Saving in variable cost of Division A by reducing division’s output

1,20,000

(1,000 units × Rs.120) Net cost (benefit) to the company

.

It is advisable that the Division C should buy the component from outside as this decision will benefit the company by Rs.5,000.

(5,000)

Ans 26 (i) Working notes:

1. Contribution per hour of Super-chips and Okay-chips: Super-chips Okay-chips Selling price per unit (Rs.) 600 120 Less: Variable cost per unit (Rs.) 300 80 Contribution per unit (Rs.) 300 40 Hours required per unit 2 0.5 Contribution per hour 150 80 (Rs.300/2 hrs) (Rs.40/0.5 hrs)

2. Details of hours utilized in meting the demand of 15,000 units of Super-chips and utilizing the remaining hours for Okay-chips out of available hours of 50,000 per annum: Rs. Hours utilized for manufacturing 15,000 units of Super-chips 30,000 (15,000 units × 2 hours) Hours utilized for manufacturing 40,000 units of Okay-chips (40,000 units × 0.5 hours)

20,000

3. Contribution of a process control unit (using an imported complex circuit board):

50,000

Rs.

192

Selling price per unit: (A) 1,400 Variable costs Circuit board (Imported) 600 Other parts 80 Labour cost (5 hours × Rs.100) 500 Total variable costs: (B) 1,180 Contribution per unit (Rs.) : [(A) – (B)] 220

4. Contribution of process control unit (using a Super-chips): Rs. Selling price per unit: (A) 1,400 Variable costs Super-chip 300 (Material + Labour costs) Other parts 80 Labour (6 hours × Rs.100) 600 Total variable costs: (B) 980 Contribution per unit (Rs.) : [(A) – (B)] 420

5. Incremental contribution per unit of a process control unit, when instead of using imported complex circuit board Super-chip is used:

Rs. Incremental contribution per unit (Rs.420 – Rs.220) (Refer to W. N. 3&4) 200

(ii) Super-chips to be transferred to Mini Computer Division to replace Circuit Boards: Out of 50,000 available hours 30,000 hours are utilized for meeting the demand of 15,000 unit of

Super-chips, the rest 20,000 hours may be used for manufacturing 40,000 Okay-chips, which yields a contribution of Rs.40 per unit or Rs.80/- per hour (Refer to working note 1) or a contribution of Rs.160 per two equivalent hours.

In case the company decides to forego the manufacturing of 20,000 units of Okay-chips in favour of 5,000 additional units of Super-chips to be used by Mini-Computer division (instead of complex imported Circuit Board) for manufacturing process control units. This decision would increase the existing contribution of Mini-computer Division by Rs.200/- per two-equivalent hours (Refer to working note 5).

Hence the entire requirement of 5,000 units of Super-chips be produced and transferred to Mini-Computer Division.

(ii) Minimum transfer price of Super-chip to Mini Computer Division: Variable cost of a Super-chip + Opportunity cost of foregoing the production

of an Okay-chip and using craftsmen time for Super-chip

= Rs.300 + 2 hours × Rs.80 = Rs.460 (iii) Super –chips to be produced for the production of 12,000 units of process control units: After meeting out the order of 15,000 Super-chips per year, the concern is left out with 20,000 hours.

Use of Super-chips for control units production would increase the existing contribution of Mini-Computer Division by Rs.200/- per unit. Out of the remaining 20,000 craftsmen hours, 10,000 units of Super-chips can be made, which may be used for the production of 10,000 process control units.

Ans 27

193

(i) Statement of the overall profit of the company (By harvesting 2,000 kgs of oil seeds, processing it into edible oil & selling the same in 2 kg cans)

Harvesting Division

Oil Mill Division

Marketing Division

Total Rs.

Output of each department

2,000 kgs of oil seed

1,000 kgs. of oil produced

500 cans of 2 kg each

Total costs Variable cost (Rs.) : (A) 5,000 10,000 1,875 16,875 (2,000 kgs ×

Rs.2.50) (1,000 kgs ×

Rs.10) (500 ×

Rs.3.75)

Fixed cost (Rs.): (B) 10,000 7,500 4,375 21,875 (2,000 kgs ×

Rs.5) (1,000 kgs ×

Rs.7.50) (500 ×

Rs.8.75)

Total cost (Rs.): (C) = [(A)+(B)]

15,000 17,500 6,250 38,750

Sales revenue (Rs.): (D) 75,000 (500 cans × Rs.150) Profit (Rs.) [(D) – (C)] 36,250

(ii) Working note: (a) Total Contribution = (Sales revenue – total variable cost) = Rs.75,000 – Rs.16,875 = Rs.58,125 (b) Amount of shared contribution in relation to variable costs:

Harvesting Division = Rs.58,125 × Rs.16,875Rs.5,000 = Rs.17,222

Oil Mill Division = Rs.58,125 × Rs.16,875Rs.10,000 = Rs.34,445

Marketing Division = Rs.58,125 × Rs.16,875Rs.1,875 = Rs.6,458

Computation of Transfer Price (for internal transfers) under the following pricing methods: (1) Shared contribution in relation to variable costs: Transfer price from harvesting Division to Oil Mill Division = Variable cost of Harvesting Division + Shared contribution of Harvesting Division in relation to

variable costs = Rs.5,000 + Rs.17,222 (Refer to working note 2) = Rs.22,222 Transfer price from Oil Mill Division to Marketing Division = Transfer price from Harvesting Division to Oil Mill Division + Variable cost of Oil Mill Division + Shared contribution of Oil Mill Division in relation to variable costs (Refer to working note 2) = Rs.22,222 + Rs.10,000 + 34,445 = Rs.66,667 (2) Market price: Transfer price from Harvesting Division to Oil Mill Division = Market price of 2,000 kgs of Oil seeds transferred to Oil Mill Division

194

= 2,000 kgs. × Rs.12.50 = Rs.25,000 Transfer price from Oil Mill Division to Marketing Division = Market price of 1,000 kgs of edible oil = 1,000 of kgs × Rs.62.50 – Rs.62,500 (iii) Statement of profitability (under different transfer prices method)

From Harvesting Division to Oil Mill Division

From Oil Mil to Marketing Division

From Marketing Division to market (500 cans of 2 Kgs.)

Rs. Rs. Rs. Shared contribution method Transfer price: 22,222 66,667 75,000 (Refer to (1) above) Less: Transfer price __ 22,222 66,667 (Refer to (ii) above) Less: Variable cost 5,000 10,000 1,875 Less: Fixed cost 10,000 7,500 4,375 (Refer to (i) above) Profit 7.222 26,945 2,083 Market price method Transfer price 25,000 62,500 75,000 (Refer to (2) above) Less: Transfer in price __ 25,000 62,500 (Refer to (ii) above) Less: Variable cost 5,000 10,000 1,875 (Refer to (ii) above) Less: Fixed cost 10,000 7,500 4,375 (Refer to (i) above) Profit 10,000 20,000 6,250 Decision: Divisional Manager of Harvesting Division would prefer the use of market price method for transferring 2,000 kgs of oil seeds to Oil Mill Division because its usage increases the profit by Rs.2,778 (Rs.7,222) over the shared contribution method. Whereas Oil Mill Division manager would prefer the use of shared contribution method over the market price method because its use would increase its profit by Rs.6,945 (Rs.26,945 – Rs.20,000). Similarly Marketing Divisional Manager would be benefited to the extent of Rs.4,167 (Rs.6,250 – Rs.2,083) by using market price method.

Ans 28 (i) Statement of profitability of Division X

No. of components Transfer price for the component to

Department Y@ Rs.90 per unit

Total cost of components (Rs.)

Profit / (Loss) (Rs.)

(a) (b) (c) (d) = {(b) – (c)} 5,000 4,50,000 5,62,500 (1,12,500) 10,000 9,000 9,00,000 __

195

15,000 13,50,000 12,37,500 1,12,500 20,000 18,00,000 15,75,000 1,25,000 25,000 22,50,000 19,12,500 3,37,500 30,000 27,00,000 22,50,000 4,50,000

Statement of profitability of Division Y No. of Components

Sale revenue on

average price basis

Component cost

(Transfer price) to Dept. Y

Manufacturing cost in

division Y

Total cost Profit/(Loss)

Rs. Rs. Rs. Rs. Rs. (a) (b) (c) (d) (e)={(c)+(d)} (f)={(b)-(e)} 5,000 19,68,750 4,50,000 14,06,250 18,56,250 1,12,500 10,000 29,85,000 9,00,000 16,87,500 25,87,500 3,97,500 15,000 37,12,500 13,50,000 19,68,750 33,18,750 3,93,750 20,000 41,70,000 18,00,000 22,50,000 40,50,000 1,20,000 25,000 45,00,000 22,50,000 25,31,250 47,81,250 (2,81,250) 30,000 45,00,000 27,00,000 28,12,500 55,12,500 (9,90,000)

(ii) Profitability of the company as a whole (a) At 30,000 units level, at which Division X’s net profit is maximum Rs. Profit of Division X 4,50,000 Profit of division Y Operating profitability / (Loss) of the company

(9,00,000)

(b) At 10,000 units level, at which Division Y’s net profit is maximum Rs. (5,40,000)

Profit of division X NIL Profit of division Y Operating profitability of the company

3,97,500

(iii) Profitability of the company, if it is not organised on profit centre basis 3,97,500

No. of components

Sales revenue on

average basis

Cost of component

to division X

Manufacturing cost in

division Y

Total cost Profit/ (Loss)

(Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (a) (b) (c) (d) (e)={(c) +

(d)} (f)={(b)–(e)}

5,000 19,68,750 5,62,500 14,06,250 19,68,750 - 10,000 29,85,000 9,00,000 16,87,500 25,87,500 3,97,500 15,000 37,12,500 12,37,500 19,68,750 32,06,250 5,06,250

20,000 4170,000 15,75,000 22,50,000 38,25,000 3,45,000 25,000 45,00,000 19,12,500 25,31,250 44,43,750 56,250 30,000 45,22,500 22,50,000 28,12,500 50,62,500 (5,40,000)

The level of output, the company will earn maximum profit, if the company is not organized on profit centre basis is 15,000 components.

196

Ans.29. Statement showing contribution P.U. of ranking (Rs.)

Particulars Product A B C D

Market Price P.U. Less: Variable Production Cost P.U Contribution P.U. Labour hours P.U. Contribution per labour hour (i)/(ii) Ranking

150 130 20 3

6.67 IV

146 100 46 4

11.5 III

140 90 50 2 25 I

130 85 45 3 15 II

(i) Allocation of 20,000 labour hours C (2,300 units x 2 L.H.) D (1,600 units x 3 L.H.) B (2,500 units x 4 L.H.) A (Balance) (200 units x 3 L.H.0

4,600 4,800

10,000 600

20,000 Product D can be transferred to Division Y, but the maximum Quantity that might be required for transfer is 2,500 units of D. Time required for 2,500 units of D =2,500 units x 3 L.H =7,500 L.H 2,500 units of Product D for Division Y can be met by sacrificing as follows: (Labour hours) Product A (200 units x 3 L.H.) Product B (Balance) (1,725 units x 4 L.H.)

600 6,900 7,500

Transfer price to be charged by Division Z to Division y on supply of 2,500 units of product D. (Rs.) Variable cost (2,500 units x Rs.85) Add: opportunity cost of contribution foregone Product A (200 units x Rs.20) Product B (1,725 units x Rs.46) Transfer Price Transfer Price P.U. (Rs.2,95,850 / 2,500 units)

2,12,500

4,000 79,350

2,95,850 118.34

(ii) Allocation of 30,000 Labour Hours C (2,300 units x 2 L.H.) D (1,600 units x 3 L.H.) B (2,500 units x 4 L.H.) A (2,800 units x 3 L.H.) Idle Labour (Balance) Total

4,600 4,800

10,000 8,400 2,200

30,000 2,500 units of Product D for Division Y can be met by sacrificing as follows: Idle labour hour Product A (1,725 units x 3 L.H.) Total

2,200 5,300 7,500

Calculation of transfer price (Rs.)

197

Variable cost (2,500 units x Rs.85) Opportunity cost of Contribution foregone of Product A (1,767 units x Rs.20) Transfer price P.U. (Rs.2,47,840 / 2,500 units)

2,12,500 35,340

2,47,840 99.14

Ans. 30

Working Notes:

(i) Hours required to meet maximum demand:

External sales Hours reqd. Total Hrs. per unit

(i) (ii) (iii) = (i) × (ii)

X 800 units 3 2,400 Y 500 units 4 2,000 Z 300 units 2

600

Total (ii) Contribution per unit:

5,000

Product X Y Z Rs. Rs. Rs.

Selling price 48 46 40 Less : Variable cost 33 24

Contribution per unit : (A)

28

15 22 12

Labour hours required per unit : (B) 3 4 2

Contribution per hour (Rs) : (A) / (B) 5 5.5 6

Ranking III II I

(a) If only 3,800 hours are available in Division A.

300 units of Z (maximum), which will take* 600 hrs. 500 units of Y (maximum), which will take 2,000 hrs. 400 units of X to use remaining hrs. 1,200 hrs.

3,800 hrs

.

*Note: Labour hours required per unit are given in the question. If 300 units of Y are to be transferred to ‘B’ division, then 1,200 hours will have to be used for production of Y instead of X. It means Division A will sacrifice production of 400 units of X, which are yielding Rs. 5 per hr. Given above is the optimum mix for Division A for 3,800 hrs. If 300 units of Y are to be transferred to ‘B’ division with time constraint of 3,800 hours, then additional 300 units of Y will have to be produced sacrificing the production of 400 units of X which is yielding contribution.

Transfer price Rs. (i) Variable cost of Y 24.00 Opportunity cost (ii) Contribution relating to ‘X’ forgone for

producing additional units of Y (4 hrs × Rs. 5*) 20.00

*Y takes 4 hours and in each hour production of X would have generated contribution of 44.00

198

Rs. 5.

(b) If 5,600 hours are available Maximum time required to meet external sales (Refer to Working note 1) 5,000 hrs. Hours now available 5,600 hrs. (i) It means 600 hrs can be easily used for the production of Y and transfer price will be variable

cost only i.e. (600 hrs. 4 hrs) × Rs. 24 Rs. 3,600 Note: Y takes 4 hours per unit (ii) For producing additional 150 units, production of X will be disturbed. Variable costs

(i) 150 units of X @ Rs. 24 Rs. 3,600 Opportunity cost (ii) Contribution of ‘X’ units

forgone (600 hrs. × Rs. 5) Rs. 3,000* 6,600 Total price for 300 units 10,200

Average transfer price should be Rs. 34 per unit *Contribution per hr. of X forgone.

Ans.31. (1) Maximum hours required to meet the present outside market requirement Maximum sales units Hours required per

unit Total hours

Vx X1 Xt

900 300 600

3 2 4

2,700 600

2,400 Maximum total hours required to meet the outside market requirement 5,700 (2) Contribution per unit, per hour and ranking (Rs.) Product V X X Selling price per units Less: Variable cost per unit Contribution per unit Labour hours required per unit Contribution per hour Ranking

24 17 7 3

2.33 II

23 12 11 2

5.5 I

20 14 6 4

1.5 III

(3) Utilisation of 4,800 available hours according to ranking (hours) 300 units of products X1 (300 units x 2 hours) 900 units of products Vx (300 units x 3 hours) 375 units of products Xt (300 units x 4 hours) Total hours

600 2,700 1,500 4,800

(a) computation of transfer price for each unit of Vx if total labour hours available in

Department x are 4,800 According to the ranking 4,800 available hours are utilized to produce 300 units of X 900 units of Vx and 375 units of X. The aforesaid product mix would give rise to optimum mix for optimum profit.

199

In case 400 units of Vx are to be supplied to Department y in addition to existing outside sale then the production of product X is to be curtailed partially and the hours thus obtained will be utilized for the production of 400 additional units of Vx. The new product mix will be as follows:

(Hours) 300 units of products X1 (300 units x 2 hours) 1,300 units of products Vx (1,300 units x 3 hours) 75 units of products Xt (75 units x 4 hours) Total hours

600 3,900

300 4,800

Computation of transfer price per unit (Rs.) Variable cost of one unit of Vx Contribution foregone (opportunity cost) per unit due to the curtailment of Xt(3 hours x Rs.1.5) Transfer price per unit

17.00

4.50 21.50

(b) Computation of transfer price for each unit of Vx, if total labour hours available in

Department x are 6,200 Hours required to meet the present outside market requirement 5,700 Remaining hours available for producing 400 additional units of Vx 500 After meeting the present outside market requirement (6,200 hours -5,700 hours) Computation of transfer price per unit: (Rs.) Total variable cost on the production of 166.67 units of Vx (500 hours / 3 hours) @ Rs.17 per unit by utilizing 500 remaining available hours Total variable cost of 233.33.units of Vx @ Rs.17 per unit (400 units – 166.67 units) produced by curtailing the production of Xt product to the tune of 700 hours. Contribution foregone (opportunity cost ) on the diversion of 700 hours of Production of Xt for producing 233.33 units of Vx (700 hours x Rs.1.50) Total cost for producing 400 additional units of Vx Transfer price for one unit of Vx (Rs.7,850 / 400 units)

2,833

3,967

1,050

7,850 19,625

Ans. 32(a) When component is purchased by Division B from outside (Rs.)

(i) Statement of contribution

Division A Division B Sales (2000x 400) Less: Cost of Purchase (2000x 200) 400000 Variable costs (200x 150) Company’s total contribution

300000

8,00,000

3,80,000

Nil

1,00,000 1,00,000

(b) When component is purchased from Division A by Division B (Rs.) Division A Sales (2000x 220) Less: Variable costs (2000x 190) Division B Sales (2000x 400) Less: Variable Costs: Purchase cost in Division A (2000x 220) 440000 Variable cost in Division B (2000x 150) Company’s total contribution

300000

4,40,000 7,00,000

8,00,000

7,40,000

60,000

60,000 1,20,000

200

Qty. Unit

Rate Rs.

Value Rs.

Q t y Unit

Sale in open market 2,400 12.00 28,800 9,600 2 Transfer to painting shop 9,600 12.00 1,15,200 Total sales : (A) 12,000 1,44,000 9,600

Thus, it will be beneficial for the company as a whole to ask Division B to buy the component from Division A. (ii) Statement of total contribution if Division A could be put to alternative use: Division A: Contribution from alternative use of facilities Division B: Sales (2000x 400) Less: Variable costs: Cost of purchase (2000x 400) 400000 Division B (2000x 150) Company’s total contribution

300000

8,00,000

7,00,000

30,000

1,00,000 1,30,000

Since, the company’s contribution when component is purchased from outside, shows as increase of Rs.30,000 as compared to when there is inter departmental transfer. Hence, it will be beneficial to purchase the component from outside. (iii) Statement of total contribution when component is available from outside at Rs.185. Division A: Division B: Sales (2000x 400) Less: Variable costs: Cost of purchase (2000x 185) 370000 Division B (2000x 150) Company’s total contribution

300000

8,00,000

6,70,000

Nil

1,30,000 1,30,000

If the component is purchased by Division B from Division A, the contribution is only Rs.1,20,000 as calculated under

(2) above. Hence it will be beneficial to buy the component from outside. (v) Fixations of transfer price

(a) When there are no alternative uses of production facilities of Dept. A: In such a case the variable cost i.e. Rs.190 per component will be charged. (b) If facilities of Division A can be put to alternative uses: (Rs.)

Variable cost Opportunity cost Transfer price

190 15

205 (c) If market price gets reduced to Rs.185 and there is no alternative use of facilities of Division A. the variable cost of Rs.190 per component should be charged.

Fastners Limited Ans. 33

(a) Present profitability of individual shops and overall profitability

Particulars Welding shop Painting shop

201

Less: Variable cost : (B) 1,14,000 (9600 units × Rs.20) 1,92,000 (12,000 units × 9.50)

Contribution : {(A) – (B)} 30,000 48,000 Less: Fixed cost 25,000 30,000 Profit 5,000 18,000

Overall profit for the company (Rs. 5,000 + Rs. 18,000) = Rs. 23,000 (b) (i) When painting shop purchases all its requirement from open market at a price of Rs. 10 per unit

Welding shop Painting shop

Qty. Unit Rate Rs.

Value

R

Q t y Unit

Rate Rs.

Value Rs.

Sale 2,400 12.00 28,800 9,600 25.00 2,40,000 Less: Variable cost 2,400 9.50 22,800 9,600 18.00* 1,72,800 Contribution 6,000 67,200 Less: Fixed cost 25,000 30,000 Profit/(Loss) (19,000) 37,200

Overall profit for the company Rs. 37,200 – Rs. 19,000 = Rs. 18,200 *It is given in the question that cost of painting including transfer price from welding shop is Rs. 20 per unit. The transfer price from welding shop is Rs. 12 per unit. Therefore, the variable cost of Rs. 8 (Rs. 20 – Rs. 12) is incurred by painting shop exclusively. The painting shop will be purchasing its requirement from open market at Rs. 10 per unit. Therefore, the variable cost per unit in painting shop will be Rs. 18 (Rs. 10 + Rs. 8). This point should be noted carefully. (b) (ii) When all the requirements of painting shop is met by transfer from welding shop at a transfer price of Rs. 10 per unit

Welding shop Painting shop

Qty. Unit

Rate Rs.

Value Rs.

Qty Unit

Rate Rs.

Value Rs.

Sale in the open

market 2,400 12.00 28,800 9,600 25.00 2,40,000 Transfer to painting shop 9,600 10.00 96,000

Total sales 12,000 1,24,800 Less:Variable cost (12,000 units×Rs.9.50) 1,14,000 (9,600 units×Rs.18) 1,72,800 Contribution 10,800 67,200 Less: Fixed cost 25,000 30,000 Profit/(Loss) (14,200) 37,200

Overall profit of the company = Rs. 37,200 – Rs. 14,200 = Rs. 23,000

For the purpose of comparison, the results of the three alternatives are summarised below: Welding shop Painting shop

Rs. Rs. Profit under (i) 5,000 18,000 Profit/(Loss) under (b)(i) (19,000) 37,200 Profit/(Loss) under (b)(ii) (14,200) 37,200

Rs. The overall profit under (a) 23,000

202

Sales Centre (S) Rs. Rs. Rs. New Board Sold

– Selling price 35,000 – Purchase price 29,000

Gross margin 6,000

b(i) 18,200 b(ii) 23,000

Alternative (b)(ii) should be accepted due to the following reasons: (a) It gives a maximum overall profit of Rs. 23,000. The discussion is confined to either b(i) or

b(ii). (b) Each shop is treated as a separate cost centre and not a profit centre.

(c) The policy of overall goal congruence of the company is followed.

Neither selling price nor total sales is given. Division A of Better Margins Ltd. expects a return of 25% on average assets employed i.e., Rs. 12,00,000.

Ans. 34

Total sales will be: Rs.

(a) Profit (25% of 12,00,000) (b) Fixed overhead (c) Variable cost (2,00,000 × Re. 1) Total sales 9,00,000 Sales per unit (Rs. 9,00,000 ÷ 2,00,000 units) Rs. 4.50

Transfer to Division B Sale to outside and sale to outside parties parties only

Sales (units) 2,00,000 1,40,000

Sales value (1,40,000 units @ Rs. 4.50) (60,000 units @ Rs. 2.25)

Less: Variable cost

Rs. 6,30,000 1,35,000 7,65,000

Rs. 6,30,000

Nil 6,30,000

(Re. 1 per unit) 2,00,000 1,40,000 Contribution 5,65,000 4,90,000 Less: Fixed overhead 4,00,000 3,60,000 * Net profit 1,65,000 1,30,000 Average assets employed 12,00,000 10,00,000 Return on investment 13.75% 13.00%

If the component is transferred to Division B as well as sold to outside parties, it is more profitable as the contribution, net profit and return on investment is more than the existing proposal. Therefore selling the components to Division B at Rs. 2.25 per unit is in the overall interest of the company. *Reduction in selling and administration expenses (fixed in nature) by Rs. 40,000.

Statement showing the contribution to profit for each assuming that all estimates and budgets materialised as expected

Ans. 35

203

(ii) Assuming Additional Costs It is noticed that all estimates and budgets are materialised except that repairs undertaken by R took an extra 10 hours and Rs. 100 of materials due to a problem not noticed by B or R. R is responsible for giving correct repair costs and, therefore, he has to bear the additional cost: Rs. Rs. Repair Centre (R)’s contribution 540 Less: Extra cost of materials 100 Extra D.L. variable cost (10 hrs × Rs. 6) 60 160 Revised contribution 380

However, full details are not given in the question. ‘B’ is a middleman passing on R’s costs to S and as such should not bear additional costs. Had the item been noticed originally then S would have paid the cost and perhaps it should be passed back. This would be particularly so if R had insufficient opportunity for a complete inspection. In that case extra cost should be:

Rs.

Material 100

Labour (10 hrs. × Rs. 15) 150

250

Reduced contribution of S = Rs. 3,800 – Rs. 250 = Rs. 3,550

Rs. Original

contribution of R 540

Add.: Saving in variable cost

[10 hrs × (Rs. 15 – Rs. 6)] 90

Increased contribution of R 630

Note: Other solutions are equally acceptable if well argued and logically justified.

(a) (i) AB sells product at external market Ans. 36:

Selling price (Rs.) 30 45 60 Less Variable cost 18 18 18 Contribution (per unit) 12 27 42 Demands (units) 60,000 40,000 20,000 Total contribution 7,20,000 10,80,000 8,40,000 Optimal output is 40,000 units at a selling price of Rs.45 AB transfer at Rs.42 to XY division then contribution of XY

204

Selling price (Rs.) 120 135 150 Less Variable cost V+TP (42+60) 102 102 102 Contribution (per unit) 18 33 48 Demands (units) 15,000 10,000 5,000 Total contribution 2,70,000 3,30,000 2,40,000 Manager will choose out put level 10,000 units at a selling price of Rs.135. Overall profit when transfer made at Rs.42 Division AB contribution on 10,000 units [42 – (18 -3)] = 2,70,000 Division XY contribution 10,000 (135 – 102) Total contribution = 6,00,000

= 3,30,000

Division AB contribution from external market sale Total profit

10,80,000

16,80,000

(ii) AB transfer at variable cost Selling price (Rs.) 120 135 150 Less Variable cost (15+60) 75 75 75 Contribution (per unit) 45 60 75 Demands (units) 15,000 10,000 5,000 Total contribution 6,75,000 6,00,000 3,75,000 Optimal is 15,000 units at the rate of 120 per unit. If AB transfer at Variable cost (Rs.15) then no contribution will be generated by AB division XY division choose 15,000 units level gives contribution 15,000 × 45 = 6,75,000 Division AB contribution from external market sale Total contribution

= 10,80,000

= 17,55,000

(iii) Contribution AB division by selling 10,000 units to new external market at Rs.32 and XY division purchasing at Rs.31.

Contribution (32 – 18) × 10,000 = 1,40,000 XY contribution [135 – (31 + 60)] = 4,40,000 Division AB contribution from external market sale Total contribution

= 10,80,000

= 16,60,000

Ans. 37

(a) The variable costs per unit of output of sale outside the company are Rs.11 for the intermediate product and rs.49(Rs.10 for A+Rs.39 for B) for the final product. Note that selling and packing expenses are not incurred by the supplying division for the transfer of the intermediate product. It is assumed that the company has sufficient capacity to meet the demand at the various selling prices.

Optional output of intermediate product for sale on external market. Selling Price (Rs.) Unit contribution (Rs.) Demand (units)

20 9

15,000

30 19

10,000

40 29

5,000

Total contribution (Rs.) 1,35,000 1,90,000 1,45,000 Optimal output is 10,000 units at a selling price of Rs.30. Optimal output for final product Selling Price (Rs.) Unit contribution (Rs.) Demand (units)

80 31

7,200

90 41

5,000

100 51

2,800

205

Total contribution (Rs.) 2,23,200 2,05,000 1,42,800 Optimal output is 7200 unit at a selling price of Rs.80. Optimal output of Division B based on a transfer price of Rs.29. Division B will regard the transfer price as a variable cost. Therefore, total variable cost per unit will be Rs.68(i.e.,29+39) and Division B’s contribution will be as follows: Selling Price (Rs.) Unit contribution (Rs.) Demand (units)

80 12

7,200

90 22

5,000

100 32

2,800

Total contribution (Rs.) 86,400 1,10,000 89,600 The manager of Division B will choose an output level of 5,000 units at a selling price of Rs.90. This is sub-optimal for the company as a whole. Profit for the company as a whole from the sale of the final product are reduced from Rs.2,23,200 (72,00 units) to Rs.2,05,000 (5000 units). Rs.2,05,000 profits would be allocated as follows: Division A Rs.95,000 (5000 units at Rs.19 i.e.,Rs.29-Rs.10) Division b Rs.1,10,000 (b) At a transfer price of Rs.12 the variable cost per unit produced in Division B contribution will be as follows: Selling Price (Rs.) Unit contribution (Rs.) Demand (units)

80 29

7,200

90 39

5,000

100 49

2,800

Total contribution (Rs.) 2,08,800 1,95,000 1,37,200 The manager of Division B will choose an output level of 7200 units and a selling price of Rs.80.This is the optimum output level for the company as a whole. Division A would obtain a contribution of Rs.14,400 (7200 units @ Rs.2 (I.e.,Rs.12-Rs.10) from internal transfers of the intermediate product whereas Division B would obtain a contribution of Rs.2,08,800 from converting the intermediate product and selling as a final product. Total contribution for the company as a whole would be Rs.2,23,200. Note that Division A would also earn a contribution of Rs.1,90,000 from the sale of the intermediate product to the external market. Ans. 38:

Opticals Ltd manufactures P( lenses) and Q ( swimming goggles ).

Division P has option to supply to Division Q or sell to outside market. Division Q has option to buy from Division P or purchase from outside market. However, both divisions have to work within their individual capacity. Variable Cost for product P in Division P = Rs 60. Variable cost for product Q in Division Q ( excluding 2 Nos P's) = Rs 80. Division P has better market price of its product P than the market price offered to Q division. For maximizing profit of the organization : Rs P division should optimise its profit by selling maximum units to outside market. Contribution per unit for sale to outside for division P 40 Contribution per unit for Div Q as follows : Sale price - Variable cost ( excluding lenses) 330 Max Contribution per unit ( if procured from P div at its variable cost i.e Rs 60) 210

206

Min Contribution per unit ( if procured at Rs 90 per unit from outside) 150 Contribution per unit at transfer price of Rs 70 i.e minimum market price 190 Option 1 : Division Q buys 5001 units from market @ Rs 70 and meets its capacity. Division P sells 3000 units to outside market @ Rs 100

Sale / Transfer Contrib. /unit

Contribution in thousand rupees

207

Rs P Div Q Div Total DivP :Sale of 3000 units to outside market @ Rs 100 40 120 120 DivQ: Sale of 2500 units with P from market @ Rs 70 190 475 475 Less : cost of rejection of one unit of product P -0.07 -0.07 Total 120 474.93 594.93 Option 2 : Division P sells 3000 units to outside market, transfer 4000 units to div Q and Division Q buys 1000 units from outside market to work within the capacity

P Division agrees to a transfer price so that profitability of Q is not affected. To maintain the same profitability of Q, contribution required from 2000 units for Div Q is Rs 400,000 i.e contribution per unit Rs 200 i.e transfer price per unit of P is Rs 65 per unit to make cost of lences Rs 130

Sale / Transfer Contrib

/unit Contribution in

thousand rupees

208

Rs P Div Q Div Total

Div P : Sale of 3000 units to outside market 40 120 120 Div P : Transfer of 4000 units to div Q at Rs 65 5 20 20 Div Q :Sale of 2000 units with P from P div @ Rs 65 200 400 400 Div Q : Sale of 500 units with P from market @ Rs 90 150 75 75 Total 140 475 615 Under Option 1, both divisions worked dis-jointly without caring for capacity utilization resulting lower profitability of the organization.

Under Option 2, both divisions worked with mutual advantages for optimizing their individual profits and overall profit for the organization has gone up by effective utilization of capacity. Product P from Division P fetches higher price from open market indicating good quality of product. Moreover, supply from P division is well assured in the long run which is the justification of establishment of two parallel divisions. Hence, Option 2 is suggested.

(ii) Division functioning as profit centers strive to achieve maximum divisional profits, either by internal transfers or from outside purchase. This may not match with the organisation’s objective of maximum overall profits. Divisions may be commercial to advice overall objects objectives, where divisional decisions are in line with the overall best for the company, and this is goal congruence. Div isions at a disadvantage may be given due weightage while appraising their performance. Goal incongruence defeats the purpose of divisional profit centre system.

(b) In an assignment minimization problem, if one task cannot be assigned to one person, introduce a prohibitively large cost for that allocation, say M, where M has a high the value. Then, while doing the row minimum and column minimum operations, automatically this allocation will get eliminated.

(a) Div A B B Ans. 39

Rs. / unit Rs. / unit Rs. / unit Direct Material (Other than A) 50 24 Direct Labour 25 14 Variable Overhead (Production) 20 2 Variable Production Cost (excl. A) 95 40 40 From A 144 From Outside ____ 160 Variable production Cost / unit 184 200 Selling Price From outside 160 300 Less: Selling Overhead 13 26

209

Net Selling Price (outside) 147 274 Net Selling Price to B 144 Net Selling Price to S 250

Net Selling Price (outside)

147

274

274 Variable Production Cost − 95 − 184 −200 Contribution / unit (outside) 52 90 74

(Sale to B & S respectively)

144

250

250

Variable Production Cost −95 −184 −200 Contribution / unit 49 66 50 Best strategy A = Maximise Production; Sell maximum no. of units @ 18,000 × 52 = 9,36,000

52 / unit (outside)

(To B) remaining units 2,000 × 49 = 98,000 Total Contribution for A 10,34,000

Best strategy for B:

Maximise contribution / unit by selling outside and procuring from A 90 / unit

Contribution × 2,000 units

Balance units can yield contribution of either 74/ unit for outside or Rs. 50 / unit to S Ltd.

Production Capacity = 28,000.

Option I Option II Outside Sales Sales to S Outside Sales × contribution /

unit 20,000 × 74 = 14,80,000 6,000 × 50 = 3,00,000 24,000 × 74 = 17,76,000 2,000 × 90 = 1,80,000 2,000 × 90 = 1,80,000

16,60,000 3,00,000

Total Contribution (16,60,000 + 3,00 ,000)19,60,000 19,56,000

(B) Choose Option I i.e. get 2,000 units from A, sell 6,000 units to S and 20,000 to outside. Make 28,000 units @ full capacity. Total Contribution Rs19,60,000.

If A and B are allowed to act independent of the group synergy, Rs.

Total contribution A – 10,34,000

B – 19,60,000 Total contribution for X Ltd. 29,94,000

Cost from X Ltd.’s Perspective

Variable Cost of production Div A Rs. 95 Div B

Variable cost of production other than A 40 40 A supplied by Division 95 A – Variable Cost

210

A purchased ____ 160 135 200

Option I Outside 26,000 units Option II

Outside 20,000 × (274 – 135) 27,80,000 20,000 (274 – 135) 27,80,000 2,000 × (274 – 200) 1,48,000 6,000 (274 – 200) 4,44,000

22,000 S Ltd. 6,000 units (250 – 200) 3,00,000 _________ 32,28,000 32,24,000

Choose Option I

Contribution = Rs. 32,28,000 for X Ltd. as a whole

Transfer (2,000 units)

Make A transfer all output to B. Sell 6,000 units of B to S and 22,000 units to out side market. This will make X Ltd. better off by 32,28,000 – 29,94,000 = Rs 2,34,000

(i.e. 18,000 units of A sold to outside increases contribution to A by 3 Rs. / unit and decreases contribution to B by 16 Rs. / unit Net negative effect = 13 × 18,000 = Rs.2,34,000).

Ans. 40: (i) Division A’s best strategy – 2011

Maximum Manufacturing capacity = 50,000 units

Per unit External Market

Spl order Transfer to B partially

Transfer to B full

Demand (units) 30,000 15,000 < 45,000 45,000 Selling price 65 55 55 60 Variable Prod cost 35 35 35 35 Variable Selling cost 10 - - - Total Variable cost 45 35 35 35 Contribution Rs. 20 20 20 25

Transfer to B in full gives maximum contribution. Hence, 45,000 units to be transferred.

Balance 5000 will be sold to the external market.

Partial fulfilment of Special order will not be possible.

Statement of profitability for best strategy in 2011 :

Rs Transfer 45000 units to B @ Rs 60 Per Unit : Contribution : 25 x 45000 11,25,000 Supply to external market : Contribution : 20 x 5000 units 100000 Total Contribution 12,25,000 Annual fixed cost Rs 4,30,000 Step fixed cost Rs 2,00,000 Fixed selling costs Rs 50,000

6,80,000 Profit in 2011 5,45,000

(ii) Company’s best strategy for 2010

211

For Division A External Market

Special Order

B – Partial B - Full

Variable cost 45 35 35 35 Price 65 55 45 50 Contribution to Division A 20 20 10 15 Margin for Division B 5 0

It is clear from the above table that the Company will have more profitability if A first satisfies external market demand and special order and then supply to B.

As quantity for special order and transfer is more than 10,000 units, Div A will always opt for fixed cost of 50,000 instead of variable selling cost of Rs 5 / unit.

The company’s strategy for Division A’s production, sales/ Transfer will be :

External Market

Special Order

B – Partial

Total

Strategy I : A’s sale/ transfer (units) 25,000 10,000 5,000 40,000 Contribution of A & B ( Rs laks) 5.00 2.00 0.75 7.75 Fixed Cost Rs Lakhs( 4.30 + 1.00 +0.5)

5.80

Net for company – Rs lakhs 1.95 Strategy II : from A ( units) 25000 10000 15000 50,000 Contribution of A & B : RS Lakhs 5.0 2.00 2.25 9.25 Fixed Cost Rs Lakhs ( 4.30 + 2.00 +0.5)

6.80

Net for company Rs. Lakhs 2.45

Thus, the strategy II will be the one for the Company for the year 2010.

(iii) B’s negotiating range in 2011 :

Upper limit: The effective price of Rs. 60 for procurement from outside source. Lower Limit : Minimum price A will look for i.e Variable cost + Maximum possible contribution from other source + additional fixed cost

= Rs ( 35 + 20 + ( 50000/45,000) = Rs 56.11

Thus, Price range for negotiation without changing A’s strategy is Rs 56.11 to Rs 60 per unit.

(a) (i) Contribution per unit against sale to outside = Rs ( 200-120-20) = Rs 60 Ans.: 41

In case of transfer, good units and rejected units are in proportion of 9:1 In case of transfer, contribution per good unit = Rs (190 – 120) = Rs 70 In case of transfer, contribution per rejected unit = Rs (150 – 120-100) = Rs -70 Thus, effective contribution per unit of transfer = Rs (70 x 0.9 – 70x 0.1) = Rs 56 As contribution per unit against outside sale is higher, the best strategy should be to sell maximum number of unit to outside marker. Contribution from outside market from sale of 900 units = Rs 54,000 {Rs.(900 x 60)}

212

Contribution from transfer of 300 units to B {Rs (300 x 56)} = Rs 16,800 Total Contribution from best strategy = Rs 70,800

(ii) If B’s demand is 540 units, total production required (540 /0.9) = 600 units. Taking outside market demand of 600, it is within production capacity of 1200 units. Now contribution from 600 units of outside sale Rs (600 x 60 ) = Rs 36,000 Contribution from rejected 60 units Rs (60 x – 70) = = Rs 31,800

Rs (4,200)

To keep same level of contribution as in (i), the contribution required from transfer of 540 unit to B (Rs 70,800 – 31,800) = Rs 39,000 Thus, contribution required per unit Rs 39,000 /540 = Rs 72.22 Hence price to be charged p. u. against transfer to B Rs (120 + 72.22) = Rs 192.2 Alternative Solution: Let x be the number of units sold outside and y be the number of units sold to B, before B returns 10% as defectives. Then, x + y = 1,200, is the limitation on production capacity of A. Department A Outside to B Rs. Rs. Selling Prices 200 190 Variable Cost – Production 120 120 Variable Cost – Sale ___20 ___Total Variable Cost 140 120

--

Contribution 60 70 Contribution on x units sold outside = 60x

Out of y units to B, 10% = 101

y. 1 = .1y is returned to A. If A scraps, amount got = 30 per unit. If A reworks and sells, it gets 150 – 100 = 50/unit. ∴Decision to reworks all defectives. i.e. (.1) (y) Contribution on good units of B = 0.9y × 70 = 63y Contribution on reworked units of B = (.1) (y) × 50 = 5y Amount of material lost on manufacture of defectives to B =12y(.1)(y)×120 ∴Contribution on y gross units transferred to B = 56y 63y + 5Y – 12y Total contribution earned by A = 60x + 56y Where x + y = 1200 To maximize contribution, maximize units sold outside. ∴900 units – sell outside. Balance 300÷1,200 units (gross transfer to B, of which B gives back defectives) Contribution: Rs.60 (900) + Rs.56 (300) = Rs.54,000 + Rs.16,800

213

Contribution = Rs.70,800 Fixed Cost (i) Profit

= Rs.36,000

= Rs.34,800

(ii) Outside demand = 600 units Contribution = 600 × Rs.60 = Rs.36,000 Balance to be got

= Rs.34,800

= Rs.70,800

Out of Rs.34,800, defectives of B will give Rs. 3,000 60 × 50 Rs. 31,800 charge to B for 540 units Contribution to be obtained from 540 units of B = Rs. 31,800 Add: Production cost of 600 units @ 120/- Amount changed for 540 units

= Rs. 72,000

= Rs.1,03,800

∴Price to be charged to B = 1,03,800÷540 = 192.22 Per good unit transferred, to maintain the same level of profit as in (a).

Ans 42: B will not pay A anything more than 13, because at 13, it will incur additional cost of Rs.2/- to modify it, 13 + 2 = 15, the outside cost.

A B C Outside

sale Transfer to B & C

Divisional variable cost of production

Transfer from A Modification

Total Variable Cost of production Selling Price Contribution

7 7 19

13 2

25

13

7 15 8

7 13 6

34 40 6

38 50 12

Option for C, Purchase all units from A @ 13: Any other option is costlier.

A B C

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Maximum external demand Exiting capacity Maximum capacity that can be added Total maximum that can be produced Additional fixed cost on expansion Units that must be sold/transfer to get this amount as contribution External demand not covered by existing capacity Decision

3,750 5,000 5,000

10,000

24,000

24,000÷6 = 4,000

-

Expand make 10,000 units 3,750 – outside 3,750 – B 2,500 – C

5,000 2,500 1,250

3,750

6,000

6,000÷6 = 1,000

Expand make 2,500 + 1,250 = 3,750 units

4,000 2,500 2,250

4,750

18,700

18,700÷6 = 1,558.33

Do not expand make only 2,500 units.

A B C

Outside sale

Transfer to B & C

Units

Contribution / unit Contribution (Rs.)

Additional Fixed Cost Net revenue addition

3,750

8 30,000

3,750 + 2,500 = 6,250

6 37,500

3,750

6 22,500

2,500

12 30,000

67,500 24,000

22,500 6,000

30,000 -

43,500 16,500 30,000 Individual strategy is the company’s best strategy.

215

Ans. 43

216

Manager of division X will sell 14,000 units outside at 110 Rs. per unit and earn contribution of Rs. 3.50 lakhs.

Excess capacity of 6,000 units can be offered to Y at a price between 70 (the variable manufacturing cost at X) and Rs. 95 (the maximum amount to equa l outside contribution). But Y can get the material outside @ 85. So, y will not pay to X anything above (Rs.85 – 6) = Rs. 79 to match external available price.

X will be attracted to sell to Y only in the range of 71 – 79 Rs. per unit at a volume of 6,000 units.

At Rs. 70, X will be indifferent, but may offer to sell to Y to use idle capacity.

Z will not buy from Y at anything above 135. If X sells to Y at 70 per unit, Y can sell to Z at 134 and earn no contribution, only for surplus capacity and if units transferred by X to Y at Rs. 70 per unit.

Y Z

Provided X sells to Y at Rs. 70 per unit

Sell 4,000 units to Z at 134 (Indifferent)

Buy 4,000 units from y at 134 (attracted)

Sell 4,000 units to Z at 135 (willingly for a contribution of Re. 1)

Indifferent, since market price is also 135

For buying from X at 71 – 79 price range, Y will be interested in selling to Z only at prices 136 – 143, which will not interest Z.

Thus Y will sell to Z only if X sells to Y at Rs. 70 per unit and Y will supply to Z maximum 4,000 units.

Ans. 44: Capacity of X division = 7000 units

X has the following option to sell following number of units:

Option Domestic Market Export Transfer Hiring out (equivalent unit) I 6000 800 200 II 5000 800 l200 III 5000 2000 IV 5000 800 400 800

According to the condition given in (iii) for procurement policy of Y,

For 7000 units, maximum amount Y is agreeable to pay at market rate i.e Rs 900 per unit

= 7000 x Rs 900 = Rs 63,00,000

If X transfers l200 units to Y, It has to incur expenses for 5800 units from market =

= 5800 x Rs 920 = Rs 53,36,000

It means for l200 units from X, Y will pay = Rs ( 63,00,000 – 53,36, 000)

217

= Rs 9,64,000 = Rs 803.33 per unit

If X transfers 2000 units to Y and Y buys 5000 units,, Y can pay to X only

= Rs ( 63,00,000 – 5000 X 920) = Rs l7,00,000 = Rs 850.00 per unit

If transfer of less than l000 units to Y, X can claim transfer price of Rs 900 per unit

Realization ( Rs) Option I 6000 x l000 + 800 x 900 + 200 x 900 Rs 69,00,000 Option II 5000 x ll20 + 800 x 900 + l200 X 803.33 Rs 72,84,000 Option III 5000 x ll20 + 2000 x 850 Rs 73,00,000 Option IV 5000 x ll20+ 800 x 900 + 400 x 900 plus

contribution from hiring out Rs 66,80,000 plus

Above table shows that Option III is preferable in comparison to Option I and II . If Option III for X, transfer price will br Rs 850.00 per unit.

For taking a decision on option IV, contribution from equivalent unit from hiring out has to be compared with contribution from minimum sales realization of Rs 775 because sales realization of Rs 775 per unit from equivalent 800 units gives the amount of Rs 6,20,000 which makes up the gap between option III and option IV. In that case, transfer price will be Rs 900 per unit.

218

Decision Making

Answer: 11

1. Material A is not yet owned. It would have to be purchased in full at the replacement cost of `6.00 per unit. Relevant cost is therefore 1,000 units at the replacement Cost.

2. Material B is used by the Company regularly. There is already existing a stock of 600 units. If these are used in the contract, a further 400 units would have to be purchased.

3. Material C: 1,000 units of material C are required. 700 units are already in stock. If it is used for the contract, a further 300 units will have to be purchased at a replacement cost of `4.00 each. The existing stock of 700 units will not be replaced. If they are used for the contract, they cannot be used @ `2.50 each unit. The realisable value of these 700 units @ `2.50 per unit represent opportunity cost.

4. Material D is already in stock and will not be replaced. There is an opportunity cost of using D in the contract. It has following two uses: It can be sold to fetch `1,200 i.e. 600 X `2 It can also be used for E, which would cost `1,500 i.e. 300 X `5. Since substitution is more useful, `1,500 is the opportunity cost.

Summary of Relevant Costs: ` Material A 1,000 units X `6 6,000 Material B 1,000 units X `5 5,000 Material C 700 units X `2.5 1,750 300 units X `4 1,200 Material D 300 units X `5 1,500 Other expenses 550 Total Relevant Cost

16,000

Contract should be accepted since offer is of `22,000 in relation to relevant Cost of `16,000. Answer: 12 Retain Present

Machine Buy New Machine

Relative Benefit of Replacement

Variable Costs: (20,000 units @ `0.30 for 3 Years

18,000 12,000 (6,000)

Sale Proceeds of Old Machine - (4,000) (4,000) Capital Cost of New Machine - 7,000 7,000 18,000 15,000 (3,000) Thus, it is advantageous to replace the equipment. Note. Depreciation charge and loss on sale of old machine should be ignored for this decision. Answer: 13 Relevant costs of producing one unit of the finished product

` Cost of material ‘M’ (realisable value) 80 Cost of labour (Being sunk cost) 0 Out-of-pocket expenses 30

110 Allocated overhead is not relevant for the decision. The customer should be charged `110 per unit. Answer: 14

219

(i) The down payment of `2,50,000 represents a sunk cost.

The lost profit from subletting the shop of `1,20,000 per annum arrived as: (18,000 × 12) – 96,000 = 1,20,000 is an example of an opportunity cost. The salary amount is not given is also an opportunity cost lost.

(ii) The relevant information for running the shop is:

(`) Net Sales 22,20,000 Less: Costs (22,02,000 – 2,50,000) (sunk cost excluded for decision making purpose) 19,52,000 Gross Margin 2,68,000 Less: Opportunity cost from subletting 1,20,000 Profit 1,48,000 As profit is more than opportunity cost, the most profitable decision is to carry on business in the shop. Ans. 15: Analysis of Cost and profit:

`(lakhs) `(lakhs) Direct material 3.60 Direct labour Prime cost 10.00

6.40

Overhead: Variable factory overhead 2.20 Fixed factory overhead 2.60 Administration overheads 1.80 Selling commission 1.00 Fixed selling overheads 0.40 Total cost 18.00

8.00

Profit Rate of profit on costs (2/18) = 1/9

2.00

Overhead absorption rate based on direct wages = (8.00 / 6.40) × 100 = 125% of direct wages Break up of new order: ` Direct Materials 36,000 Direct Labour 64,000 Overheads 125% of direct wages 80,000 Total costs 1,80,000 Profit 1/9 20,000 Selling Price 2,00,000 The following points emerge: (i) Factory overheads only are to be recovered on the basis of direct wages. (ii) The special order is a direct order. Hence commission is not payable. (iii) The budgeted sales are achieved. Hence all fixed overheads are recovered. Hence, no

fixed overheads will be chargeable to the special order. Based on the above, the factory variable overheads recovery rate may be calculated as under: Total variable factory overheads `2.20 lakhs Direct wages `6.40 lakhs

220

Factory overhead rate = (2.20 / 6.40) × 100 = 34.375% Applying this rate the cost of the special order will be as under: ` Direct materials 36,000 Direct labour 64,000 Overheads 34.375% of direct wages 22,000 Total costs 1,22,000 Price offered 1,50,000 Margin 28,000 (more than 1/9) Hence, the order is acceptable at the price of `1,50,000.

Answer: 16

Statement of minimum price which the company can afford to

quote for the new customer

(based on relevant cost)

Cost to be incurred to bring the equipment in its original condition. 29,700 Opportunity cost of the direct material 2,250 Direct wages: Dept. A : 15 man days × `120 1,800 Dept. B : 25 man days × `100 2,500 Opportunity cost of contribution lost by department B (`2,500 × `2.30) 8,000 Variable overheads 1,075 25% × (`1,800 + `2,500) Delivery costs 1,350 Supervisory overtime payable for modification 1,050 Control device to be used in another job (Refer to working note 1) (10,350) Net loss on material cost savings, in the original equipment (Refer to working note)

11,700

Opportunity cost of remaining materials which can be sold as scrap 11,400 Opportunity cost of sale drawings Total minimum price which may be quoted

1,500

Working notes: 61,975

1. Cost of control device to be used in another job: ` Cost of control device 10,500 Less: Dismantling & removal cost of control mechanism 120 (1 man day × `120) Less: Variable cost )25% × `120) Balance cost of control device

30 10,350

2. Net loss on material cost saving of equipment: Loss on material cost saving of equipment 12,000 Less: Conversion cost (2 man days × `120) 240 Less: Variable overheads (25% × `240) Net loss on material cost saving of equipment

60 11,700

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Answer: 17 Working Notes:

1. The book value of Material K `40,000 is a sunk cost and is not relevant for decision making. 2. The Scrap Value of Material K `10,000 will affect the cashflow and is relevant.

Alternative I Relevant Costs (`) Material A (Replacement Cost) (600kgs. X `70) 42,000 Direct Labour – Skilled (200 hrs X `6) 12,000 Contribution Lost (Opportunity Cost) (2000 X `2) 4,000 Unskilled (not relevant) - Variable Overheads 2,000 Total Relevant Cost 60,000 Cost per unit = `60000 / 500 units = `120 p.u. Selling Price = `150 p.u. Profit = 500 units (`150 – `120) = `15,000 Alternative II

1. The Cost of substitute material `8,000 is relevant. 2. The regular profit of a job `6,000 is not relevant.

Analysis: From the above analysis it is suggested to convert the materials into a specified product. Answer:18 Working Notes:

1. Relevant cost of labour

Grade : Nil, labour cost for Grade 1 labour as it will not be affected by the decision.

Grade 2 : `20 per hour

2. Relevant cost of material

Material A : `100 per unit, the replacement cost because the material is widely used.

Material B : `250 per unit, the net realisable value, being the opportunity cost.

3. Statement of loss of contribution from the reduction in the sale of product Y.

` `

Sales revenue per unit: (A) 700

Variable cost per unit

Grade 2 labour: (4 hour × `20) 80

Materials relevant variable costs 120

Variable production overheads: (B) 120

(4 hours × `30)

320

Contribution per unit: [(A) – (B)] 380

222

Loss of contribution from the reduction in sale of 5,000 units

19,00,000

(5,000 units × `380)

Less: Avoidable fixed factory overhead cost

Net Loss

5,90,000

Relevant costs and benefit analysis from the acceptance of the contract.

13,20,000

(`’000)

Sales revenue: (1) 20,000

(20,000 kgs. × `1,000)

Relevant costs:

Labour:

Grade 1 NIL

Grade 2 2,400

(20,000 kgs. × 6 hours × 20)

Material A (20,000 × 2 units × `1,000) 4,000

Material B (20,000 kgs. × 1 litre × `250) 5,000

Variable production overhead (20,000 kgs. × 8 hours × `30)

4,800

Total variable cost 16,200

Incremental fixed costs 2,280

18,480

Add: Loss of contribution on product Y

(Refer to working note 3)

Total relevant cost: (ii) 19,800

Excess of relevant revenue over relevant cost: 200 Advice to A Limited: to accept the contract, as it will enhance the pre-tax operating income by `2,00,000 Answer: 19:Working Notes: Calculation of contribution margin The company expects that each per cent point increase in on-time performance will result in revenue increase of `18,000 p.a. Additional revenue increase = `18,000 X 10 = `1,80,000 Contribution margin on additional revenue = `1,80,000 X 45/ 100 = `81,000 Costs incurred annually on the installation of new scheduling and tracking system (`) Additional annual cost 1,50,000 Interest Foregone on Fixed deposit

(Opportunity Cost) (10% X `2,00,000) 20,000

Total Costs 1,70,000 Expected Savings in costs on the installation of new scheduling and tracking system (`) Contribution margin from additional annual revenue (45% X `1,80,000) 81,000 Decrease in variable costs due to reduced numbers of carton lost

(3,000-1,000) X `50 1,00,000

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Total savings in cost 1,81,000 Net saving (1,81,000 - 1,70,000) 11,000 Suggestion: The expected savings are more than annual costs, hence it is suggested to install a new scheduling and tracking system. Answer: 20 Statement showing Revised Cost Estimates:

1. Steel Sheets (`12/kg. x 5,000kg.) `60,000 2. Steel Rods (1,000 kg. @ `17 kg.) 17,000 3. Bearing, hardware items, etc. 15,000 4. Labour Cost Nil 5. Overheads:

Fabrication Shop (500 hrs @ `25) 12,500 Welding Shop (300 hrs @ `16) 4,800 Planning engineers cost Nil Design engineers cost Total Estimated Relevant Cost

Nil

1,09,300

Relevant costs are estimated future costs pertinent to a decision. Imputed costs do not form part of relevant costs. All costs accumulated for stock valuation purposes may not be relevant cost. Reasons for Variation in the Cost Elements

1. Current rate of steel sheets is quite relevant. Past rate of `12 per kg has no impact on the decision and therefore not adopted in the cost estimates.

2. Steel rods purchased five years ago cannot be used (non- moving) and as such it represents sunk cost. This material can now be substituted for alloy steel rods (`17/kg). Alloy rods are cheaper than steel rods and therefore relevant to the decision.

3. Fixed costs are past costs, not relevant to the decision. Labour costs are fixed in nature. 4. It is assumed that Fabrication Shop is working at optimum level. Therefore rate charged from

outsiders (`25 per hour) is relevant. 5. It is assumed that Welding shop is not working at full capacity. Therefore variable cost of `16 per

machine hour is adopted. 6. Planning and design engineers costs are fixed cost and, therefore, irrelevant.

Answer: 21

Revised Cost Estimate 1. Direct Material:

- Paper 2,500 - Ink 3,000 5,500

2. Direct Labour (Skilled) Normal (250 hrs x `4) 1,000 Overtime (125 hrs x `1) 125 1,125 3. Variable Overhead (350 hrs x `4) 1,400 4. Printing 600 Revised Cost Estimate 8,625 Working Notes:

1. With no alternative use, the paper would not be replaced; the alternative, therefore, being to scrap the stock receiving proceeds of `2,500.

2. The surplus ink could not be used or sold and therefore the whole cost of the ink purchased should be charged to the cost of the programme.

3. The direct employees are currently usefully employed, therefore, their wage cost is being recovered from an existing customer. Before, transferring them to the work on the programme, the ability of the programme work to bear this cost must be determined.

224

4. The overtime premiums are directly caused by the programme work, which should be able to bear this additional cost.

5. There is no additional cost associated with the employment of the unskilled labour. Current idle time 200 hrs Printing Work 75 hrs

(No additional cost)

Week-end work 25 hrs 125 hrs

Paid time off 50 hrs The 50 hrs of paid time off is more than covered by the 125 hrs of idle time, which is also paid for and, therefore, there is no additional cost.

6. Variable overhead is the incremental cost. 7. The variable overhead and other variable costs associated with running the printing press have been

separately dealt with. The additional recovery required is, therefore, the lost contribution associated with 200 printing press hours.

8. Fixed production overheads are not associated with incremental cashflows, and therefore should be ignored. a) The cost of estimating time is a small cost, since it has already been incurred. It does not involve

incremental cash flow. Therefore, it has been ignored. b) In short-term decision making, resources usage is best measured by using ‘variable cost’ which

change in proportion to changes in output. When variable cost is matched with the sales revenue with which it is associated, the resulting difference or contribution gives a good indication of the expected benefit to the organisation of any course of action. If fixed assets are unaffected by a decision, contribution will be close approximation of cash flow and therefore, it is very real figure which may also be usefully used as a basis for ranking alternatives where limiting factors are involved.

c) For evaluating the economic benefit derived from a product, it is necessary to match the revenue generated with he cost incurred. Opportunity cost represents the benefit forgone for taking one course of action rather than alternative. It gives a measure of sacrifice made in order to generate income. Conventional contribution approach normally extracts variable costs from the internal costing records (i.e., stock accounts, etc.). Opportunity costs may be derived from internal or external sources depending on such factors as whether there are alternative uses for internal resources consumed and whether, if used, they would be replaced.

Answer:22: Research Project

Particulars Relevancy Reason Amount (Rs’000s)

Project cost till date Not relevant Sunk cost

Sale price of the project Relevant Incremental revenue/opportunity gain

400

Cost of materials received Not relevant Sunk cost

Cost of disposal of materials Relevant Avoidable/opportunity cost 15

Cost of labour Not relevant Common costs

Contribution lost on the alternative use

Relevant Opportunity cost [Sales – (Prime cost labour)

(125)

Absorbed Fixed overheads Not relevant Sunk cost

Cost of Research Staff Relevant Incremental / out of pocket (160)

Redundancy and severance pay

Not relevant Common costs

Share of General Not relevant Sunk costs

225

B ildi Total incremental inflow if the project is proceeded with

130

Decision: Better to continue the project. Answer. 23 Statement of cost of product NP (`) Particulars Total cost

(100000 units)

Cost per unit

Direct materials A (1,00,000 X 2.50) 2,50,000 B (60,000 X 1.00) 60,000 (40,000 X 3.00) 1,20,000 C (1,00,000 X 6.00) Direct labour

6,00,000

Skilled (25,000 hrs X `3) 75,000 Unskilled Opportunity loss (25,000 X `2) Variable overhead (1,00,000 X 1.50)

50,000

Fixed Overheads: Factory overheads: - Addl. Overheads- Foreman 36,000 Supervisor Depreciation: Type P 30,000

24,000

Type Q Total Costs

5,000

profit Sales

10,30,000

1,25,000 1,50,000

60,000

35,000 14,00,000 4,00,000

18,00,000

10.30

1.25 1.50

0.60

0.35 14.00.

4.00 18.00

Working Notes:

1. Cost of Direct Material Material A- It is in regular use and hence replacement cost of `2.50 will be charged. Material B- Total requirement is of 1,00,000 units: Stock available 60,000 units - opportunity cost `1.00 each 40,000 units - purchase price `3.00 each. Material C- Purchase price of `6.00 2. Cost of Direct Labour

Skilled Labour: (i) 1,00,000 units at `0.25 per hour (ii) Loss of contribution on existing product opportunity cost 25,000 X

2=`50,000 Unskilled labour: Available in surplus and is to be paid even without work. Hence, not relevant 3. Cost of Additional Staff (`)

Foreman Supervisor Total

36,000 24,000 60,000

4. Variable Overheads `1.50 per unit is relevant cost 5. Fixed Overheads Not relevant hence excluded 6. Depreciation Type P: The machine is used on other product. Hence, replacement cost is relevant Depreciation =`1,60,000-1,30,000 =`30,000 Type Q: Since it can be sold if not used resale value is relevant. Depreciation =`22,000-`17,000 =`5,000

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7. Market Survey Costs: It is a sunk cost. Hence it is not a relevant cost. Answer: 24 Working Notes:

1. Machine manufacturing cost Costs of `50,000 incurred to date in manufacturing the machine is irrelevant for the decision, since It is a sunk cost. The payment of `15,000 received from the customer prior to the liquidation is also not relevant for decision making.

2. Material Cost. The purchase cost of `6,000 of materials bought in the past is irrelevant for decision making. Only the scrap value of materials i.e.`6,000 is relevant for decision making since it is the opportunity cost of materials bought in the past.

3. Labour Costs. Opportunity cost of labour when the workforce, is in short supply, and switched to another job,it could fetch the additional contribution of (`30,000-`8,000-`12,000)=`10,000.

4. Consultancy fees (`) Cost of completing the work Cost of canceling the contract Incremental cost of completing of work

4,000 1,500 2,500

5. General Overheads

The general overheads are absorbed on allocation and therefore, these costs are not relevant for the decision.

Statement showing economics of proposition (`) Revenue from completing work Less: Materials (opportunity cost) Labour: Actual costs 8,000 Opportunity costs Cost of consultancy (Incremental cost)

10,000

Additional profit by accepting the offer of new customer in completion of the work.

2,000

18,000 2,500

34,000

22,500 11,500

In view of incremental profit of `11,500, the offer of new customer can be accepted. Answer: 25: For solving this question, it is necessary to take the following into consideration. SV Ltd. Has two departments A and B. Dept. A is manufacturing FLOTAP, but Dept. B is manufacturing the containers for this product. It also stores this product. This is the existing situation. Now three alternatives are given. Alternative 1.- Close Dept. B and manufacturing & storing may be given to PH Ltd. Alternative 2 – Continue Dept. B and manufacturing may be given to PH Ltd and storing to Dept. B. Alternative 3 – Continue Dept. B, Manufacturing may be done by Dept. B but storing may be given to PH Ltd. Company should either select one of the alternative or continue the existing practice. Working Notes: (i) (`) Direct Materials including germicide Use of germicide (1/5th

Direct materials other than germicide of `6,00,000)

4,20,000 1,20,000 3,00,000

This material will be avoidable cost if Division B is to Close-down. (ii) 10% of all materials = 10% of `3, 00,000

(a) Savings: `3, 00,000-`30, 000=`2, 70,000 if manufacture is given to PH Ltd. And storage is with SV Ltd.

(b) Savings: 3, 00,000- 90% of `3, 00,000=`30, 000. If manufacture is done by SV Ltd and storage given to PH Ltd.

(iii) (`) Direct Labour cost Less: Terminal benefit if B is closed Avoidable cost, if Dept .B is closed (saving)

3,00,000 45,000

2,55,000

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If manufacturing is given to PH Ltd. And SV Ltd. continues to store the product, saving on account of labour retrenchment will be only `15,000.(It means in this alterative 3,00,000-15,000=2,85,000 will be spent any way and avoidable cost will be only `15,000). If manufacturing is done by SV Ltd. Then Labour force will continue. It means impact of labour cost in 3rd

alternative will be nil.

(iv) Supervisory staff will be transferred to another department in the lst alternative. It means cash flow will not be affected. In the second and third alternative, supervisory staff will be retained and it means no additional cash flow or relevant cost due to decision.

(v) Depreciation does not affect the cash flow. Therefore it is not relevant for these decisions. (vi) The hire charges of warehouse is `54,000 per annum. The remaining space of the warehouse is idle. It

means, when department B is closed, cash outflow of `54,000 will be avoided. Therefore `54,000(and not `27,000) is the avoidable cost for this decision. If Department B continues, this expenditure of `54,000 continue. Therefore cash flow for alternatives 2 and 3 will not be isturbed on this account.

(vii) Maintenance of machine is required for manufacturing. If means `21,600 will be avoidable cost for

alternative 1 and 2. In 3rd

alternative this cost will continue to be there. Besides this machine will not be required in alternative 1 and 2. It will be sold at `1,50,000.It will be a one time cash inflow for alternatives 1 and 2.

(viii) Miscellaneous overhead of `94,500 will be avoidable cost for alternative 1. For 2nd alternative 80 % of this i.e `75,600 will be avoidable cost. For 3rd

alternative 20% of `94,500 i.e. `18,900 will be avoidable cost.

(ix) Germicide- Stock: (`) Stock in 2002 Used last year (1/5th

Balance Stock )

6,00,000 1,20,000 4,80,000

It is given that original price is `3,000 Therefore, `4,80,000/`3,000=160 tonne Germicide is there. (x) Germicide-value Alternative 1 : Storage is done by PH Ltd. Therefore it will be sold at `2,400 per tonne. Cash inflow

will be 2,400 X 160=`3,84,000. Note that original price and replacement cost are irrelevant for the decision. Alternative 2 : 10% of all material will be used. It means 90% of 160 tonne will be sold. Cash inflow

will be 160 X 0.90 X `2,400= `3,45,600 Alternative 3 : In this situation storage is done by PH Ltd. Therefore only 10% of whole quantity of

160 tonne will be sold in market at `2,400 per tonne . Cash inflow will be 16 X `2,400 `38,400.

(The replacement cost is irrelevant information in the question and it will be relevant only, when germicide has competing demands.)

(xi) Machine is used for manufacturing of containers. It is not required in alternatives 1 and 2. Therefore , it will be sold and there will be one time cash inflow of `1,50,000 under alternatives 1 and 2. Written down value is irrelevant for decision under consideration.

(`) Alternative 1 Alternative 2 Alternative 3 Division B Manufacture of containers Storage of product

Close PH Ltd PH Ltd.

Continue PH Ltd. SV Ltd.

Continue SV Ltd. PH Ltd.

Cash Inflows (Including avoidable cost)

228

Direct materials other than germicide Direct labour Rent of a part of warehouse Maintenance of machine Miscellaneous overhead Total avoidable cost p.a. (A) Cash outflows Contract fee to PH Ltd. For Manufacturer For packing and storage Total outflow (B) Net Cash outflow p.a. (A-B)-( C ) Total cash outflows for 4 years ( C X 4) One time income Sales of germicide Sale of machine Net cash outflow

3,00,000 2,55,000

54,000 21,600 94,500

7,25,100

7,50,000

9,00,000 1,50,000

(1,74,900) (6,99,600)

3,84,000 1,50,000

(1,65,600)

2,70,000 15,000

- 21,600 75,600

3,82,200

7,50,000 -

7,50,000 (3,67,800)

(14,71,200)

3,45,600 1,50,000

(9,75,600)

30,000 - - -

18,900 48,900

-

1,50,000 1,50,000

(1,01,100) (4,04,400)

38,400

- (3,66,000)

Recommendations: All the alternatives result in net cash outflow. Therefore it is interest of SV Ltd. To continue and to manufacture containers and store them in Division B. Answer: 26: Comparative Statement of Relevant Costs for use of own distribution division or use of Countrywide distributions. (`’000) Particulars Own Distribution Countrywide Distribution 95-96 96-97 97-98 95-96 96-97 97-98 Relevant Cash outflow: Operating Costs Sub-Contract costs Total Less: Relevant cash inflow: Sale of delivery vehicle On 1-4-2002 On 31-3-2005 Net Relevant Cash outflows: Total

2,100

- 2,100

- -

2,100

2,100

- 2,100

- -

+2,100

2,100

- 2,100

- 240

+1,860 =6,060

-

1,950 1,950

600 -

1,350

-

1,950 1,950

- -

+1,950 =5,250

-

1,950 1,950

- -

+1,950

Suggestion: From the above comparative statement it is observed that the net relevant cash outflow is more in case of own distribution. Hence, selection of countrywide distributors is recommended. It is based on the assumption that no portion of the common corporate cost of which `3,00,000 is apportioned to distribution division which would be avoided even if, the distribution division is closed down. (b) Reasons for reluctancy to accept countrywide distributors in distribution of Soft Drinks. (1) Loss on Sale of Delivery Vehicles presently owned by the company: (`) Cost of Vehicles (8 Vehicles on 1-4-2003) Less: Depreciation for 2003-04 Book Value on 1-4-2004 Less: Sales realization (8 Vehicles X `75,000) Book Loss on sale of Vehicles

19,20,000 4,20,000

15,00,000 6,00,000 9,00,000

6. Possibility of reduction in reported income as per Security Analyst’s recommendation Forecast of operating income as per Security Analyst (`’000)

Particulars 1995-96 1996-97 Estimated Profit when own distribution division is used Net income if the offer of countrywide distributors is accepted

630 630

660 330

Working Notes: (`’000) Projected Profit for 95-96 660

229

Add; Depreciation avoided Add: Saving in operating cost (`2,100- `1,950) Less: Book loss on the disposal of delivery vehicles Net income, if Countrywide distributors selected

420 150

1,230 900 330

Analysis: In view of short- run benefit, countrywide distributors can be opted. But when the long-run benefits are recognized, and to focus on customer needs, the company’s own distribution function is recommended.

Answer: 27: Statement showing value of total work undertaken by X Ltd. at customer’s price

(`’000)

Material costs (for appliances covered under agreement) 825

[Rate to working note 1 (i)]

Material costs (for appliances not covered under agreement) 275

[Refer to working note 2 (i)]

Labor cost (for appliances covered under agreement) 1,000

[Refer to working note 1 (ii)]

Labour cost (for appliances not covered under agreement) 240

[Refer to working note 2 (ii)] _____

Total receipts 2,340

Break up of receipts:

Big appliances 60% 1.404

Small appliances 40% 936

Profitability Statement

(`’000) Option 1 Option 2 Option 3 Income Big appliances 129.6

(60%×`216) 1,404 1.404

Small appliances 936 .

86.4

936 (40%×`216)

Total receipts: (A) .

1,065.6 1,490.4 2,340 Costs: Material 320 480 800 40%×(825+275) 60%×(825+275)

(825+275) 137.5% 137.5% 137.5%

Heat, rent, light etc. 125 50 150 Management costs 108 83 150 Service staff costs 230 440 750 Transport costs 25 220 Total costs: (B)

230 808 1,273

Profit: [(A) – (B)] 2,080

257.6 217.4 Recommendation:

260

Option 3 is most profitable one.

Working Notes: 1. Material and labour cost (for appliances under after sales agreement):

230

`

(i) Cost of Material per unit charged to customer’s by X Ltd. (`100 + 10% x `100 + 25% x `110) 137.50

Cost of material charged to customer’s by X Ltd.

Rs.10Rs.60,000

× `137.50 8,25,000

(ii) Cost of labour charged to customer by X Ltd.

Rs.100Rs.1,00,00

× `100 10,00,000

2. Material and labour cost (for appliances not covered under sales agreement):

`

(i) Cost of material charged to customer by X Ltd.

Rs.10Rs.20,000

× `137.50 2,75,000

(ii) Cost of labour charged to customer by X Ltd.

Rs.15Rs.36,000

× `100 2,40,000

Answer: 28

Statement of relevant cost of Mahila Griha Udyog Industries

If the contract is accepted/rejected

Decision Relevant costs (if contract is

accepted) `

Relevant costs (if contract is rejected)

` Cash inflows Contract price 18,00,000 - Sale of material Y - 2,10,000 (Refer to working note I) . Total cash inflows: (A)

. 18,00,000

Cash outflows 2,10,000

Material X substitute 1,35,000 - (Refer to working note 2) Adaptation required for the use of obsolete material X

- 27,000

Material Z 3,00,000 - Replacement of semi-skilled labour by skilled labour

5,70,000 -

(Refer to working note 3) Non-skilled labour cost 3,00,000 - (Refer to working note 4) Supervisory staff cost 35,000 - (Refer to working note 5) Avoidable overheads 1,25,000 -

231

(Refer to working note 6) Total cash outflows: (B) 14,65,000 27,000 Net cash inflows: (A) – (B) 3,35,000 1,83,000 The net benefit on accepting the contract is : `3,35,000 – `1,83,000 = `1,52,000.

Conclusion

The contract should be accepted as it yields a net incremental cash inflow of `1,52,000.

Working notes:

1. Material Y will have to be paid for whether or not the contract is accepted, therefore its cost is irrelevant. The relevant cost figure here is that which has an opportunity cost of `2,10,000. This means that the company can resell material Y at this price.

2. Regarding material X, if the contract is accepted, alterative material will have to be purchased for the other product at a cost of `1,35,000. If the contract is rejected material X will be adapted for a product not included in the list of special range of namkeens at a cost of `27,000.

3. The relevant skilled labour cost of `5,70,000 is the extra cost to the company because of this contract. It is the replacement cost of semi-skilled labour by skilled labour.

4. Non-skilled labour cost is the incremental cost of the contract.

5. If the company accepts the contract it will have to pay `35,000 for the two position that the supervisory staff can replace.

6. Only `1,25,000 of avoidable overheads are relevant to this contract. Answer: 29

M/s Ranka Builder’s

Statement of relevant costs on the

Acceptance of contract form Excel Ltd.

(Figure in lakh of `)

S.No. Particulars Basis for the cost to be relevant

Relevant cost if contract is accepted `

Irrelevant cost if the contract is

accepted `

1. Land cost

(Refer to working note 1)

20

2. Drawings and design - 7 (Sunk cost)

3. Registration Incremental 10 -

4. Materials :

Cement and sand Replacement 8

Bricks and Tiles Opportunity 5

Steel Incremental 10

Others

(Refer to working note 2)

9

5. Labour :

Skilled Opportunity 2

Unskilled Incremental 8

232

Supervisor’s Salary 5 (Sunk Cost)

6. Overheads :

General Relevant (avoidable)

4

Depreciation - 6 (Sunk Cost)

Replacement cost of machine

7

7. Estimated profit foregone on other project

Opportunity foregone

10

Total 93 Decision : Since the offer price of contract is `1 crore and its total relevant cost is `93 lacs; these figures clearly shows that the offer should be accepted.

Working notes :

1. `(Lacs)

Total cost of 3 grounds of land 60

Cost of ground of land will be borne by Excel Ltd. 40

Cost of 1 ground of land will be borne by M/s Ranka Builders 20

2. Others material cost is `10 lacs, it includes material worth `2 lacs, relating to interior decoration, which is a sunk cost, this material can be sold for `1 lac, (which is a relevant opportunity cost) and `8 lacs, material is an incremental cost. Hence total relevant cost of others material is `9 lacs. (`8 lacs, incremental + `1 lac, opportunity cost).

3. Since the equipment can also be used on ths contract. Its current replacement price is `32 lacs, and after one year its cost will be `25 lacs. Therefore the relevant opportunity cost of machine is : (`32 lacs – `25 lacs).

Answer: 30 Alternative 1 – (Conversion versus immediate sale)

` ` `

Sales revenue 900 units at `300 per unit (Refer to working note 1)

2,70,000

Less: Relevant costs

Material XY opportunity cost (Refer to working note 2)

21,000

Material A – units @ `90 per unit (Refer to working note 3

54,000

Material B – 1,000 units @ `45 per unit (Refer to working note 4)

45,000

Direct Labour :

Unskilled – 5,000 hours @ `3 per hour 15,000

Semi-skilled Nil

Highly skilled – 5,000 hours @ `11 (Refer to 70,000 55,000

233

working note 5)

Variable overheads 15,000 hours @ Re.1 (Refer to working note 6)

15,000

Extra selling and delivery expenses 27,000

Extra advertising 18,000 45,000

Fixed advertising

2,50,000

Nil

(To remain same, not relevant)

Excess of relevant revenues

.

Alternative 2 – (Adaptation versus Immediate Sale)

20,000

Saving on purchase of sub-assembly

Normal spending – 1,200 units @ `900 per unit 10,80,000

Less: Revised spending – 900 units @ `1,050 per unit (Refer to working note 7)

9,45,000 1,35,000

Less: Relevant costs:

Material XY opportunity cost (Refer to working note 2)

21,000

Material C – 1,000 units @ `37 (Refer to working note 8)

37,000

Direct labour

Unskilled – 4,000 hours @ `3 per hour 12,000

Semi-skilled Nil

Highly skilled – 4,000 hours @`11 per hour (Refer to working note 5, 6)

56,000 44,000

Variable Overheads – 9,000 hours @ Re.1/- per hour (Refer to working note 6)

1,23,000 9,000

Fixed overheads Nil

Net relevant savings

.

12,000

Evaluation :

The evaluation of two alternatives clearly shows that Alternative 1, yields higher net revenue of `8,000 (`20,000 – `12,000). Hence because of higher net revenue of Alternative 1, it is advisable to convert material XY into a specialized product.

Working notes :

1. There will be a additional sales revenue of `2,70,000 if Alternative 1 is chosen.

2. Acceptance of either Alternative 1 or 2 will mean a loss of revenue of `21,000 from the sale of the obsolete material XY and hence it is an opportunity cost for both of the alternatives. The original purchase cost of `75,000 is a sunk cost and thus not relevant.

3. Acceptance of Alternative 1 will mean that material A must be replaced at an additional cost of `54,000.

4. Acceptance of Alternative 1 will mean diversion of material B from the production of product Z. The excess of relevant revenues over relevant cost for product Z is `180 (`390 – `210) and each unit of product Z uses four units of material B. The lost contribution (excluding the cost of material B which is incurred for both alternatives) will therefore be `45 for each unit of material B that is used for converting the obsolete materials into a specialised product.

234

5. Unskilled labour can be matched exactly to the company’s production requirements. Hence acceptance of either alternative 1 or 2 will cause the company to incur additional unskilled labour cost at `3 for each hours. It is assumed that the semi-skilled labour will be able to meet the extra requirements of either alternatives at no extra cost to the company. Hence, cost of semi-skilled labour will not be relevant. Skilled labour is in short supply and can only be obtained by reducing the production of product L, resulting in a loss of contribution of `24 (given) or `6 per hour of skilled labour. Hence the relevant labour cost will be `6 (contribution lost per hour) + `5 (hourly rate of skilled labour) i.e. `11 per hour.

6. It is assumed that for each direct labour of input, variable overhead will increase by Re.1 hence for each alternative using additional direct labour hours, variable overheads will increase.

7. The cost of purchasing the sub-assembly will be reduced by `1,35,000 if the second alternative is chosen and so these savings are relevant to the decision.

8. The company will incur additional variable costs, of `37 for each unit of material C that is manufactured, so the fixed overheads for material C viz. `18/- per unit is not a relevant cost.

Ans. 31 Calculation minimum price to be quoted for a quotation, based on relevant costs only (`) Opportunity cost of:

(1) Retaining materials already in the original machine - Sale of Brass scrap - Sale of Steel scrap - Balance material , cost of scrapping )saved)

(2) Conversion materials - Department M - Department A

(3) Conversion work (a) Department M

Labour 60,000 Variable overhead 12,000

Contribution foregone (b) Department A

1,80,000

Labour Nil

Variable overhead 6,000 Off-loading cash flow foregone (4) Sales proceed of design and specifications

57,000

(5) Incremental fixed overhead-cost of supervision Minimum price to be quoted

1,00,000 25,000 (5,000)

12,000

3,000

2,52,000

63,000 60,000 10,000

5,20,000 Note: For the above minimum price of `5,20,000 profit can be added. The existing overheads are committed costs and are not relevant for decision making. Answer: 32

1. Value of Material X in stock : (which can be used as substitute for other materials) = `54,000 X 90 / 100 = `48,600

2. Value of Material X for which firm order has been placed

= `76,000 X 90 / 100 = `68,400

3. Value of Material Y in stock = 2 times x `62,000 = `1,24,000

4. Irrelevant Costs: Following costs are irrelevant therefore, they have been ignored

• Site manage costs – being fixed costs • Depreciation of plants • Interest on capital • Notional interest in estimated working capital

235

• Head office expense allocated to contracts. Comparative statement of Net Benefit resulting from each contract (`) Particulars Contract

AX Contract BX

Material X – in stock 48,600 Material X – firm orders placed 68,400 Material X – not yet ordered (at current cost) 1,50,000 Material Y - in stock - 1,24,000 Material Z – not yet ordered (at replacement

cost) - 1,78,000

Labour – to be paid 2,15,000 2,75,000 Travel and other expenses (future outflow) 17,000 14,000 Income from the hire of plant (15,000) Penalty for rescinding the contract ‘AX’ is relevant

- 70,000

Total Cost 4,84,000 6,61,000 Contract Price 7,20,000 8,80,000 Expected net benefit 2,36,000 2,19,000 Advice- Since the expected net benefit of contract AX, is more than Contract BX, it is suggested to continue with Contract AX. Answer: 33:Relevant Cost of ‘Jeet’ bicycle Material 300.00 Labour 200.00 Variable Overhead (0.4 X 300) 120.00 Cost of Capital (0.15 X 6,00,000) / 25,000 3.60 623.60 If Star Bicycle company accept the offer of making ‘Jeet’ for the chain stores the loss in contribution due to sale of Smart is going down by 1,00,000 units is relevant, which causes a loss of `(899-300-200-120)= `279 The price of Jeet then should be `623.60 + 279 = `902.60. This is higher than the price of `800 as offered by the chain store. So, the offer cannot be accepted. Since the chain store has decided to launch a product like ‘Jeet’, it will do so whether or not Star Bicycle Company accepts the proposal as there is excess capacity in the industry it will be able to do so. In that case, the loss of contribution is `279 is not relevant and Star Bicycle Company can accept the proposal of the chain store. Star Bicycle Company should have a closure look in the market condition and the chain store’s ability to get a replica of ‘Jeet’ from other manufacturer before Star Bicycle Company reaches a final decision. Answer 34: Minimum recommended price per unit of 5,000 units of a product (obsolete model) of ACE Ltd. (i) Historical cost of `11.50 per unit of 5,000 units of a product is irrelevant (as it is a sunk cost) for

determining the recommended price per unit.

(ii) If at all this model is sold in the market through normal distribution channels it will entail a variable selling and distribution cost of `3 per unit.

(iii) If the stock is disposed off by asking someone to take them on “as is where is basis”, the company would have to spend `5,000 over 5,000 units i.e. `1/- per unit.

In view of (ii) and (iii) the option of selling 5,000 obsolete units of the model using regular channels will nave a differential cost of `2 (`3 – Re.1) per unit.

Recommendation:

Hence, if the company can get anything more than `2/- per unit, then it is worthwhile to sell the stock of 5,000 units and earn an additional contribution.

236

Answer: 35

Statement of Increment Cost and Incremental Revenue

Capacity in units

Unit cost ` Total cost `

Incremental cost `

Unit price `

Total price `

Incremental revenue `

(a) (b) (c)=(a)×(b) (d) (e) (f)=(a)×(e) (g) 200 40 80,000 - 100 2,00,000 - 3000 35 1,05,000 25,000 95 2,85,000 85,00,000 (`1,05,000

– `80,000) (`2,85,000

- `2,00,000)

4000 34 1,36,000 31,000 94 3,76,000 91,000 `1,36,000

– 1,05,000)

(`3,76,000 – `2,85,000)

5,000 32 1,60,000 24,000 - - - (`1,60,000

– `1,36,000)

6,000 31 1,86,000 26,000 - - - (`1,86,000

– `1,60,000)

Decision:

At 4,000 units capacity told sales revenue is `3,76,000 and the total cost is `1,36,000 leaving a profit of `2,40,000. The profit figure at this level clearly shows that the fixed expenses stand fully recovered. Hence, we have to take incremental cost for further level levels of output. For an additional sales of 2,000 units

incremental cost is `50,000 (`1,86,000 – `1,36,000) and the cost per unit is `25

units 2,000Rs.50,000

Since the price quoted per unit is `28, which is more than `25, therefore, the order should be accepted.

Answer: 36 ABC Ltd is facing Direct material constraint and special steel plates are in short supply but the stock is available only 500 M.T. Alternatives available to maximize profit Alternative I: - Manufacture and Supply only 20,000 cylinders at the risk of reduced order in future. Alternative II: - Make 40,00 upper halves, buy 40,000 button halves from outside and supply 40,000

cylinders. Profitability Statement

No. of Cylinders Alternatives Differential Cost I

20,000 II

40,000 Sales Realisation @ `700 140 280 140 Welding and other costs @ 30 (6) (12) (6) Transportation, loading etc. (at `5 per half) - (2) (2) Net Differential Income 134 266 132 The additional net income when 40,000 halves are purchased is `132 lakhs which is the maximum price that ABC Ltd. Can afford to pay keeping for itself at least the contribution it would earn by its own operation (a).

237

i.e. The Price = ` 120 Lakhs 40,000

= `330 per bottom half.

Answer: 37 Option 1: Profitability to continue only in season period (`) Particulars Gift shop Restaurant Lodge Total Incremental Revenue (i) 6,000 8,000 20,000 34,000 Differential cost: Cost of Sales Supplies Electricity Charges Total (ii) Incremental revenue over differential cost (i)-(ii) Less: Cost of advertisement Net incremental revenue

3,300

300 40

3,640

2,360

4,400 800 160

5,360

2,640

- 1,600

400 2,000

18,000

7,700 2,700

600 11,000 23,000 12,000 11,000

Working Notes: (1) Incremental revenue (`) Gift shop (`48,000 X 10/80) Restaurant (`64,000 X 10/80) Lodge (`1,80,000 X 10/90) Total

6,000 8,000

20,000 34,000

(2) Differential cost of sales (`) Gift shop (`6,000 X 55/100) Restaurant (`8,000 X 55/100) Total

3,300 4,400 7,700

(3) Differential cost of supplies (`) Gift shop (`6,000 X 5/100) Restaurant (`8,000 X 10/100) Lodge (`20,000 X 8/100) Total

300 800

1,600 2,700

(4) Differential cost of Electricity Charges (`) Gift shop (`900-`640) X 10/80) Restaurant (`3,200 –`1,920)X 10/80) Lodge (`13,500-`9,900) X 10/90) Total

40 160 400 600

Option 2: Profitability to continue throughout the year including season and off season periods (`) Particulars Gift shop Restaurant Lodge Total Incremental Revenue: Season Period Off Season period Total (i) Differential Cost Cost of Sales Supplies Salaries Electricity –Fixed Electricity- Variable Total (ii) Net incremental Revenue (i)-(ii)

-

34,200 34,200

19,800 1,800 9,600 1,280 240

32,720 1,480

-

45,600 45,600

26,400 4,800 9,600 3,840 960

45,600 -

-

80,000 80,000

-

12,800 40,800 13,800 3,200 70,600 9,400

-

1,59,800 1,59,800

46,200 19,400 60,000 18,920 4,400

1,48,920 10,880

Working Notes: (a) Incremental Revenue in off season period (`)

238

Gift shop (`48,000 X 2 X 30 / 80X 95/100) Restaurant (`64,000 X 2 X 30 / 80X 95/100 Lodge (`1,80,000 X 2 X 40 / 90X 50/100 Total

34,200 45,600 80,000

1,59,800 (b) Differential Cost of Sales (`) Gift shop (`36,000 X 55/100) Restaurant (`48,000 X 55/100) Total

19,800 26,400 46,200

(c) Differential cost of supplies (`) Gift shop (`36,000 X 5/100) Restaurant (`48,000 X 10/100) Lodge (`1,60,000 X 8/100) Total

1,800 4,800

12,800 19,400

(d) Differential cost of Salaries (`) Gift shop (`4,800 X 2) Restaurant (`4,800 X 2) Lodge (`25,200-`4,800) X 2) Total

9,600 4,600

40,800 60,000

(e) Differential cost of Electricity (Fixed Element) (`) Gift shop (`640 X 2) Restaurant (`1,920 X 2) Lodge (`6,900 X 2) Total

1,280 3,840

13,800 18,920

(f) Differential cost of Electricity (Variable element) (`) Gift shop (`900-`640) X 30 X2 /80) Restaurant (`3,200 –`1,920) X 30X 2/80) Lodge (`13,500-`9,900) X 40 X 2 /90) Total

240 960

3,200 4,400

Decision : By adopting the Option 1, the net increase in incremental revenue by `120 (i.e. `11,000-`10,880) over the Option 2.Therefore, Option 1 is suggested to adopt. Incremental profitability by adopting strategies of both advertisement insertions and operating during off season period. (`) Incremental Revenue with Advertisement Incremental Revenue with the continue of operations during off season Total incremental revenue

11,000 10,880 21,880

Therefore, both the strategies can be implemented simultaneously for increase of profitability of the organization. Answer: 38 (a) Consequences of undertaking: Nagpur & Delhi Contracts (`’000) Nagpur Contract Delhi Contract Contract revenue Sales of materials held for the Nagpur contract (Note 1) Saving in material purchases by alternative use of materials of Delhi contract (Note2) Hire of plant Incremental costs:

170

48 2

220

180 24

204

239

Materials to be ordered (Note 3) Project manager’s travel, lodging etc. Local labour Penalty for canceling the other contract Excess of revenue/saving over incremental costs

40 4 70 8

122

98

34 4 56 16

110

94 Note:

(1) If the Delhi job is undertaken sales of materials no longer required for the Nagpur job would be (`)

Materials held, at cost Current money value (add 60%) Sales price )x90%) Less: transportation etc. costs (16.67%) Net sales revenue

20 32

28.8 4.8

24.0 (2) If the Nagpur job is undertaken, the materials for the Delhi job might be refused on a different

contract, thereby saving the purchase of additional materials: (`’000) Materials held Contracted for Cost of unwanted materials Saving in purchase on different contract (80%)

24 36 60 48

(3) The materials contracted for to carry out the Delhi job must be paid for whatever happens. Although

not yet received, they must be paid for whichever (if either) contract is undertaken. It is therefore not an incremental cost chargeable to the Delhi contract. For similar reason, materials already held are not an incremental cost to their respective contracts. The alternative use of materials not required is , however, significant and this has been taken into account on the revenue side of the analysis.

(4) It is assumed that the project manager’ salary is a fixed cost, whichever contract (if either) is undertaken. Incremental labour costs are therefore travel, lodging etc. and local labour.

(5) The penalty cost of failing to undertake one contract should be treated as a consequential cost of undertaking the other contract.

(6) The excess of revenue/ saving over incremental costs calculated for each contract shows the comparative effect on profits of undertaking each job in preference to the other. The difference between the two figures (`98,000 a and `94,000) shows that there is a difference between the two project of `4,000 in favour of Nagpur job.

(c) The approach usef has assumed that one project or the other will be undertaken. Some costs have already been incurred (some materials , plant): other costs have been committed (project manager’s salary, head office administration) and others are notional (interest on plant).

These are not relevant to any decision about future action. The only relevant consideration should be: (i) Future revenues or cash savings as a consequence of the decision. (ii) Future costs, incurred as an additional expense as a consequence of the decision. In the solution in part (a), incremental revenues are the revenues from the contract undertaken , alternative uses of materials held but not required and hire of plant. Incremental costs are only those additional costs which would be incurred as a result of the decision to undertake one of the contracts. The cost accounting profit or loss recorded for each contract might be: Nagpur: `1,70,000-`1,60,000 = `10,000 Delhi: `1,80,000-`1,82,000 =(`2,000) There figures are irrelevant to a decision because the costs include past , committed or notional costs, and other revenues and penalty costs to the company are ignored. ( c) Other factors to consider are: (i) The constraints on working which make the contract mutually exclusive. If there is a shortage of

labour, funds etc., it might be possible to overcome and carry out both projects: (ii) The likelihood of another contract being offered for the same period of time, which is more

profitable than either the Nagpur or Delhi jobs. (iii) Loss of goodwill and future contracts by not undertaking either projects: (iv) Reliability of the prospective customer in each contract:

240

(v) Reliability of costs forecasts, lobour availability etc. on both contacts. The net difference between the two jobs, `4,000 is relatively small and sensitivity / risk analysis will be very important:

(vi) The preference for the Nagpur contract (by `4,000) has assumed that the alternative use for the Delhi contract materials will exist. It is only a likelihood, however. Failure to obtain this saving would shift the preference strongly in favour of accepting the Delhi job.

Answer: 39 Working Notes: Calculation of Balance Capacity

Products Units Labour Hours (per unit)

Total Labur Hours

Capacity utilized (%)

‘AB’ ‘CD’ Total

5,000 10,000

5 4

25,000 40,000 65,000

25 40 65

At 65% Capacity = 65,000 Labour hours used At 100% Capacity = Labour hours used would be 1,00,000 Balance Capacity = 1,00,000 hours-65,000 hours = 35,000 hours (i) Statement of Profit for 2003-04 (`) Products ‘AB’ ‘CD’ Total Production & Sales (Units) 5,000 10,000 Sales Revenue (i) Variable Costs: Direct Material Direct Labour

4,00,000 (@`80) 50,000 (@`10) 1,25 ,000 (@`25)

10,00,000(@`100) 300000 (@`30) 200000 (@`20)

14,00,000 3,50,000 3,25,000

Products ‘AB’ ‘CD’ Total Variable overheads ( 100% on Wages) Total (ii) Contribution (i)-(ii) Less: Fixed Costs Profit

1,25,000 3,00,000 1,00,000

2,00,000 7,00,000 3,00,000

3,25,000 10,00,000 4,00,000 2,25,000 1,75,000

Working Notes: Proposals

(1) Utilise balance capacity to Produce ‘AB’ (2) Utilise balance capacity to Produce ‘CD’ (3) Utilise balance capacity to produce a new product ‘EF’ Additional Units= Balance Capacity / Labour hours per unit AB = 35,000 hrs. / 5 hrs = 7,000 units CD = 35,000 hrs. /4 hrs. = 8,750 units Less: Decrease in 1,400 units Efficiency by 16%

= EF = 35,000 hrs. / 7 hours 5,000 units

7,350 units

Statement showing utilization of Balance Capacity

Products Proposal (a0 Proposal (b) Proposal ( c ) AB - Existing

- Additional

5,000 7,000

5,000 -

5,000 -

12,000 5,000 5,000 CD – Existing

− Additional

10,000 -

10,000 7,350

10,000 -

10,000 17,350 10,000 EF – New Units - - 5,000

241

Statement showing contribution per unit of Products ‘AB’ ‘CD’ AND ‘EF’. Product AB CD EF Units Existing

5,000 Addl. 7,000

Existing 10,000

Addl. 7,350

New 5,000

Selling Price (i) 84.00 80.00 104.00 104.00 145.00 Variable Costs: Direct Material 10.50 10.50 31.50 31.50 40.00 Direct Labour 26.25 26.25 21.00 25.00 36.75 Variable Overheads (100% of Wages)

26.25 26.25 21.00 25.00 36.75

Total Variable Costs (ii)

63.00 63.00 73.50 81.50 113.50

Contribution (i) – (ii) 21.00 17.00 30.50 22.50 31.50 Note:

1. The selling price of additional units of Product ‘CD’ is assumed to be `104 as is for existing units. 2. The direct labour cost per unit of additional units of Product ‘CD’ is calculated as below:

Time taken for each additional unit of Product ‘CD’ = 35,000 hours/ 7,350 units = 4,762 hours Direct Labour Cost per unit = 4,762 hours x `5.25 per hour = `25000 The variable cost per unit of Products ‘AB’ and ‘CD’ were `60 and `70 respectively in the year 2003-04. In the year 2003-04 it became `63 and `73.50 respectively. Then the differential cost for product ‘AB’ for 5,000 units comes to `3 per unit and for product ‘CD’ for 10,000 units comes to `3.50 per unit. The differential cost per unit for each additional unit produced during unutilised capacity is equal to its variable cost. Profitability Statement using incremental revenue and differential cost approach (`) Products Units Incremental

Revenue per unit

Total Incremental revenue

Differential cost per unit

Total Differential cost

Difference

Proposal (a) AB 5,000 4.00 20,000 3.00 15,000 5,000 7,000 80.00 5,60,000 63.00 4,41,000 1,19,000 CD 10,000 4.00 40,000 3.50 35,000 5,000 Total 6,20,000 4,91,000 1,29,000 Proposal (b) AB 5,000 4.00 20,000 3.00 15,000 5,000 CD 10,000 4.00 40,000 3.50 35,000 5,000 7,350 104.00 7,64,400 81.50 5,99,025 + 1,15,375 50,000 (*) Total 8,24,400 6,99,025 1,25,375 Proposal (c) AB 5,000 4.00 20,000 3.00 15,000 5,000 CD 10,000 4.00 40,000 3.50 35,000 5,000 EF 5,000 145.00 7,25,000 113.50 5,67,500+ 1,27,500 30,000(**) Total 7,85,000 6,47,000 1,37,500 * Selling and Distribution Expenses ** Special Advertising Expenses The Profit as per Statement of Profit for 2003-04 is `1, 75,000. By utilising the Balance capacity 35,000 hours in manufacture of product ‘EF’ the said profit will increase by `1,37,500 Statement of Profit for 2004-05 with the selection of Proposal (C) to Introduce Product ‘EF’ (`) Existing Profit on manufacture of Products ‘AB’ and ‘CD’ 1,75,000 Add: Profit from Product ‘EF’ by utilising to balance capacity 1,37,500 Total Profit 3,12,500 Answer: 40

242

Differential Cost of the job

Increase ` Decrease `

Material cost 50,000 20,000

Labour cost 90,000 22,500

Additional Overheads 10,000 -

Other expenses - 2,250

Total 1,50,000 44,750

Net differential cost of the job : `1,05,250

(`1,50,000 – `44,750)

Note: Depreciation, rent, heat and light and power are not going to affect the costs.

(b) Full Cost of the jobs:

`

Cost as above at (a) 1,50,000

(i.e. increased costs)

Depreciation 9,000

Power 1,000

Rent 2,500

Heat & Light 250

Total 1,62,750

(c) Opportunity cost of taking the order:

` `

Sale of Product A 62,500

Less:

Material 20,000

Labour 20,500

Power 1,000

Other expenses 2,250

Total

45,750

(d) Sunk cost of the jobs:

16,750

`

Depreciation 9,000

Power* 1,000

Rent 2,500

Heat & Light 250

Total 12,750

*If a student treats power as a relevant cost, in that case it would not appear here. Advice regarding the jobs :

ZED Ltd. should not accept the job as there will be a chase disadvantage of `42,750/- as computed below:

` `

243

Incremental revenue

5,000 units @ `25 1,25,000

Less: Sale of product A 62,500

Differential costs (a)

62,500

Cash disadvantage 1,05,250

42,750

Ans 41:Working Notes: Contribution per hour in manufacturing Product B is as follows: (`per unit) Selling Price Less: Variable Cost Contribution per unit

100 60 40

Contribution per machine hour =`40/5 hours =`8 (`) Relevant cost per unit 10+(2M.H. X `8) Suppliers price per unit Excess of relevant cost over supplier’s price.

26 25 1

Analysis-The relevant cost of production of component is higher by Re 1 over the purchase price of component part X-100.therefore buy decision is recommended.

Ans. 42:

Selling price per unit of product ‘A’ 50

`

Less: marginal cost per unit 35

Contribution per unit 15

Contribution per hour of product ‘A’ 3

Since one unit of product ‘B’ needs 2 hours, therefore if a unit of B is produced, then the contribution lost by not producing ‘A’ = 2 hours × `3 = `6

Real cost of producing one unit of product ‘B’

`

Marginal cost per unit 5

Add: Contribution lost per unit 6

Total cost of producing a unit of Product ‘B’ 11

As the suppliers price per unit of product ‘B’ is `10 and that of producing in the factory is `11, therefore it is suggested that it is better to buy product ‘B’ from outside.

Ans. 43:

Component

Calculation of total number of hour required in department P and Q

Particulars A B C Total Demand units 900 900 1350 Department P: Hours per unit 2 2 1.5 Total hour required 1800 1800 2025 5625 Component Particulars A B C Total Department Q: Hours per unit 3 3 1 Total hours required 2700 2700 1350 6750

244

From the above, we can observe that department Q is facing the capacity constraint of 750 hours Statement showing the qualities of components to be purchased to maintain cost Particulars A C Purchase cost 129 70 Less: variable cost of manufacture 99 50 Saving in manufacture 30 20 Hours required per unit in dept. Q 3 1 Saving in manufacture per hour 10 20 Suggestion: since the saving in manufacture per hour is more in case of component C, component A should be purchased from outside. No. of components of A to be purchased from outside =750 hrs/3 hrs =250 units Ans. 44:

(a) Selling price per unit 600 Less: Variable cost of ` Component A 32 Component B 54 Component C 58 Component D 12 Component E 4 Assembly 40

Contribution per unit 400 200

Total contribution for 132 units ` 52800 Less: Fixed cost 132×316 Net profit

41712

(b) The company may buy any one of the components. The number of units that can be produced under the three options:

11088

Buy component “A” Buy component “B” Buy component “C” Component Machine Hrs reqd

Component Machine Hrs reqd

Component Machine Hrs reqd

A - B 14 C Total machine

12

Hrs/unit Total machine hours available is 4752 under all options

26

Number of units that can be manufactured, if “A” is bought = 4752/26 = 182.77 units Additional capacity that can be created (182.77 132) 100 38.5%

132− ×

=

A 10 B - C

12

22

Number of units that can be manufactured, if “B” is bought = 4752/22 = 216 units Additional capacity that can be created (216 132) 100 63.6%

132− ×

=

A 10 B 14 C

-

24

Number of units that can be manufactured, if “C” is bought = 4752/24 = 198 units Additional capacity that can be created (198 132) 100 50%

132− ×

=

(c) If the increase in demand during the next period is 50% it is not possible to meet it by buying Component “A” as additional capacity created is only 38.5%. Of the remaining two options, the cheaper one has to be accepted.

Buy “B” Buy”C” ` `

245

Market price 160 125 Less: Variable cost if made by the company

54

Additional cost to be incurred

58

106 67 Machine hours saved 14 12 Cost per hour 7.57 5.58

Since it is cheaper to increase capacity by buying “C” this option has to be exercised.

(d) Profitability statement Selling price per unit of equipment `600 Less: Variable cost of: Making A `32 Making B `54 Buying C `125 Making D `12 Making E `4 Assembly `

267 40

Contribution per unit 267

Total contribution for 198 units (Note 1) 65934 333

Less: Fixed cost (as worked out above) Net profit

41712

Net increase over period for current period 27222

Note: 1. Maximum capacity = 4752 machine hours. 13134

Machine hours reqd for one unit of equipment : 36 hours. No. of equipment that can be produced = 4752/36 = 132 Nos. Marketing department of the company anticipates 50% increase in demand during the next period. i.e. 132 + 50% = 198 Nos.

Ans. 45:

1. Present demand of components (in batches) from 10,800 (maximum) available machine hours and projected estimates of components demand (in batches) in the next year.

Working Notes:

Maximum available machine hours 10,800

Machine hours needed to manufacture components. A, B and C (Per batch of

ten numbers) of water purifier

Components Total

A 20 Machine hours

B 28 Machine hours

C 24 Machine 72 hours

Present demand (in batches) of components A, B and C (10,800 hours/ 72 hours) 150

Projected estimate of demand of components A, B and C (add 50% increase) in 225

the next year

2. Present and future fixed costs:

Present fixed cost of 150 batches @ `200/- per batch 30,000

246

Add: Increase in fixed cost to meet 50% increase in demand

Total future fixed cost for 225 batches

10,000

3. Expected purchase cost of components

40,000

View point Probability Component A B C Expected

price Expected

Price Expected

Price ` ` ` Pessimistic 0.25 30 50 40 (`120×0.25) (`200×0.25) (`160×0.25) Most likely 0.50 55 65 70 (`110×0.50) (`130×0.50) (`140×0.50) Optimistic 0.25 20 35 30 (`80×0.25) (`140×0.25) (`120×0.25) Total 105 150

140

4. Present contribution (per batch)

` `

Selling price (per batch) 800

Less: Variable production cost 320

Less: Variable assembly cost 50 370

Contribution (per batch) 430

Total Present contribution on 150 batches 64,500

(i) Maximum number of batches that could be produced in 10,800 machine hours each of the three alternatives namely buying A or B or C is considered respectively.

(a) Buy component A (from outside) No machine hour required

Make component B 28 Machine hours required

Make component C 24

Total

Machine hours required

Number of batches that could be produced internally 207.69 batches

52

(10,800 hours/52 hours)

(b) Buy component B (from outside) No machine hour required

Make component A 20 Machine hours required

Make component C 24

Total

Machine hours required

Number of batches that could be produced internally 245.45 batches

44

(10,800 hours/744 hours)

But in view of projected (expected) market demand of 225 batches, production would be restricted to 225 batches only.

(c) Buy component C (from outside) No machine hours required

Make component A 20 Machine hours required

Make component B 28 Machine hours required

247

Total 48

Number of batches that could be produced internally 225 batches

(10,800 machine hours 748 hours)

(ii) Statement of financial implication when purchases of component A, B and C are made from outside(in view of the fact that production capacity will be limited to 50% increase)

Component bought A B C ` ` ` Total variable cost per batch (I) 64 108 116 Expected purchase cost (II) 105 150 (Refer to working note 3)

140

Increase I variable cost per batch (III) = (II – I)

41 42 24

Present contribution per batch (IV)

430 430 430

(Refer to working note 4) Revised contribution per batch (V) = (IV – III)

389 388 406

Total revised contribution 80,791 87,300 91,330 (207.69

batches × `389)

(225 batches × `388)

(225 batches × `406)

Advise: Purchase component C from outside as it gives maximum contribution on manufacturing A and B internally.

(iii) Profit Statement

(When C is bought from outside and A, B were manufactured internally and extra production is made and sold)

Per Batch ` Total (for 225 batches)

` Sales revenue: (I) 800.00 1,80,000 (225

batches × `800) Less: Variable costs (`(Per batch) : (II) Production cost of A `64 Production cost of B `108 Production cost of D `24 Production cost of E `8 Production cost of C `140 (Refer to working note 3) `344 Assembly cost `50 394.00 88.650 (225 batches ×

`394) Contribution : (III) – (-II) 406.00 91,350 Less: Fixed costs 177.78 (`40,000 / 225 batches)

40,000

248

(Refer to working note 2) Profit 228.22

51.350

Ans: 46:The components are made in a machine shop using three identical machines each of which can make any of the three components.

Total machine hours required for 3 components = 4+5+6 = 15 hours Total capacity of 3 machines is 12,000 machine hours per month and is just sufficient to meet the current demand. Hence, the current demand is 12,000/15 = 800 units of product z per month. Profit made by the company for current month. Sale price 300 Less: Variable cost 48+60+80+30= 218 Contribution per unit 82 Total contribution 800 x 82= 65,600 Less: fixed cost per month Profit for current month RS.

50,000 15,600

(a) From next month onwards, the company expects the demand for z to rise by 25% i.e., 800+25% = 1,000 units per month. One component should be bought from the market. Which component ?

Statement of extra cost of component per unit Component A B C

Market price Less: Variable cost

64 48

75 60

110 80

Extra cost of buying one unit 16 15 30 Machine hours required per unit Extra cost per machine hour 16/4=

4 `4

5 15/5=`3

6 30/6=`5

Ranking II I III Because of Ist rank (lowest extra cost), component b should be bought from the market. Manufacturing Hours C 1,000 units x 6 hours = 6,000 A 1,000 units x 4 hours = 4,000 B 400 units x 5 hours = 2,000 ( Total

Balance)

12,000

Balance 600 units of B should he bought from the market. ( c) Profit made by the company

Component Element of cost Cost per unit No. of units Amount(`) A B B C

Assembling

Variable cost Variable cost Market price Variable cost Variable cost

48 60 75 80 30

1,000 400 600

1,000 1,000

48,000 24,000 45,000 80,000 30,000

Total variable cost Add: Fixed cost Total cost Sales 1,000 units at `300 per unit

2,27,000 50,000 2,77,000

3,00,000

249

Profit on 1,000 units 23,000 Ans. 47:

Statement showing Profit / Loss of company

i)

(If it accepts the order of manufacturing moulded toys)

Total available machine hours: (A) 18,000

(8 machine × 7.5 hours / day × 300 days)

Machine hours required for producing

4,20,000 cans: (B) 14,000

(4,20,000 cans /30 cans)

Balance machine hours: {(A) – (B)] 4,000

Total number of production of moulded toys in balance hours 60,000

(4,000 hours × 15 toys / hour)

Total contribution on 60,000 moulded toys (`) 6,00,000

(60,000 × `10)

Less: Fixed expenses of mould (`) 2,25,000

Net profit (`) 3,75,000

Decision: It is advisable for the company to accept the order of 60,000 moulded toys as it will increase its profit by `3,75,000.

(ii) Statement showing Profit / Loss

(If the order of manufacture of cans increase to 5,40,000)

If 5,40,000 cans are produced, no machine hours would be available for manufacturing toys

`(Lacs)

Total contribution on 5,40,000 cans 32.40

5,40,000 cans × `6)

Less: Fixed cost

Profit

20.00

Alternatively, the production would be 4,20,000 cans and 60,000 moulded toys

12.40

`(lacs)

A. Profit from 4,20,000 cans:

Contribution 25.20

(4,20,000 cans × `6)

Less: Fixed cost

Profit

20.00

B. Profit from 60,000 moulded toys 3.75

5.20

(Refer to (i) above)

Total profit: (A + B) 8.95

250

Decisions: The production of 1,20,000 additional cans instead of 60,000 moulded toys will result an additional profit of `3.45 lacs (`12.40 lacs – `8.95 lacs). Therefore, the company is advised not to accept the order of manufacturing moulded toys.

(iii) Let the minimum excess capacity needed to justify the manufacturing of any portion of the moulded toys order be x.

If toys are manufactured, the profit is = (`60 – `50) x – `2,25,000

and, if toys are sub-contracted, the profit is = (`60 – `57.50) x

Indifference point would be 10x – `2,25,000 = 2.5x

or x = 30,000 moulded toys

Toys produced per hour =15 toys

Therefore, 2,000 (30,000 toys / 15 toys) excess machine hours are required to justify manufacturing of toys by the company, instead of sub-contracting.

(iv) Profit under existing production plan:

(`Lacs)

Contribution from 4,50,000 cans 27.00

(4,50,000 × `6)

Contribution from 45,000 toys 4.50

(45,000 × `10)

Total contribution 31.50

Less: Fixed cost 22.25

(20 lacs + 2.25 lacs)

Profit 9.25

Profit from 15,000 sub-contracted toys

(15,000 × `2.50)

0.375

Total profit

If demand was accurately forecasted & 4,80,000 cans were manufactured, excess machine hour capacity available was 2,000 hrs, such excess being the pint of indifference i.e. profit from toys order would be the same by either manufacturing 30,000 toys or sub-contracting them along with the rest of 30,000 toys.

9.625

(v) Profit under properly negotiated production plan:

(`Lacs)

Contribution from 4,80,000 cans 28.80

(4,80,000 × `6)

Less: Fixed cost 20.00

Profit 8.80

Profit from Toys

60,000 Nos. sub-contracted

1.50

(60,000 × `2.5)

Total profit 10.30

251

Therefore, the loss for improper prediction and negotiation is `10,30,000 – `9,62,500 or `67,500. Ans. 48:

1. (i) Fixed manufacturing overhead per unit

Working Notes:

“XY 100”; `3,00,000 / 5,000 units or `60

“XY 200”; `3,00,000 / 12,000 units or `25

(ii) Variable manufacturing overhead per unit

“XY 100”; (`180 – `60) or `120

“XY 200”; (`60 – `25) or `35

2. Variable costs of production of “XY 100” and “XY 200”

Product Per unit

‘XY 100’ ‘XY 200’

` `

Direct material 200 200

Variable machine operating costs 150 50

Variable manufacturing overheads 120

Total variable costs per unit

35

470

3. (i) machine hours for the production of one unit of each of the two products.

285

“XY 100”; `150/-`100 per hour = 1.5 hours.

“XY 200”; `50/- `100 per hour = 0.50 hours.

(ii) Total machine hours available

5,000 units × 1.5 hours = 7,500 hours

Ranking between manufactured “XY 100” and manufactured “XY 200”

Manufactured Manufactured

“XY 100” “XY 200”

` `

Variable cost of production 470 285

(Refer to working note 2)

Variable marketing and administrative cost 80 60

Total variable cost per unit: (A) 350 345

Selling price per unit: (B) 900 600

Contribution per unit: [(B) – (A)] 350 255

Contribution per hour 233 510

[Refer to working note 3(i)] (`3.50/1.5 hrs) (`255/0.5 hrs)

Ranking II I

Ranking between manufactured “XY 100” and purchased “XY 100”

Manufactured Purchase

252

“XY 100” “XY 100”

` `

Variable cost of production 470 --

(Refer to working note 2)

Purchase price -- 650

Variable marketing and administrative cost 80 40

Total variable cost per unit: (A) 550 690

Selling price per unit: (B) 900 900

Contribution per unit: [(B) – (A)] 350 310

Ranking II I

“XY 200”: 12,000 units × 0.50 hours or 6,000 hours

“XY 100”: (7,500 – 6,000) hours = 1,500 hours

Quantity of each product that XYZ Limited should manufacture and / or purchase to maximise operating income

Manufactured “XY 200” 12,000 units

Manufactured “XY 100”: 1,500 hours / 1.5 hours 1,000

Purchased “XY 100” 6,000

Maximum number of units

Which ABC can supply.

Ans. 49: (i) Profitability as per original Budget

Rs (‘000s)

Rs(‘000s)

Sales(1,80,000 units × Rs 130) (A) 23,400 Direct Material (1,80,000 units × Rs 30) 5,400 Component ‘EH’ ( variable cost = Rs 7.20 per unit)

1,296

Direct wages (1,80,000 units × Rs 28) 5,040 Variable factory overheads (1,80,000 units × Rs 24 × 50% )

2,160

Variable selling & distribution (1,80,000 units × Rs 24 × 50% )

2,160

Total variable cost (B) 16,056 Contribution (A – B) 7,344 Fixed factory overheads 2,160 Fixed selling & distribution overheads 720 Component ‘EH’ @2.20 396 Administrative overhead 900 4,176 Profit 3,168

(ii) Export order

Rs per Unit Rs per Unit

253

Direct material 56 Direct labour (10 hours × Rs 7 per hour) 70 Variable factory overhead ( Rs 3 × 10 labour hours) 30 Selling and distribution overheads 14 Total variable cost 170 Selling price (export) 175 Contribution 5 Since the product earns contribution of `5 per unit, it should be accepted. Total units 500(per month) = 6000 units(per annum) Therefore additional contribution (6000 units× Rs 5) = `30,000 Total hours on product ‘43 grade’ (1,80,000 units × 4) = 7,20,000 Hrs Total hours on component ‘EH’ (1,80,000 units × 0.5*) = 90,000 Hrs

* hour per rate Labour produced units of No

cost LabourDirect ×

= hour per 7 Rs units 15,000

52,500 Rs×

=

0.5 Hrs Total hours utilised at 90% capacity = 7,20,000 hours + 90,000 hours = 8,10,000 hours

100% capacity hours = 90

100 hours 8,10,000 × = 9,00,000 Hrs

Balance hours available = 90,000 hours p.a Hours required for export order 60,000 hours. Both contribution per unit of export order and availability of capacity confirm its acceptance.

(iii) Component ‘EH’ make or buy (per 15,000 units) Make (`) Buy (`) Direct material 30,000 Direct labour 52,500 Variable factory overhead 25,500 Total 1,08,000 1,18,500 Per unit 7.20 7.90 If the company makes the component the out of pocket cost is `7.20 per unit whereas if the component is bought , the out of pocket cost is `7.90.

Decision : If the capacity remains idle it is profitable to make.

(iv) Alternative use of the spare capacity

Units required = 1,80,000 units and hours required = 1,80,000 × 0 .5 = 90,000 Hrs Cost of buying component ‘EH’ = (1,80,000 units × Rs 7.90) =Rs 14,22,000 Cost of making component ‘EH’ = (1,80,000 units × Rs 7.20) = Rs 12,96,000 Hence , excess cost of buying = `1,26,000 Rent income (90,000 hours × Re1) = `90,000

Contribution per unit from making component ‘GYP’ = Rs 8 - Units 15,000

1,12,500 Rs =

Rs 0.5 per unit.

Direct labour cost per unit of ‘GYP’ = Units 15,000

31,500 Rs = `2.10 per unit.

254

No. of labour hours required for one unit of ‘GYP’ = 7 Rs

2.10 Rs= 0.3 Hrs

No. of units of ‘GYP’ in 90,000 hours = hours 0.3

hours 90,000 =3,00,000

Contribution from component ‘GYP’ = 3,00,000 × Rs 0.50 = Rs 1,50,000 Since the contribution from ‘GYP’ is greater than the extra variable cost of buying component ‘EH’ , component ‘GYP’ should be manufactured and component ‘EH’ should be purchased.

Hence, accept export order and buy the component.

(i) If the reliable suppliers offered to supply P44E at a guaranteed price of `50 p.u. variable manufacturing cost p.u.

Ans. 50:

Direct material 14 Direct labour 12 Variable overheads 8 Total variable manufacturing cost 34 (`) Purchase price 50 Less: variable manufacturing cost 34 Saving, if manufactured internally 16 (ii) If the company incur additional inspection and testing charges of `56,000 p.a. = `56,000/`16 p.u. = 3500 units The company can purchase, if yhe requirement of P44E, is less then 3500 units. If the requirement is more then 3500 component, it can manufacture its own requirement. (iii) when the direct labour hours is limiting factor : Calculation of contribution per labour hour Particulars Own manufacture of

P44E Extra sale of another existing product

Selling price - 90 Cost of purchase of P44E (saving) 50 - Less: variable cost

50 34

90 50

Contribution (i) 16 40 Labour hours (ii) 4 8 Contribution per labour hour (i)/(ii) 4 5 Rank II I Analysis: since the labour hours are the limiting factor, it is suggested to opt for extra sale of another existing product then to manufacture component P44E. (iv) The cost of the machine bought last year is a sunk cost and not relevant to the present decision of ‘make or buy’. Book value of the machine is merely an accounting treatment. Ans. 51: (a)This is a make or buy decision so compare the incremental cost to make with the incremental cost buy

255

Incremental cost per unit Make the Blades Direct material `7.50 (`75000 ÷ 10,000) Direct labour `6.50 (`65000 ÷ 10,000) Variable Overhead `5.50 (`55000 ÷ 10,000) Supervision (`35,000 ÷ 10,000) `3.50 Total cost `23.00 Compare the cost to make the blades for 10,000 motors. `23.00, with the cost to buy, `25.00 There is a net loss of `2.00 if ‘X’ chooses to buy the blades.

(b) ‘X’ will be indifferent between buying and making the blades when the total costs for making and buying will be equal at the volume level where the variable costs per unit times the volume plus the fixed avoidable costs are equal to the supplier’s offered cost of `25.00 per unit times the volume.

(Direct materials + Direct labour + Variable overhead) × Volume + Supervision =, Cost to buy × Volume. Let volume in units = x (7.50 + 6.50 + 5.50) × x + 35,000 = 25.00x

19.50 x + 35,000 = 25.00 x

35,000 = 25.00 × x – 19.50 × x

35,000 = 5.50 × x x = 6,364 units of blades

As volume of production decreases, the average per unit cost of in house production increases. If the volume falls below 6,364 motors, then ‘X’ would prefer to buy the blades from the supplier.

(c) If the space presently occupied by blade production could be leased to another firm for `45,000 per year, ‘X’ would face an opportunity cost associated with in house blade production for the 10,000 units of `4.50 per unit. New cost to make = 23.00 + 4.50 = 27.50

Now ‘X’ should buy because the cost to make, 27.50, is higher than the cost to buy, 25.00.

(i) Deciding whether B Ltd. Should accept the offer from an outside vendor instead of manufacturing chains internally.

Ans. 52:

Price of chain offered by vendor `12 Less: Variable cost of (`5 + `2) Excess of quoted price over variable cost

7

Total excess of quoted price over variable cost (24,000 x `5) `1,20,000 5

Less: Avoidable cost Inspection, set-up, etc. `24,000 - Machine rent 24,000 48,000Excess of bought –out price over variable cost and avoidable cost 72,000

Decision- B Ltd. Should not accept the offer from outside vendor, because this decision will lead

to reduction in profit by `72,000. (ii) Deciding whether the use of internal facilities for upgrading the quality of chains would

be useful in comparison to purchase from outside. Incremental revenue per unit `22

256

Less: Differential cost per cycle Contribution

18

Total Contribution (24,000 x `4) `96,000 4

Less: Tooling costs Net contribution

16,000

80,000

Decision – B Ltd. Should accept the offer of alternative use of facilities for upgrading the bicycle. It will lead to increase of `80,000 in contribution. This is more than the excess of bought-out price over variable and avoidable cost [i.e.`72,000 as per (i)]. Thus company will benefit by `8,000 i.e.,(`80,000 – `72,0000) (iii) Deciding whether use of internal facilities for upgrading the bicycle ( chain) internally would be profitable, if batch size becomes 4,000 units in comparison to their purchases from an outside vendor. Bought- out price offered `12 Less: Variable internal cost Excess of bought – out cost over variable cost

7

Total excess of bought – out cost over variable cost (24,000 x `5) `1,20,000 5

Less: Inspection cost `12,000 - Machine rent 24,000 Excess of bought – out price over variable and avoidable costs

36,000

Decision – If inspection cost (Which varies with batch size) decreases, then excess of bought- out price over variable and avoidable costs would be `84,000. In comparison to this, net contribution from using the internal facilities for upgrading quality of chains will `80,000[refer to (ii).] There fore, if batch size increases and inspection cost reduces, then use of internal facilities of updation of quality of chain is advocated. If decision to update is taken in (ii), it will increase profit by `4,000 (i.e..`84,000 – `80,000)

84,000

Ans. 53: For taking a make or buy decision, it is necessary to find out the relevant cost of both the decisions, i.e. manufacturing vis-à-vis purchasing the component from outside.

Departmental Expenses Budget (`000) Items Total Allocation ratio Gadgets Components Production Variable Costs Direct material Direct labour Indirect labour Inspection and testing Power Fixed Costs Lighting Insurance Depreciation Misc. Fixed Exp. Total cost Variable cost per unit

3,840 1,536

720 480 480

7,056

40 30 96 54

220 7,276

80 : 20 75 : 25 80 : 20 75 : 25 75 : 25

24,000

3,072 1,152

576 360 360

5,520

`230

24,000

768 384 144 120 120

1,536

`64

257

(i) Variable cost of component is `64 per unit. The purchase price is `70 per unit. For each

unit net cash outflow will be `6. Therefore, company should take decision to make. (ii) Evaluation of decision to export Inflow (a) Additional contribution due to export 12,000 units x (`245 – 230) `1,80,000 (b) Saving in variable cost of components (24,000 units x `64) 17,16,000

15,36,000

Less: Outflow Payment to be made to supplier (24,000 units x `70) Net Cash Inflow

16,80,000

36,000

(a) Ans. 54

Demand 52,000 48,500 26,500 30,000 A B C D

Direct Material 64 72 45 56

M/c 48 32 64 24 Other Variable Cost 32 36 44 20 Total Variable Cost 144 140 153 100 Selling Price 162 156 173 118 Contribution (`/u) 18 16 20 18 M/s Hours per unit 6 4 8 3 Contribution (`/ M/c hr.) 3 4 2.5 6 Ranking III II IV I Sub-Contract Cost `/u) 146 126 155 108 Cont (`/u) on (Subcontract) 16 30 18 8 I Division: It is more profitable to sub-contract B, since contribution is higher sub- contract.

1st Level of Operations: 1,50,000 hours, Produce D as much as possible. Hours required = 30,000 units × 3 = 90,000 hours Balance hours available: 60,000 hours.

Produce the next best (i.e. A, Since B is better outsourced)

60,000 hrs = 10,000 units of A. 6 hrs / u

1st Level of Operation:

Contribution (units) Contribution (`)

A Produce 10,000 units 18 1,80,000 A Outsource 42,000 units 16 6,72,000 B 48,500 units

Outsource fully 30 14,55,000

258

C 26,500 units Outsource fully 18 D 30,000 units

Fully produce 18 5,40,000 Total Contribution: 33,24,000 Less: Fixed cost 10,00,000 Net Gain 23,24,000

2nd Level of Operation:

Both A and C increase contribution by own manufacture only by `2/ - per unit. 1,50,000 hrs can produce 25,000 units of A. ∴Contribution increases by 25,000 × 2 = 50,000

(Difference in Contribution sub -contract and own manufacturing) = 2

But increase in fixed Cost = 50,000

At the 2nd level of operation, the increase in contribution by own manufacturing is exactly set up by increase in fixed costs by `50,000/-. It is a point of financial indifference, but other conditions like reliability or possibility of the sub -contractor increasing his price may be considered and decision may them but towards own manufacture. 3rd Level Additional: 1,50,000 hrs available

Unit of A that are needed = [52,000 – 25,000 (2nd Level) – 10,000 (1st Level)]

= 17,000 units × 6 hrs/u = 1,02,000 hrs. Balance 48,000 hrs are available for C to produce 6,000 units. Increase in Contribution over Level 1st or 2nd :

A: 17,000 × 2 = `34,000 C: 6,000 × 2 = `12,000

= `46,000 Increase in fixed costs = `50,000

Additional Loss = `4,000 4th

Level Additional 150000 hrs. can give 150000 ÷ 8 = 18,750 unit of C

Increase in Contribution 18,750 × 2 = ` 37,500

Increase in Cost = (`50,000) Level 3rd loss c/fd = (` 4,000) Level 1st profit will order by =(` 16,500) Advice: Do not expand capacities; sell maximum No. of units by operating at 1,50,000 hrs. capacity (level 1st ) and gain `23,24,000.

Summary: Product Produce

(Units) Sub-Contract

(Units) Contribution (Production)

Contribution (Sub-Contract)

Total Contribution

A 10,000 42,000 1,80,000 6,72,000 8,52,000 B - 48,500 - 14,55,000 14,55,000

259

C - 26,500 - 4,77,000 4,77,000 D 30,000 - 5,40,000 - 5,40,000

33,24,000 Fixed Cost 10,00,000 Profit 23,24,000

Calculation of contribution per unit Ans. 55

Particulars EXE WYE (a) selling cost P.U. 375 540 Variable cost P.U. Dept. 1 Direct materials 58 100 Direct labour 5 hours

50 7.5 hours 75

Variable overheads (5 hrs*`2.40) 12 - (7.5 hrs*`2.40) - 18 (i) 120 193 Dept.2 Direct materials 21 26 Direct labour 90 120 (7.5 hrs*`3.60) 27 - (10 hrs* `3.60) - 36 (ii) 138 182 Total variable cost (i)+(ii) 258 375 Contribution P.U. (a)-(b) 117 165 Calculation of contribution per unit if facilities of Dept.1 were sub-contracted but facilities of Dept.2 used internally (`) Particulars EXE WYE Selling price per unit (a) 375 540 Cost of sub-contracting Dept.1 facilities 138 212 Cost of manufacture in Dept.2 internally 138 182 Total variable manufacturing cost per unit 276 394 Contribution per unit (a)-(b) 99 146 Calculation of contribution per unit if facilities of Dept.1 and Dept.2 are sub-contracted Particulars EXE WYE Selling price per unit (a) 375 540 Cost of sub-contracting P.U. Dept.1 Dept.2

138 150

212 192

Total variable cost P.U. (b) 288 404 Contribution P.U. (a)-(b) 87 136 Statement showing number of units to be produced and sold to earn maximum profit by using own manufacturing capacity Particulars EXE WYE Dept.1 (1,75,000 hrs/5 hrs) (1,75,000 hrs/7.5 hrs) Dept.2 (2,80,000 hrs/7.5 hrs) (2,80,000 hrs/10 hrs)

35,000 - 37,333 -

- 23,333 - 28,000

Maximum unit can be produced and sold by using facilities of 35,000 23,333

260

both departments. Maximum contribution (35,000 units* `117) (23,333 units*`165) Les: fixed cost (Dept.1 `5,00,000 + Dept.2 `10,00,000)

40,95,000 - 15,00,000

- 38,49,945 15,00,000

Maximum profit 25,95,000 23,49,945 Suggestion: by production and sale of 35,000 units of EXE is maximum, it is suggestion to manufacture EXE internally. Calculation of profit from EXE (`) Contribution on internally produced units (35,000 units * `117) Contribution when Dept.1 services were sub-contracted (2,333 units * `99) Contribution when Dept.1 & Dept.2 services were sub-contracted (1,167 units * `87)

40,95,000 2,30,967 1,01,529

Total contribution of EXE Less: fixed cost

44,27,496 15,00,000

Profit 29,27,496 Calculation of total contribution of WYE (`) Contribution on internally produced units (23,333 units * `165) Contribution when Dept.1 services were sub-contracted (4,667 units * `146) Contribution when Dept.1 and Dept.2 services were sub-contracted (3500 units * `136)

38,49,945 6,81,382 4,76,000

Total contribution of WYE Less: fixed cost

50,07,327 15,00,000

Profit 35,07,327 Suggestion: profit is maximum for product WYE. Hence 31,500 units of WYE should be produced to yield a sum of `35,07,327 as profit.

Working notes:

Ans. 56:

1.

(a) Total normal and overtime hours available.

Department

A B

Normal capacity hours 600 520

Overtime hours 300 260

(50% of normal hours in each department)

Total available hours 900 780

(b) Total hours required to meet fully the market demand of 2,500 units of P and 2,000 units of Q.

Department A B Hours required for manufacturing P 2,500 units of Product

250 500

(2,500 Units × 0.1 hour) (2,500 Units × 0.2 hour)

Hours required for manufacturing Q 2,000

600 400

261

units of Product (2,000 Units × 0.3 hour) (2,000 Units × 0.2

hour) Total hours required 850 900

2. Sub-contracting should be resorted:

To meet the market demand of 2,500 units of product P and 2,000 units of product 850 and 900 hours [Refer to working note 1(b)] are required in departments A and B respectively. In department B only 780 hours are available and thus does not meet fully the requirement of 900 hours. Hence, sub-contracting should be resorted to meet the market demand fully.

3. (i) Contribution per unit;

Product P Q

Normal hours

Overtime hours

Normal hours

Overtime hours

Director material cost (`) 10.00 10.00 5.00 5.00

Direct labour cost Dept. A (`) 1.00 1.50 3.00 4.50

(`10 × 0.1 hr.)

(`15 × 0.1 hrs.)

(`10 × 0.3 hrs.)

(`15 × 0.3 hrs.)

Dept. B: (`) 2.40 3.60 2.40 3.60

(`12 × 0.2 hrs.)

(`18 × 0.2 hrs.)

(`12 × 0.2 hrs.)

(`18 × 0.2 hrs.)

Total variable cost per unit (`) : (A) 13.40 15.10 10.40 13.10

Sub-contract price per unit (`) : (B) 18.00 18.00 12.00 12.00

Contribution / cost saving / (Loss per unit (`)

4.60 2.90 1.60 (1.10)

(C) = [(B) – (A)]

(ii) Contribution per hour

Hours required per unit

Dept. A 0.1 0.1 0.3 0.3

Dept. B 0.2 0.2 0.2 0.2

Contribution per hour

Dept. A (`) 46 29 5.33 Loss

(`4.60/0.1 hrs.) (`2.90/0.1 hr.) (`1.60/0.3 hrs.) --

Dept. B (`) 23 14.50 8.0 Loss

(`4.60/0.2 hrs.) (`2.90/0.2 hr.) (`1.60/02. Hrs.) --

4. Utilization of normal and overtime available hours to meet fully monthly market demand of 2,500 units of P and 2,000 of Q.

(i) An analysis of contribution statement (Refer to working note 3) clearly shows that 2,500 units of the product P should be manufactured by utilising the normal capacity hours of departments A and B. The

262

manufacturing of 2,500 units of P will consume 250 normal hours of department A and 500 hours of department B (Refer to working note 1(b).

(ii) For manufacturing 2,000 units of product Q, it is beneficial to utilise the remaining normal available hours of departments A and B. The normal available hours in the department B are only 20 hours, [520 hours – 500 hours] and in department A 350 hours [600 hours – 250 hours]. 100 units of product Q can be manufactured by utilising the normal available hours of departments A and B. The manufacturing of 100 units of Q in normal available hours will utilise 30 hours in department A and 20 hours in department B.

(iii) Now for manufacturing the remaining 1,900 units of product Q, we have 320 normal hours plus 300 overtime hours in department A and 260 overtime hours in the department B. The manufacturing cost per unit of product Q comes to `11.60 when normal hours of department A and overtime hours of department B are utilized.

{`5 (Material Cost) + `3 (Direct Labour in Department A) + `3.60 (Direct Labour in Department B)}

On comparing `11.60 with sub-contracting price of `12 per unit, we arrive at a contribution of 0.40 per unit. Hence maximum number of units of product Q should be manufactured by using normal hours of department A and overtime hours of department B. since 0.3 and 0.2 hours are required respectively for manufacturing one unit of product Q in the two departments, therefore, utilising 320 normal hours and 213 overtime hours in departments A and B respectively, 1066.66 units (or say 1,067 units) of product Q are manufactured.

(iv) Finally, to manufacture remaining 833 units of Q, the available time is 300 overtime hours and 47 overtime hours in department A and B respectively. According to (working note 1) the available time in department B is short by 120 hours (900 required hours – 780 available hours) therefore 833 units of Q cannot be made internally. But few units can be made by utilising the available overtime hours in departments A and B. The manufacturing cost of 1 unit of Q by utilizing overtime hours in departments A and B comes to `13.10 (Refer to working note 3) which on comparison with subcontract price of `12 gives rise to a situation of loss of `1.10 per unit {`13.10 – `12}. Hence it is advisable not to manufacture the remaining 833 units internally. These 833 units should be sub-contracted at a price of `12/- per unit.

(i) Statement of quantity of each product to be manufactured / or to be sub-contracted for fulfilling the market demand in most economical way.

Departments A B Normal

time hours Overtime

hours Normal

time hours Overtime

hours Available hours (Refer to working note 1(i)

600 300 520 260

Production 2,500 units of P 250 -- 500 -- (Refer to working note 4 (i)) (2,500 units × 0.1 hrs.) (2,500 units × 0.2 hrs.) 100 units of Q 30 -- 20 -- (Refer to working note 4 (ii) (100 units × 0.3 hrs.) (100 units × 0.2 hrs.) 1067 units of Q 320 -- -- 213 (Refer to working note 4(iii)) (1,067 units × 0.3 hrs.) (1,067 units × 0.2 hrs.)

(ii) Statement Showing Total Cost

(Based on the solution in (i) above)

Products

263

Particulars P Q Sub contract price

Total

` ` ` ` Direct Material Cost 25,000 5,835 - 30,855 (2,500 units ×

`10) (1,167 units × `5)

Direct Wages: Dept. A 2,500 3,500 -- 6,000 (250 hours ×

`10) (350 hours × `10)

Dept. B 6,000 4,074 -- 10,075 (500 hours ×

`12) (20 hours × `12 + 213 hours × `18

Fixed overhead 18,000 6,400 - 24,400 Cost of 833 units @ `12 per unit on sub-contracting

-- -- 9,996 9,996

Total Cost 51,500 19,809 9,996 81,305

(i) Option

Ans. 57:

Statement of Profit (Loss)

(if the firm discontinue all the operations during notice period of 3 months)

(`Crores)

Products A B C D Total Sales* - - - - - Costs: Material & Labour - - - - - Allocated overheads: Manufacturing 1.5 1.2 1.8 1.2 5.7 Admin. & Selling 0.6 0.3 0.9 0.6 Total allocated overheads during notice period of 3 months

2.4 2.1 1.5 2.7 1.8

Profit / (Loss)

8.1

(2.1) (1.5) (2.7) (1.8) (8.1) *The option (i) would not yield any revenue.

Conclusion: The option (i) will result in a loss of `8.1 crores due to the committed costs account of 3 months notice period.

(ii) Option

Working note:

Ascertaining profitable products (if their production is continued during 3 months of notice period) (`Crores)

Products A B C D

Sales (X) 18 13.5 21 15

264

Variable cost:

Materials 12.0 7.5 13.5 9.0

Labour 4.5 3.0 7.5 7.5

Total variable costs: (Y) 16.5 10.5 21.0 16.5

Contribution: (X – Y) 1.5 3.0 - (1.5) A review of contribution figures in the above statement of four products A, B, C and D clearly reveals that products A and B are only profitable.

Statement of Profit (Loss)

(If the firm continues the operations of profitable products A and B during 3 months of notice period)

(`Crores)

Products A B Total

Contribution (Refer to above working note) 1.5 3.0 4.5

Less: total manufacturing administrative & selling overheads (Refer to part (i) above)

Profit / (Loss)

8.1

Conclusion: Under this option the total loss is (`3.6) crores which is less than the loss of option (i).

(3.6)

(iii) Option

Working Note:

Ascertaining profitable products (when notices are issued to the staff and the landlord – only in the manufacturing unit, resort to subcontracting only on profitable products)

(`Crores)

Products A B C D Sales: (X) 72.0 54.0 84.0 60.0 Variable Cost: Materials 48.0 30.0 54.0 36.0 Sub-contracting charges 16.0 10.5 27.0 26.0 (20 lacs × (15 lacs ×

`80) (30 lacs ×

`70) (20 lacs ×

`90) Total variable costs : (Y)

`130) 64.0 40.5 81.0

Contribution: (X – Y) 62.0

8.0 13.5 3.0 (2.0) A review of contribution figures in the above statement clearly shows that products A, Band C are only profitable.

Statement of Profit / (Loss)

(If the firm resorts to manufacturing of profitable products by sub-contracting)

(`Crores)

Product Total A B C Contribution: (X) 8.0 13.5 3.0 24.5 (Refer to above working note) Total manufacturing overheads of 3 months notice period : (Y)

5.7

(Refer to option (i) above)

265

Total administrative & Selling overheads: (Z) Profit/(Loss): {X – (Y+Z)}

9.6

Decision: 9.2

Out of the three options the option (iii) is the most viable one. Not only it will help the company with a turn around, but from the year 2002, the company can look forward to even higher profitability, since the manufacturing overhead would no longer be incurred thereafter.

Working Notes:

Ans. 58:

1. FOB price of dismantled kit: FOB price of dismantled kit (in$) 510 FOB price of dismantled kit (in `) 24,000

($510 × `47.059) 2. Cost of a dismantled kit to Z Inc. If `120 is the S. P. of kit to Z Inc. then its C `100

Re 1 = Rs.120Rs.100

If `24,000 is the S. P. then C. P. is = Rs.120Rs.100

× `24,000

= `20,000 3. Cost of local procurements: 140% of the supplies made by Z Inc. or 140% × `10,000* = `14,000 *Being 50% of cost of a dismantled kit to Z Inc. 4. Landed cost of a dismantled kit: ` FOB price 12,000 (50% × `24,000) (Refer to working note 1) Add: Insurance & freight CIF price 12,500

500

Add: Customs duty 3,750 (30% × `12,500) Landed cost of a dismantled kit 5. Cost of the standard items procured locally:

16,250

48% of the cost of locally procured goods = 48% × `14,000

= `6,720 6. Royalty payment per computer: Let x = Selling price per unit of personal computer y = Royalty paid per computer Since 20% is the margin of profit on S.P. it main a margin of 25% on C.P. Therefore we have

266

X = 1.25 (`32,250+ `150 + y)

Y = 10% {x – (`6,720 + `16,250)} On solving the above equations we get: X = `43,000

Y = `2003.43 or `2,000 (Approx)

Statement showing the selling price of a personal computer in India ` A. Landed cost of a dismantled kit (Refer to working note 4) 16,250 B. Cost of local procurement (Refer to working note 3) 14,000 C. Cost of assembly and other overheads per computer D. Total cost of manufacture: (A+ B + C) 32,250

2,000

E. Technology fee per computer 150 (`3,00,00,000 / 2,00,000 computer) F. Royalty payment per unit (Refer to working note 6) G. Total cost (D + E+ F) 34,400 H. Profit (20% on selling price of 25% of total cost) I. Selling price (per computer)

8,600

43,000

Ans. 59: Capacity Output (units) FOB cost Total cost(`) Differential Differential

Statement of Differential cost

per unit (`) cost(`) cost per unit (`)

70% 70,000 97 67,90,000 − − 80% 80,000 92 73,60,000 5,70,000 57 90% 90,000 87 78,30,000 4,70,000 47

100% 1,00,000 82 82,00,000 3,70,000 37 Statement showing gain or loss for various export order

If proposal A is accepted the company will suffer a loss of `10,000 with an idle capacity of 5,000 units.

If proposals A and B are accepted, the company will suffer a loss of `10,000 with an idle capacity of `5,000 units.

If the company accepts all the three proposals, it will earn profit of `80,000 with an idle capacity of 5,000 units.

267

Therefore, the company should accept all three proposals.

Shut down point = Ans. 60:

P/V Ratio Avoidable Fixed cost - Shut down cost

= [120000-40000] - 0 1-0.8

= `400000

Ans. 61:

Continue Shut Down Fixed expenses at 50% activity 30,000 - Additional shut down cost 2,000 Fixed expenses during shut down

10,000 30,000 12,000

Additional fixed cost incurred due to continued operations = 18,000

If contribution from operation is less than 18,000, a shut down is recommended.

i.e. Contribution per unit < 18,000 5,000

i.e. Contribution < Rs 3.60 per unit i.e Selling price – variable cost < Rs 3.60 per unit or S.P. – 3.6 < Variable cost i.e. 14.00 – 3.60 < Variable Cost or variable cost is more than Rs 10.40 For a variable cost more than Rs 10.40 per unit, a shut down is recommended.

Alternative

Contribution from operation must be less than 18,000 `for a shut down. Sales value = 14x5,000 = 70,000

Sales – variable cost < 18,000

or variable cost is more than 70,000-18,000 = 52,000

Variable cost of 5,000 units above `52,000

Or Variable Cost V.C. per unit > 52,000 = `10.40 5,000

For a variable cost per unit above `10.40, shut down is recommended.

Ans. 62:

If plant is continued If plant is shutdown Sales 7,60,000 -

Less:Variable Cost - 5,70,000 Contribution 1,90,00

Less:Fixed Cost 3,50,000 1,30,00 Additional Cost 15,000

268

Operating Loss 1,60,00

1,45,00 A comparison of loss figures indicated as above points out that loss is reduced by

(16,000-14,500) `15,000 if plant is shut down.

Shut down point = 3,50,000 - 14,5000 = 20,500 = 1,02,500 units 8 - 6 2

Capacity level of shut down point:

At 100% level production is 95,000 = 1,18,750 0.80

Capacity level at shut down = 1,02,500 = 86.31% 1,18,750

Alternative Solution

` If the plant is shut down, the sunk cost or fixed expenses 1,45,00

If it is working at 80% capacity, the fixed cost 3,50,000 Additional fixed expenses 2,05,000 Contribution (95000*2) 1,90,00

0 Incremental Loss on Continuing 15,00 Decision - better to shut down

Production at shut-down point

2 x – 350000 = 1,45,000 2x = 2,05,000 x = 1,02,500 Units Capacity % = 1,02,500/(95,000/0.8) =

(a) Contribution per tin = Selling Price – Variable cost Ans. 63:

= 21 – (7.8 + 2.1+ 2.5 + 0.6)

= `8 per tin.

Loss on operation:

Fixed cost per annum = 2,00,000 units × 4 per unit = 8 lakhs ∴ Fixed cost for 1 quarter = 8/4 = 2 lakhs

` Fixed cost for the quarter 2,00,000 Less: Contribution on operation (8 × 10,000) Expected loss on operation

80,000 (1,20,000

)

Loss on shut down: `

Unavoidable Fixed Cost 74,000 Additional shut down cost Loss on shut-down

14,000 (88,000

)

269

Conclusion: Better to shut down and save `32,000. Shut-down point (number of units) = Avoidable Fixed Cost ÷ Contribution per unit

= (2,00,000 − 88,000)/8 = 14,000 units.

The Directors, Ans. 64:

XYZ Co. New Delhi Date…….

Dear Sir As desired, we have analysed the cost implications of the decision of temporary closure of the trade recession. We find that if the factory is run at 50% capacity and with reduced sales revenue, the loss likely to be incurred in one full year (the estimated period of recession), would be around `200000 as detailed below:

`In’000

Direct materials 300 Direct labour 400 Production overhead 240 Administrative overhead 120 Selling & distribution overhead

130

1190 Loss

Sales

200

If the factory is closed, the following costs will be incurred: `In ‘000 990

Fixed costs 220

Settlement cost 150

Maintenance costs 20 Cost of resuming operations

80

It is obvious from the above, that despite the fact that running at 50% capacity would imply a loss of `200000, it is better not to close down the factory since in that case the loss would be higher.

470

In our views, even if running the factory entailed a somewhat bigger loss as compared to the loss incurred by closing it down temporarily, it may be better to keep the factory in operation. This is because a closure, even if temporary, results in the loss of regular and old customers, suppliers and skilled personal. This, coupled with a loss of goodwill in the market, may give rise to substantial losses at the time of restarting the factory. We trust that the above analysis would be helpful to you in reaching an appropriate decision in the matter. We shall be glad to be of any further assistance that may be required in this regard.

Yours faithfully X and Co.

Chartered Accountants.

270

Working Note:

Production Admn. Selling overhead overhead overhead (`Lakhs) (`Lakhs) (`Lakhs) (i) Amount at 60% 2.52 1.24 1.36 (ii) Amount at 80% 2.76 1.32 1.48 (iii) Variable cost for 20% 0.24 0.08 0.12 (iv) Variable cost for 60% 0.72 0.24 0.36 (v) Fixed Cost 1.80 1.00 1.00 (vi) Amount at 50% (iii×2.5+v) 2.40 1.20 1.30

M/s supreme Ltd. Ans. 65:

(i) Comparative statement of sales and profit under marginal costing Details 2002 2003 Sales Revenue `6,00,000 5,62,500 Less: variable cost 4,50,000 4,50,000 Contribution 1,50,000 1,12,500 Less: fixed cost 1,20,000 78,750 Profit 30,000 33,750 (ii) Minimum sales required, if the firm decides to shut down in units in 2003: Minimum sales required is the sales which should yield at least the contribution, which is sufficient to meet increase in fixed cost. Increase in fixed costs in 2003 = `78,750 – 60,000 = `18,750 Sales required to yield contribution equal to increase in fixed cost X* P/V retio = `18,750 Or x = `18750 / 0.20 = `93,750 Working notes 1. Computation of variable costs, break even point, profit and fixed cost for the year 2002: Sales revenue `6,00,000 P/V ratio 25% Margin on safety 20% So, margin of safety = sales * 0.20 = `6,00,000 * 0.20 = 1,20,000 We know that margin of safety * P/V ratio = Profit So, Profit: `1,20,000 * 0.25 = `30,000 Total contribution = sales * P/V ratio = `6, 00,000 * 0.25 = `1,50,000 Variable cost = sales – contribution So, variable cost = 6, 00,000 – 1,50,000 = 4,50,000 Fixed cost = contribution – Profit = 1,50,000 – `30, 000 = `1,20,000 Break even sales * P/V ratio = fixed cost So, BES = 1,20,000 / 0.25 = `4,80,000 2. Computation of sales revenue, variable cost, fixed cost and profit in 2003 Let sales revenue for the year 2003 be x. the variable cost for the year 2003 is `4,50,000 (no. change). So, contribution = X – `4,50,000 = 20% (given) We know that P/V retio = Sales

contribution

Or, 20 100 =

X X – 4, 50,000

271

Or, 20x = `100x – `4, 50, 00,000 Or, x = `4, 50, 00,000/80 = 5, 62,500 Margin of safety = 30% (given) So, margin of safety = sales * margin of safety ratio = `5, 62,500 * 0.30 = `1, 68,750 We know that sales – margin of safety = B.E. sales So, B.E. sales = `5, 62,500 – `1, 68,750 = `3, 93,750 Ans. 66 (i)

Option I At 75% in Feb and close in

March and April (`)

Option II At 25% each from Feb

– April (`) Direct Material 5,25,000 5,25,000 Direct Labour 5,23,600 5,19,750

Factory Overhead : Indirect Material Two months idle Indirect Labour Training cost Indirect Exp. :

Repairs & Maintenance Over hauling cost Others Expenses Idle × 2

10,48,600 10,44,750

8,400 9,800

1,01,500 65,800

28,000 14,000 52,500 53,200

14,700

1,78,500

84,000

1,02,900

Office overhead: Staff Salaries Idle 67,550 × 2 Other overheads Idle

1,48,400 1,35,100

28,000 22,400

2,94,000

59,850

Total overhead cost 6,67,100 7,33,950 Total cost 17,15,700 17,78,700

The more economic course of action is to operate at 75% capacity for a month only, and close the plant for March and April. This option will save (`17,78,700 – `17,15,700) = `63,000. Ans. 68: (i)

Statement of Profitability of E Ltd. in Existing Situation A B C Total No. of units 10,000 25,000 20,000 ` ` ` Selling Price per unit 40 75 85 Less: Variable Cost per unit Direct Material 10 14 18 Direct wages 8 12 10 Variable Overhead 8 9 10

272

Contribution per unit 14 40 47 Total Contribution 1,40,000 10,00,000 9,40,000 20,80,000 Less: 1,60,000 Fixed Cost 4,50,000 4,00,000 10,10,000 Net Profit -20,000 5,50,000 5,40,000 10,70,000

Calculation of overall profit under each proposal

(ii)(a) If Product A is discontinued and capacity released is utilized for either B, either C or for both B and C Revised contribution of Product B and Product C. B(`) C (`) Selling Price per unit 73.50 80.75 (75 – 2% of 75) (85 – 5% of 85) Less: Variable cost per unit Direct Material 15.40 18.90 (14 + 10%of 14) (18 + 5%of 18) Direct Wages 12.00 10.00 Variable Overhead 9.00 10.00 Contribution per unit 37.10 41.85

Profitability Statement

Option 1 Option 2 Option3- Both B and C equally

Only B Only C B C No. of Units (as per W.N.1) 6,666 8,000 3,333 4,000 ` ` ` ` Additional contribution 2,47,308.6 3,34,800 1,23,654.3 1,67,400 2,91,054.3 Savings from Fixed Cost of A 1,60,000 1,60,000 1,60,000 Reduction in contribution from A 1,40,000 1,40,000 1,40,000 Net Increase in Profit 267308.6 3,54,800 3,11,054.3 Existing Profit 10,70,000 10,70,000 10,70,000 Total Profit 1337308.6 14,24800 3,31,054.3 Hence, it is better to produce Product C only. (ii)(b) Discontinue Product A and divert the capacity to produce Product D A B C Total Sales (units) 10,000 25,000 20,000 Labour Hrs. per unit 4 6 5 Total Labour Hours 40,000 1,50,000 1,00,000 2,90,000 Idle Capacity (hours) 2,90,000 * 20 / 80 72,500 Capacity released of A 40,000 Total hours released 1,12,500 Hours per unit 4 No. of units that can be produced 28,125

Profitability Statement No. of units 28,125 ` Selling Price per unit 60 Less: Variable Cost per unit Direct Material 28 Direct wages 12 Variable Overhead 6 Contribution per unit 14 Additional Contribution (D) 3,93,750 Less: 1,05,500 Additional Fixed Cost Additional Net Profit 2,88,250 Add: Existing Profit (B & C) 10,90,000 Total Profit 13,78,250

273

(c) If we hire out the idle capacity ` Idle hrs. 72,500 Profit per hour (10,70,000 / 2,90,000) 3.69 Total Profit 2,67,500 Existing Profit 10,70,000 Total Profit 13,37,500 Decision : Better to produce product C as per proposal (a) Working Note-1: Hours release on discontinuation of Product A = 10,000 * 4 Only B Only C B and C equally 40,000 / 6 = 6,666 40,000 / 5 = 8,000 B- 3333 and C- 4000

Ans. 69:

1. Quantity analysis Input in process A – total capacity – given = 2, 00,000 kg Less: loss in process A = 10% of Input = 20,000 kg Balance transfer to process B = 1,80,000 kg

(NRV at `1/ kg = 20,000)

Less: loss in process B = 5% of Input = 9,000 kgBalance good output available for sale =

(NRV at `2 / kg = 18,000)

2. Supplier Evaluation and Decision 1,71,000 kg

Supplier P Q R R Condition Max. 1,20,000 kg Max. 1,60,000 kg Any Quantity Qtty = 2,00,000 kg Price Var. Transport cost Total

10.00 1.20

11.20

11.20 1.00

11.60

12.20 1.00

11.00

12.60 1.00 12.00

The following can be planned in any of the following ways – Total Purchase = 2, 00,000 kg Purchase entirely from R 2,00,000 kg Purchase first kg. from P(least cost) and

balance 80,000 kg from Q (Next least cost) 1,20,000 * `11.20 + 80,000 * `12.20)

Cost incurred = (2,00,000 * `12) = 23,20,000 = 24,00,000 Decision: hence the company should Buy 1,20,000 kg from P and 80,000 kg from Q Fixed transport cost being constant is not relevant to the above decision. 3. Customer evaluation and decision Customer k L M Condition Upto 80,000 kg only Upto 1,60,000 kg only All 1,71,000 kg Selling price Less: discount 2% Net selling price Less: var. transport cost Net realization

65.00

63.70 1.30

2.60

64.00

61.10

62.72 1.28

1.44

61.80

61.28

61.80 NIL

NIL 61.80

The sales can be made in any of the following way – Total sale Quantity = 1,71,000 kg Sold entirely to M 1, 71,000 kg sell first 1,60,000 kg to L (max. revenue)and Balance 11,000 kg to K (next max. revenue) Amt realized = (1,71,000 * `61.80) (1,60,000 * `61.28 + 11,000 * `61.10) = `1,05,67,800 = 1,04,76,900 Less: fixed delivery cost NIL = `60,000 (`5,000 * 12 months) Net amount = `1,05,67,800 = 1,04,16,900

274

Decision: since revenue is higher, the company should sell the entire quantity to customer M. 4. Statement of process costs Particular Process A Process B Raw materials (`23,20,000 + fixed transport 2,00,000) Transport from previous process Direct wages Overheads

25,20,000 22,00,000 9,56,000

56,56,000 21,00,000 13,45,800

Total process costs Less: scrap value of normal loss ( as in WN Above)

56,76,000 20,000

91,01,800 18,000

Net process costs transferred to subsequent process/FG

56,56,000 90,83,800

Net profit: sales revenue – costs of production = 1,05,67,800 – 90,83,800 = `14,84,000

(i) Reorder level = Safety Stock + lead time consumption Ans. 70:

= 100 units + (3600 units/12) = 400 units (ii) Anticipated reduction in the value of the average stock investment

EOQ = 2 Annual consumption Buying cost per orderCost of carrying one unit of inventory for one year

× ×

= 2abcs

Where a = Annual consumption b= Buying cost per order c= Storage and other inventory carrying cost rate

= 2 36000 2 100

Rs. 40. .

unitsRs

× ××

The average stock to be held under new system: = minimum lavel + ½Reorder quantity

= 100 + ½* 120 = 160 units The average stock investment under new system: = 160 units * `100 = `16,000 The average stock under old system: = Minimum level + ½ EOQ

= 0 + ½ (1800 units) = 900 units The average investment under old system = 900 * `100 = `90,000 Therefore, anticipated average reduction in value of average stock investment = `90,000 – `16,000 = `74,000 (iii) The anticipated reduction in total inventory costs (in the first and subsequent years) Under new system: Annual ordering cost ((3,600/120) * `40) = `1,200 Stock holding cost (0.20 * `16,000) = Total inventory cost

3,200

Under old system: 4,400

Annual ordering cost (2 orders * `40) = ` 80 Stock holding cost (0.20 * `90,000) = Total inventory cost

18,000

Anticipated reduction in subsequent year: 18,080

Thus anticipated reduction in total inventory cost is `13,680 (i.e., `18,080 – 4,400) in subsequent years. Anticipated reduction in the first year = `13,680 – `10,000 * = `3,680

275

* In the first year 100 units will have to be purchased.

Particular Ans. 71:

Current Policy A Policy B Policy C Sales Less: variable cost at 70%

4,50,000 3,15,000

5,00,000 3,50,000

5,40,000 3,78,000

5,65,000 3,95,500

Contribution Less: fixed cost (given)

1,35,000 10,000

1,50,000 10,000

1,62,000 10,000

1,69,500 10,000

Profit before tax Less: tax at 40%

1,25,000 50,000

1,40,000 56,000

1,52,000 60,800

1,59,500 63,800

Profit after tax 75,000 84,000 91,200 95,700 Cost of good sold (VC + FC) Inventory turnover ratio (given) Average inventory (COGS /T/o ratio) Carrying cost of inv. At 5% (a) Opportunity cost at 20 % of capital blocked in average inventory (b) Total cost of inventory holding (a + b) Net benefit = total cost of inventory

3,25,000 10 times 32,500 1,625 6,500 8,125 66,875

3,60,000 8 times 45,000 2,250 9,000 11,250 72,750

3,88,000 6 times 64,667 3,233 12,933 16,166 75,034

4,05,500 4 times 1,01,375 5,069 20,275 25,344 70,356

Decision: As net benefit is Maximum under policy B, it may be chosen (alternative assumptions exist)

Working Note:

Ans. 72:

Fixed overheads `

Present sale value: (A) 15,00,000

(15,000 units ×`100)

Direct materials 4,50,000

(30% of sale value)

Direct labour 3,00,000

(20% of the value)

Variable overheads 3,00,000

(`20 per unit)

Total variable costs (B)

..

Contribution: (C) = (A) – (B) 4,50,000

10,50,000

Profit : (D) 2,25,000

(15,000 units × `15)

Fixed overheads: (C) – (D) 2,25,000

.

(current level)

Add: Additional fixed overheads due to price escalation

Total fixed overheads:

50,000

Statement of profitability for various alternatives

2,75,000

Alternatives I II III IV Rejecting

the Rejecting the

proposal for Accepting the

proposal of Accepting the

proposal of the

276

proposal for the purchase of 10,000 units and continuing with present level of sales only

the purchase of 10,000 units from a party and attaining the maximum capacity by incurring additional selling expenditure

the party to take 10,000 units @ `90 per units by installing a balancing equipment and continuing with present level of sales

party to take 10,000 units @ `90 per cent by installing a balancing equipment and attaining sale of maximum available capacity by incurring additional selling expenditure

Sale (units) 15,000 20,000 25,000 30,000 ` ` ` ` Sales Value: (A)

15,00,000 (15,000 ×

`100)

20,00,000 (20,000 ×

`100)

24,00,000 (15,000 ×

`100+10,000 × `90

29,00,000 (20,00,000 ×

`100 + 10,000 × `90)

Variable costs Direct material

4,95,000 6,60,000 8,25,000* 9,90,000*

(33% of sales value) Direct Labour 3,75,000 5,00,000 6,25,000* 9,90,000* Variable overheads

3,00,000 4,00,000 5,00,000 6,00,000

(@`20 per unit) Total variable costs: (B)

11,70,000 15,60,000 19,50,000 23,40,000

Fixed costs Fixed overheads

2,75,000 2,75,000 2,75,000 2,75,000

(Refer to working note) Additional selling expenditure

- 50,000 - 50,000

Depreciation for balancing equipment

- - 1,00,000 1,00,000

Additional administrative expenses

- - 50,000 50,000

Total fixed cost : (C)

2,75,000 3,25,000 4,25,000 4,75,000

Total cost D: [(B)+(C)]

14,45,000 18,85,000 23,75,000 28,15,000

Profit: (A)-(D) 55,000 1,15,000 25,000 85,000 Note: For computing the material and labour cost under alternative III & IV the notional sale price of `100 is taken for additional 10,000 units.

Recommendation: Alternative II is the best as it gives maximum profit.

277

Comparative profit Statement (based on Revised Cost Structure)

Ans. 73:

Proposal 1 Proposal 2 Proposal 3

Sell 20,000 units only

Secure orders for 5,000 additional units (unused capacity) and sell 25,000 units

Accept the new order for 10,000 additional units and sell 30,000 units

` ` `

Total sales revenue (A) 20,00,000 25,00,000 29,00,000

(`20,000 units × `100)

25,000 units × `100)

(30,000 units + `33)

Director Labour 5,00,000 6,25,000 7,50,000

(20,000 units × `25)

(`25,000 units × `10)

(30,000 units + `10)

Variable overhead 2,00,000 2,50,000 3,00,000

(20,000 units × `10)

(25,000 units × `10)

(30,000 units + `10)

Fixed overheads 4,40,000 4,40,000 4,40,000

(`4,00,000 + `40,000)

Add: Administrative charges

- - 60,000

Add: Sales promotion expenses

- 50,000 -

Depreciation (New equipment)

1,50,000

Total cots (B) 18,00,000 21,90,000 26,90,000

Profit (C) = [(A) – (B)] 2,00,000 3,10,000 2,10,000

Analysis

An analysis of the profit figures of M/s Unique products under three proposals clearly shows that it is maximum under proposal 2. Therefore, it is advisable for the concern to produce and sell 25,000 units @ `100/- per unit and utilise its full production capacity.

Ans. 74

(as originally envisaged by the company) (a) Statement of Profitability for the year 1993-94

Products Ethylene EDC VCL Total Annual Production Capacity (MT) Annual Planned Productions (MT) (Refer to Note -1) Cost of production of annual planned production

25,000

25,000 `

30,000

25,000 `

30,000

15,000 `

`

278

Variable costs (Refer to Note 2) Fixed cost (Refer to Note 3) Common cost (Refer to Note 4) Cost of Ethylene Cost of Ethylene (Used for EDC) Cost of EDC (25,000 MT) Cost of 10,000 MT of EDC (Refer to Note 5) Cost of 15,000 MT of EDC for (VCL) Cost of Sale (A) Sales Revenue (B) Profit (B-A)

5,00,000 5,00,000 2,50,000 12,50,000

7,50,000 9,00,000 4,50,000

12,50,000 33,50,000 13,40,000

13,40,000 15,00,000 1,60,000

6,00,000 12,00,000 6,00,000

20,10,000 44,10,000 45,00,000

90,000

57,50,000 60,00,000 2,50,000

Note: Only 25,000 metric tonne of ethylene is available and as such 25,000 metric tonne of EDC could be produced. Out of this 15,000 metric tonne of EDC is consumed for VCL production and the balance of 10,000 metric tonne of EDC is sold. Working Note: Note: 1 annual planned production Ethylene EDC VCL Proposed Sale Production: For EDC For VCL Total

- -

10,000 15,000 25,000

10,000 10,000

15,000 25,000

15,000 15,000

-

15,000 2. Variable Costs Ethylene EDC VCL 25,000 MT x `20 25,000 MT x `30 15,000 MT x `40 =`5,00,000 =`7,50,000 =`6,00,000 3. Fixed Cost (This will be based on 25,000 MT x 20 30,000 MT x 30 30,000 MT x40 Production capacity) =`5,00,000 =`9,00,000 =`12,00,000 4. Common Cost (This will also be based 25,000 MT x 10 30,000 MT x 15 30,000 MT x 20 On production capacity =`2,50,000 =`4,50,000 =`6,00,000 5. Cost of 25,000 metric tones of EDC = `33,50,000 Cost of one metric ton of EDC = `33,50,000 * 25,000 = `134 Cost of 10,000 metric tones of EDC = 10,000 x `134 = `13,40,000 Cost of 15,000 metric tones of EDC = 15,000 x `134 = `20,10,000 6. Sales Revenue EDC = 10,000 MT x `150 =`15,00,000 VCL = 15,000 MT x Rs,300 =` Total

45,00,000

60,00,000

(b) Revised Statement of Profitability (When the company decides to accept offer of X)

Products Ethylene EDC VCL Total Annual planned productions (MT) 25,000 25,000 30,000

279

Cost of production Refer (a) Variable cost (30,000 MT x `40) Production Fixed cost (30,000 MT x `40) Common Fixed cost (30,000 MT x `20) Purchases cost of 5,000 MT of EDC @ `125 per MT Total of EDC used in VCL Total cost (A) Total Sales (Refer to note 1 below (B) Profit (B-A)

` 12,50,000

` 33,50,000

6,25,000

39,75,000

`

12,00,000 12,00,000 6,00,000

39,75,000 69,75,000

80,00,000 10,25,000

Comment – Since the profit has increased the proposal of X should be accepted. Note 1: Total Sales : 20,000 MT of VCL to X @ `250 per MT =`50,00,000 10,000 MT of VCL X `300 (in open Market) =`

Hours 30,00,000

Available capacity 20,000 First product D should be produced (2,800 x 6) Balance hours 3,200

16,800

Second product A should be produced (2,000 x 1) Balance hours 1,200

2,000

Third product B should be produced (600 x 2) 1,200 Thus, if 20,000 hours is the limiting factor, all requirements of D and A can be manufactured and only 600 units of product B can be manufactured. The balance requirement of product B. i.e.,3,500-600 =2,900 units will have to be bought – out or manufactured in the second shift. (b) Because purchase price of component c is `52 and cost of manufacturing is `57, it will not be profitable to manufacture C even in second shift. It should be purchased form outside, purchased from outside. The relative position is as follows:

Cost of producing 2,900 units of product B in second shift

Solution (a) Working Notes Ans. 75:

(i) Press hours required Components A B C D Direct expenses Direct hours per unit

`10 1

`20 2

`10 1

`60 6

(ii) Marginal cost per unit vs. bought-out prices per unit

Marginal costs: Direct Materials Direct wages Direct expenses Marginal costs Bought – out price Excess of bought out price over marginal cost Process hours per unit

`37 10 10 57 60 3 1

`27 8 20 55 59 4 2

`25 22 10 57 52

(5) 1

`44 40 60 144 168

24 6

280

Excess of bought – out price per unit of limiting factor Ranking

3 11

2

111

(5) -

4 1

The bought – out price of component C is lower than the marginal cost by `5 and for this reason it should be purchased from outside. For the remaining products. Ranking is based on utilization of limiting factor. Optimal product mix has been, calculated as follows:

Calculation of optimal product mix

Variable Cost `55 Increase in direct wages

2

Total variable cost (2,900 x 57) `1,65,300 57

Additional fixed cost Hours required = 2,900 x 2=5,800 hours Extra fixed cost of 5,800 hours at `500 for each 1,000 hours or part thereof Total cost for producing 2,900 units of product B in second shift 1,68,300

3,000

Bought- out price for 2,900 units of product B will be 2,900 x `59 Disadvantage in buying B

1,71,100 2,800

For the above-mentioned reasons, it is in the interest of company to manufacture product B in the Second shift instead of buying it from outside market .The disadvantage of the decision to buy

product B from outside will be `2,800 . 80,00,000

Components Ans. 76:

P Q R S i. Direct wages ii. D.L.H. @ `8.75 p.h iii. Variable Mfg. cost iv. Purchase Price v. Saving if components are

manufactured vi. Saving per hour (5 * 2) Ranking

`17.50 2

`99.75 105.00

5.25

2.625 2

`35.00 4

`96.25 103.00

6.75

1.6875 3

`17.50 2

`99.75 91.00

- -

`105.00 12

`252.00 294.00

42.00 3.50

1

(i) Statement showing product-mix of the components to be manufactured (Available hrs. = 40,000)

Component Qty. reqd. Hrs. / unit Production Hrs. Used Balance hrs. S P Q

2,400 2,400 4,800

12 2 4

2,400 2,400 1,600

28,800 4,800 6,400

11,200 6,400 -

Components to be manufactured= S = 2,400 P = 2,400 Components to be purchased = Q = 1,600 Q = 3,200 R = 1,200 *6,400 hrs * 4 = 1,600

281

(ii) Statement showing impact of second shift working

Additional quantity of Q required = 3,200 Hours required to manufacture (3,200 x 4) = 12,800 Say = 13,000 Fixed cost (`875 * 1,0000 ) x 13,000 = `11,375 Fixed cost per component Q (11,375 * 3,200) =`3.55 Increase in labour cost (`35 x 25%) Total 12.30

8.75

Saving in cost Loss if component Q is manufactured

6.75

5.55

Hence, second shift operation is not recommended • Fixed cost given per 1,000 hours

Since S and Y are produced simultaneously from an input of raw material Z, therefore when additional 60,000 kgs. of Y will be produced then 30,000 of S will also be produced simultaneously. The input of material Z required for these additional 60,000 kgs. of Y and 30,000 kgs. of S will be 90,000 kgs. of material Z. Hence the cost of processing 90,000 kgs. of material will be as follows:

Ans. 77:

`

Cost of Raw material Z 2,70,000

(90,000 kgs. × `3)

Variable processing cost 1,80,000

(90,000 kgs. × `2)

Total cost of processing 4,50,000

Less: Sales revenue from 60,000 kgs. of Y 2,40,000

(60,000 kgs. × `8)

Balance cost to be recovered 2,10,000

Current sales revenue from the sale of 3,00,000 kgs. of S 24,00,000

(3,00,000 kgs. × `8)

Total sales revenue to be earned from the Sale of S 26,10,000

(3,00,000 kgs. + 30,000 kgs.)

Hence minimum reduced price per kg. of S to recover `26.10,000 from 7.91

the sale of 3,30,000 kgs. of S

(`26,10,000 / 3,30,000 kgs.)

Working notes: Ans. 78:

1. Statement of total available, utilized and surplus capacity hours when 9,000 units of product ‘X’ are produced.

282

Departments Available Capacity hours

Capacity utilized Surplus Capacity hours

(in % (in hours) (1) (2) (3) (4) = (2)×(3) (5)=(2)-(4) A 2,400

(300 days × 8 hours)

75 1,800 600

B 2,400 100 2,400 NIL C 2,400 70 1,680 720 D 2,400 50 1,200 1,200

2. Statement of total available, utilized and surplus capacity hours when 12,000 units of product ‘X’ are produced.

Production Department

Available capacity

hours

Capacity utilization on 9,000 units Hours

Balance capacity

hours

Unit per hour Hours required for 3,000 additional

units

Surplus capacity

hours

(1) (2) (3) (4)=(2)×(3) (5) (6) (7) (8)=(5)-(7)

A 2,400 75 1,800 600 5

hrs. 1,800units 9,000

600 Nil

B 2,400 100 2,400 Nil 3.75

hrs. 2,400units 9,000

800 Nil

C 2,400 70 1,680 720 5.36

hrs. 1,680units 9,000

560 160

D 2,400 50 1,200 1,200 7.5

hrs. 1,200units 9,000

400 800

Alternative I

Statement of net Revenue (Under Alternative I) Production Surplus

capacity hours

(Refer to W.N.-1

Hire charges per hour

Total revenue in

(`Lacs)

Incremental costs per

hour `

Total cost in (`Lacs)

Net revenue

in (`)

(a) (b) (c)=(a)×(b) (d) (e)=(a)×(d) (f)=(c)-(e) A 600 2,500 15.00 2,000 12.00 3.00 B 720 1,800 12.96 1,500 10.80 2.16 D 1,200 1,600 19.20 1,200 14.40 4.90

Total 47.16 37.20 9.96 Add: present income (10% of `1,800 lacs) Total return

180.00 189.96

283

Return on investment

= investment Total

return Total× 100 =

1,800189.96

× 100 = 10.553%

Alternative II Statement of Net Revenue when 12,000 units of product ‘X’ are produced and surplus plant capacity (hours) in departments C and D hired out. Production Surplus

capacity hours

(Refer to W.N.-2)

Hire charges per hour

Total revenue in

(`Lacs)

Incremental costs per

hour `

Total cost in (`Lacs)

Net revenue in

(`Lacs)

(1) (2) (3)=(1)×(2) (4) (5)=(1)×(4) (6)=(3)-(5) C 160 1,800 2.88 1,500 2.40 0.48 D 800 1,600 12.80 1,200 9.60 3.20

Total 15.68 12.00 3.68 Add: Revenue (in lacs) earned on 3,000 additional units sale (3,000 units is × `1,600)

Add: Present income on investment (10% × `1,800 lacs)

48.00

Total Return (in lacs) 180.00

Return on investment =

231.69

lacs 2,200lacs 231.68

× 100 = 10.53%

Evaluation of two alternative proposals : Since the return on investment under alternative I is more than that under alternative II; therefore it should be accepted.

(i) Statement of Profitability of three Joint Products resulting from the joint production process of a popular line of colognes.

Ans. 79:

Evergreen Morning Flower

Evening Flower

Total

` ` ` ` Sales revenue 4,00,000 6,00,000 6,00,000 16,00,000 (10,000 units ×

`40) (6,000 units ×

`100) (4,000 units ×

`150) --

Less: cost after point of split off

2,00,000 (10,000 units ×

`20)

2,40,000 (6,000 units ×

`40)

2,00,000 (4,000 units ×

`50)

6,40,000 --

Net realization value at the point of spilt off

2,00,000 3,60,000 4,00,000 9,60,000

Less: Joint cost apportioned (Refer to working note)

1,16,667 2,10,000 2,33,333 5,60,000

Profit 83,333 1,50,000 1,66,667 4,00,000

284

Response to the President’s question. Review of the above profitability statement clearly shows that the concern is not selling its largest-volume product viz. evergreen at a loss. It yields a profit of `83,333. In fact the figure of joint cost data given in the statement of the question is misleading. The total joint cost viz. `5,60,000 should have been apportioned ever the three joint products by using net realisable value method. The use of net realisable value method would give joint cost per-unit of three respective joint products as `11,666; `35 and `58.33. (Refer to working note)

Working note: Statement of Joint cost apportionment over three products obtained under a joint production process. Evergreen Morning

Flower Evening Flower

Total

` ` ` ` Total Joint cost 2,80,000 1,68,000 1,12,000 5,60,000 (10,000

units × `28)

(6,000 units × `28)

(4,000 units × `28)

--

Joint cost apportionment (One the basis of net realization value i.e. (`2,00,000 : `3,60,000 : `4,00,000 or (5:9:10)

1,16,667 2,10,000 2,33,333 5,60,000 --

Joint cost per unit 11,666 (`1,16,667

/ 10,000 units)

35 (`2,10,000 / 6,000 units)

58.33 (`2,33,333 / 4,000 units)

(ii) Should the company sell Morning Flower Cologne below cost: To compete successfully with the other company’s product, if the price of Morning Flower Cologne is reduced to `60, it will still contribute `20 per unit (`60 – `40) towards joint cost and profit. On a volume of 6,000 units it will contribute `1,20,000 in total. Hence the company should do so and go ahead to sell Morning Flower below cost.

(iii) Response to price reduction: (Refer to working note) A reduction in sales price of Morning Flower fails to maintain a gross margin of 20% on sales of three products obtained from the joint production process of a popular line of colognes. Hence the company cannot reduce the sales price of Morning Flower to `60. A reduction in sale price would result in a loss of revenue of `1,40,000.

Working note: `

Total joint cost (20,000 units × `28) 5,60,000

Total cost after split off (10,000 × `20 + 6,000 units × `40 + 4,000 units × `50) Total cost

6,40,000

12,00,000 Add: Profit margin (20% on ales or 25% on total cost 3,00,000 Expected desired sales revenue Less: Sales revenue of Evergreen and Evening Flower (10,000 units × `40) + (4,000 × `150)

15,00,000 10,00,000

Expected sales revenue from Morning Flower 5,00,000 By reducing sales price of morning flower to `60/- total sale revenue received will be

3,60,000

Loss of revenue resulting from the sale of Morning Flower 1,40,000 (iv) Minimum price for Morning Flower

285

Expected Sales revenue from Morning Flower to maintain a gross margin of 20% of sales: (`)

5,00,000

(Refer to (ii) part Quantity (in units) 6,000 Hence minimum price per unit (`) 83.33

(`5,00,000 / 6,600 units)

(i) (a) Statement showing apportionment of joint costs sales value at split-off Ans. 80:

Products Sales in tones (a) Selling price per ton

(`) (b) Sales value (`) (c) = (a) * (b)

Apportioned joint cost (`)

Caustic soda Chlorine

2,400 1,600

100 150

2,40,000 2,40,000

1,00,000 1,00,000

Total 4,80,000 2,00,000 *Apportioned joint cost = Total joint cost Total sale value

* sale revenue of each product.

Apportioned joint cost to caustic soda = `2,00,000 `4,80,000

* `2,40,000 = 1,00,000

Apportioned joint cost to chlorine = `2,00,000 `4,80,000

* `2,40,000 = `1,00,000

(b) Statement showing apportionment of joint costs on physical measure (tons) Products Sales in (tons) Apportioned ** joint costs (`) Caustic soda Chlorine

2,400 1,600

1,20,000 80,000

Total 4,000 2,00,000 **Apportioned joint cost = Total joint cost Total sales (tons)

* sales of each product (tons)

Joint cost apportioned to caustic soda = `2,00,000 `4000 tons

* 2,400 tons = `1,20,000

Joint cost apportioned to chorine = `2,00,000 `4,000 tons

* 1,600 tons = `80,000

(c) Statement showing apportionment of joint costs by using estimated net realizable value method Products Sales revenue (`) Further pro-cessing

cost (`) Net realizable value (`)

Apportioned ** joint cost (`)

Caustic soda (2,400 tons * `100) PVC (1,000 tons of PVC * `400)

2,40,000 4,00,000

- 40,000

2,40,000 3,60,000

80,000 1,20,000

Total 6,00,000 2,00,000 ***Apportioned joint cost = Total joint cost Total net realizable value

* Net realizable value of each product.

Apportioned joint cost for caustic soda = `2,00,000 `6, 00,000

* `2,40,000 = `80,000

286

Apportioned joint cost for chlorine = `2, 00,000 `6, 00,000

* `3, 60,000 = `1, 20,000

(ii) Statement of gross margin percentage of caustic soda and PVC under sales value at split off: physical measure (tons) and estimated net realizable value method Sale value at split off (`) Physical measure (tons) (`) Estimated net realizable

value (`) Caustic soda Sale revenue : (A) Joint cost allocated : (B) Gross margin (C) : (A)-(B) Gross margin (%) (C) * (A)

100

(b) PVC: Sales revenue (A) Joint cost allocated Further processing cost Total cost Gross margin (c) : (A)-(B) Gross margin (%) (C)

(A) *100

2,40,000 1,00,000 1,40,000 58.33% 4,00,000 1,00,000

1,40,000 40,000

2,60,000 65%

2,40,000 1,20,000 1,20,000 50% 4,00,000 80,000

1,20,000 40,000

2,80,000 70%

2,40,000 80,000 1,60,000 66.67% 4,00,000 1,20,000

1,60,000 40,000

2,40,000 60%

(iii) Consequence of the operating income of inorganic chemicals for November, 1998 by accepting the offer of daily swimming pools Ltd. to purchase, 1,600 tons of chlorine Incremental revenue (loss) due to processing of chlorine to PVC (`1, 60,000) (1,600 tons * `150) – (1,000 tons * `400 tons) Saving on further processing cost of chlorine into PVC Incremental operating income

40,000

(`1, 20,000)

The operating income of inorganic chemicals will be reduced by `1,20,000 in the month of November, 1998 if it accepts the offer of daily swimming pools Ltd., to purchase 1,600 tons of chlorine in November, 1998 at `150 per ton.

Ans. 81:

(i) Statement showing the product to be manufactured and sold and the result contribution Aristocrat deluxe Maximum possible production in unit (Note1) S. P. per unit `90.00 `80.00 Less: variable costs: Aristocrat deluxe Direct material `10.00 `10.00 Variable costs: Deptt. A (0.5*`50; 0.3 * `50) 25.00 15 Deptt. B (0.4 * `60; 0.45 * `60) 24.00 Total variable cost per unit

27.00 59.00 52.00 59.00 52.00

Contribution per unit 31.00 28.00

Total contribution per unit 6,800 * `31; 8,500 * `28 `2,10,800 `2,38000 Form the above, it is apparent that sale of `8,500 units of deluxe model produces the maximum contribution of `2,38000 within the capacity and material constraints. Therefore, 8,500 units of deluxe model should be produced.

(ii) statement showing the maximum contribution on the sale of aristocrat or deluxe models and hiring out the surplus capacity in departments A and B Aristocrat deluxe Total contribution on sale of maximum possible production as per (i) above `2,10,800 `2,38,000 Contribution on hiring capacity (Note 2):

287

Aristocrat Deluxe Deptt. A Nil 850 * `40 - 34,000 Deptt. B 1,120 * `60 15 * `60 67,200 Total contribution

900 2,78,000

It is noticed that total contribution of the company would be maximum i.e. `2,78,000 on the sale of 6,800 units of aristocrat model and hiring out the surplus capacity of the two departments.

2,72,900

(iii) Statement showing total contribution of company when 4,250 units of each product are manufactured and surplus capacity of Deptt. A and/or Deptt. B hired out Aristocrat Deluxe Total (a) Production (units) 4,250 4,250 (b) Contribution per unit as at (i) above `31 `28 Total contribution (a) * (b) `1,31,750 `1,19,000 `2,50,750 Contribution earned on hiring the surplus capacity of Deptt. B (Note 3)

13,650*

This proposal is less profitable then proposal at (ii) above 2, 64,400

Working Note: Maximum capacity or production is given in hours. But part (i) required production to be stated in units. The same has been worked out as under: Deptt. A Deptt. B Maximum capacity in hours 3,400 3,840 Aristocrat Deluxe Maximum hour per unit - Deptt. A 0.50 0.30 Deptt. B 0.40 0.45 Maximum possible production (in unit) – constant Maximum capacity Deptt. A: 3,400/0.5; 3,400/0.30 6,800 11,333 Deptt. B 3,840/0.40; 3,840/0.45 9,600 8,533 Maximum possible production (in unit) – constant Available material 17,000 kgs/2 kgs 17,000/2 kgs 8,500 8,500 Maximum possible production considering both Capacity and material constants 6,800 8,500 2. Surplus capacities Deptt.A Deptt. B (a) Maximum possible hours 3,400 3.840 (b) Capacity used when 6,800 units of aristocrat model are produced (0.50 * 6,800; 0.40 * 6,800) 3,400 (c) surplus capacity with aristocrat model

3,840 NIL

(d) Capacity used when 8,500 units of deluxe model are produced 1,120

(0.3 * 8,500; 0.45 * 8,500) 2,550 3,825 (e) Surplus capacity with deluxe model (a)-(d) 850 15 Deptt. A Deptt. B 3. Maximum possible hour as in unit Note 1 3,400 3,840 Hour utilized aristocrat 4,250 * 0.50; 4,250 * 0.45 (-) 2,125 (-) 1,700 Deluxe (-) 1,275 Surplus capacity (hours) NIL NIL

(-) 1912.5

Brightly Ans. 82:

Unit price

`

Contribution

per unit `

VolumeUnits

Total contribution (`in 000)

Incremental contribution (`000)

Labour hours

Incremental labour hours

Incremental contribution per labour hour

`

Rank

288

276 176 12000 2112 2112 24000

24000 88 2

272 172 14000 2408 296 28000

4000 74 6

268 168 16000 2688 280 32000

4000 70 7

264 164 18000 2952 264 36000

4000 66 8

260 160 20000 3200 248 40000

4000 62 9

254 154 22000 3388 188 44000

4000 47 10

Lightly Unit price Contribution

per unit Volume Total

contribution (`in 000)

Incremental contribution

(`000)

Labour hours

Incremental labour hours

Incremental contribution per labour

hour

Rank

163 103 40,000 4120 4,120 40,000 40,000 103 1 162 102 42,000 4284 164 42,000 2,000 82 3 161 101 44,000 4444 160 44,000 2,000 80 4 160 100 46,000 4600 156 46,000 2,000 78 5 156 96 48,000 4608 8 48,000 2,000 4 11 152 92 50,000 4600 (8) 50,000 2,000 (4) Loss

As the labour time is scarce source (time available 78,000 hours), the decision has to be taken on the basis of ranks based upon incremental contribution per labour hour.

Product Price Incremental volume

Incremental labour hours

Balance hours

Incremental Contribution

(in 000 `) Lightly 163 40,000 40,000 38,000 4120 Brightly 276 12,000 24,000 14,000 2112 Lightly 162 2,000 2,000 12,000 164 Lightly 161 2,000 2,000 10,000 160 Lightly 160 2,000 2,000 8,000 156 Brightly 272 2,000 4,000 4,000 296 Brightly 268 2,000 4,000 280 Total 7,288

Hence product mix is Brightly – 16,000 units and Lightly 46,000 units

Optimal contribution per month `72,88,000 Fixed costs per month `60,00,000 Optimal profit per month `12,88,000

Working Notes:

Brightly Lightly Variable cost (p.u.) 100 Rs.

12,000) 000,16(4,00,000)3 000,00,38(

=−−

60 Rs. 0,000)4 000,48(2,00,000)6 000,80,66(

=−−

Fixed cost (`) 22,00,000 38,00,000 Contribution = Unit selling price less variable cost per unit.

289

Statement showing computation of selling price per unit Ans. 83:

Months 1-3 4-9 10-12 Total Total number of unit Produced (Note 4) `28,125 `60,000 `33,750 Variable cost `2,81,250 `6,00,000 `3,37,500 `12,18,750

1,21,875

Labour cost (Note 2) 3,00,000 6,00,000 3,37,500 12,18,750 Overheads 1,12,500@ 2,40,000@ 1,35,000@ 4,87,500 Total sami variable overheads (Note 3) 72,000# Fixed overheads Total costs

1, 92,300

Add: profit: (20% on selling price or 25% on cost) 32, 08,050

Sales revenue 8, 02,013

Selling price per unit ( `40,10,063/1,21,875 on cost) 40, 10,063

32.90

Working notes 1. Average installed capacity per month (in units): = Total annual installed capacity/12 month (in units): = 1, 50,000 units/ 12 months = 12,500 units per month. 2. Total labour cost at different capacity utilization: Capacity utilization 75% 80% 90% Expected production per month ( in units) 9,375 10,000 11,250 Labour cost of expected production (`) 93,750 1, 00,000 1, 12,500 Minimum lqbour cost per month (`) 1, 00,000 1, 00,000 1, 12,500 Capacity utilization (in months) 3 6 3 Total labour cost at different capacity levels `3, 00,000 `6, 00,000 `3, 37,500 @28125 × `4; 60000 × `4; 33750 × `4 #This can also be taken based on average capacity utilization i.e. ( 121875÷150000) × 100 = 81.25%. Therefore, semi-variable overheads can also be taken as 68000 (refer note 3). In that case, selling price will be `32.87.

Ans. 84:

Part A Part B Target Price (`) 145 115 Less : Variable Cost p.u. (`) Material(1.6 kg. @ `12.5 p.kg.) (`) 20 20 Variable OH Machine A (0.6/0.25 hrs @ `80 p.h.) (`) 48 20 Variable OH: Machine B (0.5/0.55 hrs @ `100 p.h.) (`) 50 55 Total Variable Cost p.u. (`) 118 95 Contribution p.u. (`) 27 20 Number of parts can be manufactured on the basis of: Alloy Available (13000kg ÷ 1.6/1.6) 8,125 8,125 Machine A (4000 hrs ÷ 0.6/0.25) 6,666 16,000 Machine B (4500 hrs ÷ 0.5/0.55) 9,000 8,181 Maximum units that can be manufactured 6,666 8,125 Total Contribution (6,666 units × 27; 8,125 × 20) 179,982 162,500 Hence it is recommended to produce Part A. (b) Parts A to be Manufactured 6,666 units Hours utilized Idle hours Machine A usage (6,666 × 0.6) 3,999.6 0.4 Machine B usage 3,333 1167 Compensation for unutilized machine hour (1167.4 @ Rs 60/ hour) `70,044 Revised contribution after reduction of 10% in S.P. [6,666 × (145 × 0.9 – 118)] `83,325

290

Total Contribution `153,369

Ans. 85:

Cutting Finishing Capacity (units) 10,000 5,000 Selling Price 1000 Material Cost 400 Throughput contribution 600 `/u.

(i) Throughput Contribution 600

Subcontracting changes

400 200

Increase in throughput contribution = 200 x 5000 = 10,00,000

(ii) Already cutting has surplus capacity. It is not a bottleneck. Do not outsource as there will be no benefit, instead there will be reduction of or throughput contribution of outsourced.

(iii) Cutting has surplus capacity. Do not increase non-bottleneck capacity.

Contribution analysis: Ans. 86:

Product X Product Y ` ` Selling price 288 432 Variable costs: Direct materials 40 80 Direct Labour: 48 72 24 48 72 − − 96 Variable overheads 32 28 Total variable costs 216 324 Contribution per unit 72 108

The direct labour hours required to manufacture the two products in each of the four departments at the wage rate of `8 per hour are as under:

Department Product X Product Y Wage cost Hours/unit Wage cost Hours/unit

1 48 6 72 9 2 24 3 48 6 3 72 9 − − 4 − − 96 12

Department 3 is used only for product X and department 4 is used only for product Y. Hence, these two departments will determine the maximum production of these two products as under:

Department 3 : Maximum available hours:

Workers × Hours/day × Days/year 27 × 8 × 300 = 64,800 hours

291

Maximum possible production of product X:unit per hrs 9

64,800= 7,200 units

Department 4 : Maximum available hours:

Workers × Hours/day × Days/year 36 × 8 × 300 = 86,400 hours

Maximum possible production of product Y:unit per hrs 12

86,400= 7,200 units

The company can produce 7,200 units each of products X and Y provided departments 1 and 2 have capacity to process this quantity of output.

We can check the capacity of departments 1and 2 as under:

Department 1: Maximum available hours:

Workers × Hours/day × days/year 45 × 8 × 300 = 1,08,000 hours Hours required to produce 7,200 units each of X and Y: Product X 7,200 × 6 hours = 43,200 hours Product Y 7,200 × 9 hours = 64,800 hours Total = 1,08,000 hours Department 1 has capacity to produce 7,200 units each of products X and Y. Department 2 : Maximum available hours:

Workers × Hours/day × days/year 24 × 8 × 300 = 57,600 hours Hours required to produce 7,200 units each of X and Y: Product X 7,200 ×3 hours = 21,600 hours Product Y 7,200 × 6 hours = 43,200 hours Total = 64,800 hours Department 2 has scarce capacity. Since department 2 capacity is scarce, link the contribution to the key factor of department 2 hours as under:

Product X Product Y Contribution per unit 72 108 Department 2 hours per unit Hours

3 6

Contribution per hour of Department 2 ` 24 18 Rank 1 2

Optimal product mix:

Product Max. units

Lab. Hours/unit

Prod. units

Hours used

Balance hours

Cont./unit Total cont.

` ` X 7,200 3 7,200 21,600 36,000 72 5,18,400 Y 7,200 6 6,000 36,000 − 108 6,48,000

Total optimal contribution 11,66,400 Fixed costs 5,00,000 Optimal profit 6,66,400

Alternative Solution:

292

The maximum possible production of product X is 7,200 units and that of product Y is 7,200 units. The following two methods shall be used to determine the optimal profit:

(a) Produce 7,200 units of product X and use the balance capacity to produce product Y. (b) Produce 7,200 units of product Y and use the balance capacity to produce product X.

Profitability based on (a):

Direct labour hours are scarce in Department 2. Maximum available hours in Department 2 57,600

Product X requires 7,200×3= 21,600 hours Balance hours on Y 36,000

Production of Y 36,000 ÷ 6= 6,000 units

Contribution: X 7,200 units @ `72

`5,18,400

Y 6,000 units @ `108

`6,48,000

Total `11,66,400 Fixed costs `5,00,000 Profit `6,66,400 Profitability based on (b): Maximum available hours in Department 2 57,600

Product Y requires 7,200×6= 43,200 hours Balance hours on X 14,400

Production of X 14,400 ÷ 3= 4,800 units

Contribution: X 4,800 × 72 `3,45,600

Y 7,200 × 108 `7,77,600

Total `11,23,200

Fixed costs `5,00,000

Profit `6,23,200

Profitability of (a) is better.

(a) Statement of Cash Receipts, Disbursements and cumulative difference in Cash flows for four years taken together under both alternatives

Ans. 87:

(`in thousands)

Alternatives Keep old machine Buy new machine Year

1 2nd 3rd & 4th

All 4 years

year each

Year 1 2nd 3rd & 4th

All 4 years

year each

Cumulative difference in cash flows

for four years taken

together Receipts Sales revenue 150 150 600 150 150 600 Self of old - - - 8 - 8

293

equipment Total receipts : (A)

150 150 600 158 150 608

Disbursements Annual operating cost

15 15 60 9 9 36

Other cash costs 110 110 440 110 110 440 Purchase cost of “old” machine

20 - 20 20 - 20

Purchase of “new” machine

- - - 24 - 24

Total disbursements : (B)

145 125 520 163 119 520

Net cash in-flows: (A)-(B)

5 25 80 (5) 31 88 08

(b) Statement of income for each of the four years and cumulative difference in operating income. Alternatives Keep old machine Buy new machine 1st, 2nd 3rd &

4thAll

years year each

Year 1 2nd 3rd & 4th

All 4 years

year each

Cumulative difference operating income

Income Sales revenue 150 600 150 150 600 Total revenue : (A) 150 600 150 150 600 Costs: Annual operating cost

15 60 9 9 36

Other cash costs 110 440 110 110 440 Depreciation 5 20 6 6 24 (Refer to working note 1) Loss on the disposal of old machine

- - 12 - 12

(Refer to working note 2) Total costs: (B) 130 520 137 125 512 Operating income: (A)-(B)

20 80 13 25 88 08

(c) The purchase of cost old machine `20,000; the sale revenue `1.50,000 and other cash costs of `1,10,000 as irrelevant items for the presentation in requirements (a) and (b) above. These items are irrelevant because their amounts are common to both the alternatives.

(d) The net difference in requirements under (a) and (b) will not change if the cost of ‘old’ machine becomes `10,00,000 instead of `20,000. This is so because the cost of old machine is common for both the alternatives.

(e) In the decision about eh replacement of machine the book value of the machine is irrelevant because it is a past (historical) cost. All past costs are down the drains. Nothing can change what has already happened. As apparent from (a) and (b) above; we can completely ignore the cost of old machine i.e. `20,000 and still have a correct analysis.

294

Working note: 1. Depreciation (according to straight line method): Old machine New machine (i) cost of machine (`) 20,000 24,000 (ii) Terminal disposal value Zero Zero (iii) Useful life 4 4

Depreciation

(iii)

(ii) -(i)` 5,000 5,000

2. Loss on the disposal of old machine: ` `

Purchase price of old machine 20,000 Disposal value 10,000 Less: Removal cost 2,000

8,000 12,000

Evaluation of Make or Buy proposal

Ans. 88:

(All figures are in lakhs in rupees)

Year P.V. factors at 10%

When the component is manufactured

When the component is bought from an outside supplier

Cash outflow (Capital cost + manufacturing cost + opportunity cost)

Present Value Cash outflow (Buying cost)

Present Value

` ` ` ` (a) (b) (c) (d)=(b)×(c) (e) (f)=(b)×(e)

0 1.000 4 4.000 - - 1 0.909 6+2 7.272 9 8.181 2 0.826 7+2 7.434 10 8.260 3 0.751 8+2 7.510 11 8.261 4 0.683 10+2 14 8.196

Total 9.562

34.412

−=

outside. frombought iscomponent

the whenoutflow, cashof valuepresent Total

internallyedmanufactur iscomponent

the whenoutflow, cashof valuepresent total

outside) frombrought (whenoutflow cash in Saving

24.264

= `24.412 – `34.264

= `0.148 (lakhs)

Conclusion: Since there is a saving of `0.148 (lakhs) in buying the component from outside, therefore, we should stick to this decision.

295

Note: The loss of `2 lakhs cash inflow for each of the four years due to the inability of the firm to operate another machine if it manufactures the component has been treated as an opportunity cost.

Proposal I Ans. 89:

Statement of sales revenue of mild Year (a) Quantity of mild in

metric tonnes (b) Price per metric tonne (c)

Total amt of sales in (`Lacs) (d) = (b) * (c)

Discount factor @ 12% (e)

NPV of sales (`In lacs) (f) = (d) * (e)

1 2 3 4 5

15,000 15,000 15,000 15,000 15,000

950 900 850 800 750

142. 5 135.0 127. 5 120.0 112. 5

0.89 0.79 0.71 0.64 0. 57

126.825 106.65 90. 525 76.800 64.125

464. 925 Proposal II Year (a)

Quantity of medium in metric tones (b)

Price per metric tone (c)

Variable cost per metric tone (`) (d)

Net price per metric tone (`) (e) =(c)– (d)

Net sales revenue in (`Lacs.) (f) = (b) * (e)

Discount factor @ 12% (g)

PV of net sales revenue (`Lacs.) (h) = (f) * (g)

1 2 3 4 5

1,000 2,000 3,000 4,000 5,000

1,200 1,300 1,400 1,500 1,600

200 200 200 200 200

1,000 1,100 1,200 1,300 1,400

10 22 36 52 70

0.89 0.79 0.71 0.64 0.57

8.90 17.38 25.56 33.28 39.90

Total 125.02 Note: since the selling price of medium is not given after second year, therefore an individual is free to talk any selling price after second year. In view of this assumption the answer of each case may differ. Year (a) Quantity of mild

in metric tones (b)

Price per metric tone (`) (c)

Sales revenue in (`Lacs) (d) = (b) * (c)

Discount factor @ 12% (e)

PV of sales revenue in (`Lacs) (f) = (d) * (e)

1 2 3 4 5

14,000 13,000 12,000 11,000 10,000

950 900 850 800 750

133 177 102 88 75

0.89 0.79 0.71 0.64 0.57

118.37 92.43 72.42 56.32 42.75

Total 382.29 Total present value of sales of medium and mild under proposal II (`Lacs) 507.31 (`125.02 lacs – `382.29 lacs) Total net present value under proposal II (`507.31 lacs – `30 lacs) The net present value under proposal I is `464.925 lacs, and that under proposal II is `477.31 lacs. A comparison of the net present value under two proposal clearly shows that the proposal II is better as it yield a higher net present value of revenue, therefore it should be accepted. Ans: 90 (i) 15,000 tins scrapped per month can be converted into 75,000 lids. (Each rejected tin can be converted into 5 lids) unusable tins are sold as scrap at `8 per unit. Hence, `8 can be taken as raw material cost for conversion into lids. 15,000 tines at `8 1,20,000 Add: Conversion cost `50 per 100 pieces. i.e. 50 paise per piece. 15000 x 5 = 75,000 lids x 0.50 = 37,500

296

3,000 3,000 33,000 29,000

33,000 26,000

4,000 7,000 5,000 2,000

Total cost of 75,000 lids 1,57,500 Less: Value of scrapped lids and off-cuts. Weight of tins: 15,000 kgs. 75,000 x 120 gms 1,000

= 9,000 kgs

Weight of scrap .

Sales value of scrap 6,000 x 5 6,000 kgs.

Net cost of 75,000 lids 30,000 1,27,500

Cost of each lid 1,27,500 / 75,000 `1.70

Cost of buying one lid `2.00 Hence, there will be a saving of 30 paise on each lid converted instead of buying from outside. In view of saving , the proposal should be accepted. `lakhs (ii) Saving in year: Buying 1,00,000 lids x 12 Months x `2.00 24.00 Less: Conversion cost: 75,000 lids x 12 months x 1.70 = 15.30 Cost of buying the balance lids = 25,000 lids x 12 months x 2.00 = 6.00 Saving in a year

21.30

2.70

Or else, 75,000 lids x 12 months = 9,00,000 lids at Re. 0.30 each = `2,70,000 savings in a year accrue to the company if the proposal is accepted. Ans. 91:

Selling Price `/u

Order Qty 100-140 (`)

Order Qty 141-200 (`)

30,000 30,000 Commission @ 10% Sales revenue p. u. Less: Variable purchase cost Contribution / unit (before shipping) Less: Shipping cost > 110 units Contribution/ units after Shipping (i) Upto 110 units, Reference will earn a contribution of `4,000/u.

(ii) Between 110 & 140 units, contribution of 4,000 will be wiped out by 5,000 on shipping costs. Hence we should not consider 110 – 140 range.

(iii) 101 – 110 not to be considered since additional fixed costs 2,25,000 will not be covered by 10 units.

(iv) Valid consideration, 100 units or 141 to 190 units. Fixed cost of box of 50 cameras is `2,25,000

297

Units No. of Camera Boxes Cost of Cameras (`) Contribution (Rs/u) `4,000 Contribution (`) first 110 units @ 7,000/u Contribution (`) Balance units @ 2,000/u Total Contribution (F

A B

C

D

E

F

100 2

4,50,000

400,000

4,00,000

- 50 000

141 3

6,75,000

7,70,000

62,000

8,32,000

1 57 000

150 3

6,75,000

7,70,000

80,000

8,50,000

1 75 000

190 4

9,00,000

7,70,000

1,60,000

9,30,000

30 000 Best strategy buy 150 units from Comp. sell 110 at store and 40 outside. BEP

should be between 151 – 191 units

Extra Camera box cost beyond 150 units = 2,25,000

Less: Profit for 150 units = 1,75,000

Extra profit acquired = 50,000

No. of units to cover this additional costs at contribution 2000 `/u =25

∴BEP = 150 + 25 = 175 units

298

Miscellaneous Theory Chapters

Ans. 6:

(a) Calculation of cost of per 100 units of good components: (A) X Ltd. Y Ltd.

If not inspected Units required 10,000 10,000 Estimated defectives 300 500 (3%) (5%)

Cost Purchase price (Rs.) Production damage (Rs.) Total Cost (Rs.) Good component (units) Cost per 100 good component (Rs.)

Rs. 18,000

540 18,540

9,700 191.13

Rs. 17,400

900 18,300 9,500

192.63

(B)

If inspected

Defectives not detected 30 50 Defectives detected 270 450 Components paid for 9,730 9,550

Cost Rs. Rs.

Purchase cost 17,514 16,617 Inspection cost 2,400 2,400

Production damage 54 90

Total cost 19,968 19,107

Good components 9,700 9,500 Cost per 100 good components (Rs.) 205.86 201.3

Decision: (i) On the basis of the cost per 100 good component calculated at (A) and (B) above, it is

concluded that inspection at the point of receipt is not justified.

(ii) It will be advantageous to purchase the component from X Ltd. Ans. 1.

7: 2003 2004

a. Percentage of defective units shipped

40010,000

= 4%

33011000

= 3%

b. Customer complaints as a percentage of units shipped

50010000

= 5% 51711000

=4.7%

c. On-time delivery 8500 10000

= 85% 990011000

= 90%

d. Percentage of units reworked during production

600 10000

=6% 62711000

=5.7%

299

2. The calculations in requirement I indicate that ESC’s performance on both quality and timeliness has improved. Quality has improved because (a) percentage of defective units shipped has decreased from 4% to 3%,(b) customer complaints have decreased from 5% to 4.7% , and (c) percentage of units reworked during production has decreased from 6% to 5.7% . Timeliness has improved as on –time delivery has increased from 85 % to 90% . Of course , there is a relationship between the improvements in quality and timeliness. Better quality and less rework reduces delays in production and enables faster and on-time delivery to customers. 3a. 2003 2004 The output per labor- hour Between 2003 and 2004 10000 =0.11 11000Can be calculated as follows 90000 110000

=0.10

3b . Output per labor-hour may have declined from 2003 and 2004 either because workers were less productive or more likely because the initial implementation of the quality program may have resulted in lost production time as employees were trained and became more adept at solving production quality problems. As workers implement good quality practices and defects and rework decrease over time, it is possible that both quality and productivity (output per labor-hour) will increase. 3c. it is not clear that the lower output per labor-hour will decrease operating income in 2004. the higher labor costs in 2004 could pay off in many ways. Higher quality and lower defects will likely result in lower material costs because of lower defects and rework. Internal and external failure costs will also be lower, resulting in lower customer returns and warranty costs. Customer satisfaction will likely increase, resulting in higher sales, higher prices, and higher contribution margins. Indeed the 10% increase in the number of units produced and sold in 2004 may well have been due to quality improvements. Overall, the benefits of higher quality in 2004 may very well exceed the higher labor costs per unit of output. Ans.

8: (i) Classification of Quality Costs Figures Rs. ’000

2007 % of sales 2008

% of sales

Sales 6,000 6,000 Prevention Quality training 75 1.25 150 2.5 Appraisal Product Inspection 200 240 Materials Inspection 80 60 280 4.67 300 5 Internal Failure Scrap 600 300 Rework 500 400 1100 18.33 700 11.67 External Failure Product warranty 300 5 150 2.5 1755 29.25 1300 21.67

(ii) Cost reduction was effected by 7.58% (29.25 – 21.67) of sales, which is an increase in profit by Rs.4,55,000. (6 Marks) Nov/08-NC& ICWA-June/03 [Adapted] Ans. 9

Ascertainment of Total cost

: Had there been no defectives for production of 1,00,000 pieces of P 1,00,000X5=5,00,000 units of raw material would be required. In case of high quality material , defective being 10% total raw material required is 5,00,000 units/0.90 =5,55,556 units. In case of lower quality material, defective being 20%, total raw material requirement is 5,00,000 units/0.08 =6,25,000 units. Similarly labour and variable overhead requirement are to be adjusted accordingly.

I. Using high quality materials (scrap 10%) (Rs) Material (5,00,000 units/0.90X Rs.1.05) 5,83,333 Labour (2,50,000 hours/0.90X Rs.0.50) 1,38,889 Variable overhead (Rs.1,00,000/0.90) 1,11,111

300

Fixed overhead 50,000 Less: Scrap (5,00,000/0.90)-5,00,000)XRe.0.30 8,83,333 16,667 Cost of 1,00,000 pieces of P 8,66,666

II. Using lower quality materials (scrap 10%) (Rs)

Material (5,00,000 units/0.80X Rs.0.80) 5,00,000 Labour (2,50,000 hours/0.80X Rs.0.50) 1,56,250 Variable overhead (Rs.1,00,000/0.80) 1,25,000 Fixed overhead 50,000 Machine and Tooling cost 3,000 Additional laboour (1,00,000units X 0.5hours XRe.0.50) 2,500 Additional overhead for additional labour

(1,00,000 units x 0.5 hours)X (Rs.1,00,000/2,50,000 hours)

20,000

8,79,250 Less: Realizable value of scrap 5000 Cost of 1,00,000 pieces of P 8,74,250

Analysis: Hence the high quality material should be used. Ans. 10(I) If each components is tested before being sent to the agents for sales

:-Let the defectives be’d’

No: of components in a batch Rs.2000 Cost of testing each components Rs.20 Cost of rectification before dispatch Rs.200 Total Cost Rs.(2000x25)+200d

(II) If components dispatch without pre-testing and defectives received back for rectification under warranty. Total Cost 400d In difference point of two alternatives (2000x25)+200d 400d 400d-200d 2000x25 200d 50,000 D 50000/20 250 Defective Components 250 components Percentage of defectives to total components 250/2000*100 =12.5% Analysis: If defectives exceed 12.5% of the total number of components per-testing is recommended. Ans. 11

Cost per unit. (Rs.) : Present Position (Based on 1,000 units Production)

Direct material 10 Direct wages (8 hours @ Re.0.50) 4 Overheads (8 hours @ Rs.1.75) 14 Total 28

Per unit Units Total

Particular Sales price Profit / Loss Profit Loss Firsts 30 2 900 1,800 - Seconds 20 (-) 8 50 - 400 Thirds 10 (-) 18 50 - 900 1,800 1,300 Net Profit 500

Reprocessing of Inferior units (a) Additional expenditure for reprocessing per unit (Rs.) Direct Material 4 Direct Wages 8 hrs. 4 Variable overhead @ 0.875 7 15 Total expenditure for 100 units Rs.1,500

301

.

(b) Additional Revenue (Rs.) Second (Rs.30-Rs.20)x50units 500 Thirds (Rs.30-Rs.10)x50 1000 1500

Note: No change in the profit position hence this need not be considered.

Ans. 1

2: (a)

Existing After TQM

Programme

i. Total production units (Preinspection)

Total sales requirements 5,000 5,000

Specification losses 5% 250 2.5% 125

5,250 5,125

Downgrading at inspection

×5.875.12 5,250

750

×5.925.7 5,125

416

Total units before inspection 6,000 5,541

ii Purchase of material ‘X’(Sq Mtr)

Material required to meet pre inspection production requirement 6,000 × 8 SqMtr

48,000 SqMtr

5,541×8 SqMtr

44,328 SqMtr

Processing loss ×964 48,000 2,000

×5.975.2 44,328

1,137

Input to the process 50,000 45,465

Scrapped material ×955

50,000

2,632

×973 45,465

1,406

Total purchases 52,632 46,871

iii Gross Machine Hours

Initial requirements 6,000 × 0.6

3,600 5,541 × 0.5 2,771

Idle time ×8020 3,600 900 ×

5.875.12 2,771 396

Gross time 4,500 3,167

(b) Profit and loss statement

Rs Rs

Sales revenue 5,000 Units× Rs 1,000

50,00,000

50,00,000

Sales downgraded 5,25,000 416 Units × Rs 700 2,91,200

302

750 Units×Rs 700

55,25,000

52,91,200

Costs:

Material 52,632 Sq Mtr ×Rs 40 21,05,280

46,871Sq Mtr × Rs 40

18,74,840

Inspection and storage costs 52,632 Sq Mtr ×Re 1

52,632

46,871Sq Mtr × Re 1

46,871

Machine cost 4,500 Hrs × Rs 400

18,00,000

3,167 Hrs× Rs 400 12,66,800

Inspection and other cost 2,50,000 2,50,000 × 60% 1,50,000

Product liability (3% × 50,00,000

1,50,000 1% × 50,00,000 50,000

Sundry cost of selling, distribution and administration.

6,00,000

6,00,000 × 90%

5,40,000

Preventive programme cost 2,00,000 6,00,000

51,57,912

45,28,511

Net profit 3,67,088 7,62,689 Ans. 13(a) (i) Units

:

Components worked on in the process 6120 Less: planned defective units 612 replacements to customer (2% X 5400) 108 Components invoiced to customers 5400 Therefore actual result agree with planned results (ii) Planned components cost = (3 X Rs.18 for material A) + (2 X Rs.9 for material B) + Rs.15 variable cost =Rs.87 Comparing with the data in appendix: Materials = Rs.440 640/6120 =Rs.72 Variable overhead = Rs.91 800/6120 = Rs.15 This indicates that prices were at the planned levels. (b) Internal failure costs = Rs.53 244(612 units X Rs.87) External failure costs = Rs.9396 (108 units X Rs.87) (c) (i) Period 2 (units) Period 3 (units) Components invoiced to customers 5500 5450 Planned replacement (2%) 110 109 Unplanned replacement 60 (170-110) -69 (40-109) Components delivered to customers 5670 5490 Planned process defects (10% of worked on in the process) 620 578 Unplanned defects (difference to agree with with final row) -90 -288 Components worked on in the process 6200 5780 (ii) Period 2(Rs.) Period 3(Rs.) Internal failure costs 46,110 (620-90) XRs. 87 25,230 (578-288) X Rs.87 External failure costs 14,790 (110+60) X Rs.87 3,480 (109-69) X Rs.87 Appraisal costs 10,000 15,000 Prevention costs 5,000 8,000 (iii) The following points should be included in the report:

303

1. Insufficient detail is provided in the statistics shown in the appendix thus results in the need to for an improvement in reporting.

2. The information presented in (c) (i) indicate that free replacement to customers were 60 greater than planned in period 2 but approximately 70 less than planned in period 3. in contrast, the in process defects were 90 less than planned (approximately 15%) in period 2 and 288 less than plan (approximately 50%) in period 3.

3. Internal failure costs show a downward trend from period 1-3 with a substantial declined in period 3.External failure costs increased in period 2 but declined significantly in period 3.

4. The cost savings arising in period 2 and 3 are as follows: Period 2(Rs.) Period 3(Rs.) Increase /decrease from previous period: Internal failure costs -1734(Rs.53244-Rs.46110) -20880(Rs.46110-Rs.25230) External failure +5394(Rs.9396-Rs.14790) -11310(Rs.14790-Rs.3480) Total decrease -1740 -32190 The above savings should be compared against the investment of Rs.10000 appraisal cost and Rs.5000 prevention cost for period 2 and Rs.15,000 and Rs.8,000 respectively in period 3. it can be seen that the cost exceed the savings in period 2 but the savings exceeds the cost in period 3. There has also been an increase in the external failure cost from period 1 to period 2. Investigations should me made relating to the likely time lag from incurring prevention/appraisal costs and their subsequent benefits. 5. The impact on customer goodwill from the reduction in replacements should also be explained.

Return of 12% net (after tax of 40%) on capital employed is equivalent to 12%÷(1-0.4) = 20% (gross) on capital employed.

Ans. 27:

Let selling price per unit to be ‘x’

Since Total sales = Total cost + profit

i.e., 80,000x = 14,60,000+20% (12,00,000+0.5×80,000×)

Or, 80,000x = 14,600+2,40,000+8,000x

Or, 72,000x = 17,00,000

Or, ‘x’ = 000,72

000,00,17 = Rs. 23.61

Hence selling price per unit will be Rs. 23.61

Ans. 28:

(i) Statement showing price of Product Z

Direct Material Deptt. A 30 Deptt. B 25 55

Direct Labour Deptt. A 30

Deptt. B 40 70

Variable overhead Deptt. A 3×6 18

Deptt B 4×3 12 30

Variable selling and distribution overhead 30,000/1,500 20

Total Variable Cost per unit 175

Total hours required for a target of 1,500 units of product Z

304

Deptt. A1500 × 3 4500 hours

Deptt. B1500 × 4 6000 hours

10500 hours

10500 hours represent 30% capacity

So total capacity per month 10500 / 0.30 = 35000 hours. Yearly

capacity is 35000 × 12 = 420000 hours.

Fixed capital employed in both department = 40.00 Lakhs

(25 lakhs + 15 Lakhs)

Expected return = 0.21 × 40,00,000 = 840000

Contribution per hour = 840000 / 4200000 = 2.00 per hour

Working Capital = 0.21 × 400000 = 84000

Contribution per unit 84000 / 18000 unit = 4.67 per unit

Total contribution required Rs.

To cover fixed cost 3 hours of A and 4 of B = 7 × 2 = 14.00

To working capital = 4.67

18.67

Fixed charges recovery is based on usage. Full capacity is not being used by product Z and departments are also producing other products using same plant and machinery. Price of Product = Variable cost + contribution required = 175 + 18.67 = 193.67 per unit.

(ii) Price of product when product is well established in market:

Variable Cost 175 Fixed Cost (24 + 16) 40 Total price 215 The product is first time launched in the market, and then variable cost Rs.175 should form the basis for price fixation.

(a) Rs./u of alloy Ans. 29:

Materials:

Iron 10kg @ Rs.5/- 50 Copper 5 kg @ Rs.8/- 40 90

Wages X : 3 hrs @ 15 Rs./Hr. 45 Y : 5 hrs @ 12 Rs./Hr 60 105

Variable OH (Production) X : 8 hrs × 3 hrs 24 Y : 5 hrs × 5 hrs 25 49

305

Variable OH – Selling 20 Total Variable Cost 264 Fixed Off:

X : 8/hrs × 3 hrs. 24 Y : 5/hrs × 5 hrs 25 49

Total Cost 313 (i) If pricing strategy is to penetrate the market, the minimum price for a new product

should be the variable cost i.e. Rs.264/-. In some circumstances, it can also be sold below the variable cost, if it is expected to quickly penetrate the market and later absorb a price increase. Total Variable Cost is the penetration price.

(ii) When the alloy is well established, the minimum selling price will be the total cost – including the fixed cost i.e. Rs.313 per unit. Long run costs should cover at least the total cost.

Ans. 30: Sales in X (rearranged for the purpose of ranking

XYZ Ltd.

Rank Category Stock(Rs.’000) Cum. Sales(Rs.’000) % )

1 OTC 175 175 21.9 2 Toiletries 150 325 40.6 3 Photo 125 450 56.3 4 Food/ Drink 100 550 68.8 5 Baby 50 600 75.0 5 San. Prod. 50 650 81.3 5 Other 50 700 81.3 8 Foot Care 30 730 91.3 9 Cosmetics 25 755 94.4 10 Hair-care 25 780 97.5 11 Perfume 20 800 100.0 Stock in X (rearranged for the purpose of ranking) Rank Category Stock(Rs.’000) Cum. Sales(Rs.’000) % 1 Toiletries 60 60 26.1 2 Cosmetics 40 100 43.5 3 OTC 35 135 58.7 4 Photo 20 155 67.4 4 Food/ Drink 20 175 76.1 6 Other 13 188 81.7 7 Baby 10 198 86.1 7 San. Prod. 10 208 90.4 7 Hair 10 218 94.8 7 Perfume 10 228 99.1 11 foot care 2 230 100.0 Sales in Z (Rearranged for ranking) Rank Category Stock(Rs.’000) Cum. Sales(Rs.’000) % 1 OTC 120 120 24 2 Toiletries 100 220 44 3 Food/ Drink 75 295 59 4 Photo 60 355 71 5 Cosmetics 30 385 77 6 Baby 25 410 82 6 San. Prod. 25 435 87 6 Other 25 460 92 9 Foot care 20 480 96 10 Hair 10 490 98 11 Perfume 10 500 100

306

Sales in Z (Rearranged for ranking) Rank Category Stock (Rs.’000) Cum. Sales(Rs.’000) % 1 Toiletries 65 65 30.2 2 Cosmetics 45 110 51.2 3 OTC 40 150 69.8 4 Food/ Drink 20 170 79.1 5 Photo 12.5 182.5 84.9 6 Perfume 7.5 190 88.4 7 Baby 5 200 93.0 7 San. Prod. 5 200 93.0 7 foot care 5 205 95.3 7 Hair 5 210 97.7 7 Other 5 215 100.0

Ans. 46:

Annual Relevant Costs of Current Production System and JIT Production System for Evans Corporation.

Relevant

Relevant Costs under

Costs under

Current JIT Production Production

Relevant Items System Annual tooling costs - Rs.1,50,000

System

Required return on investment: 12% per year x Rs.9,00,000 of average inventory per year Rs.1,08,000 - 12% per year x Rs.2,00,000 of average inventory per year - 24,000 Insurance , space, materials handling , and setup costs 2,00,000 1,40,000Rework costs 3,50,000 2,80,000

a

Incremental revenues from higher selling prices - (90,000)b

Total net incremental costs c

Rs.6,58,000 Annual difference in favor of JIT production Rs.1,54,000

Rs.5,04,000

aRs. 200,000 (1-0.30) = Rs.140,000 bRs. 350,000 (1-0.20) = Rs.280,000 c

Rs. 3x30,000 units = Rs.90,000

(a) Personal observation by production line workers and managers is more effective in JIT plants than in traditional plants. A JIT plant’s production process layout is streamlined. Operations are not obscured by piles of inventory or rework. As a result, such plants are easier to evaluate by personal observation than cluttered plants where the flow of production is not logically laid out. Besides personal observation, non financial performance measures are the dominant methods of control. Non financial performance measures provide most timely and easy to understand measures of plant performance. Examples of non financial performance measures of time, inventory, and quality include:

• Manufacturing lead time • Units produced per hour • Machine setup time / manufacturing time4 • Number of defective units / number of units completed.

In addition to personal observation and non financial performance measures. Financial performance measures are also used. Examples of financial performance measures include.

• Cost of rework • Ordering costs • Stock out costs • Inventory turnover

(3b) The success of a JIT system depends on the speed of information flows from customers to manufactures to suppliers. The Enterprise Resource Planning (ERP) system has a single database, and gives lower-level managers, workers, customers, and suppliers access to operating information. This benefit, accompanied by tight coordination across business function, enables the ERP system to rapidly transmit information in response to changes in supply and demand so that manufacturing and distribution plans may be revised accordingly. Ans. 47: (i) Comparative Statement of cost for purchasing from Y Co Ltd under current policy & JIT

307

Particulars Current Policy JIT Rs Rs Purchasing cost 18,20,000 18,20,260 (13,000 × 140) (13,000 × 140.02) Ordering cost 26 260 (2×13 orders) (2×130 orders) Opportunity carrying cost 10,500.00 1,050.15 (1/2×1000×140×15%) (1/2×100×140.02×15%) Other carrying cost(Insurance, material handling etc) 1,550.00 155 (1/2×1000×3.10) Stock out cost 200 (4 × 50) Total relevant cost 18,32,076 18,21,925.15

Comments: As may be seen from above, the relevant cost under the JIT purchasing policy is lower than the cost incurred under the existing system. Hence, a JIT purchasing policy should be adopted by the company. (ii) Statement of cost for purchasing from Z Co Ltd.

Particulars Rs. Purchasing cost 1,76,800 (13,000x13.60) Ordering Cost 260 (2x130 orders) Opportunity Carrying 102 Cost (1/2×100×13.60× 15%) Other Carrying Cost 150 (1/2×100×3.00) Stock out Cost 2,880 (8x360) Inspection Cost 650 (13,000 x .05) Customer Return Cost 6,500.00 ( 13,000 x 2% x 25) Total Relevant Cost 1,87,342

Comments : The comparative costs are as follows, Under current policy Rs 18,32,076.00 Under purchase under JIT Rs 18,21,925.10 Under purchase from Z Co Ltd Rs 1,87,342.00 Packages should be bought from Z Co as it is the cheapest.

308

A B Rs.

4 2 10 1 1 4

80 60

1

Ans:7 Linear Programming

The problem may be summarized as follows:

Chemical Chemical Cost per mix

Supplier X Supplier X2

Units required

Let x1 be the number of mixes to be purchased from supplier X1 and x2 be of those to be purchased from supplier X2.

The conditions of the problem when symbolised, take the form: Minimize Z = 10 x1 + 4 x2 Subject to the restrictions x1 ≥ 0, x2 ≥ 0 4x1 + x2 ≥ 80, 2x1 + x2 ≥ 60. For the line 4x1 + x2 = 80, let x1 = 0,so that x2 = 80; let x2 = 0,so that x1 = 20. For the line 2x1 + x2 = 60, let x1 = 0,so that x2 = 60; let x2 = 0,so that x1 = 30.

Feasible region is shaded in the diagram which appears to be unbounded. We now try to deter- mine the additional hidden conditions in the problem for which the feasible region becomes bounded. The column vector for the values of the objective function is given by

309

Since 260 is the smallest element in EC, the minimum value is reached at the extreme point E2, whose coordinates are (10,40).

Thus, to honour the contract and yet to minimize cost, the company should purchase 10 mixes from X1 and 40 mixes from X2. Ans.8:

Maximize z = 80x + 100y subject to x + 2y ≤ 720 5x + 4y ≤ 1800 3x + y ≤ 900 x ≥ 0 y ≥ 0 where x = No. of units of A y = No. of units of B

By the addition of slack variables s1, s2 and s3 the inequalities can be converted into equations. The problem thus become

z = 80x + 100y subject to x + 2y + s1

5x + 4y + s = 720 2

3x + y +s = 1800

3

and x ≥ 0, y ≥ 0, s = 900

1 ≥ 0, s2 ≥ 0, s3

Table I ≥ 0

80 100 0 0 0 Profit/unit Qty. X Y S S1 S2 3 S 0 1 720 Ι 2 1 0 0 360

2720

=

S 0 2 1800 5 4 0 1 0 1800/4 = 450

S 0 3 900 3 Ι 0 0 1 900/1 = 900 Net evaluation row

80 100 0 0 0

1800 – 720 ×4/2 = 360 900 - 720×1/2 = 540 5 – I×2 = 3 3 - 1× ½ = 5/2 4 – 2 × 2 =0 I – 2 ×1/2 = 0 0 - I×2 = - 2 0 – I ×1/2 =- 1/2 I - 0×2 = I 0 – 0 ×1/2 = 0 0 - 0×2 = 0 I- 0×1/2 = I

Table 2:

80 100 0 0 0 Program Profit/unit Qty. X Y S S1 S2 3

310

Y 100 360 ½ I ½ 0 0 360÷1/2=720 S2 0 360 3 0 −2 1 0 360÷3=120 S3 0 540 5/2 0 −1/

2 0 I 540÷5/2=216

Net evaluation row

30 0 −50 0 0

360 – 360 × 1/6 = 300 540 – 360 × 5/6 = 240 ½ - 3 ×1/6 = 0 5/2 –3 × 5/6 = 0 1- 0× 1/6=1 0 – 0 × 5/6 = 0 ½ - -2 × 1/6 = 5/6 -1/2 - -2 ×5/6 = 7/6 0 – 1 ×1/6 = - 1/6 0 – 1 × 5/6 = -5/6 0 – 0 ×1/6 = 0 1-0 × 5/6 = 1

Table 3:

80 100 0 0 0 Program Profit/unit Qty. X Y S S1 S2 Y

3 100 300 0 I 5/6 -1/6 0

X 80 120 I 0 −2/3 1/3 0 S3 0 240 0 0 7/6 -5/6 I Net evaluation row

0 0 -500/6 +160/3

+100/6 -80/3

0

= 6

180 = 660

−

All the values of the net evaluation row of Table 3 are either zero or negative, the optimal program has been obtained. Here X = 120, y = 300 and the maximum profit

= 80×120 + 100× 300 = 9600 + 30,000 = Rs. 39,600. Ans. 9: Formulation of Linear Programming (LP) model :

Let X1 and X2

be the units of products A and B respectively which were manufactured and sold (within sales constraints) by the company in a month, by utilizing monthly available budgeted capacity in department A and B so as to maximize the profit of the company. The formulated LPP based on the given data is as under :

Max Z = 80 x1 + 100 x2

(Refer to working note)

2 x1 + 4x2

< 1,400 -- Department P Constraint

5x1 + 4x2

< 2,000 -- Department Q constraint

X1

< 400 -- Product A Sales constraint

311

X2

< 400 -- Product B sales constraint

X1

, X2 > 0

Graphical Solution : Draw the above four constraints by selecting X1 and X2 axes as shown in the diagram.

X2 - AXIS

X1 < 400 (0,500) X2 <

400

(0,350) P (200, 250) 0 (400,0) (700,0) Put x2 = 0 in (i), then x1

= 700

Put x1 = 0 in (i), then x2

= 350

Put x2 = 0 in (ii); then x1

= 400

Put x1

= 0 in (ii); then x2 = 500

The point of intersection of (i) and (ii) viz, P is given by (200, 250) The marked area represents the feasible area (common to all of the four constraints). The corner points of the identified feasible region are (0,0); (400,0); (200,250) and (0,350). According to Dantzig, the objective function is maximum or minimum at the corner points of the feasible region.

312

Z (0,0) = 0,0 Z (400, 0) = 32,000 Z (0, 350) = 35,000 Z (200, 250) = 41,000 The objective function has maximum contribution viz, Rs. 41,000 at the point (200, 250). Hence, the concern should manufacture and sell 200 units of A and 250 units of B product. Optimal contribution (Rs) 41,000 (200 units x Rs. 80 + 250 units x Rs. 100) Less : Fixed costs 34,000 (Rs. 14,000 + Rs. 20,000) _____ Optimal profit

7,000

Working note : Product A Product B Selling price per unit : (i) 300 200 Variable manufacturing costs 160 60 Sales commission 60

40

Total variable cost per unit : (ii) 220

100

Contribution per unit : (ii – I) 80

100

Ans. 11: Let x1, x2 x3

Then the profit gained by the industry is given by be the number of units produced of products A, B and C respectively.

Z = 3x1 + 8x2 + 2xHere it is assumed that all the units of products A and B are sold.

3

In first operation, A takes 3 h of manufacturer’s time and B takes 4 h of manufacturer’s time. Therefore, total number of hours required in first operation becomes. 3x1 + 4xIn second operation, per unit of A takes 2 h of manufacturer’s time and per unit B takes 5 h of manufacturer’s time. Therefore, the total number of hours used in second operation becomes

2

3x1 + 5xSince there are 18 h available in first operation and 21 h in second operation, the restrictions become

2

3x1 + 4x2 ≤ 18 …… (1)

313

3x1 + 5x2

Since the maximum number of units of C that can be sold is 5, therefore, ≤ 21 …… (2)

X3

Further, the company gets three units of by product C for every unit of product B produced, therefore ≤ 5 …… (3)

X3 = 3x2

Now, the allocation problem of the industry can be finally put in the following linear programming problem:

…… (4)

Maximise Z = 3x1 + 8x2 + 2xSubject to the constraints

3

3x1 + 4x2

3 x ≤ 18

1 + 5x2

x ≤ 21

3 ≤ 5, x3 = 3x x

2

1, x2, x3

Ans. 15: ≥ 0

Let X1, X2 and X3

(i) Phosphorus content must not exceed 0.03%

respectively be the amounts in tons of grades A, B, and C used. The constraints are

.02 X1+ .04X2 + 0.3 X3 ≤ .03 (X1 + X2 + X3

2X)

1 + 4 X2 + 3X3 ≤ 3 (X1 + X2 + X3) or – X1 + X2

(ii) Ash content must not exceed 3% ≤ 0

3X1 + 2 X2 + 5 X3 ≤ 3 (X1 + X2 + X3) or – X2 + 2X3

(iii) Total quantity of fuel required is not more than 100 tons. X ≤ 0

1 + X2 + X3

The Mathematical formulation of the problem is ≤ 100

Maximize Z = 12 X1 + 15X2 + 14 X Subject to the constraints:

3

- X1 + X2

- X ≤ 0

2 + X3

X ≤ 0

1 + X2 + X3

X ≤ 100

1, X2, X3

Introducing slack variable X > 0

4 >0, X5>0, X6

>0

12 15 14 0 0 0 C Yb Xb Yb Y1 Y2 Y3 Y4 Y5 0

6 Y 0 4 -1 1* 0 1 0 0

0 Y 0 5 0 -1 2 0 1 0 0 Y 100 6 1 1 1 0 0 1 Z -12 -15 -14 0 0 0

C Yb Xb Yb Y1 Y2 Y3 Y4 Y5 6

314

15 Y 0 2 -1 1 0 1 0 0 0 Y 0 5 -1 0 2 1 1 0 0 Y 100 6 2* 0 1 -1 0 1 Z -27 -14 15 0 0 C Yb Xb Yb Y1 Y2 Y3 Y4 Y5 15

6 Y 50 2 0 1 1/2 1/2 0 1/2

0 Y 50 5 0 0 5/2* 1/2 1 1/2 12 Y 50 1 1 0 1/2 -1/2 0 1/2 Z 0 0 -1/2 3/2 0 27/2 C Yb Xb Yb Y1 Y2 Y3 Y4 Y5 15

6 Y 40 2 0 1 0 2/5 -1/5 2/5

14 Y 20 3 0 0 1 1/5 2/5 1/5 12 Y 40 1 1 0 0 -3/5 -1/5 2/5 Z 0 0 0 8/5 1/5 68/5 The optimum solution is X1 = 40, X2 = 40 and X3

Ans.16: = 20 with maximum Z = 1360.

Table 1

C

j

Qty

40 60 0 0 0 Ratio

Cj Variable X1 X2 X3 X4 X5

0 X3 36 3 3 1 0 0 12 0 X4 60 5 2 0 1 0 30 0 X5 60 2 6 0 0 1 10 Zj 0 0 0 0 0 0 Zj-Cj -40 -60 0 0 0

Table 2

Cj Qty

40 60 0 0 0 Ratio

Cj Variable X1 X2 X3 X4 X5 0 X3 6 2 0 1 0 - ½ 3 0 X4 40 13/3 0 0 1 -1/3 120/13

60 X2 10 1/3 1 0 0 1/6 30 Zj 600 20 60 0 0 10 Zj-Cj -20 0 0 0 10

Table 3

Cj

40 60 0 0 0

315

Qty Cj Variable X1 X2 X3 X4 X5 40 X1 3 1 0 ½ 0 -1/4 0 X4 27 0 0 -13/6 1 3/4

60 X2 9 0 1 -1/6 0 1/4 Zj 660 40 60 10 0 5 Zj-Cj 0 0 10 0 5

Since all Zj –Cj are positive or zero, this is the optimum solution with, X1 =40 &

X2 = 60 and optimum Z = 660. Note: Alternatively, Cj-Zj may be used whereby maximum positive value may be considered. Ans. 18:

Under the usual notations where S1, S2, S3 are stock Variables, A4 = the artificial variable S4 = Surplus Variable

We have, Max. Z = 100x1 + 80x2 + 0S1 + 0S2 + 0S3 + 0S4 – M A4. S.t.

3x1 + 5x2 + S1 = 150 x2 + S2 = 20

8x1 + 5x2 + S3 = 300 x1 + x2 + - S4 + A4 = 25

x1 x2 S1 S2 S3 S4 A4

Basis Cj

CB

100

80

0

0

0

0

- M

S1

S2

S3

A4

0

0

0

- M

3

0

8

1

5

1

5

1

1

0

0

0

0

1

0

0

0

0

1

0

0

0

0

-1

0

0

0

1

150

20

300

25

√

√

√

√ Zj

Cj-Zj

- M

100+M - M

80+M 0

0 0

0 0

0 M

-M -M

0 -25M √

√ Ans.20:

(i) Simplex Table

Basis

Cj → 8 6 0 0 (1 mark) CB x1 x2 s1 s2

316

X1 X2 S1 S2

X1 8 X 1 = 8 8 X 0 = 0 8 X 1/3 = 2.2/3 8 X - 1/ 1.1/

X2 6 X 0 = 0 6 X 1 = 6 6 X - 1/6 = - 1 6 X 1/3 Adding Zj 8 6 5/3 2/3

x1

x2

Zj

NER

8 6

→ Cj - Zj

1 0

6 0

0 1

6 0

⅓ -⅙

5

3

− 5 3

-⅙ ⅓ ⅔ -⅔

2 marks 1 marks

Note: Zj values are obtained by multiplying each row with cost and adding the values of the respective column as under:

6 =

3 = 2

Net Evaluation Row (NER) is obtained by deducting Zj from Cj as under: 8 – 8 = 0 6 – 6 = 0 0 – 5/3 = - 5/3 0 – 2/3 = - 2/3

Since the values of NER ar≤e 0, the solution represented by this tableau is optimal. (ii)

S1 S2 Rs. M I X1 60 x 5/3 100 M II X2 48 x - 2/3 32 Total optimal contribution 132

Ans.21:

Let pidj be the variable to denote the number of units of product from the ith plant to the jth destination, so that

P1d1 = transport from plant P1 to D1

P2d2 = transport from plant P2 to D2 etc.

Objective function

Minimize z = 400 p1d1 + 600 p1d2 + 800 p1d3 + 1000 p2d1 + 1200 p2d2 + 1400 p2d3

+ 500 p3d1 + 900 p3d2 + 700 p3d3.

Subject to:

p1d1 + p1d2 + p1d3 ≤ 65

p2 d1 + p2 d2 + p2 d3 ≤ 24 (Plant constraints)

p3 d1 + p3 d2 + p3 d3 ≤ 111

and p1d1 + p 2 d1 + p 3 d1 ≥60 p1d2 + p 2 d2 + p 3 d2 ≥ 65 (destination constraints)

317

p1d3 + p 2 d3 + p 3 d3 ≥ 75

all pidj ≥ 0 Ans.22:

Route I Residence HO 600 400 300 180 Residence Route II Residence 500 300 200 40 Br. Residence No. of vehicles 4 10 20 Max. capacity 80 80 100 220 No. of passengers 260

Let i be the ith route,

and j be the type of vehicle, so that

S11 = no. of vans (vehicles on Route I, Type I)

S12 = no. of 8 seater cars on Route I

S13 = no. of 5 seater cars on Route I

S21 = no. of vans ─ on Route II

S22 = no. of 8 seater cars on Route II S23 = no. of 5 seater cars on Route II Ans. 23:

Formulation. Let xi be the number of times cutting alternative i (j = 1,2, .....6) is employed.

Minimise (waste produced) Z = 1x3 + 1x4 + 1x5 + 1x6 subject to

6x1 + 1x3 + 4x6 ≤ 3000 3x1 + 3x2 + 1x3 + 4x5+ 2x6 ≤ 2000 2x2 + 1x3 + 2x4 + 1x5+ 1x6 ≤ 1500

1x3 + 1x4 ≤ 1000 xj ≥ 0, for

all j Ans.24:

The profits for each arrangement are:

Economy = 6.00 – 4 (0.20) – 2(0.25) – 8 (0.15) = Rs. 3.50 May time = 8.00 – 8 (0.20) – 5 (0.25) – 10 (0.15) – 4 (0.22) = Rs. 2.77 Spring colour = 10.00 – 9 (0.20) – 10 (0.15) – 9 (0.20) – 6 (0.22) = Rs. 3.58 Deluxe rose = 12.00 – 12 (0.20) – 12 (0.20) – 12 (0.22) = Rs. 4.56

Let x1, x2, x3, x4 be number of units arrangements of type Economy, May time, Spring colour & Deluxe rose. Then the objective is Maximise Z = 3.5x1 + 2.77x2 + 3.58x3 + 4.56x4

subject to 4x1 + 9x3 + 12x4 ≤ 800

318

3 2

2x1 + 5x2 ≤ 456 8x1 + 10x2 + 10x3 ≤ 4000 8x + 9x+ 12x ≤ 920 4x2 + 6x3 + 12x4 ≤ 422

All xi's ≥0

Ans. 26: The information given in the question can be presented in the following tabular form.

Products

Raw material (in kg) required to produce one kg of product Selling price (per kg) X X1 X2 3

Y 1/2 1 1/4 1/4 Rs.90 Y 3/7 2 2/7 2/7 Rs.100 Y -- 3 2/3 1/3 Rs.120

Cost of raw material (Per kg)

Rs.30 Rs.50 Rs.120

Availability of raw material

20 kg 15 kg 10 kg

From the above table, the cost of producing 1 kg of Y1, Y2 and Y3

Cost to produce 1 kg of Y can be calculated as given below:

1

= Rs.15 + Rs.12.50 + Rs.30 = ½ Rs.30 + ¼ Rs.50 + Rs.120

= Rs.57.50 ∴ Profit per kg of Y1

Similarly, cost to produce 1 kg of Y = Rs.90 – Rs.57.50 = Rs.32.50

2

= 1/7 (Rs.90 + Rs.100 + Rs.240) = 3/7 Rs.30 + 2/7 Rs.50 + Rs.120

= Rs.430/7 = Rs.61.43 Profit per kg of Y2

and cost to produce 1 kg of Y = Rs.100 – Rs.61.43 = Rs.38.57

3

Profit per kg of Y = 2/3 Rs.50 + 1/3 Rs.120 = Rs.220/3 = Rs.73.33

3

Let the manufacturer produce y = Rs.120 – Rs.73.33 = Rs.46.67

1, y2 and y3 units of the products Y1, Y2 and Y3

Since the manufacturer wants to maximise the profit, the objective function is given by respectively.

Maximise Z = 32.50 y1 + 38.57 y2 + 46.67 y½ y

3 1 + 3/7 y2 ≤ 20 or 7 y1 + 6 y2

¼ y ≤ 280

1 + 2/7 y2 + 2/3 y3 ≤ 15 or 21 y1 + 24 y2 + 56 y3

¼ y ≤ 1,260

1 + 2/7 y2 + 1/3 y3 ≤ 10 or 21 y1 + 24 y2 + 28 y3

where Y ≤ 840

1, Y2 and Y3

≥ 0

Ans. 27: Let x1 X

= No. of units of product 1 produced 2 = No. of units of product 2 produced

319

X3

= Amount of money borrowed

The profit contribution per unit of each product is given by the selling price minus the variable cost of production. Total profit ay be computed by summing up the profits from producing the two products minus the cost associated with borrowed funds (if any):-

The objective function is thus stated as Maximize Z = (14 – 10 ) x1 + (11 – 8) X2 - 0.05 X3

= 4 x

1 + 3 X2 - 0.05 X(Note that the interest rate is 20% per annum, hence 5% for a period of three months)

3

Subject to the following constraints: The production capacity constraints for each department, as given by table 1 are: 0.5x1 + 0.3X2 0.3x

≤ 500 ……….(1) 1 + 0.4X2

0.2x ≤ 400 ……….(2)

1 + 0.1X2

The funds available for production include both Rs.3,00,000 cash that the firm possesses and any borrowed funds maximum up to Rs.2,0,000. Consequently production costs. The constraint expressing this relationship is

≤ 200 ……….(3)

Funds required for production ≤ Funds available. i.e 10x1 + 8X2 ≤ Rs. 3,00,000 + X or 10x

3 1 + 8X2 - X3

≤ Rs. 3,00,000 ……….(4)

The borrowed funds constraint (from condition (iii) of the Question) is X3

≤ Rs. 2,00,000 ……….(5)

The constraint based on the acid-test condition is developed as follows:-

Surplus cash on hand after production + Accounts receivable Bank Borrowings + Interest accrued thereon

≥ 1

i.e. (3,00,000 +X3 - 10x1 – 8X2 ) + 14x1 + 11X2 (X

≥ 1 3 + 0.05X3

)

or, 3,00,000 +x3 +4x1 +3x2 > (x3 +0.05x3) Or, - 4x1 - 3X2 + 0.05X3

≤ 3,00,000 ……….(6)

Thus, the linear programming problem is given by Maximize Z = 4x1 + 3X2 - 0.05X

3

Subject to 0.5x1 + 0.3X2 ≤ 500 0.3x

……….(1) 1 + 0.4X2

0.2x ≤ 400 ……….(2)

1 + 0.1X2 10x

≤ 200 ……….(3) 1 + 8X2 - X3

X ≤ Rs. 3,00,000 ………..(4)

3 - 4x

≤ Rs. 2,00,000 ……….(5) 1 – 3X2 + 0.05X3 ≤ Rs. 3,00,000 ……….(6)

320

Where x1 X2 X3

≥ 0.

Ans. 28: Let x1, x2 and x3

Since the average yield of radish is 1,500 kg per acre, and the selling price for radish is Rs.5/kg hence the selling amount which the agriculturist gets from one acre is:

be the number of acres allotted for cultivating radish, mutter and potato respectively.

Rs.5 × 1,500 = Rs.7,500 To produce 100 kg of radish, the manure cost is Rs.12.50, so the manure cost per acre will be Rs.12.50 × 1,500/100 = Rs.12.50 × 15. Labour cost per acre for radish = Rs.40 × 6 = Rs.240 Profit per acre for radish = Rs.7,500 – Rs.12.50 × 15 – Rs.240 = Rs.7,072.50 Similarly, the selling price, manure cost, labour cost and profit per acre of land for mutter and potato are also calculated and presented in the following table.

Per acre Radish Mutter Potato

Selling price Rs.5 × 1,500 = Rs.7,500

Rs.4 × 1,800 = Rs.7,200

Rs.5 × 1,200 = Rs.6,000

Manure cost 100

1,500 Rs.12.50× 100

1,800 Rs.12.50× 80

1,200 Rs.12.50×

Labour cost Rs.40 × 6 = Rs.240 Rs.40 × 5 = Rs.200 Rs.40 × 6 = Rs.240 Profit (Rs.7,500-Rs.187.50

– Rs,240) = Rs. 7,072.50

(Rs.7,200 – Rs.255 - Rs.200) = Rs.6,775

Rs.6,000–Rs.187.50 – Rs.240) = Rs.

5572.50

Since, the agriculturist wants to maximise the total profit, hence the objective function of the problem is given by: Maximise Z = 7,072.5x1 + 6,775x2 + 5572.5x Subject to following constraints:

3

x1 + X2 + X3

6x

≤ 125 …… (1) (land constraint)

1 + 5x2 + 6x3

Where x ≤ 500 …… (2) (man day constraint)

1, x2 and x3

≥ 0

Ans. 29: Maximize Z = 60 (9x1 + 5x2) + 90 (7x1 + 9x2)

= 1170x1 + 1110x2

Subject to 9x1 + 5x2 ≥ 500 commitment for A

7x1 + 9x2 ≥ 300 commitment for B

5x1 + 3x2 ≤ 1500 availability of Q

321

7x1 + 9x2 ≤ 1900 availability of P

2x1 + 4x2 ≤ 1000 availability of R

and x1 ≥ 0, x2 ≥ 0. Ans. 30: Let x1, X2 and X3

denote the number of P III, P II and Celeron Computers respectively to the manufactured in the company. The following data is given:

P III P II Celeron

Selling Price per unit (Rs.) 3,000 5,000 15,000 Labour, Material and other Variable Costs p.u. (Rs.) 2,000 4,000 8,000 Profit per unit (Rs.) 1,000 1,000 7,000

From the data given for time required for various models and the total number of hours available for machine time and assembly time, we get the following constraints: 20x1 + 15x2 + 12x3

5x ≤ 1,000 (Machine Time Restriction)

1 + 4x2 + 3x3

The level of operations in the company is subject to availability of cash next month i.e.; the cash required for manufacturing various models should not exceed the cash available for the next month.

≤ 1,500 (Assembly Time Restriction)

The cash requirements for x1 units of P III, x2 units of P II and x3

2,000x units of Celeron computers are:

1 + 4,000 x2 + 8,000x3

The cash availability for the next month from the balance sheet is as below: …… (1)

Cash availability (Rs.) Cash balance (Rs. 2,10,000) Loan to repay to Nationalized bank (Rs. 50,000) Interest on loan from XYZ cooperative bank and Nationalized bank (Rs. 1500)

Interest on long term loans

×

12000,00,218.0

Salary to staff (Rs. 15,000) Or, Cash availability = Rs. 2,10,000-(Rs. 50,000 + Rs. 1,500 + Rs. 3,000 + Rs. 15,000)

= Rs. 1,40,500 ..…. (2) Thus, from (1) and (2), 2000 X1 + 4000 X2 + X3 < Rs. 1,40,500 The company has also promised to deliver 3 P III, 2 P II and 5 Celeron computers to M/s. Kingspen Ltd.

Hence, X1 > 3, X2 > 2, X3 > 5 Since the company wants to maximize the profit, hence the objective function is given by: Maximize Z = 1000X1 + 1000X2 + 7000X3- (Rs. 15000 + Rs. 3000 + Rs. 1500) The LP formulation of the given problem is as follow: Maximize Z = 1000 X1 + 1000X2 + 7000 X3 – (Rs. 15000 + Rs.15000) Subject to the constraints:

20X1 + 15X2 + 12X3 < 1000 5X1 + 4X2 + 3X3 < 1500

322

2000 X1 + 4000 x2 + 8000 X3 < Rs. 1,40,500 X1 > 3, X2 > 2, X3 > 5 X1, X2 and X3 can take only positive integral values.

Ans. 31: Let the firm produce x1 units of product A, x2 units of products B and x3

The profit per unit of products A, B and C is Rs. 50, and Rs. 80 respectively. Since the objective of the firm is to maximize the profit, therefore, the objective function is given by

units of product C.

Maximize Z = 50x1 +50x2 +80x

3

The firm uses two types of raw materials I and II of which 5,000 and 7,500 units respectively are available. As per the given data, the raw material constraints can be formulated as given below:

3x1 +4x2 +5x3 and 5x

< 5,000 ………….. (i) 1 +3x2 +5x3

< 7,500 (ii)

The labour time for each unit of product A is twice that of product B and three times that of product C. Also the entire labour force can produce the equivalent of 3,000 units.

∴ X132

32 XX+ + < 3,000

or, 6x1 +3x2 +2x3

< 18,000 (iii)

The minimum demand of the three products is 600, 650 and 500 units respectively.

Hence, x1 > 600, x2 > 650 and x3

> 500

Since the ratios of the number of units produced must be equal to 2:3:4, therefore,

½ x1 = 1/3 x2, and 1/3 x2 = ¼ x or, 3x

3 1 = 2x2 and 4x2 =3x3

(iv)

The linear programming model can be formulated as follows: Maximize Z = 50x1 +50x2 +80X3

(v)

Subject to the constraints: 3x1 +4x2 +5x3 5x

< 5,000 1 +3x2 +5x3

6x < 7,500

1 +3x2 +2x3 3x

< 18,000 1 = 2x2 and 4x2

x =3x3

1 >600, x2 > 650 & x3

> 500.

Ans. 32: Renco Foundries has to decide the amount of funds to be allocated to projects A, B, C, D, E and money market instruments. Let us define the decision variables as

323

a : Rs. Invested in investment A b : Rs. Invested in investment B c : Rs. Invested in investment C d : Rs. Invested in investment D e : Rs. Invested in investment E Si

: Rs. Invested in money market instruments at time i (for i = 0,1,2)

The objective of Renco Foundries is to draw up the capital budget in such a way that will “maximize cash on hand at time 3”. Now at time 3, the cash on hand for Renco Foundries will be the sum of all cash inflows at time 3. Since the firm earns interest at 8% p.a. by parking the un-invested funds in money market instruments, hence Rs. S0 which are invested in these instruments at time 0 will become 1.08 S0 at time 1. Similarly an investment of Rs. S1 at time 1 will become 1.08 S1 at time 2, and an investment of Rs. S2 at time 2 will become 1.08 S2From the table giving the description of various investments, it can be computed that at time 3,

at time 3.

Cash on hand = a×Re. 0+b×Re.1+c× Re. 0+d× Rs.1.9+ e× Rs. 1.5+ 1.08S = Rs. (b+1.9d+1.5e+1.08S

2 2

)

The objective of Renco Foundries is to maximize the cash on hand at time 3. hence the objective function will be Maximize Z = b+ 1.9d+ 1.5e +1.08 S2

…………….(i)

It may be noted that Cash available for investment at time t = cash on hand at time t ………..(ii) At time 0, funds to the tune of Rs. 1,00,000 are available for investment. From the table, it can be seen that funds are invested in investment A, C, D and S0

at time 0.

Hence, a+c+d+S0

= 1,00,000………………….(iii)

At time 1, Rs. 0.5 a, Rs. 1.2 c and Rs. 1.08 S0 will be the available returns as a result of investments made at time 0. From the table Rs. B and Rs. S1 are invested in investment B and money market instruments respectively at time 1. Using equation (ii), we get 0.5a+ 1.2c+ 1.08S0 = b+ S1

……………….(iv)

At time 2, Re. 1 a, Rs. 0.5 b and Rs. 1.08S1 will be available for investment. However, Rs. E and Rs. S2

are invested at time 2………………………………..(v)

Further, since the firm will not commit an investment exceeding Rs. 75,000 in any project, we get the following constraints:

324

a < 75,000 (vi) b < 75,000 (vii) c < 75,000 (viii) d < 75,000 (ix) e < 75,000 (x) Also a, b, c, d, e and Si (for i

= 0, 1, 2) are all > 0

Combining all the constraints, the linear programming model for the Renco Foundries is as given below: Maximize Z = b+ 1.9d+ 1.5e+ 1.08S

2

Subject to following constraints a+c+d+S0 = 1,00,000 0.5a +1.2c +1.08 S0 = b+S 1a+ 0.5b +1.08S

1 1 = e+ S

2

a < 75,000 b < 75,000 c < 75,000 d < 75,000 e < 75,000 a, b, c, d, e and si (I =0, 1, 2) are all > 0

Ans. 33: Let x1 and x2

Maximise Z = 0.1x

be the amount to be invested in first and second stock portfolio respectively. The average rate of return for first portfolio is 10% and for second portfolio, it is 20%. Since the company wishes to maximize the return from investment, the objective function is as given below:

1 + 0.2xThe maximum amount available for investment is Rs.1,00,000.

2

Hence, x1 + x2

Further, the maximum investment allowed in either portfolio set is Rs.75,000. ≤ 1,00,000 …… (1)

Therefore, x1

and x ≤ 75,000 …… (2)

2

The first portfolio has a risk rating of 4 (on a scale from 0 to 10) and the second has 9. The company will not accept a risk factor above 6.

≤ 75,000 …… (3)

Therefore, 4x1 + 9x2 ≤ 6 (x1+x2

Further, the company will not accept an average rate of return below 12%. ) …… (4)

Hence, 0.1x1 + 0.2 x2 ≥ 0.12 (x1 + x2

Also, x) …… (5)

1 and x2

The linear programming model for the given problem can now be formulated as follows: ≥ 0 …… (6)

Maximise Z = 0.1x1 + 0.2xSubject to the constraints

2

x1+x2 ≤ 1,00,000 …… (1)

325

x1

x ≤ 75,000 …… (2)

2

4x ≤ 75,000 …… (3)

1 + 9x2 ≤ 6 (x1 + x2

or – 2x)

1 + 3x2

0.1x ≤ 0 …… (4)

1 + 0.2x2 ≥ 0.12 (x1+x2

or – 0.02x)

1 + 0.08x2

where x ≥ 0 …… (5)

1, x2

The problem is solved graphically below: ≥ 0

The point of intersection for the lines - 2x1 + 3x2

and x = 0

1 + x2

is given by B (60,000, 40,000) = 1,00,000

The point of intersection for the lines X1

and x = 75,000

1 + x2

is given by C (75,000, 25,000) = 1,00,000

Similarly, the lines x1

and – 0.02x = 75,000

1 + 0.08x2

intersect at point D (75,000, 18,750) = 0

Thus, the feasible region is bounded by ABCDA and feasible points are A (0, 0); B(60,000, 40,000); C(75,000, 25,000) and D(75,000, 18,750). Value of the objective function at the above mentioned feasible points is calculated below: At A, Z=0 At B, Z=0.1 × 60,000 + 0.2 × 40,000 = 6,000 + 8,000 = Rs.14,000 At C, Z=0.1 × 75,000 + 0.2 × 25,000 = 7,500 + 5,000 = Rs.12,500

326

At D, Z=0.1× 75,000 + 0.2 × 18,750 = 7,500 + 3,750 = Rs.11,250 We find that the value of the objective function is maximum (Rs.14,000) at point B(60,000, 40,000). Hence, the company should invest Rs.60,000 in first portfolio and Rs.40,000 in second portfolio to achieve the maximum average rate of return of Rs.14,000. Ans. 35:

Contribution analysis: Products A B (Rs.) (Rs.) Selling price (A) 500 450 Variable costs: Direct Materials 100 100 Direct Labour 80 40 Painting 30 60 Variable Overheads 190 175 Total variable costs (B) 400 375 Contribution (A – B) 100 75 Direct Material per unit 100/25 = 4 kg. 100/25 = 4 kg. Direct Labour hour per unit 80/20 = 4 hours 40/20 = 2 hours Painting hour per unit 30/30 = 1 hour 60/30 = 2 hours

Let A be the units to be produced of product A and B be the units to be produced of product B.

LP Problem formulation:

Z Max 100A + 75B Maximisation of contribution

Subject to:

4A + 4B ≤ 480 Raw material constraint

4A + 2B ≤ 400 Direct Labour hour constraint

A + 2B ≤ 200 Painting hour constraint

A, B ≥ 0 Non negativity constraint

Raw Material Constraint : Put B = 0, A = 120

Put A = 0, B = 120

Direct Labour Constraint : Put B = 0, A = 100

Put A = 0, B = 200

327

Painting Constraint : Put B = 0, A = 200

Put A = 0, B = 100

The graphical representation will be as under:

Q Intersects 4A + 2B = 400 (1)

and 4A + 4B = 480 (2)

Subtracting (2) from (1), we get −2B = −80

⇒ B = 80/2 = 40

Putting value of B in (1), we get 4A + 2 × 40 = 400

⇒ A = 400 − 80 = 80

4

R Intersects 4A + 4B = 480 (3) and A +

2B = 200 (4) Multiplying (4) by (2) and then subtracting

from (3), we get

2A = 80

⇒ A = 40

Putting the value of A in (4), we get 2B = 200 – 40

⇒ B = 80.

328

Evaluation of corner points:

Point Products Contribution Total Contribution

A B A (Rs.) 100 per unit

B (Rs.) 75 per unit

Rs.

P 0 100 0 7,500 7,500 Q 80 40 8,000 3,000 11,000 R 40 80 4,000 6,000 10,000 S 100 0 10,000 0 10,000

Optimal product mix is Q

Product Units Contribution Rs.

A 80 8,000 B 40 3,000 Total contribution 11,000 Less: Fixed costs 400 D.L. Hrs. × Rs. 17.50 7,000

Optimal Profit 4,000

(iii) If the painting time can be sold at Rs. 40 per hour the opportunity cost is calculated as under:

A

(Rs.) B

(Rs.) Income from sale per hour 40 40 Painting variable cost per hour 30 30 Opportunity cost 10 10 Painting hours per unit 1 2 Opportunity cost 10 20 Revised contribution 100 – 10 = 90 75 – 20 = 55

Hence, modification is required in the objective function.

Re-formulated problem will be:

329

Z Max.

Subject to: 90A + 55B Maximisation of contribution

4A + 4B ≤ 480 Raw Material constraint 4A + 2B ≤ 400 Direct Labour hour constraint A + 2B ≤ 200 Painting hour constraint A, B ≥ 0 Non-negativity constraint

Ans 40: Dual:

Minimise 140u1 + 120u2 + 50u3

S.T. 6u1 + 10u2 + 10u3 ≥ 100

4u1 + 10u2 + 12u3 ≥ 90

8u1 + 2u2 + 6u3 ≥ 40

4u1 + 6u2 + 2u3 ≥ 60 u1, u2 u3 u4 ≥ 0

330

Ans. 6 Transportation

(a) 3

-- 9

---- 6

4

4

--- 6

--- 8

3

5

40

50

30

(ii) Initial allocation under NW corner rule is as above. Initial cost: 20×3 = 60 20×4 = 80 20×4 = 80 30×3 = 90 30×5 =

150

(a) 460

3

-- 9

---- 6

4

4

--- 6

--- 8

3

5

40 50 30

1 1 1 4 1 1 1 1 Initial solution 20×3 = 60 20×4 = 80 50×3 = 150 20×6 = 120 10×5 = __100 __

460

Checking for optimality 3

4 6

3 5

V1 =3 v2 = 3 v3 = 5

20 20 40 60 120

20 20

30 30

20 20 3 40 0 0 2 60 2 2 2

20 20

30 30

U1 = 0 U2 = 1 U3 = 0

331

Ui+ vj

3

5

4

3

3 3 5 ∆ij = Cij- (ui-vj)

6 1 0

5 ∆ij > 0 ∴ Solution is optimal Conclusion: The solution under VAM is optimal with a zero in R2C2 which means that the cell C2R2 which means that the cell C2R2 can come into solution, which will be another optimal solution. Under NWC rule the initial allocation had C2R2 and the total cost was the same Rs. 460 as the total cost under optimal VAM solution. Thus, in this problem, both methods have yielded the optimal solution under the 1st allocation. If we do an optimality test for the solution, we will get a zero for ∆ij in C3R2

indicating the other optimal solution which was obtained under VAM.

Ans. 8 The new transportation costs table, which consists of both production and transportation costs, is given in following table.

Store P Q R S Supply A 2+2=4 4+2=6 6+2=8 11+2=13 50 B 10+3=13 8+3=11 7+3=10 5+3=8 70

Factories C 13+1=14 3+1=4 9+1=10 12+1=13 30 D 4+5=9 6+5=11 8+5=13 3+5=8 50 Demand 25 35 105 20 200 185

Since the total supply of 200 units exceeds the total demand of 185 units by 200-185 =15 units of product, there fore a dummy destination (store) is added to absorb the excess supply. The associated cost coefficients in dummy store are taken as zero as the surplus quantity remains lying in the respective factories and is, in fact, not shipped at all. The modified table is given below. The problem now becomes a balanced transportation one and it is a minimization problem. We shall now apply Vogel’s Approximation method to fine an initial solution.

0 1 0

332

P Q R S Dummy Supply Difference A 25

4 5

6 20

8 13

0 50/25/20/0 4 2 2 2 5

B 13 11 70

10 8

0 70/0 8 2 2 2 2 2

C 14

30

4 10 13 0 30/0 4 6 _ _ _ _

D 9 11 15 20 15 50/35/15/0 8 1 1 3 3 5 13 8 0 Demand 25/0 35/5/0 105/85/15/0 20/0 15/0 200 Difference 5 2 2 0 0 5 2 2 0 - 5 5 2 0 - - 5 2 0 - - - 2 0 - The initial solution is shown in above table. It can be seen that 15 units are allocated to dummy store from factory D. This means that the company may cut down the production by 15 units at the factory where it is uneconomical. We will now test the optimality of the solution. The total number of allocations is 8 which is equal to the required m+n-1 (=8) allocation. Introduce ui’s, vj’ s, i= (1,2,- - - - -4) and j =(1,2,- - - -5) ∆ ij=cij-(ui+vj) for allocated cells. We assume that u4 =0 and remaining uj’s, vj’s and ∆ ij

’s are calculated below”

P Q R S Dummy Supply UA

i 25

4 5

6 20

8 13

+10 0

+5 50 U1= -5

B 13

+7 11

+3 70

10 8

+3 0

+3 70 U2 =

C 14

+1 30

4 10

+4 13

+12 0

+7 30 U3 = -7

D 9

0 11 15 20 15 50 U4 = 0

0 13 8 0 Demand 25 35 105 20 15 V Vj 1 2 =9 2 0 0 Please not that figures in top left hand corners of the cell represent the cost and the one in the bottom right hand corner of the non basic cell are the values of ∆ ij=cij-[(ui+vj

Since opportunity cost in all the unoccupied cells is positive, therefore initial solution is an optimal solution also. The total cost (transportation and production together) associated with this solution is

)]

Total cost = 4×25+6×5+8×20+10×70+4×30+13×15+8×20+0×15 = 100+30+160+700+120+195+160 = Rs.1,465/- Ans.9:

333

The given problem is an unbalanced transportation problem since the availability of trailers (= 10+4+6+5=25) is less than the requirement (=13+10+6+6=35). Therefore, it is first converted into a balanced problem by adding a dummy terminal with an availability of 10 trailers and cost elements for various plants as zero. The problem becomes as given below.

Plants Terminals A B C D Availability

U 20 36 10 28 10 V 40 20 45 20 4 W 75 35 45 50 6 X 30 45 40 25 5

Dummy 0 0 0 0 10 Requirement 13 10 6 6

The objective of the company is to minimize transportation cost. To achieve this objective, let us find an initial feasible solution by applying Vogel’s Approximation Method to the above matrix.

Plants

Terminals A B C D Availability Difference U 3

20

36 6

10 1

28

10/4/1/0

10/10/8/8 V

40 4

20

45

20

4/0

0/0/0/- W

75 6

35

45

50

6/0

10/10/15/15 X

30

35

40 5

25

5/0

5/5/5/5 Dummy 10

0

0

0

0

10/0

0/-/-/- Requirement 13/3/0 10/6/0 6/0 6/1/0

Difference 20 20 10 20 10 15 30 5 10 15 0 5 10 0 - 5

The initial solution is as given below which is tested for optimality.

334

Plants Terminals A B C D Availability

U 3 20

36

6 10

1 28

10

V 40

4 20

45

20

4

W 75

6 35

45

50

6

X 30

35

40

5 25

5

Dummy 10 0

0

0

0

10

Requirement 13 10 6 6 The number of allocation is 7 which is one less than the required m+n-1 (=8) allocations. Introduce a very small quality e in the least cost independent cell (Dummy, B0. Let us also introduce uj, vj; I- (1,2 – 5) j = (1,2,3,4) such that ∆ ij = cij-(u1+vj) for allocation cells. We assume that u1=0 and remaining ui’s, vj’s and ∆ ij’

’s are calculated as below:

Terminals A B C D ui’s U 3 +θ

20 16

36 6

10 1 -θ

28

0 V 20

40 4 -θ

20 35

45 -8 +θ

20

0 W 40

75 6

35 20

45 7

50

15 X 13

30 18

35 33

40 5

25

-3 Dummy 10 -θ

0 e +θ

0 10

0 -8

0

-20 vj’s 20 20 10 28

Since some of the ∆ ij’ ’s are negative, the above solution is not optimal. Introduce in the cell (V,D) with the most negative ∆ ij an assignment θ. And the reallocated solution as obtained from above is given below. The values of u i ’s and vj’’s and ∆ ij’

’s also calculated.

335

Terminals A B C D ui’s U 4

20 16

36 6

10 8

28

0 V 20

40 3

20 35

45 1

20

0 W 40

75 6

35 20

45 15

50

15 X 5

30 10

35 25

40 5

25

5 Dummy 9

0 1

0 10

0 0

0

-20 vj 20 ’s 20 10 20 -20

Since all ∆ Ij’s for non basic cells are positive, therefore, the solution obtained above is an optimal one. The allocation of terminals to plants and their cost is given below.

Terminal Plant Cost

U A 4 × Rs.20 = Rs.80 U C 6 × Rs.10 = Rs.60 V B 3 × Rs.20 = Rs.60 V D 1 × Rs.20 = Rs.20 W B 6 × Rs.35 = Rs.210 X D 5 × Rs.25 = Rs.125 = Rs.555

Ans. 10:

Answer

(a) The problem may be treated as an assignment problem. The solution will be the same even if prices are halved. Only at the last stage, calculate the minimum cost and divide it by 2 to account for fall in oil prices.

A B C X 15 9 6 Y 21 12 6 Z 6 18 9

Subtracting Row minimum, we get

A B C X 9 3 0 Y 15 6 0 Z 0 12 3

Subtracting Column minimum,

336

A B C

No of lines required to cut Zeros = 3

Cost / u Units Cost Revised Cost

Allocation: X B 9 10 90 45 Y C 6 10 60 30 Z A 6 10 60 30 210 105 Minimum cost = 105 Rs.

Alternative Solution I

Least Cost Method

X – B Y – C Z – A Test for optimality

No. of allocation = 3

No. of rows m =3, no. of column = 3

337

m + n – 1 = 3 + 3 – 1 = 5

2 very small allocation are done to 2 cells of minimum costs, so that , the following table is got :

A B C

X

15

10 9

e 6

Y

21

12

10 6

Z

10 6

18

e 9

m + n – 1 = 5

Now testing for optimality

ui

9 e 0

6

0

6 e 0

vj 6 9 6

ui + vj for unoccupied cells

A B C X 6 - - Y 6 9 - Z - 9 -

Diff = Cij – (ui + vj)

A B C

X 9 - - Y 15 3 - Z - 9 -

All Δij > 0, Hence this is the optimal solution.

338

Original Costs Reduced Costs due to Oil Price

Qty. Cost

X – B

Y – C

Z – A

9

6

6

4.5

3

3

10

10

10

45

30

30

105 Total cost of transportation is minimum at Rs.105

Alternative Solution II

No. of rows + no. of column – 1

m + n – 1 = 5

No. of allocation = 3

339

3 - - 3 4.5 - - 4.5 -

Hence add ‘e’ to 2 least cost cells so that

Now m + n – 1 = 5 Testing for optimality, ui, vj table

A B C ui

X 4.5 e 0

Y 3

0

Z 3 e 0

vj 3 4.5 3

ui + vj for unoccupied cells

3 - - 3 4.5 - - 4.5 -

Cij u i+vj

7.5 - - 11.5 6 -

- 9 - Δij = Cij – (ui + vj)

4.5 - - 11.5 1.5 - 8.5 4.5 -

All Δij > 0. Hence the solution is optimal.

Qty. Cost/u Total Cost X – B

Y – C

Z – A

10

10

10

4.5

3

3

45

30

30 Total minimum cost at revised oil prices 105

340

9 2 5 6 2 C1 C2 C3 C4 C5

8 6 4 11 2 8 6 2

10 9 9 12 9 6

8 7 6 3 7 7

2 0 2 9 3 5 6 11

12 8 8 8 4

Ans.11:

The concept tested in this problem is Degeneracy with respect to the transportation problem. Total of rows and columns = (4 + 5) = 9. Hence, the number of allocations = 9

– 1 = 8. As the actual number of allocation is 7, a ‘zero’ allocation is called for. To resolve this, an independent cell with least cost should be chosen. R4C2 has the least cost (cost = 3), but this is not independent. The next least cost cell R4C3 (cost = 5) is independent.

Total

0R1 18

0R2 10

−2R3 8

0R4 4

Total 40

Forming Equations through allocated cells

Basic equation Setting R1 = 0 other values R1 + C2 = 2 Setting R1 = 0, C2 = 2 R1 + C4 = 6 C4 = 6 R1 + C5 = 2 C5 = 2 R2 + C1 = 9 R2 = 0 R3 + C3 = 3 R3 = −2 R4 + C1 = 9 C1 = 9 R4 + C3 = 5 C3 = 5 R4 + C4 = 6 R4 = 0

Evaluate unallocated cells

R1C1 = 11 − 0 − 9 = 2 R3C1 = 7 + 2 − 9 = 0 R1C3 = 8 − 0 − 5 = 3 R3C2 = 6 + 2 − 2 = 6 R2C2 = 9 − 0 − 2 = 7 R3C4 = 7 + 2 − 6 = 7

R2C3 = 12 − 0 − 5 = 7 R3C5 = 7 + 2 − 2 = 7 R2C4 = 9 − 0 − 6 = 3 R4C2 = 3 − 0 − 2 = 1 R2C5 = 6 − 0 − 2 = 4 R4C5 = 11 − 0 − 2 = 9

Since all the evaluation is 0 or +ve, the optimal solution is obtained.

Optimal cost = (8 × 2) + (6 × 6) + (4 × 2) + (10 × 9) + (8 × 3) + (2 × 9) + (0 × 5) + (2 × 6) = 16 + 36 + 8 + 90 + 24 + 18 + 10 + 12 = Rs. 204.

Note: As regards allocation of the zero values, the solution to the above problem is also obtained by allocating the zero value in other independent cells such as R1C3, R2C2, R2C3, R3C1, R3C2, R3C4,

341

38 40 43 0 190/100/0 38/1/1/3 90/0 110/10/0 160/0 60/0 0 0 0 0 10* 2 6* 0

3 7 0 4 0 52 0

38 40

40 50 52 50 37

28 25 –12

2 –2 –14 –1 14

11 18 12

e 2

R3C5. In such situation there will be one more iteration.

Ans. 12 The optimum distribution for this company to minimize shipping costs

Availabilities = 160 +150 +190 = 500 Requirements = 80 +90 +110 +160 = 440 Availabilities –Requirement = 500 – 440 = 60

Therefore, a dummy warehouse H is introduced, and initial solution is obtained below by VAM in just one table.

D E F G H Available Diff.

160 e

A 42 48 38 37 0 160/0 37/1/1/1

80 10 60

B 40 49 52 51 0 150/90/10/0 48*/9/11*/1

90 100

C 39

Reg. 80/0

Diff. 0

1

since there are only 6 (one less than m+n –1) allocations, an infinitesimally small allocation e is placed in the least cost and independent cell (1, 5). This solution is tested for optimality below. (N.B.: if allocations were m +n –2 we would place two e’s, e ,

which are virtually zero in the 2 least cost independent cells). This device enables us to apply to optimality test on (m +n –1) allocations.

V j 0 0 –12

V j 4 0 50 52 3 7 0

(ui + vj) matrix

Δ ij m atrix

Since there are –ve Äij ‘s the initial solution is not optimal. Reallocation is done below by ticking the most -ve Äij cell (1, 3) and involving it in the loop.

θ mx

342

√ 160 e Note that the maximum that can be tansferred to the ticked cell is e. Since e is infinitestimally small it leaves other corner allocations unaffected. (Intermediate i.e. non corner allocations are never altered in the process of reallocations).

80 10 60 90 100

e 160

80 10 60 90 100

38 37 40 52 0

38 40

26 36 –14 50 51

28 39 –12

16 12 14 –1 0

11 4 12

160 80 √ 10–θ 60

90–θ 100+θ

e 160 80 10 60

80 110

⎭ ⎩

3 8 3 7

4 0 4 9 0 0 - 3 8 4 0

⎧e − θ = 0 ⎫ ⎪ ⎪

min ⎨10 − θ = 0 ⎬ ⎪ = e⎪

Reallocation

This solution is tested for optimally below :

38

52

40

-12 -2 0 -1 -52

(ui+vj) matrix)

Δ j matrix

Since there are –ve ΔØ, this solution too is not optimal. Reallocation is done below :

⎛10 − θ = 0 ⎞ θmax = min ⎜ ⎟

⎝ 90 − θ = 0 ⎠

Reallocation

Since there are –ve Δij this solution too is not optimal. Reallocation is done below. This solution is tested for optimality below:

u i –1 3 0 –1 1

V i 4 0 4 9 5 1 5 0 0

343

2 7 2 6 – 1 3 5 1 5 0

2 9 3 9 – 1 1

1 5 1 2 1 3 1 1

1 0 4 1 1

3

j

( v i + v j)

Δ ij m a t rix Since all Δij’s are +ve, this solution is optimal. Ans. 15: The initial solution is found by VAM below: Factory Godown Availability Diff.

1 2 3 4 5 6 1 7 20 5

7 7 5 40 3 60/40/0 2/4/0

2 10 9

11 10 6 11 ∞ 5 20/10/0 1/3

3 11

10 30 6 20 2 40 2 8 90/70/30/0 0/4/2/5

4 50 9

10 9 6 9 12 50/0 3/0

Demand 60

0 50 0

20 40

0 10 0

20 0

40 0

40

Diff. 2 5 0/1 4 3 2

The above initial solution is tested for optimality. Since there are only 8 allocations and we require 9(m+n-1 =9) allocations, we put a small quantity in the least cost independent cell (2, 6) and apply the optimality test. Let u= 0 and then we calculate remaining ui and v

vj uFactory

i Godowns

1 2 3 4 5 6 1 7

20 5

7

7

5

40 3

2 10 9

11

10 6

11

∞

e 5

3 11

10

30 6

20 2

40 2

8

4 50 9

10

9

6

9

12

Vj 9 7 6 2 2 5

Now we calculate Δij = cij – (ui +vj) for non basic cells which are given in the table below:

0 3 7 5 4 9 ∞

2 3 3 3 3 4 7 7

Δ ij matrix

- 2 0 0 0

344

Since all Δij are positive, the initial solution found by VAM is an optimal solution. The final allocations are given below: Factory to Godown Unit Cost Value

1 2 20 5 100 1 6 40 3 120 2 1 10 9 90 2 3 10 6 60 3 3 30 6 180 3 4 20 2 40 3 5 40 2 80 4 1 50 9

450

Total cost Rs. = The above solution is not unique because the opportunity cost of cell (1,2) is zero. Hence alternative solution exists. Students may find that the alternative solution is as given below:

1,120

Factory to Godown Unit Cost Value 1 1 10 7 70 1 2 20 5 100 1 6 30 3 90 2 3 10 6 60 2 6 10 5 50 3 3 30 6 180 3 5 40 2 80 3 4 20 2 40 4 1 50 9

450

Total cost (Rs.)

1,120

Ans. 16 The given problem is a balanced minimization transportation problem. The objective of the company is to minimize the cost. Let us find the initial feasible solution using Vogel’s Approximation method (VAM)

Outlets Plants A B C D Capacity Difference X

4 400

6

8 300

6 700/300/0 2 2 0 0

Y

3 50

5 350

2

5 400/50/0 1 2 0 0

Z 400

3

9

6 200 600/200/0 2 2 4 0

Requirement 400/0 450/400/0 350/0 500/300/0 Difference 0 1 4 0 0 1 - 0 - 1 - 0 The initial feasible solution obtained by VAM is given below:

345

Outlets Plants A B C D Capacity X

4 400

6

8 300

6 700

Y

3 50

5 350

2

5 400

Z 400

3

9

6 200

5 600

Requirement 400 450 350 500 Since the number of allocations = 6= (m+n-1), let us test the above solution for optimality. Introduce ui (i=1,2,3) and vj (1,2,3,4) such that ∆ ij= Cij –(ui+vj) for allocated cells. We assume u1=0, and rest of the ui’s, vj’s and ∆i j

Outlets

’s are calculated as below:

Plants A B C D UX

i 0

4 400

6 5

8 300

6 0

Y 0

3 50

5 350

2 0

5 -1

Z 400

3 4

9 4

6 200

5 -1

V 4 j 6 3 6 On calculating ∆i j ’s for non-allocated cells, we found that all the ∆i j

The optimal allocations are given below. ≥0, hence the initial solution obtained above is optimal.

Plants Outlet Units Cost Total Cost X →B 400 × 6 = 2,400 X →D 300 × 6 = 1,800 Y →B 50 × 5 = 250 Y →C 350 × 2 = 700 Z →A 400 × 3 = 1,200 Z →D 200 × 5 = 1,000 7,350

The minimum cost = 7,350 thousand rupees. Since some of the ∆i j

’s = 0, the above solution is not unique. Alternative solutions exist.

Ans.17: The given problem is a transportation problem. The profit matrix for various factories and sales counters is calculated below:

346

Factory Sales Centres Capacity (kgms) 1 2 3

A 3 2 4 100 B 0 -1 1 20 C 4 3 5 60 D 2 1 3 80

Demand (kgms) 120 140 60 Since this is an unbalanced transportation problem (demand > capacity), let us introduce a dummy factory with profit as Rs.0 per unit for various sales centres and capacity equal to sixty units. The resulting matrix would be as below:

Factory Sales Centres Capacity (kgms) 1 2 3

A 3 2 4 100 B 0 -1 1 20 C 4 3 5 60 D 2 1 3 80

Dummy 0 0 0 60 Demand (kgms) 120 140 60

The above profit matrix can be converted into a loss matrix by subtracting all its elements from the highest payoff of the matrix i.e. 5. The loss matrix so obtained is given below:

Factory Sales Centres Capacity (kgms) 1 2 3

A 2 3 1 100 B 5 6 4 20 C 1 2 0 60 D 3 4 2 80

Dummy 5 5 5 60 Demand (kgms) 120 140 60

The initial solution is obtained by applying Vogel’s approximation method.

Factory Sales Centres Capacity Difference 1 2 3

A 100 3

1

100/0

1 1 - 2

B 5

20 4

20/0

1 1 1 6

C 1

2

60 60/0

1 - - 0

D 20 60

347

3 4 2 80/60/0 1 1 1 Dummy

5 60

5 60/0

0 0 0 5

Demand 120/20/0 140/120/60/0 60/0 Difference 1 1 1

1 1 - 2 1 -

The solution obtained by VAM is as given below:

Factory Sales Centres Ui 1 2 3

A 100 0 3

E 1

3 2

B 0 5

20 0 4

6 6

C 0 1

0 2

60 2 0

D 20 60 0 2

4 3 4

Dummy 1 5

60 2 5

5 5

Vj -1 0 2 Since all ∆ ij

From Factory

≥ 0 for the non allocated cells, hence the solution given by above matrix is optimal. The optional solution for the given problem is given below:

To Sales Centre Quantity Profit per unit (Rs.)

Total Profit (Rs.)

A 1 100 3 300 B 2 20 -1 -20 C 3 60 5 300 D 1 20 2 40 D 2 60 1 60

Dummy 2 60 0 0 Total Profit = 660

(Note: since some of the ∆ ij’s

are equal to zero, alternative solutions also exist.)

Ans.18: The given problem is an unbalanced transportation problem which is converted into a balanced on by adding a dummy investment as given below:

348

Year Net Return data (in paise) of Investment Dummy Amount Payable P Q R S

1 95 80 70 60 0 70 2 75 65 60 50 0 40 3 70 45 50 40 0 90 4 90 40 40 30 0 30

Maximum Investment

40 50 60 60 20

The values in the table represent net return on investment of one rupee till the end of the fourth year. The objective of the company is to maximize the net return. For achieving this objective, let us convert this maximization problem into minimization problem by subtracting all the elements of the above payoff matrix from the highest payoff i.e. 95, and apply Vogel’s approximation method for finding the initial feasible solution.

Year Loss Matrix – Investment type Dummy Amount Available

Difference

P Q R S

1 40 0

30 15

25

35

95

70/30/0

15/10 _ _

2 20

20 30

20 35

45

95

40/20/0

10/5/5/10

3 25

50

40 45

50 55

95

90/50/0

10/40/20 /0/0

4 35

55

55

10 65

20 95

30/20/0

10/3/0

Maximum Investment

40/0 50/20/0 60/40/0 60/10/0 20/0

Difference 20 15 10 10 0

- 15 10 10 0

- 20 10 10 0

- - 10 10 0 solution obtained by VAM is as given below

349

Year Loss Matrix – Investment type Dummy Amount Available

P Q R S

1 40 0

30 15

25

35

95

70

2 20

20 30

20 35

45

95

40

3 25

50

40 45

50 55

95

90

4 35

55

55

10 65

20 95

30

Maximum Investment

40/0 50/20/0 60/40/0 60/10/0 20/0

This initial solution is tested for optimality. There are 8 (=m+n-1) independent allocations. Let us introduce ui, vj, i=(1,2,3,4); = (1,2,3,4,5 such that Dij = cij = (ui+vj

Year

) for allocation cell. We assume u1 = 0 and remaining u1’s vj’s and Dij’s are calculated.

Loss Matrix – Investment type Dummy Amount Available

P Q R S

1 40 0

30 15

5 25

5 35

35 95

0

2 5 20

20 30

20 35

0 45

20 95

15

3 0 25

10 50

40 45

50 55

10 95

25

4 0 35

5 55

55

10 65

20 95

35

vj 0 ’s 15 20 30 60 On calculating Aij

Year Invest in Net Return

s for non-allocated cells, we found that their values are positive, hence the initial solution obtained above is optimal. The optimal allocations are given below:

1 Invest Rs 40 lacs in investment P 0.95xRs.40 lacs = Rs. 38,00,000

350

Rs 30 lacs in investment Q 0.80xRs.30 lacs = Rs. 24,00,000 2 Invest Rs 20 lacs in investment Q 0.65xRs.20 lacs = 13,00,000 Rs 20 lacs in investment R 0.60xRs.20 lacs = 12,00,000 3 Invest Rs 40 lacs in investment R 0.50xRs.40 lacs = Rs. 20,00,000 Rs 50 lacs in investment S 0.40xRs.50 lacs = Rs. 20,00,000 4 Invest Rs.10 lacs in investment S 0.30xRs.10 lacs = Rs.3,00,000 Total Rs.130,00,000 Ans. 19: The given information can be tabulated in following transportation problem:

Profit Sales offices

Capacity in units

Plant 1 2 3 4 5 1 2 3

Demand

9 -1 8

80

11 3 9

100

6 1

10 75

5 9

14 45

5 1 4

125

150 200 125

Where entries in the cells of the above table indicate profit per unit received by selling one

unit of item from plant i (1 =1,2,3) to the sales office (i=1,2,3,4,5). The profit per unit is calculated using the following formula.

Profit = sales price –(production cost +Shipping cost) The objective of the company is to maximize the profit. For achieving this objective, let us

convert this maximization problem into minimization problem by subtracting all the elements of the above payoff matrix from the highest payoff i.e. Rs. 14.

Loss matrix

Sales offices Capacity in units

Plant 1 2 3 4 5 1 2 3

5 15 6

3 11 5

8 13 4

9 5 0

9 13 10

150 200 125

Demand 80 100 75 45 125 The problem is an unbalanced transportation problem since capacity (=475 units) is 50 units

more than the demand. Hence a dummy sales office is added with cost equal to zero for all plants and demand equal to 50 units. Now, let us apply Vogel’s Approximation method to the resultant balanced matrix for finding the initial feasible solution.

351

Sales offices Plant 1 2 3 4 5 Dummy Capacity Difference

1 50

5

100

3

8

9

9

0

150/50/0

3/3/2/2/4

2 25

15

11

13

5

125

13

50 0

200/150/125/0 5/11/2/2/2/2

5

75 45

3 6 5 4 0 10 0 125/80/5/0 0/4/1/1/4/4 Demand 80/30 100/0 75/0 45/0 125/0 50/0 /25/0 differ 1 2 4 5 1 0 1 2 4 -- 1 0 1 2 4 -- 1 -- 1 2 -- -- 1 -- 1 -- -- -- 1 -- The initial solution obtained by VAM is given below which is tested for optimality.

Plant 1 2 3 4 5 Dummy Capacity

in units 1 50

5 100 3

8

9

9

0

150

2 25 15

11

13

5

125 13

50 0

200

3 5 6

6

75 4

45 0

10

6

125

Demand in units

80

100

75

45

125

50

These are m +n –1 =8 independent allocations. Let us now introduce ui, vj, I = (1,2,3); j =

(1,2-----6) such that ∆ ij = Cij –(ui +vj) for allocation cells. We assume u2 = 0 and remaining ui’s vj’s and ∆ij’s are calculated as below:

Sales offices Plant 1 2 3 4 5 Dummy Ui’s

1 50 5

100 3

5 8

10 9

6 9

10 0

-10

2 25 -θ 15

-2 11

10 13

-4 + θ

5

125 13

50 0

0

3 5 + θ 6

1 5

75 4

45 - θ

0

6 10

9 0

-9

Vj 15 ’s 13 13 9 13 0

352

Since some of the Δ ij ’s are negative, therefore, the above solution is not optimal. Introduce in the cell (2,4) with the most negative Δ ij, an assignment. The value of θ and reallocated solution as obtained from above is given below. The reallocated solution is again tested for optimally. Hence, the values ui’s vj’s and Δ ij

’s are again calculated.

Sales offices

Plant 1 2 3 4 5 Dummy Ui’s 1 50

5 100 3

5 8

10 9

2 9

6 0

-6

2 4 15

2 11

4 13

25 5

125 13

50 0

0

3 30 6

1 5

75 4

20 0

2 10

5 0

-5

11 Vj’s 9 9 5 13 0

Since all Δ ij

’s for non-basic cells are positive, therefore, the solution obtained above is an optimal one. The allocation of plants to sales officers and their profit amount is given below:

Plant Sales units profit per profit Office unit 1 1 50 9 450 1 2 100 11 1,100 2 4 25 9 225 2 5 125 1 125 2 Dummy 50 0 0 3 1 30 8 240 3 3 75 10 750 3 4 20 14 Total

280

3,170

Ans.20: Convert the given profit matrix into a loss matrix by subtracting each element of the matrix from the highest value viz.44.The resulting loss matrix is as follows:

Loss Matrix Customer ------------------------------------------------ Factory A B C D supply P 4 19 22 11 100 Q 0 9 14 14 30 R 6 6 16 14 70 Demand 40 20 60 30 150/200 The loss matrix, obtained as above is an unbalanced one, We introduce a dummy column to make it a balanced one.

353

Loss Matrix Customers Factory A B C D Dummy Supply

______________________________________

P 4 19 22 11 0 100 Q 0 9 14 14 0 30 R 6 6 16 14 0 70 Demand 40 20 60 30 50 200/200 By using Vogal’s approximation method, the following initial feasible solution is found Customers Factory A B C D Dummy Supply P 10 60 30 e 100 4 19 22 11 0 -------------------------------------------------------------------------------------------------------------- Q 30 30 0 9 14 14 0 ---------------------------------------------------------------------------------------------------------------- R 20 50 70 6 6 16 14 0 ----------------------------------------------------------------------------------------------------------------- Demand 40 20 60 30 50 200/200 Since the number of allocation’s in the initial feasible solution are 6 and for applying optimality test they should be equal to (m+n-1)=7, therefore we enter a very small assignment equal to e in the minimum cost so that no loop is formed. Let us introduce the variables Ui and Vj such that Ui + Vj = Cij for allocated cells. We thus have the following relations: U1 + V1 = 4 U2 + V1 U

= 0 1 + V3 = 22 U3 + V2

U = 6

1 + V4 = 11 U3 + V5U

= 0 1 + V5

Put U + 0

1V

= 0,we get 1 = 4;V3 = 22; V4 = 11; V5 = 0; U3 = 0;V2 = 6 and U2

= (-4)

Compute: Cij – (Ui + Vj) for non-allocated cells. U1V2 U

=19 - (0 + 6) = 13 2V2 = 9 - (- 4 + 6) =7

354

U2V3U

= 14 - ( - 4 + 22) = (-4) 2V4

U = 14 - (- 4 + 11) = 7

2V5 U

= 0 - (- 4 + 0) = 4 3V1

U = 6 - (0 + 4) = 2

3V3U

= 16 - (0 + 22) = (-6) 3V4

= 14 - (0 + 11) = 3

Since the value of Cij - (Ui + Vj)is negative in two cells therefore the initial solution is not optimal, Introduce an assignment 0 in the cell U3V3 and construct a loop shown as below, after adjusting. Customers Factory A B C D Dummy Supply Ui -------------------------------------------------------------------------------------------------------------------------------- P 10 60-0 30 e+0 100 U1

= 0

4 19 22 11 0 30 Q 30 U2

0 9 14 14 0

= (-4)

20 0 50-0 R 70 U3

6 6 16 14 0

= 0

Demand 40 20 60 30 50 200/200 Vj V1= 4 V2 = 6 V3 = 22 V4 =11 V5

= 0

Maximum value of 0 = 50 Apply optimality test once again. Introduce Ui and Vj’

s and determine their values

Compute Cij - (Ui + Vj) for non-allocated cells, since it comes out to be negative for U2V3 cell, therefore we repeat the aforesaid process by introducing 0 in U2V3

cell, the minimum value 0f 0 is 10.

355

Customers Factory A B C D Dummy Supply U

i

P 10+θ 10-θ 30 50 100 U1

=0

4 19 22 11 0 0 Q 30-θ 30 U2

=(-4)

0 9 14 14 0 R 20 50 70 U3

= ( - 6)

6 6 16 14 0 Demand 40 20 60 30 50 200/ 200 V1 V1=4 V2=12 V3=22 V4=11 V5

=0

The second improved solution obtained is as under: Apply optimality test to the solution once again after determining the values of Ui and Vj. Since Cij - (Ui + Vj

) for non-allocated cell is positive, therefore the following solution is optimal one.

Customers Factory A B C D Dummy Supply Ui ------------------------------------------------------------------------------------------------------------------------------ P 20 30 50 100 U1=0 4 19 22 11 0 10 Q 20 30 U2=(-4) 0 9 14 14 0 R 20 50 70 U3=(-2) 6 6 16 14 0 Demand 40 20 60 30 50 200/200

356

Vj V1=4 V2=8 V3=18 V4+11 V5=0 Transferring the solution to the original profit matrix, we get; Customers Factory A B C D Dummy Supply ------------------------------------------------------------------------------------------------- P 20 30 50 100 40 25 22 33 0 Q 20 10 30 44 35 30 30 0 R 20 50 70 38 38 28 30 0 Demand 40 20 60 30 50 Maximum profit =20 Rs.40+30Rs.33+20*Rs.44+10*Rs.30+20*Rs.38+50*Rs.28+50*Rs.0 =Rs.800+Rs.990+Rs.880+Rs.300+Rs.760+Rs.1,400 =Rs.5,130

Ans. 21

The given information can be tabulated in following transportation problem: Project

Auditor 1 2 3 Time available (Hours)

(Rs.) (Rs.) (Rs.) 1 1,200 1,500 1,900 160 2 1,400 1,300 1,200 160 3 1,600 1,400 1,500 160

Time Required 130 140 160 (Hours)

The given problem is an unbalanced transportation problem. Introducing a dummy project to balance it, we get

357

Project Auditor 1 2 3 Dummy Time

available (Hours)

1 1,200 1,500 1,900 0 160 2 1,400 1,300 1,200 0 160 3 1,600 1,400 1,500 0 160

Time Required

(hrs.)

130 140 160 50 480

The objective here is to maximize total billing amount of the auditors. For achieving this objective, let us convert this maximization problem into a minimization problem by subtracting all the elements of the above payoff matrix from the highest payoff i.e. Rs. 1900.

Project Auditor 1 2 3 Dummy Time available

1 700 400 0 1900 160 2 500 600 700 1900 160 3 300 500 400 1900 160

Time required

(Hrs)

130 140 160 50 480

Now, let us apply Volgel’s Approximation Method to the above matrix for finding the initial feasible solution.

Project (Figure of payoff’s in Rs. 00’s) Auditor 1 2 3 Dummy Time

Available Difference

1

7

4

160 0

19

160/0

4/-/-/-

2

5

110 6

7

50 19

160/50/0

1/1/13/13

3

130 3

30 5

4

19

160/30/0

1/2/14/-

Time 130/0 140/110/0 160/0 50/0 Required Difference 2/2/-/- 1/1/1/1 4/-/- 0/0/0

The initial solution is given below. It can be seen that it is a degenerate solution since the number of allocation is 5. In order to apply optimality test, the total number of allocations should be 6 (= m + n -1). To make the initial solution a non-degenerate, we introduce a very small quantity in the least cost independent cell which is cell of Auditor 3, Project 3.

358

Project Auditor 1 2 3 Dummy Time Available

1

7

4

160 0

19

160

2

5

110 6

7

50 19

160

3

130 3

30 5

e 4

19

160

Time Required

130 140 160 50

Introduce ui’s and vj’s such that ∆ ij = Cij– (ui+vj) (for I, = 1 to 3; j = 1,2,3, dummy). To determine the values of ui’s and vj’s we assume that u3 = 0, values of other variables i.e. ui’s, vj’s

Project and … are calculated as follows:

Auditor 1 2 3 Dummy Uj

’s

U1

=-4

U2

=1

U3=0

1 8

7

3

4

160

0

5

19

2 1

5

110

6

2

7

50

19

3 130

3

30

5

e

4

1

19 Vj’s v1=3 v2= 5 v3=4 v4

Since all for non basic cells are positive, therefore the initial solution obtained above is optimal. The allocation of projects to auditors and their billing amount is given below: Here an auditor may be involved in more one project as apparent from the following solutions.

=18

Auditor Project Billing amount (Rs.)

1 3 160xRs. 1900 = 3,04,000 2 2 110xRs. 1300 = 1,43,000 3 1 130xRs. 1600 = 2,08,000 3 2 30xRs. 1400 = 42,000 Total billing = 6,97,000

Hence, the maximum total billing during the next month will be Rs. 6,97,000

359

Assignment

Ans. 1:

I II III IV 1 16 52 34 22 2 26 56 8 52 3 76 38 36 30 4 38 52 48 20

Step 1: Subtract the smallest element of each row from every element of the corresponding row

I II III IV 1 0 36 18 6 2 18 48 0 44 3 46 8 6 0 4 18 32 28 0

Step 2: Subtract the smallest element of each column from every element in that column

I II III IV

1 0 28 18 6

2 18 40 0 44

3 46 0 6 0

4 18 24 28 0 Step 3: Drew minimum number of horizontal and vertical lines to cover all the zeros

I II III IV

1 0 28 18 6

2 18 40 0 44

3 46 0 6 0

4 18 24 28 0

The optimal assignment is 1 ─ I = 16 2 ─ III = 8 3 ─ II = 38 4 ─ IV =

20

Minimum time taken = 82 hours 82 hours

Ans. 2:

(a) Consider the following assignment problem: Division N E W S

360

A 14 20 11 19 B 12 10 15 9 Marketing Executives C 16 19 18 15 D 17 13 15 14

Step 1 Select the minimum element of first row and subtract it from all the elements of the row. On repeating the step with all the rows of the above matrix, we get the following

Division

N E W S A 3 9 0 8 B 3 1 6 0 Marketing Executives C 1 4 3 0 D 4 0 2 1

Step 2 Select the minimum element of first column and subtract it from all the elements of the column. On repeating this step with all the columns of the above matrix; we get the following

Division N E W S A 2 9 0 8 B 2 1 6 0 Marketing Executives C 0 4 3 0 D 3 0 2 1

Step 3 On drawing the minimum number of lines in the above matrix, so as to cover at the zeros, we get the following matrix. Division

N E W S A 2 9 0 8 B 2 1 6 0 Marketing Executives C 0 4 3 0 D 3 0 2 1

Since the minimum number of lines drawn under the step is equal to number of marketing executives or number of divisions, therefore we go over to the final step for determining the required optimal solution. Step 4 For determining the optimal solution scan each row in turn for a single uncovered zero in it, encircle it and pass a line in its column.

361

Division N E W S A 2 9 0 8 B 2 1 6 0 Marketing Executives C 0 4 3 0 D 3 0 2 1

The optimal assignment obtained in this case is as under: Marketing Division Cost Executive Rs. A W 11 B S 09 C N 16 D E Total minimum cost

13

49

Using the information that the factory works effectively 7 hours (=420 minutes) a day and the time required by each operator for producing each of the products, we obtain the following production and profit matrices:

Ans. 5:

Production Matrix (units) Profit Matrix (in Rs.) Operator Product Operator Product

A B C D A B C D P 70 42 30 35 P 210 84 120 35 Q 60 84 140 105 Q 180 168 560 105 R 70 60 42 42 R 210 120 168 42 S 21 42 28 28 S 63 84 112 28

In order to apply the assignment algorithm for minimizing losses, let us first convert this profit matrix to a loss matrix by subtracting all the elements of the given matrix from its highest element which is equal to Rs.560. The matrix so obtained is given below:

Operator Product A B C D

P 350 476 440 525 Q 380 392 0 455 R 350 440 392 518 S 497 476 448 532

Now apply the assignment algorithm to the above loss matrix. Subtracting the minimum element of each row from all elements of that row, we get the following matrix:

362

Operator Product A B C D

P 0 126 90 175 Q 380 392 0 455 R 0 90 42 168 S 49 28 0 84

Now subtract the minimum element of each column from the elements of that column to get the following matrix:

Operator Product A B C D

P 0 98 90 91 Q 380 364 0 371 R 0 62 42 84 S 49 0 0 0

Draw the minimum number of lines to cover all zeros. The minimum number of lines to cover all zeros is three which is less than the order of the square matrix (i.e.4) thus the above matrix will not give the optimal solution. Subtract the minimum uncovered element (=62) from all uncovered elements and add it to the elements lying on the intersection of two lines, we get the following matrix:

Operator Product A B C D

P 0 36 90 29 Q 380 302 0 309 R 0 0 42 22 S 111 0 62 0

The minimum number of lines which cover all zeros is 4 which is equal to the order of the matrix, hence, the above matrix will give the optimal solution. Specific assignments in this case are as below:

Operator Product A B C D

P 0 36 90 29 Q 380 302 0 309 R 0 0 42 22 S 111 0 62 0

Operator Product Profit (Rs.) P A 210 Q C 560 R B 120 S D 28

Total Profit (Rs.) 918 Ans. 8:

363

(i)

4 12 16 8 20 28 32 24 36 44 48 40 52 60 64 56

Subtracting minimum element – each row.

0 8 12 4 0 8 12 4 0 8 12 4 0 8 12 4

Subtracting minimum element – each column,

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Minimum no. of lines to cover all zeros = 4 = order of matrix. Hence optional assignment is possible.

Minimum cost = 4 + 28 + 48 + 56 = 136.

= AR1 + BR2 + CR3 + DR4

Since all are zeros, there are 24 solutions to this assignment problem.

Viz. A B C D R1 R2 R3 R4 R2 R3 R4 R1 R3 R4 R1 R2 R4 R1 R2 R3 R1 R3 R4 R2 etc.

A can be assigned in 4 ways, B in 3 ways for each of A’s 4 ways.

(ii) SP – VC = 100 Rs.

A B C D R1 96 88 84 92 R2 80 72 68 76 R3 64 56 52 60 R4 48 40 36 44

Subtracting the highest term

0 8 12 4 16 24 28 20 32 40 44 36 48 56 60 52

Subtracting minimum term of each row.

364

0 8 12 4 0 8 12 4 0 8 12 4 0 8 12 4

Which is the same as the earlier matrix

Maximum contribution = Rs. (96 + 72 + 52 + 44) = Rs. 264. Alternative Solution:

Maximisation of contribution is same as minimizing cost. Hence, same assignments as in (i) will be the optional solution.

Maximum Contribution Rs. (400 – 136) = Rs. 264

(iii) (a) The relative cost of assigning person i to region r does not change by addition or subtraction of a constant from either a row, or column or all elements of the matrix.

(b) Minimising cost is the same as maximizing contribution. Hence, the assignment solution will be the same, applying point (i) above.

(c) Many zero’s represent many feasible least cost assignment. Here, all zeros mean maximum permutation of a 4 × 4 matrix, viz. 4 × 3 × 2 × 1 = 24 solutions are possible.

Reducing minimum from each column element (figure in ’000s) Ans. 9:

Step 1 Step 2

R R1 R2 R3 4 R R1 R2 R3

C

4

1 1 1 − − C 0 1 0 − −

C − 2 0 − 0 C − 2 0 − 0

C 0 3 − 0 − C 0 3 − 0 −

C − 4 − 2 1 C − 4 − 1 0

Number of lines to connect all zeros nos. is 4 which is optional.

Alternatively you may also reduce the minimum from each row.

Step 1 Step 2

R R1 R2 R3 4 R R1 R2 R3

C

4

0 1 1 − − C 0 1 1 − −

C − 2 0 − 0 C − 2 0 − 0

C 1 3 − 0 − C 0 3 − 0 −

C − 4 − 0 1 C − 4 − 0 0

Number of lines to connect all zeros nos. is 4 which is optional.

All diagonal elements are zeros and are chosen. The minimum cost is Rs.15,000 C1 – R1 4,000; C2 – R2 4,000; C3 – R3 2,000; C4 – R4

5,000; (Total) = 15,000.

Let us first formulate the preference ranking assignment problem. Ans.10:

MANAGERS

365

Room No. M1 M2 M3 M4 M5 301 – 4 2 – 1 302 1 1 5 1 2 303 2 – 1 4 – 304 305 – 3 4 2 –

3 2 3 3 3

We have to find an assignment so that total preference ranking is minimum. In a cell (-) indicates that no assignment is to be made in that particular cell. Let us assign a very large ranking value M to all such cells. Step 1 : From each row, subtract the minimum element of that row, from all the elements of that row to get the following matrix.

MANAGERS

Room No M1 M2 M3 M4 M5 301 M 3 1 M 0 302 0 0 4 0 1 303 1 M 0 3 M 304 1 0 1 1 1 305 M 1 2 0 M

Draw the minimum number of lines in the above table to cover all zeros. In this case the number of such lines is five, so the above matrix will give the optimal solution. The assignment is made as below:

MANAGERS

Rooms No. M1 M2 M3 M4 M5 301 M 3 1 M 0 302 0 0 4 0 1 303 1 M 0 3 M 304 1 0 1 1 l 305 M 1 2 0 M

Thus, the assignment is M1 → 302, M2 → 304, M3 → 303, M4 → 305, M5 → 301 and the total minimum ranking = 1 + 2 + 1 + 2 + 1 = 7

Ans. 11:

Dummy machine (M5) is inserted to make it a balanced cost matrix and assume i ts installation cost to be zero. Cost of install at cell M3 (J) and M2 (L) is very high marked as é.

J K L M N M1

M2

M3

M4

M5 (Dummy)

18

24

é

28

0

22

18

22

16

0

30

é

28

24

0

20

20

22

14

0

22

18

14

16

0 Step 1

Subtract the minimum element of each row from each element of that row

J K L M N

366

M1 M2 M3

0 6 é

4 0 8

12 é

14

2 2 8

4 0 0

M4 14 2 10 0 2 M5 (Dummy) 0 0 0 0 0

Step 2

Subtract the minimum element of each column from each element of that column

J K L M N M1 M2 M3 M4

M5 (Dummy)

0 6 é 14 0

4 0 8 2 0

12 é

14 10 0

2 2 8 0 0

4 0 0 2 0

Step 3

Draw lines to connect the zeros as under:

J K L M N M1 0 4 12 2 4 M2 6 0 é 2 0 M3 é 8 14 8 0 M4 14 2 10 0 2

M5 (Dummy) 0 0 0 0 0

There are five lines which are equal to the order of the matrix. Hence the solution is optimal. We may proceed to make the assignment as under:

J K L M N M1

M2

M3

M4

M5 (Dummy)

0

6

e

14

0

4

0

8

2

0

12

e

14

10

0

2

2

8

0

0

4

0

0

2

0

The following is the assignment which keeps the total cost at minimum:

Machines Location Costs Rs. M1 J 18 M2 K 18

367

M3 N 14 M4 M 14

M5 (Dummy) L 0 Total 64

Since the Executive Director of the 5 star hotel is interested in maximizing the revenue of the hotel, therefore, the objective of the given problem is to identify the preferences of marriage parties about halls so that hotel management could maximize its profit. To solve this problem first convert it to a minimization problem by subtracting all the elements of the given matrix from its highest element which is equal to Rs. 10,000. The matrix so obtained which is known as loss matrix is given below:

Ans. 12:

Loss matrix/Hall

Marriage party 1 2 3 4 A 0 1000 M M

B 2000 0 2000 5000 C 3000 0 4000 2000

D 0 2000 M M

Now apply the assignment algorithm to the above loss matrix. Subtracting the minimum element of each column from all elements of that column, we get the following matrix.

Loss matrix/Hall

Marriage party 1 2 3 4 A 0 1000 M M

B 2000 0 0 3000 C 3000 0 2000 0

D 0 2000 M M

The minimum number of lines to cover all zeros is 3 which is less than the order of the square matrix (i.e. 4), the above matrix will not give the optimal solution. Subtracting the minimum uncovered element (= 1000) from all uncovered elements and add it to the elements lying on the intersection of two lines, we get the following matrix

Marriage party 1 2 3 4

A 0 0 M M

B 3000 0 0 3000 C 4000 0 2000 0

D 0 1000 M M

Since the minimum number of lines to cover all zeros is 4 which is equal to the order of the matrix, the above matrix will give the optimal solution which is given below:

Marriage party 1 2 3 4 A 0 0 M M B 3000 0 0 3000 C 4000 0 2000 0 D 0 1000 M M

368

and the optimal schedule is :

Revenue (Rs.) Marriage party A → Hall 2 9,000 B → Hall 3 8,000 C → Hall 4 8,000 D → Hall 1 10,000 Total 35,000

The following matrix gives the cost incurred if the typist (i = A, B, C, D, E) executes the job (j = P, Q, R, S, T). Ans. 14:

Job Typist P Q R S T

A 85 75 65 125 75 B 90 78 66 132 78 C 75 66 57 114 69 D 80 72 60 120 72 E 76 64 56 112 68

Subtracting the minimum element of each row from all its elements in turn, the above matrix reduces to Job

Typist P Q R S T A 20 10 0 60 10 B 24 12 0 66 12 C 18 9 0 57 12 D 20 12 0 60 12 E 20 8 0 56 12

Now subtract the minimum element of each from all its elements in turn, and draw minimum number of lines horizontal or vertical so as to cover all zeros . All zeros can be covered by four lines as given below:

2 2 0 4 0 6 4 0 10 2 0 1 0 1 2 2 4 0 4 2 2 0 0 0 2

Since there are only 4 lines (<5) to cover all zeros, optimal assignments cannot be made. The minimum uncovered element is 2. We subtract the value 2 from all uncovered elements. Add this value to al junction values and leave the other elements undisturbed. The revised matrix to obtained is given below:

2 2 2 4 0 4 2 0 8 0 0 1 2 1 2 0 2 0 2 0 2 0 2 0 2

369

Since the minimum no. of lines required to cover al the zeros is only 4(<5), optimal assignment cannot be made at this stage also. The minimum uncovered element is 1, repeating the usual process again, we get the following matrix.

2 1 2 8 0 4 1 0 7 0 0 0 2 0 2 0 1 0 1 0 3 0 3 0 3

Since the minimum number of lines to cover all zeros is equal to 5, is this matrix will give optimal solution? The optimal assignment is made in the matrix below:

Typist P Q R S T A 2 1 2 3 0 B 4 1 0 7 0 C 0 0 2 0 2 D 0 1 0 1 0 E 3 0 0 0 3

Cost ( Rs.) Thus typist A is given job 75 T : Thus typist B is given job 66 R : Thus typist C is given job 66 Q : Thus typist D is given job 80 P : Thus typist E is given job S 112 Total Rs.399 Note: In case the above solution is not unique. Alternate solution also exists.

Ans. 17: (a) Sum of the proportion = (8 + 7 + 5 + 4) = 24

Assuming Rs. 1,000 as one unit, the effective matrix is as follows:

Effective Matrix Managers

East West North South Z (8/24) × 240 = 80 (8/24) × 192 = 64 (8/24) × 144 = 48 (8/24) × 20 = 40 N (7/24) × 240 = 70 (7/24) × 192 = 56 (7/24) × 144 = 42 (7/24) × 120 = 35 O (5/24) × 240 = 50 (5/24) × 192 = 40 (5/24) × 144 = 30 (5/24) × 120 = 25 P (4/24) × 240 = 40 (4/24) × 192 = 32 (4/24) × 144 = 24 (4/24) × 120 = 20

Convert the maximization problem to minimization problem

The resultant loss matrix is as follows:

Loss Matrix

Managers East West North South M 0 16 32 40

370

N 10 24 38 45 O 30 40 50 55 P 40 48 56 60

Row operation

Managers East West North South M 0 16 32 40 N 0 14 28 35 O 0 10 20 25 P 0 8 16 20

Column operation

Managers East West North South M 0 8 16 20 N 0 6 12 15 O 0 2 4 5 P 0 0 0 0

Managers

East

West

North

South

M 0 6 14 18 N 0 4 10 13 O 0 0 2 3 P 2 0 0 0

Managers

East

West

North

South

M 0 2 10 14 N 0 0 6 9 O 4 0 2 3 P 6 0 0 0

Managers

East

West

North

South

M 0 2 8 12 N 0 0 4 7 O 4 0 0 1 P 8 2 0 0

Assignment Sales

Rs.

M – East N – West O – North P – South

371

1,86,000

Ans. 20

The initial matrix relating to nurse-patient combination is as under:

Nurse Patients W X Y

K 10 10 30 L 30 10 20 M 20 30 20

Deducting the lowest element of each row from the other elements of the same row, we get the following matrix:

0 0 20 20 0 10 0 10 0

We deduct the lowest element of each column from the other elements of the same column. Since there is zero in each column, the same matrix will be returned.

Draw lines to connect zeros as under:

0 0 20 20 0 10 0 10 0

There are three lines as required by the order of matrix of three.

Hence the solution is optimal.

Allocation of patients to nurses as under to minimize the cost

0 0 20 0 0 10

K W 10 400 400

L X 10 400 400

M Y 20 800

800 Total minimum cost

1600

(iii) With the introduction of a new patient and a new nurse, the original matrix of nurse-patient combinations will stand revised as under:

Nurse Patients W X Y Z

K 10 10 30 40 L 30 10 20 40

M 20 30 20 40 N 50 50 50 50

372

9

Deducting the lowest element of each row from the other element of the same row, we get the following matrix:

0 0 20 30 20 0 10 30 0 10 0 20 0 0 0 0

Deduct the lowest element of each column from the other elements of the same column. Since there is zero in each column, the same matrix will be returned. Draw lines to connect zeros as under:

0 0 20 30 20 0 10 30 0 10 0 20 0 0 0 0

There are four lines as required by the order of matrix of four

Hence the solution is optimal.

Proceed to allocate the patients to nurses as under to minimize the cost.

0 0 20 20 0 10 0 10 0 0 0 0

K W 10 400 400 L X 10 400 400 M Y 20 800 800 N Z 50 2000 2000

Total minimum cost

3600 (iv) The cost of new nurse per hour is Rs. 50 in respect of any patient and the cost of the existing

nurses for attending to the new patient is Rs. 40 per hour. Both these rates are greater than the values of other elements of existing nurse-

patient combination matrix. Thus the new nurse row and new patient column will have a higher value than the element of the existing matrix. Hence the new nurse can be allocated to the new patient without having to redo the assignment exercise. Hence we need not to a fresh assignment. N will be assigned to patient Z at 50/ hr is Rs. 2000/ week. This will be the extra minimum cost to the hospital i.e. 2000 + 1600 = 3600.

373

Ans. 12 PERT & CPM

(i) The required network is given below:

(ii) Critical path : B,E,F =7+7+6 = 20 days Ans. 13 The network is constructed as given in figure below:

(i) The TE’s and TL

Event No.: ’s for various events computed on the network are as follows:

1 2 3 4 5 6 7 8 9 10 T 0 E 4 1 5 7 11 15 17 18 25 T 0 L 12 1 13 7 17 15 17 18 25

(ii) Activity floats are computed using the following formula:

374

Float = TL (Head event) – TE

Activity (Tail event) – Duration

Duration TE T (Tail Event) L Float (Head Event) 1-2 4 0 12 8 1-3 1 0 1 0 2-4 1 4 13 8 3-4 1 1 13 11 3-5 6 1 7 0 4-9 5 5 18 8 5-6 4 7 16 5 5-7 8 7 15 0 6-8 1 11 17 5 7-8 2 15 17 0 8-9 1 17 18 0

8-10 8 17 25 0 9-10 7 18 25 0

Critical path is given by all those activities which have zero floats. Along the zero float activities, there are two such critical paths: (i) 1 → 3 → 5 → 7 → 8 → 9 → 10 (ii) 1 → 3 → 5 → 7 → 8 → 10 The project duration is 25 weeks.

Ans. 16(i)

A D F = 16+ 10+12 = 38 B E F = 20+ 6+ 12= 38 (ii) A-C –E- F = 16+8 +6 +12 = 42 Critical Path (iii) Total float and free float for each activity

375

(iii) Total float and free float for each activity

Activity Normal Earliest Time Latest Time Float Free Time start finish start finish total Days A 16 0 16 0 16 0 0 B 20 0 20 4 24 4 4 C 8 16 24 16 24 0 0 D 10 16 26 20 30 4 4 E 6 24 30 24 30 0 0 F 12 30 42 30 42 0 0

Ans. 18

(a) 20 204

Z −= = 0; Probability = 0.50

(b) 18 204

Z −= = –0.50; Probability = 0.31

(c) 24 204

Z −= = 1; Probability = 0.84

Ans. 19

Tcp = 60 S.D. = 9 = 3.

60 + 3 × 2.3 = 67 weeks (Answer)

Ans. 21 The required network is drawn below:

376

(i) From the above network, it can be noted that the critical path is 1 – 2 – 4 – 6 – 8. (ii) Expected cost of construction of the plant = (5 + 3 + 4 + 9 + 2 + 12 + 20 + 7 + 14 + 4) millions of Rs. = Rs.80 million (iii) Expected time required to build the plant = 4 + 6 + 9 + 1 = 20 months. (iv) It is given that the time required for one activity is independent of the time and cost of any other activity and variations

are expected to follow normal distribution, the S.D. Hence, the variance of the expected time is determined by summing the variance of critical activities and is = 1 + 2 + 5

+ 1 = 9. Standard Deviation of the expected time = √9 = 3 months.

Ans. 24 The earliest expected completion time, latest allowable completion time and slack time for each event is:- Event δ2 te Earliest Earliest Latest Latest Slack (I – j) start finish start finish 1 – 2 2 4 0 04 0 4 0 1 – 3 3 5 0 5 16 21 16 2 – 4 01 20 4 24 4 24 0 2 – 5 10 20 4 24 14 34 10 3 – 4 2 3 5 08 21 24 16 3 – 6 4 8 5 13 24 32 19 4 – 5 4 10 24 34 24 34 0 4 – 6 2 6 24 30 26 32 2 5 –7 1 8 34 42 34 42 0 6 – 7 8 10 30 40 32 42 2

-

The critical path is 1 2 4 5 7 = 42 Variance of project time

δ2 = 2 + 1 + 4 + 1 = 8

Therefore, δ2 = 8 and scheduled time T5

= 38

Z = 84238 −

= 84−

= - 1.41

From table on normal curve, the area of Z = 1.41 is given as 0.4207 Therefore the probability of completion of the project by the scheduled time = (0.5 – 0.4207) = 7.93%

377

Ans. 25

Calculation of expected time and variance of each activity:

Activity Optimistic Most likely Pessimistic Expected Variance Days Days Days Duration

1−2 4 10 16 10 4 1−3 3 6 9 6 1 1−4 4 7 16 8 4 2−5 5 5 5 5 0 3−5 8 11 32 14 16 4−6 4 10 16 10 4 5−6 2 5 8 5 1

The network diagram is as under:

According to probability values given in the question probability is 11.9% To obtain 95% confidence level:

Critical Path: 1-3 3-5 5-6 Duration (days) 6 14 5 = 25 days Standard deviation: 1 + 16 + 1 = 18 18 = 4.24 Probability that the project will be completed five days earlier:

Z = 24.4

2520 −= 1.18

According to probability values given in the question probability is 11.9% To obtain 95% confidence level:

1.65= 24.4

25−X

X – 25 = 6.996 X = 32 days

378

Ans. 26:

i. Activity to tm tp

2

60tpt2σ

−= Expected Variance

----------------------------------------------- duration (in weeks) te = (t0 + 4tm + tp

) / 6

1-2 3 6 15 7 4 1-3 2 5 14 6 4 1-4 6 12 30 14 16 2-5 2 5 8 5 1 2-6 5 11 17 11 4 3-6 3 6 15 7 4 4-7 3 9 27 11 16 Critical Path 1-2-6-7

Expected project duration = (7+11+18)=36 week (iv) Probability of project completion in 38 weeks o = 4 + 4 +16 = 24 o = 24 = 4.90 o

38 - 36 2s Z = -------- = --------- = 0.41 4.9 4.9 Value of Z = 0.41 in Z tables is 0.1591 P(Z) = 0.5+ 0.1591 Probability of project completion in 38 weeks is 66%

379

(v) Project duration (say x weeks) with 95% chances of completion: x - 36 1.65 = --------- 4.9 or 8.085 = x - 36 or x = 44 weeks

Ans. 27: The earliest and latest expected time for each event is calculated by considering the expected time of each activity as shown in the table below:

Activity (i – j)

t t0 tm tp e = (t0 + 4tm + tp 2

60tpt2σ

−=

) / 6

1-2 2 2 14 4 4 1-3 2 8 14 8 4 1-4 4 4 16 6 4 2-5 2 2 2 2 0 3-5 4 10 28 12 16 4-6 4 10 16 10 4 5-6 6 12 30 14 16

(a) The project network is drawn below:

(i) Critical Path is : 1 – 3- 5 – 6 (ii) The expected duration and variance of each activity is shown in the table above. The expected project length is the sum of the duration of critical activities. Hence, Expected project Length = 8 + 12 + 14 = 34 months

380

(iii) Variance of the project length is the sum of the variances of critical activities. Variance of project length = σ² = 4 + 16 + 16 = 36 months Therefore, Standard Deviation = σ = √36 = 6 (iv) Probability that the project will be completed at lest 8 months earlier than the expected time of 34 months is

given by

Prob.

−−=

−≤

6348)(34

eσeTsT

Z = Prob.[Z ≤ - 1.33]

But Z = -1.33 from the normal distribution table is 0.0918. Students may please note that the values for the Prob. For a Z value correspond tot e shaded area as shown in the

diagram below:

Thus, the probability of completing the project within 26 months is 9.18%. (v) If the project due date is 38 months, then the probability of not meeting the due date is given by

Prob.

−=

−>

634)(38

eσeTsT

Z = Prob.[Z > 0.67]

But Z = 0.67 from the normal distribution is 0.2514. Thus, the probability of not meeting the due date is 25.14%.

Ans. 28: The required network is drawn below:

381

The expected time marked in the above network diagram for various activities is calculated in the table below:

Activity Time (in weeks) Expected time (weeks) te = (t0 + 4tm

+ tp

Variance

) / 6

2

60tpt2σ

−= Optimistic

(to

Most likely (t) m

Pessimistic (t) p)

1-2 3 3 3 3 0 2-3 3 6 9 6 1 2-4 2 4 6 4 4/9 3-5 4 6 8 6 4/9 4-6 4 6 8 6 4/9 5-6 0 0 0 0 0 5-7 3 4 5 4 1/9 6-7 2 5 8 5 1

(i) Variance of each of the activities has been calculated in the last column of the above table. (ii) Critical path is given by 1 – 2 – 3 – 5 – 6 – 7 and the expected project length is 20 weeks. (iii) Variance of the critical path = σ² = 0 + 1 + 4/9 + 0 + 1 = 22/9 = 2.444 Mean = x = 20 weeks

To calculate the probability of completing the project in 23 weeks, we will first calculate the normal Z as below:

Z = σ

xD −=

444.22023−

= 1.92

P (x < 23) = P (z < 1.92) = 0.9726 (from the normal table) Thus, the probability that the project will be completed in 23 weeks is 97.26%.

Ans. 29:

382

The network for the given problem is drawn below:

1 2 9

4 6 817

17.8317.8319

17.67

3 722.83

5

20

16.6

7

In the table below, we have calculated the expected duration and variance of each activity.

Activity Time Expected duration

{(a+4m+b)÷6}

Variance {(b-a)÷6}2 Optimistic

a

Most Likely

m

Pessimistic

b

1-2

2-3

2-4

2-8

3-4

3-5

4-6

5-7

5-9

6-7

6-8

7-9

14

14

13

16

-

15

13

-

14

-

-

16

17

18

15

19

-

18

17

-

18

-

-

20

25

21

18

28

-

27

21

-

20

-

-

41

17.83 17.83 15.17

20 -

19 17 -

17.67 - -

22.83

16.67

3.36 1.36

4

17.36

20.08

383

8-9 14 16 22

Variance paths are: 1-2-3-5-7-9 77.49

1-2-3-5-9 72.33 1-2-3-4-6-7-9 75.49 1-2-3-4-6-8-9 69.33 1-2-8-9 54.5 1-2-4-6-8-9 66.67 1-2-4-6-7-9 72.83

Hence the critical path is 1-2-3-5-7-9 with duration of 77-49 days or 78 days approximately.

Variances of various activities on critical path have been calculated in the last column of the above table.

Hence standard deviation of critical path = √ 26.08 = 5.12

Now we want to find out that within how many days the project should be completed so as to provide 95% probability of break even.

Z0.95

= 1.65

Hence, 1.65 = {(D-77.49)÷5.12}

Or, D = 1.65× 5.12+77.49 = 85.94 or 86 days

The fixed cost of the project is Rs. 8 lakhs and the variable cost is Rs. 9,000 per day.

Thus, amount to bid = Rs. 8 lakhs+ Rs. 9,000×86

= Rs. 8 lakhs + Rs. 7,74,000

= Rs. 15,74,000 Ans. 34:

(a) Critical Paths:

All are critical paths:

384

(i) 1 – 2 – 5 – 6 2 + 8 + 5 = 15 (ii) 1 – 3 – 5 – 6 3 + 7 + 5 = 15 (iii) 1 – 4 – 5 – 6 4 + 6 + 5 = 15 (iv) 1 – 3 – 4 – 5 – 6 3 + 1 + 6 + 5 = 15 (i) Choose 5 – 6, common path; Crash by 1 day (ii) Choose: 1 – 2, 1 – 3, 1 – 4

Or

(iii) Choose: 1 – 2, 3 – 5, 4 – 5

Or

(iv) Choose: 2 - 5 , 3 – 5, 4 – 5 Or

(v) Choose: 1 – 3, 1 – 4, 2 - 5 Ans. 35: (i) Assuming that the duration of activity 3 – 5 is 4 weeks.

The various critical paths are: 1-2-5-8-9 15 weeks 1-3-4-7-8-9 15 weeks 1-3-4-6-7-8-9 15 weeks 1-3-5-8-9 15 weeks

(ii) Note: Since the duration for activity 3-5 is not specified it is open for you to assume the duration. Depending upon the duration assume three possibilities emerge.

1. If the duration assumed is more than 4 weeks then that path (13, 35, 58, 89) alone will be critical. In that case you can choose any of the activity in the critical path.

2. If the duration assumed is exactly 4 weeks then it will be one of the 4 critical paths and the various possibilities are given below.

3. If the duration assumed is less than 4 weeks then the solution should be based on 3 of the critical paths namely 12,589, 1346789 and 134789. This has 16 combinations.

Reduce in the following ways, the project duration is. Since all the paths are critical, reduction is possible by combining activities. The activities can be independent, common to few paths and common to all the paths. The various categories are as follows: 1. Common to all the paths. 8-9 2. Independent : Combination 1. 1-2,3-5,4-6 and 4-7. Combination 2. 2-5,3-5,4-6 and 4-7. Combination 3. 1-2,3-5,4-7, 6-7. Combination 4. 2-5,3-5,4-7, 6-7. 3. Activities common to two of the paths. Combination 1. 1-2,1-3. Combination 2. 1-3,2-5. Combination 3. 3-4,5-8. Combination 4. 5-8,7-8.

385

4. Activities common to two of the paths and two independent activities. Combination 1. 1-2,3-4,3-5. Combination 2. 1-2,3-5,7-8. Combination 3. 2-5,3-4,3-5. Combination 4. 2-5,3-5,7-8. Combination 5. 4-6,4-7,5-8. Combination 6. 4-7,5-8,6-7. (Any three of the above combination.)

Ans. 36: (i) Project network based on the given activities is as under :

(ii) A review of the above network clearly shows that there are four paths 1 – 4 – 5; 1 – 2 –5 ; 1 –2 – 3 – 5;&

1 – 3 – 5 of duration 10 days; 11 days; 13 days and 4 days respectively. The longest path of 13 days viz,. 1 – 2 – 3 – 5 is the critical path of the drawn network.

(iii) The optimum duration of a project is that duration of the project for which the total cost (direct & indirect)

will be minimum. The cost corresponding to optimal duration is known as resultant cost of the project. To determine optimum duration and resultant cost of the project based on the given activities we proceed as follows:

Activity Normal Crash Normal Crash Cost slope Time Time Cost Cost per day (days) (days) Rs. Rs Rs. 1 – 2 4 3 1,500 2,000 500 1 – 3 2 2 1,000 1,000 -- 1 – 4 5 4 1,875 2,250 375

386

2 – 3 7 5 1,000 1,500 250 2 – 5 7 6 2,000 2,500 500 3 – 5 2 1 1,250 1,625 375 4 – 5 5 4 1,500 Total direct cost 10,125

2,125 625

The normal total cost (direct & Indirect) of completing the project in 13 days is : Normal direct cost : (Rs) 10,125 Indirect cost 6,500 13 days x Rs. 500 ______ Total normal cost : (Rs)

16,625

To determine the optimum duration and resultant cost we crash activities on the critical path by properly selecting them as under :

Activities 1 – 2 2 – 3 3 – 5 No. of available crash days 1 2 1 Cost slope per day (Rs) 500 250 375 Indirect cost per day (Rs) 500 500 500 Saving in cash -- 250 125 Ranking -- 1 2 The above ranking clearly shows that we should select the activity 2 – 3 and crash it for one day, as it

results in maximum saving of Rs. 250 per day. Let us crash 2 – 3 by 2 days. Rs. Normal direct cost 10,125 Cost slope (2 days x Rs. 250) 500 Indirect cost (11 days x Rs. 500) 5,500 ______ Total cost

16,125

After crashing the activity 2 – 3 we are left with the following paths as under : 1 – 2 2 – 3 3 – 5 of 11 days duration 1 – 2 2 – 5 of 11 days duration 1 – 4 4 – 5 of 10 days duration

387

1 – 3 3 – 5 of 4 days duration 1 – 2 is a common activity in the first two paths with cost slope of Rs. 500/- per day. There is no profit or

loss in crashing this actively. Hence crash it by one by. Rs. Normal direct cost 10,125 Total cost slope (Rs. 500 + 1 day x Rs. 500) 1,000 Indirect cost (10 days x Rs. 500) 5,000 ______ Total cost

16,125

Now we have the following four paths are as under : 1 – 2 2 – 3 3 – 5 of 10 days duration 1 – 2 2 – 5 of 10 days duration 1 – 4 4 – 5 of 10 days duration 1 – 3 3 – 5 of 4 days duration To reduce the duration of project further, we are required to select the activities on all the three paths.

These activities may be 3 – 5, 2 – 5, and 1 – 4. if all of these activities are crash by even 1 day each, then the total increase in cost would be (Rs. 375 + Rs. 500 + Rs. 375) or Rs. 1,250/- for saving Rs. 500. At this stage, we stop the process of crashing.

Hence optimal project duration

10 days

Resultant project cost/optimal cost : (Rs)

16,125

Ans. 38: (i) The required network is given below:

The various paths in the network are:

388

1 – 2 – 4 – 5 with project duration = 16 days 1 – 4 – 5 with project duration = 17 days 1 – 3 – 4 – 5 with project duration = 20 days The critical path is 1 → 3 → 4 → 5. The normal length of the project is 20 days and minimum project length is 12

days. (ii) Since the present schedule consumers more time than the minimum project length, the duration can be reduced by

crashing some of the activities. Also, since the project duration is controlled by the activities lying on the critical path, the duration of some of the activities lying on critical path can be reduced. It is given that overhead cost is Rs.60 per day. Step I: First, the crashing cost of activity (3, 4) being minimum, the duration of this activity can be compressed from 10 days to 9 days. The total cost for 19 day’s schedule

= Rs.15 + Rs.19 × 60 = Rs.1,155 Step II: Since the critical path remains unchanged, the duration of activity (3, 4) can be further reduced from 9 days to 8 days resulting in an additional cost of Rs.15 so that total cost for 18 days schedule = Rs.30 + Rs.60 × 18 = Rs.30 + Rs.1,080 = Rs.1,110. Step III: Continue this procedure till the minimum project length schedule. The calculations are given below:

Normal Project

length (days)

Job crashed Crashing Cost (Rs.) Overhead cost @

Rs.60 / day

Total Cost. (Rs.)

20 -- -- 20×60 1,200 19 3–4 1 × 15 = 15 19×60 1,155 18 3–4 2 × 15 = 30 18×60 1,110 17 3–4 3 × 15 = 45 17×60 1,065 16 4–5 3×15+1×40 = 85 16×60 1,045 15 3–4, 1–4 4×15+1×40+1×30= 130 15×60 1,030 14 1–3, 1–4, 2–4 130+1×30+1×25+1×10=195 15×60 1,035 13 1–3, 1–4, 2–4 195+1×25+1×30+1×10=260 13×60 1,040 12 1–3, 1–4, 1–2 260+25+30+20=335 12×60 1,055

(iii) Since the total cost starts increasing from 14 days duration onwards, the minimum total cost of Rs.1,030 for the optimum project duration of 15 days occurs for optimum duration of each job as given below: Job: (1,2) (1,3) (1,4) (2,4) (3,4) (4,5) Optimum: 9 8 14 5 6 1

Duration (day)

389

Path 1 → 2 → 4 → 5 = 9 + 5 + 1= 15 days Path 1 → 4 → 5 = 14 + 1 = 15 days Path 1 → 3 → 4 → 5 = 8 + 6 + 1 = 15 days. Hence, the optimum duration of the project is 15 days. Ans. 39 :

(a) (i) Net work diagram

Critical Path is 1-2-5-6-7-8 = 32 weeks Associated Cost = 4220 + 32×50 = 5820

(ii) Total floats

Activity Duration weeks

Early start Latest start

Early finish

Latest finish

Total float

390

The critical path activities are 1-2 2-5 5-6 6-7 7-8 Slope 100 45 45 70 200

1-2 2-3 2-4 2-5 3-5 4-5 5-6 6-7 6-8 7-8

3 3 7 9 5 0 6 4

13 10

0 3 3 3 6 10 12 18 18 22

0 4 5 3 7 12 12 18 19 22

3 6 10 12 11 10 18 22 31 32

3 7

12 12 12 12 18 22 32 32

0 1 2 0 1 2 0 0 1 0

(iii) Calculation of crashing

Activity Nt Nc Ct Cc Slop = (Cc-Nc) / (Nt-Ct)

1-2 2-3 2-4 2-5 3-5 4-5

3 3 7 9 5 0

300 30

420 720 250 0

2 3 5 7 4 0

400 30

580 810 300

0

100 0 80 45 50 0

5-6 6 320 4 410 45 6-7 6-8 7-8

4 13 10

400 780 1000

3 10

9

470 900

1200

70 40

200

Two activities cost slope cost is minimum (2-5 and 5-6) but activity 5-6 is common and critical, it also continuing so reduce by 2 weeks, then reduce activity 2 -5 by one week.

Activity From-to Project durations Cost I 5-6 6-4 weeks 32-2 = 30 4220 + (2×45) + (30×50) = 5810 II 2-5 9-8 30-1 = 29 4220+90+(1×45)+(29×50) = 5805 After this reduction now two paths are critical 1-2-3-5-6-7 = 28 and 1-2-5-6-7 = 28

So 1-2 3-5 6-7

391

2-5 Slope cost 100 50+45=95 70 As cost per week for every alternative is greater than Rs.50 (overhead cost p er week). Therefore, any reduction in the duration of project will increase the cost of project completion. Therefore, time for projects is 29 weeks, minimum cost is Rs.5805.

Answer 40: The network is given below:

(i) The critical path of the project is ACEG or 1-2-3-4-6-7 with normal duration of 25 days. The minimum duration of the project is 18 days. (ii) The cost slope for various activities is given below:

Activity Normal Duration

Crash duration

Normal cost (Rs.)

Crash cost (Rs.)

Cost slope (Rs.)

A (1-2)

B (2-4)

C (2-3)

D (2-5)

E (4-6)

F (5-6)

G (6-7)

7

4

5

6

7

5

6

5

2

5

4

4

2

4

500

400

500

800

700

800

800

900

600

500

1,000

1,000

1,400

1,600

20057500900

=−−

10024400600

=−−

N.A.

10046800000,1

=−−

10047700000,1

=−−

20045800400,1

=−−

40046800600,1

=−−

392

Total 4,500

Step –1: Various paths of the network are given below:

1-2-3-4-6-7 With duration = 25 days 1-2-4-6-7 With duration = 24 days 1-2-3-5-6-7 With duration = 23 days 1-2-5-6-7 With duration = 24 days

In order to determine the cost of completing the project in 21 days, let us crash that activity on the critical path, which has minimum cost slope. It can be seen that the minimum cost slope of Rs.100 corresponds to activity E (4-6) and it lies on the critical path. Hence, we crash activity E (4 –6) by 1 day at an additional cost of Rs. 100. Step- 2: Various paths now are: 1-2-3-4-6-7 With duration = 24 days 1-2-4-6-7 With duration = 23 days 1-2-4-6-8 With duration = 23 days 1-2-4-6-9 With duration = 24 days An examination of the above four paths clearly points out that there are two critical paths namely 1-2-3-4-6-7 and 1-2-5-6-7, each with duration = 24 days. To reduce the project duration by three days more, there are following possible combination of activities. 1. Crash activities 4-6 on the path 1-2-3-4-6-7 and 5-6 on the path 1-2-5-6-7 by one day each at

an addition cost of Rs. 100 +Rs. 200 = Rs. 300. 2. Crash activities 4-6 on path 1-2-3-4-6-7 and 2-5 on path 1-2-5-6-7 by one day each at an

additional cost of Rs. 100 +Rs. 100 = Rs. 200 3. Crash activity 1-2 by one day at an additional cost of Rs. 200.

It can be observed that the additional cost of reducing the project duration by one day in combination 2 as well as combination 3 is Rs. 200. Hence any of these two can be selected for crashing. However, since crashing activity 1-2 by 1 day reduces the duration of all the paths by1 day, we will crash it by I day. The project duration becomes = 23 days at an additional cost = Rs. 200. Step 3: Crash activity 1-2 by 1 day further, it would reduce the project duration to 22 days at an additional cost = Rs. 200. Step 4: Activity 1-2 can not be crashed further. So, we now select the combination 2 stated above for crashing. Crash activities 4-6 and 2-5 by one day each at an additional cost of Rs. 100 +Rs. 100 = Rs. 200. Hence, in order to complete the project in 21 days, an additional cost of Rs. 100 +Rs. 200 +Rs. 200 +Rs. 200 = Rs. 700 will be incurred. The normal cot of completing the project in 25 days =Rs. 4,500. Hence, the percentage increase in cost to complete the project in 21 days

393

= 500,4.

700.RsRs

×100 = 15.5%.

Answer 42

The requires network based on the given activities and duration is drawn below :

The critical path of the network is 1-3-4-5-6 i.e. B-E-G-H. The duration of the project is 14 weeks. E = 4 L = 6 A C E = 14 4 D E = 9 3 L = 14 3 L = 9 3 E = 0 B H L = 0 E 2 G 2 7 F E = 11 2 L = 11 E = 7 L = 7

The time scale diagram for various activities along the resource accumulation table showing the number of workers required on each day are drawn on next page.

C(2) 3 7 A(4) D(4) 4 3 2 B(2) E(6) G(3) H(4) 7 2 2 3 F(3) 2 2

Crew size

1

2

6

5

3

4

2

1 3 4 5 6

394

1 2 3 4 5 6 7 8 9 10 11 12 13 14

6 6 6 6 8 -2

8 -2

8 -2

9 9 3 3 4 +2

4 +2

4 +2

6 6 6 6 6 6 6 9 9 3 3 6 6 6

It can be seen that the demand on the resources is not even. On the 8th and 9th week, the demand of workers is as high as 9 whereas on the 10th and 11th

As can be seen from the above network diagram, activity C has a float of 7 weeks and activity

week, it is only three. If 9 workers are to be hired for the entire project duration of 14 weeks, then during most of the days they will be idle. We will attempt to re-schedule our activities in such away so as to utilize the workers in a fairly uniform manner.

F has a float of 2 weeks. The maximum demand on the resources occurs during 5th week to 7th week. (i.e. 8 workers) and during 8th to 9th week (i.e. 9 workers). We will shift activity C by seven weeks so that it starts on 12th week instead of 5ht week. This reduces the demand of the workers from 8 to 6 during 5th to 7th

weeks. The modified resource requirements are shown in the last row of the above table.

Activity F has a float of two weeks. It is shifted by two weeks so that it starts on 10th week instead of 9th

Crew size

workers required earlier. The modified resource accumulation table is given:

1 2 3 4 5 6 7 8 9 10 11 12 13 14

6 6 6 6 8

8

8

9 -3

9 -3

3 +3

3 +3

4

4

4

6 6 6 6 6 6 6 9 9 6 6 6 6 6

It is evident from the last row of the above table that there is a uniform demand of 6 workers throughout the duration of the project.

Ans. 46: The network diagram is drawn below: E= 4 L = 4 4 8 E = 0 4 L = 0 6 6 E = 14 L = 14

E = 8 3 L = 8

2

5

4

1

3

395

4 E = 3 L = 4 The critical path is 1-2-4-5. The total floats of all the activities are calculated below: 1-2 4 0

Activity Duration Total float

1-3 3 1 1-4 6 2 2-4 4 0 2-5 8 2 3-4 4 1 3-5 4 7 4-5 6 0 (b) The resource allocation table is given below:

Starting day 1 4st 5th 9th 10th 13th 18th 21th st Equipment X job done No. of men required day completed

(1,2) 30 4

(1,2) 30 4

(2,4) 30 8

(4,5) 30 18

(4,5) 30 18

Equipment Y Job done No. of men required Day completed

(1,3) 20 3

(3,4) 20 12

(3,4) 20 12

(3,5) 20 21

(3,5) 20 21

Equipment Z Job done No. of men required Day completed

(1,4) 20 9

(1,4) 20 9

(1,4) 20 9

(2,5) 20 17

(2,5) 20 17

Total no. of men 50 50 50 40 40 50 50 20 Explanation:

This is basically a problem of resource-leveling whereby the main constraint would be on the resources. It the maximum demand on any resource is not to exceed a certain limit, the activities will have to be rescheduled so that the total demand on the resources at any time will be within the limit and consequent the project duration time is exceeded. The criterion to be followed in such a case is to delay the job with a large float. In this way we tend to absorb the float and cutdown the demand on the resource. If two or more jobs are competing

Ans. 47:

396

Paths Duration

1-2-5-7-8 7+16+9+8 = 40 1-2-4-7-8 7+12+19+8 = 46 1-4-7-8 6+19+8 = 33 1-3-4-7-8 8+6+19+8 =41 1-3-6-7-8 8+24+7+8 =47 1-3-6-8 8+24+4 = 36

Critical path = 1-3-6-7-8 = 47 days

397

Ans. 6 Simulation

The numbers 00-99 are allocated in proportion to the probabilities associated with each event as given below:

Daily Demand Probability Cumulative Probability

Random Numbers Allocated

0 0.01 0.01 00-00 10 0.20 0.21 01-20 20 0.15 0.36 21-35 30 0.50 0.86 36-85 40 0.12 0.98 86—97 50 0.02 1.00 98-99

Let us simulate the demand for the next 10 days using the given random numbers in order to find out the stock position if the owner of the bakery decides to make 30 breads every day. We will also estimate the daily average demand for the bread on the basis of simulated data.

Day Random Number Simulated Demand Stock if 30 breads are prepared every

day 1 48 30 0 2 78 30 0 3 19 10 20 4 51 30 20 5 56 30 20 6 77 30 20 7 15 10 40 8 14 10 60 9 68 30 60

10 9 10 80 Total 220

Daily average demand of the basis of simulated data = 22

Ans. 7:

The random numbers are established as in Table below: Production probability cumulative Random number Per day probability 196 0.05 0.05 00-04 197 0.09 0.14 05-13 198 0.12 0.26 14-25 199 0.14 0.40 26-39 200 0.20 0.60 40-59 201 0.15 0.75 60-74 202 0.11 0.86 75-85 203 0.08 0.94 86-93

398

204 0.06 1.00 94-99 Based on the 15 random numbers given we simulate the production per day as above in table 2 below.

Random No. Estimated No. of mopeds waiting No. of empty Production spaces in the lorry Per day Opening current current Total Balance excess short waiting Production production 1 82 202 -- 2 -- 2 --- 2 89 203 2 3 --- 5 --- 3 78 202 5 2 --- 7 --- 4 24 198 7 -- 2 5 --- 5 53 200 5 --- -- 5 -- 6 61 201 5 1 --- 6 --- 7 18 198 6 --- 2 4 --- 8 45 200 4 --- -- 4 --- 9 04 196 4 --- 4 0 --- 10 23 198 0 --- 2 0 2 11 50 200 0 -- -- -- --- 12 77 202 0 2 -- 2 --- 13 27 199 2 --- 1 1 --- 14 54 200 1 -- -- 1 --- 15 10 197 1 --- 3 _-- Total

__2 42

__4

Average number of mopeds waiting = 1542

= 2.80

Average number of empty spaces in lorry = 154

= 0.266

Ans. 8: If the numbers 00-99 are allocated in proportion to the probabilities associated with each category of work, then various kinds of dental work can be sampled, using random number table :-

Type Probability Random Numbers Filling 0.40 00-39 Crown 0.15 40-54 Cleaning 0.15 55-69 Extraction 0.10 70-79 Checkup 0.20 80-99 Using the given random numbers, a work sheet can now be completed as follows :-

FUTURE EVENTS PATIENT SCHEDULED ARRIVAL RN CATEGORY SERVICE TIME

1 8.00 40 Crown 60 minutes 2 8.30 82 Checkup 15 minutes 3 9.00 11 Filling 45 minutes

399

4 9.30 34 Filling 45 minutes 5 10.00 25 Filling 45 minutes 6 10.30 66 Cleaning 15 minutes 7 11.00 17 Filling 45 minutes 8 11.30 79 Extraction 45 minutes Now, let us simulate the dentist’s clinic for four hours starting at 8.00 A.M.

STATUS Time Event Number of the patient Patients being served (time to go) waiting

8.0 1st patient arrives 1st

8.30 2(60) -

nd “ arrives 1st(30) 2 9.00 1

nd st

3 departs

rd “ arrives 2nd(15) 3 9.15 2

rd nd departs 3rd

9.30 4(45) -

th “ arrives 3rd(30) 4 10.00 3

th rd

5 departs

th “ arrives 4th(45) 5 10.30 6

th th “ arrives 4th(15) 5th & 6

10.45 4th

th departs 5th(45) 6 11.00 7

th th “ arrives 5th(30) 6th & 7

11.30 5th

th

8 departs

th “ arrives 6th(15) 7th & 8 11.45 6

th th departs 7th(45) 8

12.00 End 7th

th(30) 8 12.30 - 8

th th

(45) -

The dentist was not idle during the entire simulated period :- The waiting times for the patients were as follows :- Patient Arrival Service Starts Waiting (Minutes) 1 8.00 8.00 0 2 8.30 9.00 30 3 9.00 9.15 15 4 9.30 10.00 30 5 10.00 10.45 45 6 10.30 11.30 60 7 11.00 11.45 45 8 11.30 12.30 60 Total

285

The average waiting time of a patient was 28515

= 35.625 minutes.

Ans. 9: Random allocation tables are as under: Time Arrival Arrivals Random Time Service Service Random (Mts) (Proba.) cumulative No. (Mts) (Proba.) Cumulative No.

Probability allocated Probability allocated

400

1 0.05 0.05 00-04 1 0.10 0.10 00-09 2 0.20 0.25 05-24 2 0.20 0.30 10-29 3 0.35 0.60 25-59 3 0.40 0.70 30-69 4 0.25 0.85 60-84 4 0.20 0.90 70-89 5 0.10 0.95 85-94 5 0.10 1.00 90-99 6 0.05 1.00 95-99 Simulation of ten trails:

R. No. Arrival Mts. Time Start R. No. Time Mts. Finish Time

Waiting Time

Clerk Passanger 60 4 9.04 9.04 09 1 9.05 4 16 2 9.06 9.06 12 2 9.08 1 08 2 9.08 9.08 18 2 9.10 − 36 3 9.11 9.11 65 3 9.14 1 38 3 9.14 9.14 25 2 9.16 − 07 2 9.16 9.16 11 2 9.18 − 08 2 9.18 9.18 79 4 9.22 − 59 3 9.21 9.22 61 3 9.25 − 1 53 3 9.24 9.25 77 4 9.29 1 03 1 9.25 9.29 10 2 9.31 _ 4 Total 6 6

In half an hour trial, the clerk was idle for 6 minutes and the passengers had to wait for 6 minutes. Ans. 10:

From the frequency distribution of arrivals and service times, probabilities and cumulat ive probabilities are first worked out as shown in the following table:

Time between arrivals

Frequency

Probability

Cum. Prob.

Service

Time

Frequency

Prob.

Cum. Prob.

1

2

3

4

5

6

5

20

35

25

10

5

0.05

0.20

0.35

0.25

0.10

0.05

0.05

0.25

0.60

0.85

0.95

1.00

1

2

3

4

5

6

1

2

4

2

1

0

0.10

0.20

0.40

0.20

0.10

0.00

0.10

0.30

0.70

0.90

1.00

1.00 Total 100 10

The random numbers to various intervals have been allotted in the following table:

Time between arrivals

Probability Random numbers allotted

Service Time Probability Random numbers allotted

401

1 2 3 4 5 6

0.05 0.20 0.35 0.25 0.10 0.05

00-04 05-24 25-59 60-84 85-94 95-99

1 2 3 4 5 6

0.10 0.20 0.40 0.20 0.10 0.00

00-09 10-29 30-69 70-89 90-99

-

Simulation Work Sheet

Random Number

Time till next

arrival

Arrival Time a.m.

Service begins a.m.

Random number

Service time

Service Ends a.m.

Clerk Waiting

time

Customer waiting Time

Time spend by customer in system

Length of

waiting line

64 4 11.04 11.04 30 3 11.07 04 - 3 - 04 1 11.05 11.07 75 4 11.11 - 2 6 1 02 1 11.06 11.11 38 3 11.14 - 5 8 2 70 4 11.10 11.14 24 2 11.16 - 4 6 2 03 1 11.11 11.16 57 3 11.19 - 5 8 2 60 4 11.15 11.19 09 1 11.20 - 4 5 2 16 2 11.17 11.20 12 2 11.22 - 3 5 2 18 2 11.19 11.22 18 2 11.24 - 3 5 2 36 3 11.22 11.24 65 3 11.27 - 2 5 1 38 3 11.25 11.27 25 2 11.29 - 2 4 1 07 2 11.27 11.29 11 2 11.31 - 2 4 1 08 2 11.29 11.31 79 4 11.35 - 2 6 1 59 3 11.32 11.35 61 3 11.38 - 3 6 1 53 3 11.35 11.38 77 4 11.42 - 3 7 1 01 1 11.36 11.42 10 2 11.44 - 6 8 2 62 4 11.40 11.44 16 2 11.46 - 4 6 2 36 3 11.43 11.46 55 3 11.49 - 3 6 2 27 3 11.46 11.49 52 3 11.52 - 3 6 1 97 6 11.52 11.52 59 3 11.55 - - 3 - 86 5 11.57 11.57 63 3 12.00 2 - 3 - 20 57 54 6 56 26

Average queue length = Number of customers in waiting lineNumber of arrivals

= 26 1.320

=

Average waiting time per customer = 56 2.820

= minutes

Average service time = 54 2.720

= minutes

Ans. 11: Cumulative frequency distribution for Ramu is derived below. Also fitted against it are the eight given random numbers. In parentheses are shown the serial numbers of random numbers.

402

10 4 01 (2) 00 (7) 03 (8) 20 10 30 20 14 (1) 40 40 50 80 44 (4) 61 (5) 60 91 82 (6) 70 96 95 (3) 80 100

Thus the eight times are: 30, 10, 70, 50, 60, 10 and 10 respectively. Like wise we can derive eight times for Raju also.

Col-1 Col-2 Col-3 (2× Col-2) 10 4 8 20 9 18 30 15 30 25 (4) 40 22 44 36 (1) 34 (8) 41 (6) 50 32 64 55 (3) 56 (7) 60 40 80 76 (2) 70 46 92 80 50 100 97 (5)

(Note that cumulative frequency has been multiplied by 2 in column 3 so that all the given random numbers are utilized). Thus, Raju’s times are: 40, 60, 50, 30, 80 40, 50 and 40 seconds respectively. Ramu’s and Raju’s times are shown below to observe for waiting time, if any.

1 2 3 4 Ramu Cum. Times Raju Initial Raju’s cumulative time with 30 seconds

included 30 30 40 70 10 40 60 130 70 110 50 180 50 160 30 210 50 210 80 290 60 270 40 330 10 280 70 400 10 290 40 440

Since col. 4 is consistently greater than Co.2, no subsequent waiting is involved.

Ans. 12: The numbers 00-99 are allocated in proportion to the probabilities associated with each event. If it rained on the previous day, the rain distribution & the random no allocation are given below:

403

Event Probability Cumulative Random Probability numbers Assigned

No rain 0.50 0.50 00-49 1 cm rain 0.25 0.75 50-74 2 cm rain 0.15 0.90 75-89 3 cm rain 0.05 0.95 90-94 4 cm rain 0.03 0.98 95-97 5 cm rain 0.02 1.00 98-99

Table 1 – Rain on previous day Similarly, if it did not rain the previous day, the necessary distribution and the random number allocation is given below:

Event Probability Cumulative Random Probability numbers Assigned

No rain 0.75 0.75 00-74 1 cm rain 0.15 0.90 75-89 2 cm rain 0.06 0.96 90-95 3 0.04 1.00 96-99

Table 2- No rain on previous day Let us now simulate the rain fall for 10 days using the given random numbers. For the first day it is assumed that it had not rained the day before:

Day Random Numbers Event 1 67 No rain (from table 2) 2 63 No rain (from table 2) 3 39 No rain (from table 2) 4 55 No rain (from table 2) 5 29 No rain (from table 2) 6 78 1 cm rain (from table 2) 7 70 1 cm rain (from table 1) 8 06 No rain (from table 1) 9 78 1 cm rain (from table 2) 10 76 2 cm rain (from table 1)

Hence, during the simulated period, it did not rain on 6 days out of 10 days. The total rain fall during the period was 5 cm.

Ans.13: The probabilities of occurrence of A, B and C defects are 0.15, 0.20 and 0.10 respectively. So, tile numbers 00-99 are allocated in proportion to the probabilities associated with each of the three defects Exists Random Exists? Random Exists? Random

Defect-A Defect-B Defect-C

Numbers numbers numbers Assigned assigned

Yes 00-14 yes 00-19 yes 00-09 assigned

No 15-99 No 20-99 no 10-99

404

Let us now simulate the output of the assembly line for 10 items using the given random numbers in order to determine the number of items without any defect, the number of items scrapped and the total mi Item RN for RN for RN for whether Rework

Remarks

nutes of rework time required:

No. defect A defect B defect C any defect time (in 1 48 47 82 none -- --

Exists minutes)

2 555 36 95 none -- -- 3 91 57 18 none -- -- 4 40 04 96 B 15 -- 5 93 79 20 None -- -- 6 01 55 84 A -- Scrap 7 83 10 56 B 15 --- 8 63 13 11 B 15 --- 9 47 57 52 None -- -- During the simulated period, 5 out of the ten items had no defects, one item was scrapped and 90 minutes of total rework time was required by 3 items.

10 52 09 03 B,C 15+30 =45 --

Answer 14: The question is not happily worded, if we go by the language of the question, the following solution can be worked out: First of all, random numbers 00-99 are allocated in proportion to the probabilities associated with demand as given below:

Demand Probability Cum. Probability Random Nos. 0 0.05 0.05 00-04 1 0.10 0.15 05-14 2 0.30 0.45 15-44 3 0.45 0.90 45-89 4 0.10 1.00 90-99

Based on the ten random numbers given, we simulate the demand per day in the table given below. It is given that stock n hand = 8 and stock on order = 6 (expected next day). Let us now consider both the options stated in the question. Option A: Order 5 Books, when the inventory at the beginning of the day plus orders outstanding is less than 8 books:

Day Random No.

Sales Demand

Op. Stock in

hand

Qty. Order

Qty. Recd. At end of the day

Total Qty. on order

Closing Stock

1 89 3 8 - - 6 5 2 34 2 5 - 6 - 9 3 78 3 9 - - - 6 4 63 3 6 5 - 5 3

405

5 61 3 3 - - 5 0 6 81 3 0 0 7 39 2 8 16 2 9 13 1

10 73 3

Now on day 6, there is stock out position since 5 units will be received at the end of the day and demand occurring during the day can not be met. Hence, it will into be possible to proceed further and we will have to leave the answer at this stage.

Random No.

Sales Demand

Opening Stock in

hand

Qty. Order

Qty. Recd. At end of the day

Total Qty. on order

Closing Stock

1 89 3 8 -- -- 6 5 2 34 2 5 -- 6 -- 9 3 78 3 9 -- -- -- 6 4 63 3 6 8 -- 8 3 5 61 3 3 -- -- 8 0 6 81 3 0 -- 8 -- 7 39 2 8 16 2 9 13 1

10 73 3

Now on day 6, there is stock out position since 8 units will be received at the end of the day and demand occurring during the day can not be met. Hence, it is not possible to proceed further and we may leave the answer at this stage. Alternatively, if we assume that the demand occurring during the day can be met out of stock received at the end of the day, the solution will be as follows: Stock in hand = 8 and stock on order = 6 (expected next day)

Random No.

Sales Demand

Opening Stock in

hand

Qty. Order

Qty. Recd. At end of the day

Total Qty. on order

Closing Stock

1 89 3 8 -- -- 6 5 2 34 2 5 -- 6 -- 9 3 78 3 9 -- -- -- 6 4 63 3 6 5 -- 5 3 5 61 3 3 -- -- 5 0 6 81 3 0 5 5 5 2 7 39 2 2 5 -- 10 0 8 16 2 0 -- 5 5 3 9 13 1 3 -- 5 -- 7

10 73 3 7 5 -- 5 4

406

Carrying Cost = 39 × 0.50 = Rs.19.50 Ordering Cost = 4 × 10 = Rs.40.00 Total Cost = Rs.59.50 Option B: Order 8 Books, when the inventory at the beginning of the day plus orders outstanding is less than 8 books:

Random No.

Sales Demand

Opening Stock in

hand

Qty. Order

Qty. Recd. At end of the day

Total Qty. on order

Closing Stock

1 89 3 8 -- -- 6 5 2 34 2 5 -- 6 -- 9 3 78 3 9 -- -- -- 6 4 63 3 6 8 -- 8 3 5 61 3 3 -- -- 8 0 6 81 3 0 -- 8 -- 5 7 39 2 5 8 -- 8 3 8 16 2 3 -- -- 8 1 9 13 1 1 -- 8 -- 8

10 73 3 8 -- -- -- 5

Carrying Cost = 45 × 0.50 = Rs.22.50 Ordering Cost = 2 × 10 = Rs.20.00 Total Cost = Rs.42.50 Since Option B has lower cost, Manager should order 8 books.

Ans.15 Demand (Tons) Probability Cumulative Probability Random Nos. Allocated 1 0.15 0.15 00-14 2 0.30 0.45 15-44 3 0.45 0.90 45-89 4 0.10 1.00 90-99

Option-I RN Demand Opening

Stock Receipts Closing

Stock Op.Stock on Order

Order Cl.Stock on Order

88 3 8 - 5 - - 6 41 2 5 6 9 - - - 67 3 9 - 6 - 5 5 63 3 6 - 3 5 - 5 48 3 3 - 0 5 5 10 74 3 0 5 2 5 5 10 27 2 2 - 0 10 - 10 16 2 0 5 3 5 - 5 11 1 3 5 7 - 5 5 64 3 7 - 4 5 - 5 49 3 4 - 1 5 5 10 21 2 1 5 5 4 - 5

407

44 (Rs.) No of order placed 5 Ordering cost (5x1000) Closing Stock 44 Carrying cost (44x50) Total

5,000

2,200 7,200

Option-II

RN Demand Opening Stock

Receipts Closing Stock

Op.Stock on Order

Order Cl.Stock on Order

88 3 8 - 5 - - 6 41 2 5 6 9 - - - 67 3 9 - 6 - 8 8 63 3 6 - 3 8 - 8 48 3 3 - 0 8 - 8 74 3 0 8 5 - 8 8 27 2 5 - 3 8 - 8 16 2 3 - 1 8 - 8 11 1 1 8 8 - - - 64 3 8 - 5 - 8 8 49 3 5 - 2 8 - 8 21 2 2 - 0 8

47 - 8

(Rs.) No of orders 3 Ordering cost 3 x 1000 Closing stock 47 Carrying cost 47x50 Total

3,000 2,350 5,350

Analysis: Since the cost of inventory is less in Option II, it is suggested to implement. Ans. 16 (i) Allocation of random numbers

Demand Probability Cumulative probability Allocated RN 0<300 0.18 0.18 00—17 300 < 600 0.32 0.50 18—49 600 < 900 0.25 0.75 50—74 900 < 1200 0.15 0.90 75—89 1200 <1500 0.06 0.96 90—95 1500 < 1800 0.04 1.00 96—99

(ii) Simulation: twelve months sales, monthly and annual profit/loss

Month RN Demand Sold Return Profit on sales (Rs.)

Loss on return (Rs.)

Net (Rs.)

Loss on lost units

408

1 27 450 450 300 3375 12000 2175 2 15 150 150 600 1125 2400 -1275 3 56 750 750 -- 5625 -- 5625 4 17 150 150 600 1125 2400 -1275 5 98 1650 750 -- 5625 --- 5625 900 6 71 750 750 -- 5625 -- 5625 7 51 750 750 -- 5625 -- 2175 8 32 450 450 300 3375 1200 5625 9 62 750 750 -- 5625 -- 5625 300 10 83 1050 750 -- 5625 -- 5625 900 11 96 1650 750 -- 5625 -- 5625 12 69 750 750 -- 5625 5625 54000 7200 46800 2100

(iii) Loss on lost sale 2100×7.5 = Rs15750. Ans. 17 The demand and supply patterns yield the following probability distribution. The numbers 00-99 are allocated in proportion to the probabilities associated with each event.

Availability (Kg.)

Prob. Cum. Prob.

Random Numbers allocated

Demand (Kg)

Prob. Cum. Prob.

Random number

allocated 10 0.08 0.08 00-07 10 0.10 0.10 00-09 20 0.10 0.18 08-17 20 0.22 0.32 10-31 30 0.38 0.56 18-55 30 0.40 0.72 32-71 40 0.30 0.86 56-85 40 0.20 0.92 72-91 50 0.14 1.00 86-99 50 0.08 1.00 92-99

Let us simulate the supply and demand for the next six days using the given random numbers in order to find the profit if the cost of the commodity is Rs.20 per kg, the selling price is Rs.30 per kg, loss on any unsatisfied demand is Rs.8 per kg and unsold commodities at the end of the day have no saleable value.

Day Random no.

Supply availability

Random no.

Demand Buying cost Rs.

Selling cost Rs.

Loss for unsatisfied

demand

Profit

1 31 30 18 20 600 600 -- -- 2 63 40 84 40 800 1200 -- 400 3 15 20 32 40 400 600 160 40 4 07 10 32 30 200 300 160 -60 5 43 30 75 40 600 900 80 220 6 81 40 27 20 800 600 -- -200

During the simulated period of six days, the net profit of the retailer is = (400 + 40 + 220) – (60 + 200)

409

= 660 – 260 = Rs.400 Ans. 19:

Random No. Coding Table - Receipts Amount (Rs. In crores) Probability Cum. Probability Random No. Interval

30 0.20 0.20 00-19 42 0.40 0.60 20-59 36 0.25 0.85 60-84 99 0.15 1.00 85-99

Random No. Coding Table - Payments

Amount (Rs. In crores) Probability Cum. Probability Random No. Interval 33 0.15 0.15 00-14 60 0.20 0.35 15-34 39 0.40 0.75 35-74 57 0.25 1.00 75-99

Simulation Table

Week Op.Balance Receipts Payments Cl.Balance Random

No. Amount

(in crores) Random

No. Amount

(in crores)

1 15 17 30 78 57 -12 2 -12 43 42 16 60 -30 3 -30 74 36 35 39 -33 4 -33 31 42 23 60 -51 5 -51 72 36 44 39 -54 6 -54 46 42 92 57 -69 7 -69 51 42 58 39 -66 8 -66 68 36 8 33 -63 9 -63 93 99 58 39 -3 10 -3 54 42 78 57 -18 11 -18 96 99 54 39 42 12 42 9 30 77 57 15

(i) Probability is = 10 ÷ 12 = 0.83 (ii) Total Shortfall is Rs. 399 crores. Therefore average shortfall is 399 ÷ 12 = Rs. 33.25 crores Alternatively, average shortfall is 399 ÷ 10 = Rs. 39.90 crores (iii) There will be a shortfall in 5 months i.e. 4,5,6,7,8. therefore the probability is 5 ÷ 12 = 0.42

410

Ans. 6 (i) Actual learning curve rate is 80%. Learning Curve

Time taken to produce the first machine = 600 hours

Average time taken to produce two machines = 600 × 80% hours

= 480 hours. Cumulative time taken to produce two machines = 480 × 2 hours

= 960 hours.

Time taken to produce the second machine = (960 − 600)hours

= 360 hours.

(ii) Actual learning curve rate is 90%.

Time taken to produce the first machine = 600 hours

Average time taken to produce two machines = 600 × 90% hours

= 540 hours. Cumulative time taken to produce two machines = 540 × 2 hours

= 1080 hours.

Time taken to produce the second machine = (1080 − 600) hours

= 480 hours.

The time taken to produce the second machine is lower at 80% learning rate and hence 80% learning rate shows faster learning rate.

Ans. 10: (i) Rs/u 1st unit Avg/u after 4th at

Variable Cost Labour Target Contribution Price to be quoted

2000 1000

2000 810

1500 4310 (Rs./u)

(ii) No, the company cannot quote this price for varying products because the learning curve Ratio does not apply to non-repeated jobs. Each product will carry a different price according to its direct labour hours.

Ans. 13:

5,000 units 20,000 units Material 1,50,000 6,00,000 Direct Labour 1,00,000 2,56,000 Refer to W Note i Variable Overhead 50,000 2,00,000 Total Variable Cost 3,00,000 10,56,000 Fixed Cost 1,50,000 1,50,000 Total Cost 4,50,000 12,06,000 Total cost / unit 90 60.3 Sales 100 × 5,000 5,00,000 5,00,000 15,000 × x(assumed selling price) 15,000 x (Total Sales less Total Cost) = Profit 50,000 15,000 x – 7,06,000

Or minimum selling price = 50.4(refer to Working Note ii)

Working Note: I

411

Units Hours 5,000 5,000 10,000 10,000 × 1 × .8 = 8,000 hours 20,000 20,000 × 1 × .8 × .8 = 12,800 hours Working Note: II

15,000 x – 7,06,000 > 50,000

15,000 x > 7,56,000

or x > 50.4

Alternative Solution:

Total cost / unit of capacity 20,000 = 60.3

Weighted average selling price > 80.4

i.e. 5,000 × 100 + 15,000 x > 60.3 20,000

= 5,00,000 + 15,000 x > 60.3 × 20,000

= 15,000 x > 12,06,000 – 5,00,000

Or

15,000 x > 7,06,000

x > 47.06

Minimum price to cover production Cost = 47.06

Minimum price to cover same amount of profit = 50.40 (refer to W orking Note 1)

Working Note 1 (− 47.06 + 50.04) × 15,000 units

= Rs. 50,000

Ans. 14: Units Average/ hrs/u.

1 2,000

2 1,600

4 1,280

8 1,024

Material Cost / u = 10,000

Variable cost = 2,000

Variable Cost = 12,000

Option I

If both the orders came together, learning rate 80% applies and 8 units can be made, with average time of 1,024 hours per unit. Cost to PQ:

Variable cost excl. labour = Rs.12,000

Labour cost 1,024 hrs × 4 Rs./hr = Rs. 4,096

412

Y X Selling Price Rs.17,200 Rs.14,000 Variable Cost (excl. labour) Rs.12,000 Rs.12,000 Labour cost:

1280 × 4 Rs.5,120

= Rs.16,096

In this case,

Y X Selling Price p. u. Rs.17,200 Rs.16,500 → (under option I) Variable Cost p. u. Rs.16,096 Rs.16,096 Contribution p. u. Rs.1,104 Rs.404 No. of units 4 4 Contribution (Rs.) 4416 1616 6032 Option II

If X Ltd supplies its labour. 80% learning curve will apply to 4 units each of PQ & X. Hence: hrs/ u = 1280

1280 × 1 . Rs.1280

Total Variable Cost Rs.17,120 Rs.13,280 Contribution Rs.80 Rs.720 Units 4 4 Contribution (Rs.) 320 2,880 3,200 PQ should not take labour from X Ltd. It should choose option I.

Ans. 16: Working notes : (1) By the theory of learning curve YX = KX5 ……………………… (i) Here X is the cumulative number of units or lots produced, Y is the

cumulative average unit time of those X units. K is the average time of the first unit or lot, s is the improvement exponent or the learning coefficient or the index of learning.

Taking log on both sides of relation (i) we have Log YX = log K + s log X ……………(ii)

(2) Time required for 30 units order (when the time required for the first unit is 40 hours)

Log 40 + (-0.322) log 30 = 1.6021 + (- 0.322) (1.4771) = 1.6021 – 0.4756 = 1.1264 Anti log of 1.1264 = 13.38 Hence hours required Per unit = 13.38 Total time required for 30 units = 30 units x 13.38 hours = 401.40

413

(3) Time required for 50 units order (When the time required for first unit is 40 hours) log 40 + (-0.322) log 50 = 1.6021 + (-0.322) 1.6990 = 1.055 Anti log of 1.055 = 11.35 Hence hours required per unit 11.35 hours Total time required for 50 units = 11.35 x 50 units = 567.5 hours (4) Fixed overhead recovery rate per labour hour Total labour hours 2,000 10 men x 25 days x 8 hours Less : 25% downtime (in hours) 500 _____ Total effective hours 1,500 Total fixed overheads per month (Rs.) 7,500 Fixed overhead recovery rate per labour hour (Rs) 5 (Rs. 7,500/1,500 hours) (i) Computation of cost per unit of the first order of 30 units Rs. Direct material cost 1,800.00 (30 units x Rs. 60) Direct labour cost 2,408.40 (401.4 hours x Rs. 6) Variable overheads 401.40 (401.40 hours x Re 1) Fixed overheads (401.4 hours x Rs. 5)

2,007.00

Total cost of 30 units Cost per unit 220.56

6,616.80

(Rs. 6,616.80/30 units) (ii) Cost per unit, when a repeat order for 20 units is also placed. Rs. Direct material cost 1,200.00 (20 units x Rs. 60) Direct labour 996.60 (567.5 hours – 401.40 hours) x Rs. 6 Variable overheads 166.10 (1.66.1 hours x Re 1) Fixed overheads 830.50 (166.1 hours x Rs. 5) ________ Total cost of 20 additional units

3,193.20

Cost per unit 159.66 (Rs. 3,193.20/20 units) Price to be quoted to yield a profit of 25% on selling price

414

If selling price is Rs. 100 then profit is Rs. 25 and cost is Rs. 75 Hence selling price per unit = 100 75

x 159.66

= Rs. 212.88 Ans. 18 (i) Price per unit for first order of 100 units

Rs Rs Direct material 500.00 Direct labour Dept A 20 Hrs @ 10 = 200

Dept B 40 Hrs @ 15 = 600 800.00

Variable Overhead 20% of Rs 800 160.00 Fixed Overhead Dept A 20 Hrs @ 8 = 160

Dept B 40 Hrs @ 5 = 200 360.00

Total cost 1,820.00 Profit 25% 455.00 Selling price per unit

2,275.00

(ii) Price per unit for second order of 60 units Learning will be applicable only in department B. Cumulative output becomes 100 units + 60 units = 160 units i.e 1.6 times for which

learning is 86.1 % from the tables. Therefore Total Hrs for 160 units = 160 units ×40 × .861 = 5,510.4 Hrs Therefore Hrs for 60 units = Hrs for 160 units less Hrs for 100 units Or 5510.4 less 40 × 100 = 1510.4 Hrs

Therefore Hrs per unit = 60

4.1510 = 25.17

Calculation of selling price per unit Rs Direct materials 500.00 Direct labour Dept A 20 Hrs @ 10 = 200

Dept B 25.17 Hrs @ 15 = 377.55 577.55

Variable Overhead 20% of 577.55 115.51 Fixed Overhead Dept A 20 Hrs @8= 160

Dept B 25.17 Hrs @5=125.85 285.85

Total cost 1,478.91 Profit 25% 369.73 Selling price per unit 1,848.64

(iii) Price per unit for third order of 40 units Cumulative output becomes 100 + 60 + 40 = 200 units i.e. 2 times for which learning is 80% from the table

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Total Hrs for 200 units = 200 ×40 × .80 = 6,400 Hrs Hrs for 40 units = Hrs for 200 units less Hrs for 160 units Or 6,400 less 5510.4 = 889.6 Hrs

Therefore Hrs per unit = 40

6.889 = 22.24

Calculation of selling price per unit Rs Direct materials 500.00 Direct labour Dept A 20 Hrs @ 10 = 200.00

Dept B 22.24 @ 15 = 333.60 533.60

Variable Overhead 20% of 533.60 106.72 Fixed Overhead Dept A 20 Hrs @ 8 = 160

Dept B 22.24 Hrs @ 5 = 111.20 271.20

Total cost 1,411.52 Profit 25% 352.88 Selling price per unit 1,764.40

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