Mang Account

8/2/2019 Mang Account

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Dr. Shailendra Kumar, LMTSOM, Thapar University, Patiala 16-1

Chapter 16

Volume-Cost-Profit

Analysis


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VOLUME-COST-PROFITANALYSIS

BREAK-EVEN ANALYSIS


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Volume-Cost-Profit Analysis

The cost-volume-profit (CVP) analysis is a tool to show therelationship between various ingredients of profit

planning, namely, unit sales price (SP), unit

variable cost (VC), fixed costs (FC), salesvolume, and sales-mix (in the case of

multi-product firms).

The crucial step in this analysis is the determination of

break-even point (BEP), which is defined as the saleslevel at which the total revenues equal total costs.

It is the level at which losses cease and beyondwhich profit starts.


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Break-Even Point

BEP can be determined by the followingtwo methods

(1) Algebraic Methods (2) Graphic Presentation

a) Contribution marginapproach

b) Equation technique

a) Break-even chart

b) Volume-profit graph


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1(a) Contribution MarginApproach

Contribution margin is the excess of unit sale price over unit variable cost

Example 1: How many ice-creams, having a unit cost of Rs 2 and a selling

price of Rs 3, must a vendor sell in a fair to recover the Rs 800 fees paid by

him for getting a selling stall and additional cost of Rs 400 to install the

stall? The answer can be determined by dividing the fixed cost by thedifference between the selling price (Rs 3) and cost price (Rs 2). Thus

BEP (units) =Fixed cost (Entry fees + Stall expenses)

(Sales price Unit variable cost)

(Rs 800 + Rs 400)/(Rs 3 Rs 2) = 1,200 units

BEP (units) =Fixed costs

Contribution margin (CM) per unit

BEP (amount)/BEP (Sales revenue)/BESR = BEP (units) Selling price (SP)

per unit = 1,200 Rs 3 = Rs 3,600


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BEP (amount) =Fixed costs

Profit volume ratio (P/V ratio)

P/V ratio =

Contribution margin per unit

Selling price per unit

BEP (amount) = Rs 1,200 0.3333 = Rs 3,600

From the P/V ratio, the variable cost to volume ratio (V/V ratio) can be easily

derived:

V/V ratio = 1 P/V ratio

In the vendors case, it is = 11/3 = 2/3 = 66.67 per cent

The V/V ratio, as the name suggests, establishes the relationship between

variable costs (VC) and sales volume in amount. The direct method of its

computation is:

Variable cost = Rs 2 Rs 3 = 66.67 per centSales revenue

Thus, P/V ratio + V/V ratio = 1 or 100 per cent

(1/3 + 2/3) = 1 (33.33 per cent + 66.67 per cent) = 100 per cent


7/40Dr. Shailendra Kumar, LMTSOM, Thapar University, Patiala 16-7

Margin of Safety

Margin of safety is the excess of actual sales revenue over the break-evensales revenue.

The excess of the actual sales revenue (ASR) over the break-even sales revenue(BESR) is known as the margin of safety. Symbolically, margin of safety = (ASR

BESR)

When the margin of safety (amount) is divided by the actual sales (amount), themargin of safety ratio (M/S ratio) is obtained. Symbolically,

M/S ratio = (ASR BESR)/ASR

Assume in the vendors case that sales is 2,000 units (Rs 6,000); margin ofsafety (Rs 6,000 Rs 3,600) = Rs 2,400; and the M/S ratio is Rs 2,400 Rs 6,000= 40 per cent.

The amount of profit can be directly determined with reference to the margin ofsafety and P/V ratio. Symbolically,

Profit = [Margin of safety (amount)] P/V ratio

Or Profit = [Margin of safety (units) CM per unit]

In the vendors case, profit = Rs 2,400 0.3333 (33.33 per cent) = Rs 800 or 800 Re 1 = Rs 800.

The reason is that once the total amount of fixed costs has been recovered,profits will increase by the difference of sales revenue and variable costs.


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1( b) Equation technique

The equation technique is particularly useful in

situations where unit price and unit variable costs arenot clearly defined. The excess of actual sales over theBE sales is the margin of safety. When margin of safetyis divided by the actual sales, we get margin of safetyratio which indicates the percentage by which actualsales may decline without causing any loss to the firm


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Sales revenue-Total costs = Net profit

Breaking up total costs into fixed and variable, Sales revenue Fixed

costs Variable costs= Net profit. Or Sales revenue = Fixed costs +

Variable costs + Net profit.

If S be the number of units required for break-even and sales revenue

(SP) and variable costs (VC) are on per unit basis, the above equation

can be written as follows:

SP (S) = FC + VC (S) + NI

Where SP = Selling price per unit

S= Number of units required to be sold to break-even

FC= Total fixed costs

VC= Variable costs per unit

NI= Net income (zero)

SP (S)= FC + VC (S) + zero

SP (S) VC (S)= FC


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Example 2

SV Ltd, a multi-product company, furnishes you the following datarelating to the current year:

Particulars First half of the year Second half of the year

Sales

Total costs

Rs 45,000

40,000

Rs 50,000

43,000

Assuming that there is no change in prices and variable costs andthat the fixed expenses are incurred equally in the two half-year

periods, calculate for the year:(i)The profit-volume ratio, (ii) Fixed expenses, (iii) Break-even sales,and (iv) Percentage margin of safety.

Solution

Sales revenue Total costs = Net profitRs 45,000 Rs 40,000 = Rs 5,000 (first half)

Rs 50,000 Rs 43,000 = Rs 7,000 (second half)

On a differential basis: Sales revenue, Rs 5,000 Total costs, Rs3,000 = Total profit, Rs 2,000.


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We know that only VC changes with a change in sales volume and, hence,

change in total costs are equivalent to VC (Rs 3,000). Accordingly, theadditional sales of Rs 5,000 has earned a contribution margin of Rs 2,000 [Rs

5,000 (S) Rs 3,000 (VC)].

P/V ratio = Rs 2,000 Rs 5,000 = 40 per cent.

V/V ratio = 100 per cent 40 per cent = 60 per cent.

Accordingly, 60 per cent of the total costs are made up of variable costs and

the balance represents the total fixed costs (FC).

Sales revenue = Fixed costs + Variable costs + Net profit

Rs 95,000 = FC + 0.60 (Rs 95,000) + Rs 12,000

Rs 95,000 = FC + Rs 57,000 + Rs 12,000Rs 95,000 Rs 69,000 = FC or Rs 26,000 = FC

BEP (amount) = Rs 26,000 0.40 = Rs 65,000


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Verification

Particulars Amount Per cent

Break-even sales

Variable costs

Contribution

Fixed costs

Net income

Rs 65,000

39,000

26,000

26,000

Nil

100

60

40

40

Nil

M/S ratio =(Rs 95,000 Rs 65,000

= 31.58%

Rs 95,000


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Break-Even Application

Sales Volume Required to Produce Desired Operating Profit

(Fixed expenses + Desired operating profit) P/V ratio

In Example 2, if the desired operating profit of SV Ltd is Rs 14,000,required sales volume = (Rs 26,000 + Rs 14,000)/0.40 = Rs 1,00,000

Operating Profit at a Given Level of Sales Volume[Actual Sales Revenue (ASR) Break-even Sales Revenue (BESR)] P/V ratio

Effect on Operating Profit of a Given Increase in Sales Volume

[Budgeted Sales Revenue (BSR) BESR] P/V ratioSuppose that SV Ltd forecasts 10 per cent increase in sales next

year, the projected profit will be: (Rs 1,04,500 Rs 65,000) 0.40 =Rs 15,800


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Additional Sales Volume Required to Offset a Reduction

in Selling Price

Suppose that SV Ltd reduces its selling price from Rs 10a unit to Rs 9. The sales volume needed to offset

reduced selling price/maintain a present operating profit

of Rs 12,000 would be:

Desired profit (P) + Fixed expenses (FC) = Rs (12,000 + Rs 26,000)

0.3333 = Rs 1,14,000Revised P/V ratio (Rs 3/Rs 9)

The required sales volume of Rs 1,14,000 represents an

increase of about 20 per cent over the present level. Themanagement should explore new avenues of sales

potential to maintain the existing amount of profit


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Effect of Changes in Fixed Costs

A firm may be confronted with the situation of increasing fixed costs. An

increase in the total budgeted fixed costs of a firm may be necessitated

either by external factors, such as, an increase in property taxes, insurancerates, factory rent, and so on, or by a managerial decision of an increase in

salaries of executives. More important than this in the latter category are

expansion of the present plant capacity so as to cope with additional

demand. The increase in the requirements of fixed costs would imply the

computation of the following:

(a) Relative break-even points.

(b) Required sales volume to earn the present profits.

(c) Required sales volume to earn the same rate of profit on the proposed

expansion programme as on the existing ones.

The effect of the increased FCs will be to raise the BEP of the firm. Assume

the management of SV Ltd decides a major expansion programme of its

existing production capacity. It is estimated that it will result in extra fixed

costs of Rs 8,000 on advertisement to boost sales volume and another Rs

16,000 on account of new plant facility.


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(a) The relative BEPs will be:

Present facilities = Fixed costs P/V ratio = Rs 26,000/0.40 = Rs

65,000.

Proposed facilities = (Present FCs + Additional FCs) P/V ratio.

= (Rs 26,000 + Rs 24,000)/0.40 = Rs 125,000.

It may be noted that increase in FCs (from Rs 26,000 to Rs 50,000)

has caused disproportionate increase in the BEP (from Rs 65,000 to

Rs 1,25,000).(b) The required sales volume to earn the present profit

[Present FCs + Additional FCs + Present profit (NI)] P/V ratio.

= [Rs 26,000 + Rs 24,000 + Rs 12,000] 0.40 = Rs 1,55,000.

(c) The required sales volume to earn the present rate of profit oninvestment:

(Present FCs + Additional FCs + Present return on investment +

Return on new investment) P/V ratio.


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Let us assume that the present investment is Rs 1,00,000 and the newinvestment will involve an additional financial outlay of Rs 60,000. Therequired sales volume will be (Rs 26,000 + Rs 24,000 + Rs 12,000+ Rs 7,200(0.12 Rs 60,000)/0.40 = Rs 1,73,000.

These computations may be reported in a summary form to the managementas follows (Table 1).

Table 1: Effect of Changes in Fixed Costs

Particulars Presentfacilities

Prospectivefacilities

Increase

Fixed costs Rs 26,000 Rs 50,000 Rs 24,000

BEP sales volume 65,000 1,25,000 60,000

BEP sales volume (units) 6,500 12,500 6,000

Sales volume to earn existingprofit

95,000 1,55,000 60,000

Sales volume in units to earn

existing profit

9,500 15,500 6,000

Sales volume to earn existing ROI 95,000 1,73,000 78,000

Sales volume to earn existing ROI(in units)

9,500 17,300 7,800


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Effect of Changes in Variable Costs

Assuming an increase of VC by Re 1 a unit for SVLtd, the new contributionmargin will be: Rs 3 (Rs 10 Rs 7) and the revised P/V ratio 0.30 that is, (Rs 3 Rs 10).

Revised BEP = (Rs 26,000)/0.30 = Rs 86,667

Desired sales volume to earn existing profit = Rs 38,000/0.30 = Rs 1,26,667

Assuming that variable costs of SVLtd decline by Re 1 per unit, revised BEP= Rs 26,000/0.50 = Rs 52,000.

Desired sales volume to maintain existing profit = Rs 38,000/0.50 = Rs 76,000.

Effects of Multiple Changes

So far we have assumed that a change takes place in one of the threevariable affecting profitscost, price and sales volume. In cases where morethan one factor is affected, the BEP analysis can be applied as shown below:

FC + FC (new) +Desired NI

1 tax rate

[Contribution margin per unit (New SP New VC) New selling price (NewSP)]


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Assuming the following set of new Figures for SV Ltd:

Particulars Existing data New data

Selling price per unit Rs 10 Rs 11

Fixed costs 26,000 40,000

Variable cost per unit 6 5.50

Contribution margin per unit 4 5.50

Desired net income after taxes (to maintain

the existing ROI)

12,000 25,000

Tax rate 35 per cent

Solution

Desired sales volume (on the basis of new data) [Rs 26,000 + Rs 14,000 +(Rs 25,0000.65)] 0.50, that is (Rs 5.5 Rs 11) = (Rs 78,461.5) 0.50 = Rs

1,56,923

Desired sales volume on the basis of existing data = [Rs 26,000 + (Rs12,000 0.65)] 0.40 (Rs 4 Rs 10) = Rs 44,462 0.40 = Rs 1,11,154.


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Multi-product Firms (Sales-mix)

Example 3

The Garware Paints Ltd presents to you the following income statement in a

condensed form for the first quarter ending March 31:Particulars Product Total

X Y Z

Sales

Variable costs

Contribution

Fixed costs

Net income

P/V ratio

Break-even sales

Sales-mix (per cent)

Rs 1,00,000

80,000

20,000

0.20

0.50

Rs 60,000

42,000

18,000

0.30

0.30

Rs 40,000

24,000

16,000

0.40

0.20

Rs 2,00,000

1,46,000

54,000

27,000

27,000

0.27

1,00,000

100

If Rs 40,000 of the sales shown for Product Xcould be shifted equally toproducts Yand Z, the profit and the BEP would change as shown in Table 2.


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Table 2 Break-even Point

Particulars Product Total

X Y Z

Sales

Less: Variable costs

Contribution

Less: Fixed costs

Net income

P/V ratio

BE sales


Rs 60,000

48,000

12,000

0.20

0.30

Rs 80,000

56,000

24,000

0.30

0.40

Rs 60,000

36,000

24,000

0.40

0.30

Rs 2,00,000

1,40,000

60,000

27,000

33,000

0.30

90,000

100

Example 3 shows that by increasing the mix of high P/V products (Y from 30to 40 per cent, Z from 20 to 30 per cent) and decreasing the mix of a low P/V

product (X from 50 to 30 per cent), the company can increase its overallprofitability. In fact, it can further augment its total profits, if it can make, andthe market can absorb, more quantities of Y and Z, say Rs 1 lakh each (Table3).


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Table 3

Particulars Product Total

Y Z

Sales

Less: Variable costs

Contribution

Less: Fixed costs

Net income

P/V ratio

BE sales


Rs 1,00,000

70,000

30,000

0.30

0.50

Rs 1,00,000

60,000

40,000

0.40

0.50

Rs 2,00,000

1,30,000

70,000

27,000

43,000

0.35

77,143

100

From the above, it can be generalised that, other things being equal,management should stress products with higher contribution margins. For

individual product line income statements, fixed costs should not beallocated or apportioned.


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2(a) Break-Even ChartThe break-even chart is a graphic presentation of the relationship between

costs, profits, and sales. It shows not only the break-even sales but alsothe estimated costs and profit at various levels of the sales revenue. It is,therefore, also referred to as volume-cost-profit (VCP) graph/chart

Assumptions Regarding the VCP Graph are

1. Costs can be bifurcated into variable and fixed components.

2. Fixed costs will remain constant during the relevant volume range ofgraph.

3. Variable cost per unit will remain constant during the relevant volumerange of graph.

4. Selling price per unit will remain constant irrespective of the quantitysold within the relevant range of the graph.

5. In the case of multi-product companies, in addition to the above fourassumptions, it is assumed that the sales-mix remains constant.

6. Finally, production and sales volumes are equal.


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Example 4

Selling price per unit

Fixed costs

Variable costs per unit

Relevant range (units) : Lower limit

: Upper limit

Break-up of variable costs per unit:

Direct material

Direct labour

Direct expenses

Selling expenses

Actual sales, 18,000 units (Rs 1,80,000)Plant capacity, 20,000 units (Rs 2,00,000)

Tax rate, 50 per cent

Rs 2

1.50

1

0.50

Rs 10

60,000

5

6,000

20,000


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Revenueandcosts(in000rupees)

Sales volume (in thousand units)

Y

X

Figure 1: Volume-Cost-Profit Graph (Traditional)

200

6 8 12 16 18 20 24 28 30

180

160

120

140

100

60

40

4

20

0

0

Or Rs 60 Rs 120 Rs 180 Rs 240 Rs 300

Sales revenue (in thousand units)

Per cent of plant capacity

20% 40% 60% 80% 100%

80

Relevant range

BEP

Margin of safety

(units)

Variable cost area

Fixed cost line

Fixed cost line


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Figure 1 has been drawn by using a sales line and a total cost line (including bothfixed and variable costs). The steps involved in drawing the VCP graph areenumerated as follows:

1. Select an appropriate scale for sales volume on the horizontal axis, say, 2,000 units

(Rs 20,000) per square, and plot the point for total sales revenues at relevantvolume: 6,000 units Rs 10 = Rs 60,000. Draw the sales line from the origin to Rs2,00,000 (the upper limit of the relevant range). Ensure that all the points, 0, Rs60,000 and Rs 2,00,000 fall in the same line. This should be ensured for the totalcost line also.

2. Select an appropriate scale for costs and sales revenues on the vertical axis, say,Rs 10,000 per square. Draw the line showing Rs 60,000 fixed cost parallel to thehorizontal axis.

3. Determine the variable portion of costs at two volumes of scales (beginning andending): 6,000 units Rs 5 = Rs 30,000; 20,000 units Rs 5 = Rs 1,00,000.

4. Variable costs are to be added to fixed costs (Rs 30,000 + Rs 60,000 = Rs 90,000).Plot the point at 6,000 units sales volume and Rs 1,00,000 + Rs 60,000 = Rs1,60,000. Point is to be plotted at 20,000 units sales volume. This obviously is thetotal cost line.

5. The point of intersection of the total cost line and sales line is the BEP. To the rightof BEP, there is a profit area and to the left of it, there is a loss area.

6. Verification: FC CM per unit = Rs 60,000 Rs 5 per unit = 12,000 units or Rs1,20,000


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Figure 1 has been drawn using different scales for the horizontal andvertical axis. Figure 2 has been drawn on a uniform scale for both axes.Since the scales are the same, the 45 line will always be the proxy of thesales line. Any amount of sales revenue on the horizontal axis willcorrespond to costs and revenue on the vertical axis. Let us illustrate

taking two sales levels.

1. Rs 60,000: FC = Rs 60,000

VC = 30,000 (50 per cent variable cost to volume ratio)

TC = 90,000

Loss = 30,000 (TC, Rs 90,000 Rs 30,000, sales revenue)

Thus, Rs 60,000 = Rs 60,000 + Rs 30,000 Rs 30,000. Point A in Figure 2clearly shows these three relevant figures at the sales volume of Rs 60,000.

2. Rs 1,80,000: FC = Rs 60,000

VC = 90,000

TC = 1,50,000

Profit = 30,000

Thus, Rs 1,80,000 = Rs 60,000 (FC) + Rs 90,000 (VC) + Rs 30,000 (Profit).Point B in Figure 2 portrays these three relevant figures at the sales volumeof Rs 1,80,000.


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Revenueand

costs(in000rupees)

Sales revenue (in 000 rupees)

Y

X

Figure 2: Volume-Cost-Profit Graph, Same Scale

40

0

0

BEP

Fixed cost line80

120

160

200

240

40 60 80 120 240160 180 200140


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The VCP graph in Figure 3 is drawn with the details of the individual segmentof variable cost and is more informative. The steps involved in drawing thegraph include an additional step of adding variable costs to the fixed cost.

This is to be repeated four times for four different components: material,

labour, direct expenses and selling expenses. In fact, fixed costs can also befurther split-up into parts. Such a graph provides a birds-eye view of theentire cost structure to the management. By drawing a line perpendicularfrom any volume (horizontal axis), the corresponding cost and profitvariables can be ascertained on the vertical axis.

For instance, at 20,000 unit level, following are the various cost figures, asshown by the VCP graph (line A).

Fixed costs

Variable costs:

MaterialLabour

Direct expenses

Selling expenses

Profit before taxes

Rs 60,000

40,00030,000

20,000

10,000

40,000


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Revenueand

costs(in000rupe

es)

Sales Volume (in thousand units)

Y

X

Figure 3: Volume-Cost-Profit Graph, Cost-Wise

40

BEP

80

120

160

200

4 8 12 16 20

Rs 20,000 Net income

Rs 20,000 Income tax

Rs 10,000 Selling expenses Variablecosts&exp

enses

Totalcosts

and

expenses

Rs 20,000Direct

expenses

Rs 30,000Direct labour

cost

Rs 40,000 Direct materialcost

Rs 60,000

Fixed expenses(Factory,

administration,selling)


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The VCP graph can be modified to show the changes in the

profitability factors of Example 4, such as,

1.Change in fixed costs (Rs 10,000 both ways)

2.Change in variable costs (20 per cent both ways)

3.Change in selling price (25 per cent both ways).

Table 4 provides a summary of the results due to the above changes.

Only one change is taken at a point of time.


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Table 4

Variable Effect on BEP Margin of safety Operating profit

Fixed costs (Rs 10,000):

Increase

Decrease

(Figure 4)

Variable costs:

Increase (to 60 per cent)

Decrease (to 40 per cent)

(Figure 5)

Selling price (25 per cent):

Increase

Decrease

(Figure 6)

Increase (Rs 20,000)

Decrease (Rs 20,000)


















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Revenueandcosts(in000rupees)

Y

Figure 4: Volume-Cost-Profit Graph, Change in Fixed Cost


40 80 120 160 200 240 280 320

4500

0

Profits (FC Rs 70)

FC line (A)

FC line (B)

BEP (FCRs 50)

BEP (FCRs 70)

Profit (FC Rs 50)

Margin of safety(MS)

X

280

320

240

200

160

120

80

40


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Revenue

andcosts(in000r

upees)

X

Y

Figure 5: Volume-Cost-Profit Graph, Change in Variable Cost


300

260

220180

150

140

100

60

20

40 80 120 160 200 240 280 320

450

Profits Rs 12,000(VC 60%)

FC line

Margin ofsafety(MS)

BEP (VC40%)

BEP (VC60%)

Profits Rs 48,000(VC 40%)

(MS)

0

0


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Revenueand

costs(in000rupe

es)

40 80 120 160 200 240 280 320

450


Profit (at higher SP)

BEP (at lower SP)

Profit (at higher SP)

FC line

Margin of

safety

320

320

320

200

160

120

80

40

0

0

Figure 6:Volume-Cost-Profit Graph, Change in Selling Price

X

Y


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Important Points Regarding Figure 6

In Figures 4 and 5, there are two cost lines to show the increase and

decrease. But Figure 6, which is designed to reveal the change due to the

selling price, has only one sales line (45). The impact of change in the

sales price is reflected indirectly in the variable cost line (which is merged

with FC line and is represented by the total cost line). This is due to the fact

that the V/V ratio which is an essential input for drawing the chart gets

changed when the selling price is changed. In other words, Figure 6 is like

Figure 5. The new V/V ratio has been determined as follows.

(1) When there is an increase in selling price by 25 per cent

Sales price ( revised) = Rs 5.50 (Rs 10 + 25 per cent) or 125 per cent (Rs 12.5

per unit).

Variable costs = Rs 5 or 50 per cent (existing).

V/V Ratio = (Rs 5 Rs 12.50) or (50 125) or 40 per cent.


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(2) When there is a decrease in sales price by 25 per centSales price= Rs 7.50 (Rs 10 Rs 2.50) or 75 per cent (Rs 7.5 per unit).

Variable costs= Rs 5 or 50 pr cent (existing).

V/V Ratio= (Rs 5 Rs 7.50) or (50 75) or 66.67 per cent .

Total cost line= Rs 60,000 + 66.67 per cent sales.

Since the V/V ratio assumes a fractional form, care has been taken to plot

points at sales levels of Rs 1,50,000 and Rs 2,40,000 so that corresponding

variable cost figures can be whole numbers, that is, Rs 1,00,000 and Rs

1,60,000 respectively.

Figure 7 portrays VCP relationships of a sales-mix for multi-product firm

(Example 3).


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140

160

120

100

80

60

40

20

20

X

Y

40 60 80 90 100 120 140 160

Revenueandcos

ts(in000rupees)


BEP (original)

BEP (changed mix)

Total cost line (original mix)

FC line

450

00

Figure 7: Volume-Cost-Profit Graph, Change in Sales Mix


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Cash Break-Even Point

The VCP relationship can also be used to show the liquidity position of the

firm. This is done through the computation of cash break-even point or

cash break-even sales revenue (CBEP/CBESR). Algebraically:

CBEP =Total cash fixed cost (CFC)

Equation 1Contribution margin per unit

CBESR =Total cash fixed cost

Equation 2

P/V ratioGraphically, the CBEP is determined at the point of intersection of total

cash cost line and total sales line. The area to the left of the curve

signifies cash losses and the area on the right side is indicative of cash

profits.

Assuming for Example 4, the cash fixed cost to be Rs 15,000, the CBESRusing Equation 2 would be Rs 30,000 = Rs 15,000 0.50

Figure 8 portrays the graphic presentation of the cash break-even sales

revenue.


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16 40

60

50

40

30

20

10

0 10 20 30 40 50 60

Costsandprofit(in000rupees)


Total cash fixed cost

Cash BEP

Figure 8: Cash Break-even Point

X

Y

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