2. CAPITAL BUDGETING - Welcome to Master Minds budgeting1412.pdf · 2015-12-14 · IPCC_34.5e_F.M_...

IPCC_34.5e_F.M_ Capital Budgeting_Assignment Solutions ____________________1

No.1 for CA/CWA & MEC/CEC MASTER MINDS

2. CAPITAL BUDGETING

SOLUTIONS TO ASSIGNMENT PROBLEMS

Problem No.1

Calculation of ARR for machine A and B:

Particulars Machine – A Machine - B

Step 1:

Average Profit After Tax = YearsofNo.

ProfitTotal=

5

25,00020,00010,0005,000 000,15

= 15,000

=5

5,00010,00020,00025,000 000,15

= 15,000.

Step 2:Average investment in the project

=2

1(Initial Investment - Salvage Value)

+ Salvage Value + Additional Working Capital

=2

1 (50,000 – 2,000) + 2,000

+ 4,000

= 30,000

=2

1 (50,000 - 2,000) + 2000

+ 14,000

= 40,000.

Step 3:

100ojectPrtheinInvestmentAverage

PATAverageARR = %50100

000,30

000,15 = %5.37100

000,40

000,15

Problem No.2

Problem No.3

Payback reciprocal = %20000,20

100X000,4

IPCC_34.5e_F.M_ Capital Budgeting Assignment Solutions ____________________2

Ph: 98851 25025/26 www.gntmasterminds.com

The above payback reciprocal provides a reasonable approximation of the internal rate of return, i.e. 19%.Problem No.4

Problem No.5



Problem No.6

Step 1: P.V. of Cash outflows (Rs. in. Lakhs)

Particulars Amount (Rs.) Amount (Rs.)Cost of New Equipment 175Less: Subsidy from State Govt. 25Add: Investment in W.C 20Add: Investment in additional equipment 12.5P.V. thereof = 12.5 x PVF (12%, 3 yr) = 12.5 x 0.712 8.9P.V of Cash Outflows 178.9

Step 2: P.V of Operating Cash inflowsGiven that selling price per unit = Rs.120Variable Cost ratio = 60%Therefore, Contribution ratio = 1 - Variable Cost ratio = 1 - 60% = 40%Contribution per unit = 120 x 40% = Rs.48

Particulars Year 1 Year 2 Year 3 Year 4-5 Year 6-8a. Sales Volume (Lakhs of

Units)0.72 1.08 2.6 2.7 1.8

b. Contribution per Unit (120 x 40%) (Rs.)

Rs.48 Rs.48 Rs.48 Rs.48 Rs.48

c. Total contribution (a x b) 34.56 51.84 124.8 129.6 86.4d. Fixed Cost 18 18 18 18 18e. PBDT (c-d) 16.56 33.84 106.8 111.6 68.4f. Depreciation (WN -1) 21.875 21.875 21.875 24.125 24.125



g. PBT / (Loss) (e - f) (5.315) 11.965 84.925 87.475 44.275h. Brought forward of Loss - (5.315) - - -i. Profit after set off (g - h) (5.315) 6.65 84.925 87.475 44.275j. Tax @ 30% (i x 30%) - 1.995 25.4775 26.2425 13.2825k. PAT (5.315) 4.655 59.4475 61.2325 30.9925l. CFAT (k + f) 16.56 26.53 81.3225 85.3575 55.1175m. PVF @ 12% 0.892 0.797 0.711 1.2025 1.361n. Present Value (l x m) 14.77 21.144 57.82 102.64 75.01

P.V of Operating Cash Inflows = 271.384 Lakhs

Step 3: P.V. of Terminal Cash inflows

Particulars Amount (Lakhs)GSP / NSP on sale of initial equipment at the end of 8th year 0GSP / NSP on sale of additional equipment at the end of 8th year 1.25Add: Recovery of Working Capital 20

Terminal Cash Inflows 21.25

Present value there of = 21.25 x PVF (12%, 8) = 21.25 x 0.404 = 8.585 Lakhs

Step 4: Calculation of NPV

NPV = P.V. of Cash Inflows – P.V of Cash Outflows= P.V of Operating Cash Inflows + P.V of Terminal Cash Inflows - P.V of Cash Outflows= Step 2 + Step 3 - Step 1= 271.384 + 8.585 -178.9= 101.069 Lakhs

WN-1: Calculation of Depreciation per annum

Depreciation p.a. =Life

scrap-cost

Depreciation on Original Equipment =8

0175 = 21.875

Depreciation on Additional Equipment =5

25.15.12 = 2.25

Problem No.7 (Rs. In Lakhs)

Step 1: Calculation of Present Value of Cash Outflows

Particulars AmountCost of windmillCost of land

300.0015.00

Less: Subsidy from Govt. receivable at the end of 1st yearPresent value thereof [15 x PVF (15%, 1y)] = 15 x 0.870

15315.00

13.05Present Value of Net Cash Outflows 301.95

Step 2: Calculation of Present Value of Operating Cash Inflows

Particulars Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 Y9 Y10

a. Lakhs of unitsgenerated (Note1) 24 24 24 24 24 24 24 24 24 24



b. Cost per unit (in Rs.) 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.25 4.75 5.25c. Savings in Electricity

Cost (a x b) (in Lakhs) 54 60 66 72 78 84 90 102 114 126

d. Maintenance Cost 4 6 8 10 12 14 16 18 20 22e. Depreciation 300 - - - - - - - - -f. PBT (c-d-e) (Loss) (250) 54 58 62 66 70 74 84 94 104g. Tax (Tax Shield) @

50% (125) 27 29 31 33 35 37 42 47 52

h. PAT / (Loss) (f-g) (125) 27 29 31 33 35 37 42 47 52i. CFAT (h + e) 175 27 29 31 33 35 37 42 47 52j. PVF @ 15% 0.87 0.756 0.658 0.572 0.497 0.432 0.376 0.327 0.284 0.247k. Present Value (i x j) 152.25 20.41 19.08 17.73 16.40 15.12 13.91 13.73 13.35 12.84

Therefore, Present Value of Operating Cash Inflows = 294.82 Lakhs

Step 3: Calculation of Present Value of Terminal Cash Inflows (At the end of the project)

Particulars Land Wind Milla. Gross Sale Proceeds 60 0

b. WDV / Book Value 15 0

c. Capital Gains (a - b) 45 0

d. Capital Gains tax @ 50% (Note 3) 0 0

e. Net Sale Proceeds (NSP) (a – d) 60 0

Terminal Cash Inflows 60 Lakhs

Net Sale Proceeds on Sale of Assets = 60 Lakhs

Present value there of = 60 x PVF (15%, 10y) = 60 x 0.247 = 14.82 Lakhs

Step - 4: Calculation of NPV

NPV = PV of cash inflows – PV of cash outflows

= PV of Operating Cash Inflows + PV of Terminal Cash Inflows – PV of cash outflows.

= 294.82 + 14.82 - 301.95 = 7.69 Lakhs

Conclusion: Since NPV is positive it is beneficial for the company to accept the proposal.

Note 1: No. of units of electricity generated = 25,00,000

Less: Electricity freely supplied to State Govt. @ 4% = 1,00,000

No. of units of Electricity that can be utilised = 24,00,000 units

Note 2: It is given in the problem that cost of windmill has to be written off 100% in the first year for income taxpurposes.

Note 3: It is given that tax on capital profit should be ignored. Therefore, Gross Sale Proceeds will be equal toNet Sale Proceeds.

Assumptions: Cash flows are assumed to accrue at the end of each year. Interim cash inflows at the end of each year are assumed to be reinvested at the rate of cost of capital. Cash flows given in the problem are assumed to be certain.

Problem No.8Computation of initial cash outlay

(Rs. in lakhs)Equipment Cost (0)Working Capital (0)

12015

135



Calculation of Cash Inflows:

Years 1 2 3 – 5 6 – 8Sales in units 80,000 1,20,000 3,00,000 2,00,000

(Rs.) (Rs.) (Rs.) (Rs.)Contribution @ Rs. 60 p.u. 48,00,000 72,00,000 1,80,00,000 1,20,00,000Fixed cost 16,00,000 16,00,000 16,00,000 16,00,000Advertisement 30,00,000 15,00,000 10,00,000 4,00,000Depreciation 15,00,000 15,00, 000 16,50,000 16,50,000Profit /(loss) (13,00,000) 26,00,000 1,37,50,000 83,50,000Tax @ 50% NIL 13,00,000 68,75,000 41,75,000Profit/(Loss) after tax (13,00,000) 13,00,000 68,75,000 41,75,000Add: Depreciation 15,00,000 15,00, 000 16,50,000 16,50,000Cash inflow 2,00,000 28,00,000 85,25,000 58,25,000

Computation of PV of CIF

Year CIF (Rs.) PV Factor @ 12% Rs.

1 2,00,000 .893 1,78,600

2 28,00,000 .797 22,31,600

3 85,25,000 .712 60,69,800

4 85,25,000 .636 54,21,900

5 85,25,000 .567 48,33,675

6 58,25,000 .507 29,53,275

7 58,25,000 .452 26,32,900

8 58,25,000 .404 29,99,700

WC 15,00,000

SV 1,00,000

2,73,21,450

PV of COF 0 1,35,00,000

Additional investment = Rs. 10,00,000 × .797 7,97,000 1,42,97,000

NPV 1,30,24,450

Recommendation: Accept the project in view of positive NPV.

Problem No.9



Problem No. 10Calculation of Net Cash flowsContribution = (3.00 – 1.75) × 50,000 = Rs. 62,500Fixed costs = 40,000 – (1,25,000 – 30,000)/5 = Rs. 21,000Year Capital (Rs.) Contribution (Rs.) Fixed costs (Rs.) Adverts (Rs.) Net cash flow (Rs.)0 (1,00,000) (1,00,000)1 (25,000) 62,500 (21,000) (10,000) 6,5002 62,500 (21,000) (15,000) 26,5003 62,500 (21,000) 41,5004 62,500 (21,000) 41,5005 30,000 62,500 (21,000) 71,500

Calculation of Net Present ValueYear Net cash flow (Rs.) 10% discount factor Present value (Rs.)

0 (1,00,000) 1.000 (1,00,000)1 6,500 0.909 5,909

= 6923



2 26,500 0.826 21,8893 41,500 0751 31,1674 41,500 0.683 28,3455 71,500 0.621 44,402

31,712The net present value of the project is Rs. 31,712.

Problem No.11Step 1: Calculation of Present value of Net Cash outflows.

Machine – A:

Year Particulars Cash flow PVF @ 14% PV0 Purchasing Cost 7,50,000 1 7,50,000

1-3 Running Cost p.a. 2,00,000 2.5313(PVAF@9%, 3y)

5,06,260

PV of Net cash outflows 12,56,260

Machine – B:

Year Particulars Cash flow PVF @ 14% PV0 Purchasing Cost 5,00,000 1 6,00,000

1-3 Running Cost p.a. 3,00,000 1.7591(PVAF@9%, 2y)

5,27,730

PV of Net cash outflows 10,27,730

Step 2: Calculation of Equivalent Present Value of Annual Net Cash outflows.

1. Machine A)PVAF(9%,3y

12,56,260

2.5313260,56,12

=4,96,290

2. MachineB)PVAF(9%,2y

10,27,730

1.759110,27,730 =5,84,236

Conclusion: Since Equivalent Present Value of Net Cash Outflow is less, it is beneficial to purchase MachineA.

Problem No.12Statement showing the Evaluation of Two MachinesMachines A BPurchase cost (Rs.): (i) 1,50,000 1,00,000Life of machines (years) 3 2Running cost of machine per year (Rs.): (ii) 40,000 60,000Cumulative present value factor for 1-3 years @ 10%: (iii) 2.486 -Cumulative present value factor for 1-2 years @ 10%: (iv) - 1.735Present value of running cost of machines (Rs.): (v) 99,440 [(ii) × (iii)] 1,04,100 [(ii) × (iv)]Cash outflow of machines (Rs.): (vi)=(i) +(v) 2,49,440 2,04,100Equivalent present value of annual cash outflow 1,00,338 [(vi)÷(iii)] 1,17,637 [(vi) ÷(iv)]Decision: Company X should buy machine A since its equivalent cash outflow is less than machine B.

Problem No.13First of all we shall find an approximation of the payback period:

= 425,000

1,00,000

Now we shall this figure in the PVAF table corresponding to 6 year row.The value 4 lies between values 4.111 and 3.998 correspondingly discounting rates 12% and 13% respectively.NPV @ 12%NPV12%= (1,00,000) + 4.111 x 25,000 = 2,775


No.1 for CA/CWA & MEC/CEC MASTER MINDSNPV13%= (1,00,000) + 3.998 x 25,000 = (50)The internal rate of return is, thus, more than 12% but less than 13%. The exact rate can be obtained byinterpolation:

IRR = %)%(X)(,

x,% 121350775210775212

IRR = 12.98%Problem No.14

Problem No.15



Problem No.16

Working notes:

Depreciation on machine. X =

Life

ValueScrap-Cost =

5000,50,1 = Rs.30,000

Depreciation on machine. Y =

Life

ValueScrap-Cost =

6000,40,2 = Rs.40,000

Particulars Machine X Machine YAnnual savings:WagesScrapTotal savings(A)

90,00010,000

1,00,000

1,20,00015,000

1,35,000

Annual estimated cash cost:Indirect materialSupervisionMaintenanceTotal cash cost(B)

6,00012,0007,000

25,000

8,00016,00011,00035,000

75,00030,000

1,00,00040,000

45,00013,500

60,00018,000

31,50030,000

42,00040,000

Annual cash savings(A-B)Less: depreciationAnnual savings before taxLess: tax @ 30 %Annual profit after taxAdd: depreciationAnnual cash in flows

61,500 82,000

Evaluation of alternatives:

(i) ARR = average annual net savings Average investment

Machine X = 100x000,75500,31 = 42%

Machine Y = 100x000,20,1000,42

= 35%

Decision: Machine X is better.


No.1 for CA/CWA & MEC/CEC MASTER MINDS[Note: ARR can be computed alternatively taking initial investment as the basis for computation (ARR =Average Annual Net Income/Initial Investment). The value of ARR for Machines X and Y would then changeaccordingly as 21% and 17.5%respectively]

(ii) Present Value Index MethodPresent Value of Cash Inflow = Annual Cash Inflow x P.V. Factor @ 10%Machine X = 61,500 x 3.79

= Rs.2,33,085Machine Y = 82,000 x 4.354

= Rs.3,57,028

P.V index = present value of cash inflowInvestment

Machine X = 5539.1000,50,1085,33,2

Machine Y = 4876.1000,40,2028,57,3

Decision: Machine X is better.

Problem No.17

Particulars Project C Project DNPV 4,139 (I) 3,823 (II)IRR 26.5% (2) 37.6% (1)

From the above figures, NPV supports Project C and IRR supports Project D. Therefore there is a conflict inranking of projects between NPV & IRR.

Reasons for conflict in rankings:1. The projects are mutually exclusive2. Cash flow disparity/ Time disparity3. NPV assumes that interim cash inflows are reinvested @ cost of capital where as IRR assumes that the

interim cash inflows are reinvested @ IRR

Decision: The objective of Financial Management is to maximize shareholders wealth. NPV ranks theproposals in accordance with this objective. Therefore it is beneficial to select the project being preferred byNPV i.e., Project “C”.

Problem No. 18



Problem No.19

Problem No.20(i) Cost of Project

At 15% internal rate of return (IRR), the sum of total cash inflows = cost of the project i.e initial cash outlay

Annual cost savings = Rs. 96,000

Useful life = 5 years

Considering the discount factor table @ 15%, cumulative present value of cash inflows for 5 years is 3.353

Hence, Total Cash inflows for 5 years for the Project is 96,000 x 3.353 = Rs. 3,21,888



Hence, Cost of the Project = Rs. 3,21,888

(ii) Payback Period

Payback period = Cost of the Project / Annual Cost Savings

= Rs. 3,21,888 / 96,000

Payback Period = 3.353 years

(iii) Net Present Value (NPV)

NPV = Sum of Present Values of Cash inflows – Cost of the Project

= Rs. 3,37,982.40 – 3,21,888 = Rs. 16,094.40

Net Present Value = Rs. 16,094.40

(iv) Cost of Capital

Profitability index = Sum of Discounted Cash inflows / Cost of the Project

1.05 = Sum of Discounted Cash inflows / 3,21,888

∴Sum of Discounted Cash inflows = Rs. 3,37,982.40

Since, Annual Cost Saving = Rs. 96,000

Hence, cumulative discount factor for 5 years = Rs. 3,37,982.40 / 96,000

From the discount factor table, at discount rate of 13%, the cumulative discount factor for 5 years is 3.52

Hence, Cost of Capital = 13%

Problem No. 21

(a)Payback Period Method:A = 5 + (500/900) = 5.5 yearsB = 5 + (500/1200) = 5.4 yearsC = 2 + (1000/2000) = 2.5 years

Net Present Value:

ANPV = (- 5000) + (900 - 6.145) = (5000) + 5530.5 = Rs.530.5

BNPV is calculated as follows:

Year Cash flow (Rs.) 10% discount factor Present value (Rs.)0 (5,000) 1.000 (5,000)1 700 0.909 6362 800 0.826 6613 900 0.751 6764 1,000 0.683 6835 1,100 0.621 6836 1,200 0.564 6777 1,300 0.513 6678 1,400 0.467 6549 1,500 0.424 636

10 1,600 0.386 6181591


No.1 for CA/CWA & MEC/CEC MASTER MINDSNPVC = (-5000) + (2000×2.487) + (1000×0.683) = Rs.657Internal Rate of ReturnIf ANPV = 0, present value factor of IRR over 10 years = 5000/900 = 5.556

From tables, AIRR = 12 per cent.

IRRB

Year Cash flow(Rs.)

10% discountfactor

Presentvalue (Rs.)

20%discount

factor

Presentvalue (Rs.)

0 (5,000) 1.000 (5,000) 1.000 (5,000)1 700 0.909 636 0.833 5832 800 0.826 661 0.694 5553 900 0.751 676 0.579 5214 1,000 0.683 683 0.482 4825 1,100 0.621 683 0.402 4426 1,200 0.564 677 0.335 4027 1,300 0.513 667 0.279 3638 1,400 0.467 654 0.233 3269 1,500 0.424 636 0.194 291

10 1,600 0.386 618 0.162 2591,591 (776)

Interpolating: IRRB =),(

x,776591110591110

= 10+6.72 = 16.72 per cent

IRRC

Year Cash flow(Rs.)

15%discount

factorPresent

value (Rs.)18%

discountfactor

Presentvalue (Rs.)

0 (5,000) 1.000 (5,000) 1.000 (5,000)1 2,000 0.870 1,740 0.847 1,6942 2,000 0.756 1,512 0.718 1,4363 2,000 0.658 1,316 0.609 1,2184 1,000 0.572 572 0.516 516

140 136

Interpolating: IRRC = 52.115)136140(

3x14015

= 16.52 per cent

Accounting Rate of Return

ARRA: Average capital employed =2000,5 = Rs.2,500

Average accounting profit =10

)000,5000,9( = Rs.400

ARRA =500,2

)100x400( = 16 per cent

ARRB: Average accounting profit =10

)000,5500,11( = Rs.650

ARRB =500,2

)100x650( = 26 per cent

ARRC = Average accounting profit =4

)000,5000,7( = Rs.500

ARRC =500,2

)100x500( = 20 per cent



(b) Summary of Results

Project A B CPayback (years) 5.5 5.4 2.5ARR (%) 16 26 20IRR (%) 12.4 16.7 16.5NPV (Rs.) 530.5 1,591 657

Comparison of Rankings

Method Payback ARR IRR NPV1 C B B B2 B C C C3 A A A A

PROBLEM NO. 22

Although from NPV point of view Project A appears to be better but from IRR point of view Project B appears tobe better. Since, both projects have unequal lives selection on the basis of these two methods shall not beproper. In such situation we shall use any of the following method:

(i) Replacement Chain (Common Life) Method: Since the life of the Project A is 6 years and Project B is 3years to equalize lives we can have second opportunity of investing in project B after one time investing.The position of cash flows in such situation shall be as follows:

NPV of extended life of 6 years of Project B shall be £ 8,82,403 and IRR of 25.20%. Accordingly,with extended life NPV of Project B it appears to be more attractive.

(ii) Equivalent Annualized Criterion: Method discussed above has one drawback when we have to comparetwo projects one has a life of 3 years and other has 5 years. In such case the above method shall requireanalysis of a period of 15 years i.e. common multiple of these two values. The simple solution to thisproblem is use of Equivalent Annualised Criterion involving following steps:a) Compute NPV using the WACC or discounting rate.

b) Compute Present Value Annuity Factor (PVAF) of discounting factor used above for the period of eachproject.

c) Divide NPV computed under step (a) by PVAF as computed under step (b) and compare the values.

Accordingly, for proposal under consideration:

Project A Project B

NPV @ 12% £6,49,094 £5,15,488

PVAF @12% 4.112 2.402

Equivalent Annualized Criterion £1,57,854 £2,14,608Thus, Project B should be selected.

PROBLEM NO. 23

Option -1Purchase Machinery and Service the Part at

the end of year 1

Option -2Purchase Machinery and replace the Part at

the end of year 2

Company has 2 options


No.1 for CA/CWA & MEC/CEC MASTER MINDSOption 1: Purchase the machinery and service the part at the end of year 1.

Year Particulars Cash flow PVF @ 10% PV0 Cost of machine (50,000) 1 (50,000)1 Cost of service (10,000) 0.909 (9,090)

1-3 Operating Net cash inflows 18,000 2.487 44,7663 Salvage value 12,500 0.751 9,388

NPV (4,936)

Option 2: Purchase machinery and replace the part at the end of Year 2

Year Particulars Cash flow PVF @ 10% PV0 Cost of machine (50,000) 1 (50,000)

1-3 Net cash inflows 18,000 2.487 44,7662 Cost of replacement (15,400) 0.826 (12,720)4 Operating Cash inflows 18,000 0.683 12,2944 Salvage value 9,000 0.683 6,147

NPV 487

Conclusion: Since NPV is positive in case of option 2, it is beneficial for the company to purchase themachinery and replace the part at the end of year 2.

If the Supplier gives a discount of Rs. 5,000/-

In such a case revised NPV will be as follows:

Option 1: NPV = (4,936) + 5,000 = + 64

Option 2: NPV = 487 + 5,000 = 5,487

Conclusion: Since supplier is providing discount for both the options decision making will remain same.

PROBLEM NO. 24



THE END

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