Break Even Point Theory and Cases for Students

Volume-Cost-Profit Volume-Cost-Profit Analysis

Learning Objectives i. ii. iii. iii.

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Introduction Profit planning is a function of the selling price of a unit of product, the variable cost if  making and selling the product, the volume of product units sold, and, in the case a multi-product companies, sales-mix and, finally, the total fixed costs. The volume cost-profit (VCP) analysis is a management accounting tool to show the relationship  between  between these ingredient ingredientss of profit profit planning. planning. The entire entire gamut gamut of profit profit planning planning is associated wit VCP inter-relationships. inter-relati onships. A widely-used technique to study VCP relationships is break-even analysis. A break-even analysis is concerned with the study of revenues and costs in relation to sales volume and, particularly, the determination of that volume of sales at which the firm’s revenues and total costs will be exactly equal (or net income zero. Thus, the  break-even  break-even point point (BEP) may be defined as a point at which the firm's total revenues are exactly equal to total costs, yielding zero income. The “no-profit, no-loss” point is a  break-even  break-even point point or a point point at which which losses losses cease and and profits profits begin. begin. Break-even analysis, as a technique, seeks to provide answers to the following questions: 1. 2. 3. 4.

What hat sal sales es volu volume me is nece necess ssar ary y to to pro produ duce ce an X  an X amount amount of operating profit? What hat wil willl the the oper operat atin ing g prof profit it or loss loss at X  at X sales sales volume be? What hat pr profit fit wil willl re result fro from m an an X per  X per cent increase in sales volume? What What is is the the addi additio tional nal sales sales vol volum umee requ require ired d to make make goo good d an an X per  X per cent reduction in selling prices so as to maintain the current profit level? 5. What What will will the the effec effectt on oper operati ating ng pro profit fit be be if the the compa company ny’s ’s fixed fixed costs costs hav havee increased? 6. What What will will the the effe effect ct on incom incomee be if the firm firm achie achieves ves a red reduc uctio tion n in var variab iable le costs (say, material or direct labour)? 7. What What is the require required d sales sales volu volume me to cove coverr the the addit additiona ionall fixed fixed charges charges from the  proposed  proposed new project? project? 8. What What will will the the effec effectt on operatin operating g profi profitt of of the the firm firm be be if the sales sales mix mix is change changed? d? 9. What What will will the the effe effect ct on incom incomee be if there there is an an incre increase ase in in fixed fixed cost costss by an an X  amount the to new plan but will decrease the labour costs by Y amount Y amount per unit? 10. What What sales sales volu volume me is needed needed to achie achieve ve the the budg budgeted eted profit? profit?

Section 1 Break-Even Analysis A break-even analysis shows the relationship between the costs and profits with sales volume. The sales volume which which equates total revenue with related costs and resale in neither profit nor loss is called the break-even volume or point (BEP). If all costs are assumed to be variable with sales volume, the BEP BEP would be at zero sales. If all costs were fixed, profits would vary disproportionately with sales and the BEP would be at a  point where where total sales sales revenue revenue equaled equaled fixed costs. However, However, but but are purely purely hypothetical situations. In actual practice, costs consist consist of both fixed and variable elements. Break-even point is the sales volume at which revenue equals cost (i.e. no profit no loss).

The BEP can be determined by two methods: 1. Algebraic Algebraic methods: methods: (a) Contribution Contribution margin approach approach and and (b) Equation Equation technique, and 2. Graphic presentation: presentation: (a) (a) Break-even Break-even chart and and (b) Profit volume volume graph. graph.

Algebraic Methods Contribution Margin Approach: Approach: The logic underlying the determination of the BEP under the approach can be stated by answering the following question: “How many icecreams, having a unit cost of Rs 2 and a selling price of Rs 3, much 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 to dividing the fixed cost  by the difference difference between between the selling selling price (Rs 3) and cost cost price (Rs (Rs 2). Thus, Thus,

BEP (units) =

Fixed cost (Entry fees + Stall expenses) (Sales price - Unit vari able cost) (7.1)

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

Fixed costs Contributi on m arg in (CM ) per unit (7.2)

Or, BEP (amount)/BEP (Sales revenue)/ BESR  BESR

Or,

= BEP (units) X Selling price (SP  (SP ) per  unit = 1,200 X Rs 3 = Rs 3,600

(7.3)

BEP (amount) =

P / V ratio1

Fixed costs Pr ofit volume ratio (P/V ratio) (7.4)

Contribution margin per unit =

Selling price per unit (7.5)

Re1 Re 3

=

or 33.33 per cent

BEP (amount) = Rs 1,200 ÷ 0.333 = Rs 3,600 Sum the P/V ratio, the variable cost to volume ratio (V/V  ( V/V ratio) ratio) can be easily derived: V/V ratio V/V ratio = 1 – P/V ratio

(7.6)

In the vendor’s case, it is = 1-1/3 = 2/3 = 66.67 per cent The V/V ratio, V/V ratio, as the name suggests, establishes the relationship between variable costs (VC) and sales volume in amount. amount. The direct method of its computation is: Variable cost Sales revenue

=

Rs 2 ÷ Rs 3 = 66.67 per cent (7.7)

Thus, P/V ratio + V/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

(7.8)

Margin of Safety The excess of the actual sales revenue (ASR) over the break-even sales revenue (BESR) is know as the margin of safety. Symbolically, margin margin of safety = (ASR – BESR) (7.9)

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

(ASR - BESR) ASR  (7.10)

The M/S  The M/S ratio ratio indicates the percentage by which the actual sales may be reduced before they the below the break-even sales volume. It is important that there should be a reasonable margin of safety, lest a reduced level of activity should prove disastrous. The higher the margin of safety ratio, the better it is from the point of view of the company as it indicates that a “sizeable” sales volume can fall before the BEP is reached. This measure measure acquires special significance in depression/recession. depression/recess ion.

Assume in the vendor’s case that sales is 2,000 units (Rs 6,000); margin of safety (Rs 6,000 to 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 of safety and P/V ratio. Symbolically, Profit = [Margin of safety (amount)] (amount)] x P/V P/V ratio Or Profit = [Margin of safety (units) X CM per CM per unit]

(7.11) (7.12)

In the vendor’s case, profit = Rs 2,400 x 0.3333 (33.33 per cent) = Rs 800 or 800 x 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. Equation Technique This is the most general form of analysis, which can be applied to any cost-volume-profit situation. It is based on an income equation: equation: Sales revenueTotal costs = Net profit Break up total costs into fixed and variable, Sales revenue –  Fixed costs – Variable Variable costs Net profit. Or sales revenue = Fixed costs + Variable Variable costs + Net profit.

If S  If S be be the number of units required for break-even and sales revenue (SP  ( SP ) and variable costs (VC) are on per unit basis, the above equation can be written as follows: SP(S) = FC + VC (S) + NI 

(7.13)

Where SP = SP = Selling price per unit S = S = Number of units required to be sold to break-even FC = Total fixed costs VC = Variable costs per unit  NI =  NI = Net income (zero) SP ( SP (S ) = FC + VC (S) + zero SP ( SP (S ) – VC (S  (S ) = FC or  S ( S (SP – SP – VC) = FC S  =

FC SP − VC (7.14)

It can be seen that Eq. 7.14 is identical to Eq. 7.2 (contribution margin approach). Yet, it is specially is specially useful in situations situations in which which unit price and and unit variable costs are not clearly identifiable. Example 7.1 SV Ltd, SV Ltd, a multi-product company, furnishes you the following data relating to the current year:

 Particulars  Particulars Sales

First half of the year Rs 45,000

Second half of the year  Rs 50,000

Total costs

40,000

43,000

Assuming that there is no change in prices and variable costs and that 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 profit Rs 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, Rs 3,000 = ∆ Total  profit, Rs Rs 2,000 2,000 We know that only VC changes with a change in sales volume and, hence, change in total costs are equivalent equivalent to VC (Rs 3,000). Accordingly, the additional 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 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 represents the the total fixed fixed costs costs (FC). Sales revenue = Fixed costs + Variable costs + Net profit Rs 95,000 = FC + 0.60 X (Rs 95,000) + Rs 12,000 Rs 95,000 = FC + Rs 57,000 + Rs 12,000 Rs 95,000 – Rs 69,000 = FC or Rs 26,000 = FC BEP (amount) = Rs 26,000 ÷ 0.40 = Rs 65,000

TABLE 7.1 Verification  Particulars  Particulars Break-even sales Variable costs Contribution Fixed costs  Net income income  M/S  ratio =

Amount Amount Rs 65,000 39,000 26,000 26,000 Nil (Rs 95,000 - Rs 65,000) Rs 95,000

=

31.58 per cent

Per cent  100 60 40 50 Nil

Break-Even Analysis Applications Sales Volume Required to Produce Desired Operating Profit One application of a BE analysis is a determine the required sales volume to generate a budgeted amount of   profit. The required required sales sales are given given by Eq. 7.15. 7.15.

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

(7.15)

In Example 7.1, if the desired operating profit of SV  of  SV ltd ltd is Rs 14,000, required sales volume = (Rs 26,000 + Rs 14,000)/0.40 = Rs 1,00,000 A variant of the above approach is that the management may be interested in knowing the required sales volume to produce produce the desired profit after taxes. In this case, the analysis must be expanded slightly. Assume that SV ltd SV ltd wants a net income after taxes of Rs 13,500 and that its current tax rate is 35 per cent, the net income after  taxes is 65 per cent of the net income before taxes. Re quired sales volume

=

=

Fixed costs + [Desired income after taxes/(1 - tax rate)]  P/V  ration (7.16)

Rs 26,000 + [ Rs1,35,00 /(1 − 0.35)] 0.40

=

Rs 1,16,923

Table 7.2 Verification

Sales volume Less: Variable costs Contribution Less Fixed costs Profits before taxes Less: Taxes (0.35) Profit after taxes

Rs 1,16,923 70,154 46,769 26,000 20,769 7,269 13,500

Operating Profit at a Given Level of Sales Volume [Actual Sales Revenue (ASR) –  Break-even Sales Revenue (BESR)] X P/V ratio Effect on Operating Profit of a Given Increase in Sales Volume [Budgeted Sales Revenue (BSR) – BESR] X P/V ratio (7.18)

Suppose that SV Ltd SV Ltd forecasts 10 per cent increase in sales next year, the projected  profit will will be: (Rs 1,04,500 – Rs 65,000) X 0.40 = Rs 15,800 Additional Sales Volume Required to Offset a Reduction in Selling Price The sales manager on the basis of a market research/survey may report to the management that

due to increased competition in the market and the liberal import policy of the government, the present price is relatively higher. He may advise reduction in prices to stay in competition. Suppose that SV Ltd SV Ltd reduces its selling price form Rs 10 a 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 ) Re vised P/V  ratio (Rs 3 / Rs 9)

=

Rs (12,000 + Rs 26,000) ÷ 0.3333 = Rs 1,14,000

The required sales volume of Rs 1,14,000 represents an increase of about 20 per cent over the present level. The management should explore new avenues of sales potential to maintain the existing amount of profit. On the other hand, if the firm has the opportunity to increase the unit selling price of  the product, the impact of increased sales price would be that the BEP will be reached sooner because an increase in the selling price will raise the contribution margin, assuming no change in the variable costs. An increased contribution margin will decrease the sales volume necessary to reach a desired goals. Assume that the management of SV  of SV Ltd Ltd increase the selling price of its product from Rs 10 to Rs 12, the desired sales volume would be:  FC + P  = Rs 38,000 ÷ 0.50 (Rs 6 ÷ Rs 12) = Rs 76,000 Re vised P/V  ratio 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, insurance rates, 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 expansion of the present  plant capacity capacity so as to cope cope with additional additional demand. demand. The increase increase in the the requirements requirements of fixed costs would imply the computation of the following: (a) (a) Relati lative ve bre break ak-e -eve ven n poi point ntss (b) Requ Require ired d sales sales vol volum umee to earn earn the the pre presen sentt profi profits. ts. (c) Requir Required ed sales sales volum volumee to earn earn the same rate rate of prof profit it on the the propos proposed ed expans expanskio kion n  programme  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  production capacity. capacity. It is estimated estimated that it will result result in extra extra fixed costs of Rs 8,000 8,000 on advertisement to boost sales volume and another Rs 16,000 on account of new plant facility. (a) The relative BEPs will be: Present facilities = Fixed costs ÷ P/V ratio = Rs 26,000/0.40 = Rs 65,000 Proposed facilities = (Present FC s + Additional FC s)  s) ÷ P/V  ÷ P/V ratio ratio (7.19) (Rs 26,000 + Rs 24,000)/0.40 = Rs 125,000

(b)

(c)

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). The required sales volume to earn the present profit: [Present FC s + Additional FC s + Present profit ( NI ) ÷ P/V ration (7.20) = [Rs 26,000 + Rs 24,000 + Rs 12,000] ÷ 0.40 = Rs 1,55,000 The required sales volume to earn the present rate of profit on investment: (Present FC s + Additional FC s + Present return on investment + Return on new investment) P/V  investment) P/V ratio ratio (7.21)

Let us assume that the present investment is Rs 1,00,000 and the new investment will involve as additional financial outlay of of Rs 60,000. 60,000. The required sales volume will be (Rs 26,000 + Rs 24,000 + Rs 12,000 + Rs 7,200 (0.12 X Rs 60,000)/0.40 = Rs 1,73,000 These computations may be reported in a summary form to the management as follows (Table 7.3). Table 8.3 (Effect of Changes in Fixed Costs

 Particulars  Particulars Fixed costs BEP sales volume BEP sales volume (units) Sales volume to earn existing profit Sales volume in units to earn existing profit Sales volume to earn existing ROI Sales volume to earn existing ROI (in units)

Present facilities Rs 26,000 65,000 6,500 95,000 9,500 95,000 9,500

Prospective Prospective  Increase  facilities Rs 50,000 Rs 24,000 1,25,000 60,000 12,500 6,000 1,55,000 60,000 15,500 6,000 1,73,000 78,000 17,300 7,800

Effect of Changes in Variable Costs Assuming an increase of VC by Re 1 a unit for  SV Ltd, SV Ltd, the new contribution margin will be: Rs (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 SV  of SV Ltd Ltd 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 three variable affecting profits-cost, price and sales volume. In case where more than one factor is affected, the BEP analysis can be applied as shown below:

 FC + FC (new) + [Desired  NI  / (1 - tax rate)] [Contributi on margin per unit (New SP - New VC )] ÷ New selling price (New SP )] (7.22)

Assuming the following set of new Figures for SV  for  SV Ltd: Ltd:  Particulars  Particulars Selling price per unit Fixed costs Variable cost per unit Contribution margin per unit Desired net income after taxes (to maintain the existing ROI) Tax rate

Existing data New data Rs 10 Rs 11 26,000 40,000 6 5. 50 4 5. 50 12,000 25,000 35 per cent

Solution Desired sales volume (on the basis of new data) [Rs 26,000 + Rs 14,000 + (Rs 25,000 ÷ 0.65)] = 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 + (Rs 12,000 ÷ 0.65)] ÷ 0.40 (Rs 4 ÷ Rs 10) = Rs 44,462 ÷ 0.40 = Rs 1,11,154. VCP Analysis and a Segment of the Business The fundamental approach of applying the VCP analysis to a segment of the business is the same as applying it to the business as a whole. The VCP approach “may be applied to problems problems relative to individual  product  product lines, territories, territories, methods methods of of sale, channels channels of of distribution distribution or any particular  particular  2 segment of the business which is under scrutiny” . In all these decisions, fixed costs and P/V ratio are the required inputs. Where fixed costs are inclusive of allocated costs also, in additional to direct costs, two BEPs may be determined.

SV Ltd has four sales divisions. The relevant data for its northern northern division Example 7.2 SV Ltd is reproduced below: Direct fixed costs, Rs 10,000 P/V ratio, 0.40 Allocated fixed costs from head office, Rs 5,000 The sales volume required to cover direct expenses would be: Direct fixed costs/ P/V ratio = Rs 10,000/0.40 = Rs 25,000 (7.23) The total sales volume required to cover all fixed costs would be higher as shown by equation 7.24:

Direct FCs + Allocated FCs P/V ratio (7.24)

= (Rs 10,000 + Rs 5,000) ÷ 0.40 = Rs 37,500 Multi-product Firms (Sales-mix) So far, we have confined our discussion to a one product  product company. company. However However many many manufacturers manufacturers make more more than one type type of product product.. The relative proportion of each product sold in the aggregate sales is known as the sales-mix. A change in the mix of products sold usually affects the weighted average P/V ratio and, hence, the BEP. BEP. Thus when the products have different P/V ratios, changes in the sales-mix/product-mix will affect the BEP and the results from operation.

Example 7.3 The Garware Paints Ltd presents to you the following income statement in a condensed form for the first quarter ending March 31:

 Particulars  Particulars Sales Variable costs Contribution Fixed costs  Net income income P/V ratio Break-even sales Sales-mix (per cent)

Product  X Rs 1,00,000 80,000 20,000

Total Y 

 

X

Rs 60,000 42,000 18,000

Rs 40,000 24,000 16,000

0.20

0.30

0.50

0. 30

Rs 2,00,000 1,46,000 54,000 27,000 27,000 27,000 0. 40 0.27 1,00,000 0. 20 100

If Rs 40,000 of the sales shown for product  X could  X could be shifted equally to products Y  and Z  and Z , the profit and the BEP would change as shown in Table 7.4. Table 7.4 Break-even Point

 Particulars  Particulars Sales  Less: Variable costs Contribution  Less: Fixed costs  Net income income P/V ratio BE sales Sales-mix (per cent)

Product  X

Total Y  Rs 80,000 56,000 24,000

Rs 60,000 48,000 12,000

 

X

Rs 60,000 36,000 24,000

0.20

0.30

0.40

0.30

0. 40

0.30

Rs 2,00,000 1,40,000 60,000 27,000 33,000 33,000 0.33 90,000 100

Example 7.3 shows that by increasing the mix of high P/V products ( Y from Y from 30 to 40 per cent, Z  cent, Z from from 20 to 30 per cent) and decreasing the mix of a low P/V product ( X from  X from 50 to 30 per cent), the company can increase its overall profitability. In fact, it can further augment its total profits, if it can make, and the market can absorb, more quantities of Y  of Y and and Z   Z , say Rs 1 lakh each (Table 7.5).

Table 7.5  Particulars  Particulars Sales  Less: Variable costs Contribution  Less: Fixed costs  Net income income P/V ratio BE sales Sales-mix (per cent)

Product Y Rs 1,00,000 70,000 30,000

Total Z  Rs 1,00,000 60,000 40,000

0.30

0.40

0.50

0.520

 

Rs 2,00,000 1,30,000 70,000 27,000 43,000 43,000 0.35 77,143 100

From the above, it can be generalized that, other things being equal, management should stress product with higher higher contribution margins. For individual product line income statements, fixed costs should not be allocated or apportioned. Finally, it may be stressed that there is a need for a closer study of cost structures of  individual product line/department within the same firm or of two different companies. It may be possible that the two departments/companies may have the same profits but very different cost structures. For instance, observe the Figures Figures in Table 7.6 of two departments of SV  of SV Ltd. Ltd.

Table 7.6 Particulars Sales revenue Less: Variable costs Contribution / P/V ratio Less: Fixed costs Profit BEP (amount) Margin of safety (MS) Margin of safety ratio

Department X  Amount  Amount Rs 1,00,000 70,000 30,000 20,000 10,000 66,667 33,333 0.3333

Department Y   Per cent  Amount   Per cent  cent   Amount  (100) Rs 1,00,000 (100) (70) 20,000 (20) (30) 80,000 (80) 70,000 10,000 87,500 12,500 0.125

Department Y is Y is operating closer to the BEP than Department X  Department X . Department Y has Y has a narrower margin of safety (12.5 per cent) compared to 33.33 per cent of  X   X . The margin of safety ratio signifies that if the sales of Y  of Y decreases decreases by more than 12.5 per cent, it will operate at a loss. In other words, words, the margin/cushion of safety is relatively smaller.  X  will not operate at a loss unless its sales volume drops by more than 33.33 per cent. This type of profit analysis for two different companies is of special significance from the point of view of outside investor who want to invest in one of the two companies. Assuming companies X  companies X and and Y in Y in place of the departments X  departments X and and Y in Y in the above tabulation, Company X  Company X is is certainly less risky than Company Y .

Graphic Presentation Under the algebraic technique of break-even analysis, separate computations were needed to arrive at the above set of figures. The utility of the graphical technique is that such a set of figures can be determined without involving any separate calculations. Break-Even Chart/Volume Cost Profit (VCP) Graph The break even chart is a graphic relationship between volume, costs and profits. It shows not only the BEP but also the effects of costs and revenue at varying levels of of sales. The break-even chart can, therefore, be more appropriately called the volume-cost-profit graph (VCP graph).

Assumptions Regarding the VCP Graph are 1. Costs Costs can be bifurc bifurcated ated into into variable variable and and fixed fixed compon component ents. s. 2. Fixed costs costs will remain remain constant constant during during the the relevant relevant volume volume range range of graph. graph.

3. Variable cost per unit unit will remain constant constant during during the the relevant relevant volume volume range range of  graph. 4. Selling price per per unit will remain remain constant constant irrespective irrespective of the the quantity quantity sold sold within the relevant range of the graph. 5. In the case of multi-product multi-product companies, companies, in addition addition to the above above four  four  assumptions, it is assumed that the sales-mix remains constant. 6. Finally Finally,, producti production on and and sales sales volumes volumes are equal equal.. The VCP graph graph may be prepared in a simple or elaborate manner. Figure 7.1 is an example of a simple and traditional form. In Figure 7.1, sales are shown on on the horizontal axis; the vertical axis measures costs and revenues corresponding to varying volume of sales. Sales are expressed in terms of units, rupees and percentage level of  of  activity. The VCP relationships portrayed in such a graph are valid only only within the relevant range that underlies the construction of the graph. The importance of a relevant range should be recognized because in practice most firms will progressively reduce fixed costs as the volume tends to decrease towards zero activity. Similarly, fixed costs are to be increased beyond a certain volume. Accordingly, in Figure 7.1 the lower limit and upper limit of the VCP have been drawn. The BEP lies at the point of intersection of the sales line and the total cost line. The vertical distance between the sales revenue and the total cost line measures the estimated net income (after the BEP) and the estimated net loss (before the BEP) at the related sales volume. The fixed cost line is parallel to the horizontal axis. The variable cost line is superimposed on the fixed cost line and moves upward uniformly with sales volume at the variable cost to volume ratio. This is total cost line. The sales revenue line starts from the point of origin and moves moves upward uniformly with volume. volume. The meeting point of the total cost line and sales line is the BEP. BEP. At the point, an angle is formed known as the angle of incidence. The management objective should be to have an angle of as large a size as possible because a high angle is a sign of a high rate of   profit after after the fixed fixed costs have have been been covered; covered; the narrower narrower angle angle will will signify that  profits after after the fixed fixed costs have been been covered; covered; the narrower narrower angle will will signify that  profits will will increase increase at a lower lower rate after after the BEP, BEP, showing showing that that variable variable costs form form a large part of cost of sales. Figure 7.1 is based on the following data relating to Hypothetical Ltd (Example 7.4).

Example 7.4 Selling price per unit Fixed costs Variable costs per unit Relevant range (units) Lower limit Upper limit  Break-up of variable variable costs per unit: 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)

Rs 10 60,000 5 6,000 20,000 Rs 2 1.50 1 0.50

Tax rate, 50 per cent

Figure 7.1 Volume-Cost-Profit Graph (Traditional)

Figure 7.1 has been drawn by using a sales line and a total cost line (including both fixed and variable costs). The steps involved in drawing the VCP graph are enumerated as follows: 1. Select an appropriate appropriate scale for for sales volume volume on on the horizontal horizontal axis, axis, say, say, 2,000 2,000 units (Rs 20,000) per square, and plot the point for total sales revenues at relevant volume: 6,000 units X Rs 10 = Rs Rs 60,000. Draw the sales line from the origin to Rs 2,00,000 (the upper upper limit of the relevant range). Ensure that all the points, points, 0, Rs 60,000 and Rs 2,00,000 fall 2,00,000  fall in the the same line. line. This should be ensured for the total cost line also. 2. Select an appropriate appropriate scale for for costs and and sales sales revenues revenues on the vertical axis, axis, say, Rs Rs 10,000 per square. Draw the line showing Rs 60,000 fixed cost cost parallel to the horizontal axis. 3. Determine Determine the variable variable portion portion of of costs at at two volumes volumes of scales (beginn (beginning ing and ending): 6,000 units X Rs 5 = Rs 30,000; 20,000 units X Rs 5 = Rs 1,00,000. 4. Variable costs costs are to be added added to fixed fixed costs costs (Rs 30,000 30,000 + RS 60,00 60,000 0 = Rs 90,000). 90,000). Plot the point at 6,000 units sales volume and Rs 1,00,000 + Rs 60,000 = Rs 1,60,000. Point is to be plotted at 20,000 units sales volume. This obviously is the total cost line.

5. The point point of of intersection intersection of of the total cost cost line and sales sales line is the BEP. To the the right right of BEP, there is a profit area and to the left of it, there is a loss area. 6. Verification: FC ÷ CM per CM per unit = Rs 60,000 ÷ Rs 5 per unit = 12,000 units or Rs 1,20,000 Figure 7.1 has been drawn using different scales for the horizontal and vertical axis. Figure 7.2 has been drawn drawn on a uniform uniform scale for both axes. Since the scales are the same, the 45º line will always be the proxy of the sales line. Any amount of sales revenue on the horizontal axis will correspond to costs and revenue on the vertical axis. Let us illustrate taking two sales levels. 1. Rs 1. Rs 60,000: 60,000:

FC = Rs 60,000 VC = 30,000 (50 per cent variable cost to volume

ratio) TC = TC = 90,000 Loss = 30,000 (TC  ( TC , Rs 90,000 – Rs 30,000, sales revenue) Thus, Rs 60,000 – Rs 60,000 60,000 + Rs 30,000 – Rs 30,000. 30,000. Point A in Figure 7.2 clearly shows these three relevant figures at the sales volume of Rs 60,000. 2. Rs 2. Rs 1,80,000 1,80,000::

FC =

Rs

60,000

VC = TC = TC = Profit =

Figure 7.2 Volume-Cost-Profit Graph, Same Scale

90,000 1,50,000 30,000

Thus, Rs 1,80,000 = Rs 60,000 60,000 (FC) + Rs 90,000 (VC) + Rs Rs 30,000 (Profit). Point  B in Figure 7.2 portrays these three relevant figures at the sales volume of Rs 1,80,000. The VCP graph in Figure 7.3 is drawn with the details of the individual segment of variable cost and is more informative. The steps involved in drawing the graph 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 be further split-up into parts. Such a graph provides a bird’s-eye view of the entire cost structure to the management. By drawing a line perpendicular from any volume (horizontal axis), the corresponding cost and profit variables can be ascertained on the vertical axis. For instance, at 20,000 unit level, following are the various cost figures, as shown by the VCP graph. Fixed costs Variable costs: Material Labour Direct expenses Selling expenses Profit before taxes

Rs 60,000 40,000 30,000 20,000 10,000 40,000

Application of the P/V Ratio 1. Determ Determinat ination ion of BEP BEP = FC ÷ P/V P/V ratio ratio 2. Determination Determination of profit profit at given/bu given/budgeted dgeted sales volume volume = (Actual sales –  BE sales)  BE sales) X P/V ratio  P/V ratio 3. Determ Determinat ination ion of sales sales volume volume to earn earn budge budgeted ted profit profit = (FC + DP  + DP ) ÷ P/V ratio 4. Determination Determination of of change is sales volume volume to to maintain maintain the current current level level of profit profit if  there is (a) a change is sales price, (b) change in variable cost = (FC + DP  +  DP ) ÷ Revised P/V ratio. 5. Determination Determination of of the percentage percentage of of net profit profit with the help help of margin margin of safety ratio ratio = (P/V ratio X MS  X MS ratio) ratio) (7.25)

Cash Break-Even Point The VCP relationship can also be used 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). CBESR). Algebraically: Cash break-even point is total cash fixed cost divided by contribution margin per unit.

CBEP =

Total cash fixed cost (CFC ) Contributi on margin per unit (7.26)

CBESR

Total cash fixed cost =

 P/V  ratio

(7.27)

Graphically, 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 7.4, the cash fixed cost to be Rs 15,000, the CBESR  using Equation 7.27 would be Rs 30,000 = Rs 15,000 ÷ 0.50 Figure 7.4 portrays the graphic presentation of the cash break-even sales revenue. To conclude, the uses of break-even analysis, as a technique for profit planning, have been discussed in detail in this chapter. In brief, break-even analysis shows the interplay of profit factors, that is, cost, revenue and volume in a way, which assists management in choosing the best feasible alternative now and in the future. “The breakeven system is at once an X-ray, exploratory and planning tool intended for frequent use and a proper cost-volume-profit analysis supported by the break-even chart can eliminate many of the time-consuming reports now being prepared at the company.” 3 The graphs can be used to analyse the impact of various alternative proposals under  consideration on the profit structure. Thus, the break-even system provides more readily understandable facts than conventional accounting or statistical data regarding the profit structure of the company

Figure 7.4 Cash Break-even point

However, it is important to recognize its limitations which originate from the given assumptions. The greater the deviation of actual facts from the given assumptions, the more imperfect, incorrect and invalid are the break-even calculations. These limitations limit the usefulness of the break-even chart and must be borne in mind by those who prepare or or interpret the break-even chart. These limitations suggest that the validity of the break-even chart is in proportion to the validity of the assumptions. One of the the assumptions of the break-even analysis is that an enterprise’s cost are either perfectly variable or absolutely fixed over all ranges of operating volume. In other words, variable cost is a linear function of volume: fixed costs are assumed not to be affected by volume volume at all. In practice, these assumptions are not likely to be valid over all ranges of volume. volume. Even within the relevant range of volume, volume, there is a likelihood of some degree of imprecision and to that extent validity of the results is affected. For instance, variable costs are likely to increase as the firm approaches full capacity. The reason may be due to less efficient labour or costly overtime having been resorted to. This limitation can be overcome by studying studying the relationship between total costs and volume, non-linear, to correspond with economic reality. Another assumption of the break-even analysis is that it is possible to classify total costs of an enterprise as either fixed or variable. Many costs defy clear division  because they they are partly fixed fixed and partly variable. variable. These costs costs are known known as semivariable costs.

Yet another assumption of the break-even analysis is that selling price per unit remains unchanged, irrespective of volume. In other words, total sales revenue is  perfectly variable with with its physical physical sales sales volume. volume. For some some firms, firms, operating operating in the the seller’s market, this assumption may be perfectly valid. For most others, others, however, it is not a realistic assumption because price reductions may be necessary to increase the sales volume. Once again, this limitation can be remedied by studying the relationship  between  between total sales sales revenue revenue and costs. costs.

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Profit planning is a function of coordinating the selling price of a unit of product, the variable cost per unit of making and selling the product, the volume of sales, sales-mix in the case of multiple-product firms and the total fixed cost. The volume-cost-profit analysis (VCP) is a tool to show the relationship between these ingredients of profit planning. A widely-used technique to study VCP relationship is break-even analysis (BE). The break-even analysis shows the relationship between costs and profits with the sales volume. The sales volume that that equates the total revenues with the total related costs and results in neither profit nor loss is called the BE sales/point. In other words, the no-profit-no-loss point is BEP at which losses cease and beyond which profits begin. The BPE can be determined by two methods: (1) Algebraic, comprising, (a) Contribution margin approach, (b) Equation technique, and (2) Graphic  presentation.  presentation. According According to the contributio contribution n margin margin approach, approach, BEP BEP is compute computed d on the basis of the relationship between the fixed costs and the contribution margin (CM). The CM represents the differences between sales revenue and variable costs. The equation technique is specially useful in situations in which unit price and unit variable costs are not clearly identifiable. The excess of of actual sales over the BE sales is the margin of safety. When the margin of of safety is divided by actual sales, we get the margin of safety radio which indicates the percentage by which actual sales may decline without the firm suffering a loss. Under the algebraic technique, separate computations are required. The utility of  the graphic techniques/presentation lies in the fact that a set of figures can be determined without separate calculations. The VCP chart portrays the relationship between sales, costs and profits. It not only shows BE sales but also the effect of costs and revenues at varying sales levels. It is, therefore, also referred to as the volume-cost-profit chart graph). Both the algebraic and graphic approaches can be applied to analyse the VCP relationship profit planning to reflect changes in fixed costs, variable costs and selling price. The following are the more specific applications:  Sales volume required to produce desired profit  Operating profit at a given level of sales volume  Effect on operating profits of a given percentage change in sales  Additional sales volume required to offset reduction in selling price  Effect of changes in fixed costs  Effect of changes in variable costs  Effect of multiple changes: cost, price and volume simultaneously

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Application to segments of a business Sales-mix in multi-product firms.

References 1. Wilson, J.D., “Practical Application Application of of Cost-Volum Cost-Volume-Profit e-Profit Analysis” quoted quoted by Anderson, D.L and DL. Raun, Informa Raun,  Information tion Analysis Analysis in Management Management Accounting  Accounting  (John Wiley, New York, 1978), p 162. 2. Tuckk uckker er,, S.A S.A., ., Break-E  Break-Even ven System: System: A Tool Tool for for Profit Plannin Planning, g, (Prentice Hall, Englewood Cliffs, N.J. 1963).

Solved Problems P.7.1 From the following data, calculate the: 1. Break-e Break-even ven point point express expressed ed in terms terms of sale amount/re amount/reven venue. ue. 2. Number Number of units units that must must be sold to earn a profit profit of Rs Rs 60,000 60,000 per year.

Sales price (per unit Variable manufacturing cost per unit Variable selling cost per unit Fixed factory overheads (per y ear) Fixed selling costs (per year)

Rs 20 11 3 5,40,000 2,52,000

Solution 1. BEP (amount) = (Fixed factory overheads + Fixed selling costs)/P/V ratio (Sales price – Variable manufacturing cost – Variable selling cost) ÷ Sales price = (Rs 5,40,000 + Rs 2,52,000)/0.30 (Rs 6 ÷ Rs 20) = Rs 26,40,000 2.  Desired sales sales volume volume (in units) units) to earn earn a profit profit of Rs of Rs 60,000 = (Rs 7,92,000 + Rs 60,000)/ Rs 6 (CM per unit) = Rs 1,42,000 units businesses, AB Ltd and CD Ltd, sell the same type of product in the same P.7.2 Two businesses, AB type of market. Their budgeted profit and loss accounts for the current year year ending March 31, are as follows:  Particulars  Particulars AB Ltd Ltd CD Ltd  Ltd  Sales Rs 1,50,000 Rs 1,50,000 Less: Variable costs Rs 1,20,000 Rs 1,00,000 Fixed costs 15,000 1,35,000 35,000 1,35,000  Net budgeted budgeted profit profit 15,000 15,000 15,000 15,000 You are required to: 1. Calcula Calculate te the break break-ev -even en points points of of each busin business; ess; and and 2. State which which business business is likely likely to earn earn greater greater profits in conditions conditions of: of: (a) heavy heavy demand for the product, (b) low demand for the product.

Solution 1.

BEP BEP (am (amou ount) nt) = Fix Fixed ed cost/ cost/ P/V P/V rat ratio; io; P/V ratio ratio = Con Contri tribu butio tion/S n/Sale aless rev reven enue ue BEP (AB Ltd) = Rs 15,000/0.20 = Rs 75,000 P/V ratio = Rs 30,000/ Rs 1,50,000 = 20 per cent BEP (CD Ltd) = Rs 35,000/0.3333 = Rs 1,05,000

P/V ratio = Rs 50,000/ Rs 1,50,000 = 33.33 per cent 2.

Proj Projec ecte ted d pro profi fitt (he (heav avy y de demand mand for for the the prod produ ucts) cts):: (a) CD Ltd is likely likely to to earn earn large largerr profits profits in cond conditio itions ns of of heavy heavy demand demand of the the  product  product because because its P/V ratio is higher higher than than that of AB Ltd. (b) AB Ltd is likely likely to to earn earn large largerr profits profits in cond conditio ition n of of low demand demand of the the  product  product because because its burden burden of fixed fixed costs costs is much much smaller smaller than that that of CD Ltd. P.7.3 The Soft-Flow Ink Ltd’s income statement for the preceding year is presented  below. Except Except as noted noted the cost/reve cost/revenue nue relationship relationship for for the coming coming year year is expected expected to follow the same pattern as in the preceding year. Income statement for the year ending March 31 is as follows: Sales (2,00,000 bottles @ Rs 2.5 each) Variable costs Fixed costs Pre-tax profit Less: Taxes Profit after tax

Rs 5,00,000 Rs 3,00,000 1,00,000

4,00,000 1,00,000 35,000 65,000

1. What What is the break break-eve -even n point point in amou amount nt and and units? units? 2. Suppose Suppose that a plant expansio expansion n will add add Rs 50,00 50,000 0 to fixed fixed costs and and increase increase capacity by 60 per cent. How many bottles would have to be sold after the addition to break-even? 3. At what what level of sales will will the company company be be able to maintain its present present pre-tax  profit position position even even after expansio expansion? n? 4. The company company’s ’s management management feels feels that it should should earn at lease lease Rs 10,00 10,000 0 (pre-tax  per annum) annum) on the new investment. investment. What sales sales volume volume is required required to enable the the company to maintain existing profits and earn the minimum required return on new investments? 5. Suppose Suppose the plant plant operates operates at full full capacity capacity after the the expansion, expansion, what what profit profit will  be earned? earned?

Solution 1. BEP (amount) (amount) = Rs Rs 1,00,000/0 1,00,000/0.40 .40 (Rs 2,00,0 2,00,000 00 ÷ Rs 5,00,0 5,00,000) 00) = Rs 2,50,0 2,50,000 00 BEP (units) = Rs 1,00,000/Re 1.0 = 1,00,000 units 2. BEP (increase (increase in FC) FC) = [Rs 1,00,000 1,00,000 + Rs Rs 50,000 50,000 (Additional (Additional FC)] FC)] ÷ Re 1.0 1.0 per  unit = 1,50,000 units 3. Desired sales sales volume volume to maintain maintain a pre-tax profit profit of of Rs 1,00,000 1,00,000 = [Rs 1,50,0 1,50,000 00 (FC) + Rs 1,00,000]/0.40 = Rs 6,25,000 (or 2,50,000 bottles) 4. Desired sales sales volume volume to earn a profit profit of Rs 1,10,00 1,10,000 0 (Rs 1,00,000 1,00,000 + Rs 10,000) 10,000) = Rs 1,50,000 = Rs 1,10,000]/0.40 = Rs 6,50,000 (or 2,60,000 bottles) 5. Present capacity (assumed (assumed operating operating at 100 per cent cent capacity) capacity) (bottles) (bottles) 2,00,000  Add: Additional capacity (60 per cent) 1,20,000 Total capacity (bottles) 3,20,000 Statement of income (3,20,000 units)

Sales (3,20,000 bottles @ Rs 2.5) Less: Variable costs, 0.60 Contribution Less: Fixed costs Pre-tax profits Less: Income tax Profits after income tax Sales (4,000 units @ Rs 25 each Variable costs: Materials consumed Labour charges Variable overheads Fixed overheads  Net profit profit

Rs 8,00,000 4,80,000 3,20,000 1,50,000 1,70,000 59,500 1,10,500 Rs 1,00,000 Rs 40,000 20,000 10,000 18,000

88,000 12,000 12,000

Calculate: 1. Number Number of units by by selling which the company company will break-eve break-even. n. 2. Sales Sales needed needed to earn earn a profit profit of 20 per per cent cent on sales. sales. 3. Extra units, units, which which should should be sold to obtain the present present profit profit if it is propose proposed d to reduce the selling price by 20 per cent and 25 per cent. 4. Selling price price to be be fixed to to bring down its break-even break-even point point to 600 600 units units under  under   present conditio conditions. ns.

Solution 1. BEP (units), (units), Fixed Fixed overheads overheads = Rs 18,000 18,000/CM /CM per units, units, Rs 7.50 7.50 = 2,400 2,400 units Determination of CM per unit Sales revenue (4,000 units)  Less: Variable costs Materials consumed Rs 40,000 Labour charges 20,000 Variable overheads 10,000 Contribution (4,000 units) CM per unit (Rs 30,000 ÷ 4,000)

Rs 1,00,000

70,000 30,000 7.5

2. (a) Sales Sales revenue revenue (SR) (SR) is a sum sum of of total total costs costs (TC) (TC) and tota totall profits profits (TP) (TP) OR (SR = TC + TP). (b) TC can can be split split into into FC FC and VC VC ( c) Accordingly, SR = FC + VC (SR) + TP TP (SR). Let us suppose, SR = 100 per  cent; TC = 80 per cent; TP = 20 per cent; VC = 70 per cent (Rs 70,000/Rs 1,00,000); FC = Rs 18,000 Substituting the values, we have, 100% SR = Rs 18,000 + 0.70 SR + 0.20 SR  0.10 SR = Rs 18,000 SR = Rs 18,000/0.10 = Rs 1,80,000 Verification Sales revenue Less: Variable cost (0.70)

Rs 1,80,000 Rs 1,26,000

Less: Fixed overheads  Net profit profit  Net profit profit as percentage percentage of of sales revenue revenue

18,000

1,44,000 36,000 36,000 20

3. Revised contribution contribution margin margin per per unit and and additional additional units units required required to maintain maintain profit of Rs 12,000  Particulars  Particulars Revised selling price Less: Variable cost (0.70 X Rs25, original sales price) Contribution Desired sales volume (FC + NP) ÷ CM  Number  Number of units units required required Less: Existing number of units sold Extra units to be sold to maintain a profit of Rs 12,000

Selling price reduced by  20 per cent 25 per cent   Rs 20.00 Rs 18.75 17.50 17.50 2.50 1.25 30,000/2.50 30,000/1.25 12,000 12,000 24,000 24,000 4,000 4,000 8,000 20,000

4. BEP BEP = FC/C FC/CM M per per unit unit CM per unit = FC/BEP = Rs 18,000/600 units = Rs 30 Sales price (per unit) = CM per unit + Variable cost per unit = Rs 30 + Rs 17.50 = Rs 47.5 P.7.5 ABC Ltd  ABC Ltd manufactures and sells four types of products under the brand names of  41.67, 16.67 and 8.33 per cents  A,  A, B,  B, C and C and D  D.. The sales-mix in value comprises 33.33, 41.67, for products A, products A, B, C and C and D  D respectively. The total budgeted budgeted sales (100 per cent) are as Rs 60,000 per month. Operating costs are: Variable costs as per cent of selling price: Product A, Product A, 60, B, 60, B, 68, C, 80, and D and D 40. Fixed costs, Rs 14,700 per month.

Calculate the break-even point for the products on an over-all basis.

Solution Determination of weighted PV ratio  Product  Product Sales revenue revenue (%) Variable Variable costs (%) Contribution Contribution  A Rs 20,000 (33.33) Rs 12,000 (60) Rs 8,000  B 25,000 (41.67) 17,000 (68) 8,000 C  10,000 (16.67) 8,000 (80) 2,000  D 5,000 (8.33) 2,000 (40) 3,000 Total 60,000 (100) 39,000 (65) 21,000 BEP = Fixed costs/ Weighted P/V ratio = Rs 14,700/0.35 = Rs 42,000 Confirmation Variable costs (0.65 X RS 42,000 Fixed costs Total costs Total sales revenue

P/V ration ration (%) (%) 40 32 20 60 35

Rs 27,300 14,700 42,000 42,000

P.7.6 The XYZ  The XYZ Ltd Ltd operates a chain of shoe stores. The stores sell 10 different styles of  men’s shoes with identical purchase costs and selling prices. The company is trying to

determine the desirability of opening another store, which would have the following expense and revenue relationships per pair. Variable data: Selling price Cost of shoes Salesmen’s commission Total variable expenses Annual fixed expenses: Rent Salaries Advertising Other fixed expenses

Rs 30.00 19.50 1.50 21.00 60,000 2,00,000 80,000 20,000 3.60,000

Required (consider each question independently): 1. What is the annual break-even break-even point point in sales amount amount and in unit sales? sales? 2. If 35,000 35,000 pairs pairs of shoes shoes are sold, sold, what would the store’s store’s net income income be? be? 3. If the store store manager manager was paid paid Rs 0.30 0.30 per per pair commissio commission, n, what what would would the annual annual  break-even  break-even point point be in sales amount amount and in unit sales? 4. Refer to the the original original data. data. If the store manager manager were paid Rs 0.30 0.30 per pair pair as commission on each pair sold in excess of the break-even point, what would be the store’s net income if 50,000 pairs were sold? 5. Refer to the the original original data. data. If sales sales commissions commissions were were discontinu discontinued ed in in favour favour of Rs Rs 81,000 increase in fixed salaries, what would the annual break-even point be in amount and in unit sales? 6. If the manager manager wants wants to comput computee separate break-ev break-even en points points for gent’s gent’s and ladies shoes, what additional assumption will you make and what information would you need? 7. If the store store wants to build build up stocks stocks by by the end end of the the accounting accounting period, will your  your  analysis still hold good?

Solution 1. Selling price  Less: Variable costs CM per unit (pair) P/V ratio (%) BEP (amount) = Rs 3,60,000/0.30 = Rs 12,00,000 BEP (units) = Rs 3,60,000/ CM per unit = Rs 3,60,000/Rs 9 = Rs 40,000 units

Rs 30 21 9 30

2. Income Income if 35,00 35,000 0 pairs pairs of of shoes shoes are are sold sold Contribution (35,000 X Rs 9) Rs 3,15,000 Less: Fixed cost 3,60,000 Loss (45,000) 3. Contribution Contribution is Rs 8.70 8.70 (less by by 30 paise paise commission commission paid to store manager): manager): (Rs (Rs 30  – Rs 21.30) 21.30) BEP (units) = Rs 3,60,000/Rs 8.70 = 41,380 pairs P/V ratio = Rs 8.70 Rs 30 = 29 per cent

4. CM per per unit beyond beyond the BEP BEP X Margin Margin of of safety in in units = Income Income Rs 8.70 8.70 X 10,000 (50,000 – 40,000) = Rs 87,000 5. Revi Revised sed CM and and P/V P/V ratio ratio Sales price Rs 30.00 Cost of shores 19.50 CM 10.50 P/V ratio (%) 35 Fixed costs = Rs 3,60,000 + Rs 81,000 = Rs 4,41,000 BEP (in units) = Rs 4,41,000/Rs 10.50 = 42,000 units BEP (amount) = Rs 4,41,000/0.35 = Rs 12,60,000 Alternatively, 42,000 X Rs 30 = Rs 12,60,000 6. Additio Additional nal informa information tion require required: d: (i) (i) Sepa Separa rate te data data of fixe fixed d cos costt for for the the two two type typess of of sho shoes es.. (ii) (ii) Selli Selling ng pric pricee as as well well as as varia variabl blee cost cost per per pair pair of of shoe shoess bot both h for for gen gents ts and and ladies are the same (assumption). 7. No, the the analysis analysis will not not hold true because because in the the volume-cost-pr volume-cost-profit ofit relationship, relationship, it is assumed that production is equal to sales in the manufacturing firms or purchases are equal to sales in the case of trading firms.

Financial Management

Mini Cases 7.C.1 (Break-even Point) Sybergrid Solutions is a Web Publishing firm involved in the design and hosting of websites for corporates and business houses. As the initial investment required to start web publishing is low, several new entrants have entered/are planning to enter this business. There are also some established players who are willing to operate at low margins. Website publishing is highly competitive coupled with low market demand.

A website consists of a number of web pages. On average, any website would be made up of 50 web pages. The costs, revenues and time are calculated on the basis of   production  production of one web web page, page, that is 1 unit = 1 web web page (selling as Rs 1,000). 1,000). Besides, Biplab Saha, the owner of Sybergrid Solutions, there are three  permanent  permanent employees—a employees—a visualiser visualiser who who does does the conceptu conceptualizing alizing and and designing designing the graphics, a DTP operator to enter data and make the design on the computer and an office boy. One contract programmer is also hired as and when when Sybergrid gets an order  for developing a website. The total hours available in a month are (7.5 x 25 x 3) 564 hours. The annual capacity is (564 x 12) 6,768 hours. The total man-hours per web  page to make 1 web page page are 8 hours consisting consisting of 3 hours hours each each taken taken by visualiser visualiser and and owner/entrepreneur and 2 hours by the DTP operator. The monthly man-power expenses are a follow: (i) Owner/entrepreneur, Rs 12,000 (ii) Visualiser, Rs. 5,000, (iii) DTP operator, Rs. 4,000 and (iv) Office boy, Rs. 1,500. The investments and operational expenses are summarized below: Capital cost: Computer (2) Printer (1) Scanner (1) Internet connection per annum Fixed cost per month: Rent Telephone Electricity Floppy disk, stationery and office expenses Books Magazines/newspapers Conveyance The variable costs are given below: Cost Rate Additional labour Rs 30/hr Telephone 1.5.minute

Rs. 80 8 0,000 12,000 35,000 15,000

Rs 1,42,500

3,000 600 1,000 500 250 150 1,000

6,500

Time taken per web page 1 hour   10 minutes

Electricity

Rs 20 per web page

These costs are classified into fixed and variable in Exhibit 1.

EXHIBIT 1 Fixed and Variable Costs Cost element

Labour: Owner/entrepreneur Visualiser DTP operator Office boy

Fixed cost (annual)

Variable cost per 100 web page  Direct   Direct  Selling  labour  expenses expenses Rs 3,000

Rs 1, 1,44,000 60,000 48,000 18,000 2,70,000 36,000

Rent Telephone Rs 1,500 Electricity 2,000 Internet connection Floppy disks, stationery and office expenses 6,000 1,000 Rs 200 Depreciation (10%)* 12,700 Interest (13%)** 16,500 Conveyance 12,000 500 Magazine/newspapers 1,800 Books 3,000 Total 3,92,000 3,000 4,500 700 *Rs 1,27,000 (Rs 80,000 + Rs 12,000 + Rs 35,000) X 0.10 **Rs. 1,27,000 x 0.13 (This is the opportunity cost of interest lost on owners funds used to buy computer, scanner and printer).

Required (a) (b) (c) (d)

Compu Compute te break break-eve -even n sales sales reven revenue ue to to establ establish ish viabi viability lity of busi business ness.. Compu Compute te numbe numberr of order orderss to make make operati operating ng profit profit of of Rs 15,00 15,000 0 per mont month. h. Determi Determine ne sales sales volum volumee require required d to offset offset redu reductio ction n in sale sale price price from from Rs 1,00 1,000 0 to Rs 700 to maintain operating profit of Rs 15,000 per month. Determi Determine ne sellin selling g price price at which which Sybe Sybergr rgrid id would would not not suffer suffer cash cash losse losses. s.

7.C.2 (Break-even Analysis) Amit Behki is an automobile engineer. After graduating from the IIT-Delhi, he is planning to set up an automobile service station in NOIDA. The Amit Automobile Service Station (AASS) would carry out three activities: (i) free services of new vehicles under warranty, (ii) paid services including changing of parts and (iii) denting and painting of cars/vehicles.

The land on which the AASS would be set up, the estimated cost of which is Rs. 44,00,000 is owned by his family. A feasibility analysis conducted by Amit has revealed that the initial fixed cost of setting up of the AASS would be as detailed in Exhibit 1.

EXHIBIT I Initial Fixed Cost Estimates  Item/Description  Item/Description Salary and wages Staff welfare Repair and maintenance Conveyance Printing/stationery General expenses Consumable stores (LUBES) Postage/Telephone Professional fee Electricity Local taxes

Amount  Amount  Rs 1,57,776 6,852 32,166 11,184 2,816 1,539 3,656 8,948 15,000 18,000 10,000 2,67,937

The feasibility analysis also estimates the revenues and operating cost associated with the three workshop activities as detailed below: Free Service of New Vehicles The service charges would be reimbursed by the Vehicle Dealer. The average reimbursement for the first, second and third third services would be Rs 233 per vehicle. The variable costs related to the various service jobs performed by the cleaners/washers in servicing the vehicles are estimated as shown below. • Detergents • Diesel Cloth • Polish • Grease • Stationery • • Customer hospitality (cold drink)

Rs 20 18 20 20 30 5 20 133 Paid Services The variable costs would be the same as in the case of free servicing. An additional cost on parts changed would average Rs 1,000 per vehicle.

The per vehicle average revenue would be Rs 275. There would also be a 10 per  cent margin on the parts changed. Denting and Paining The lumpsum charged for full painting average Rs 8,000 per  vehicle. The variable costs per vehicle are also shown below:

(i) Labour (painter) cost (ii) (ii) Mater terial ial cost costs: s: ― Cleanser (4 litres X Rs 26) ― Additive solvent (8 litres X Rs 126) ― Putty ― Paint (4 litres X Rs 350) ― Sheet metal ― Sand paper ― M-seal ― Carbide for welding gas (8 X Rs 32) ― Welding rod ― Files (2 X Rs 375) ― Rubbing and polish ― Rubber seal compound ― Nut bolts

Rs 1,500 Rs 104 1,008 450 1,400 110 100 350 256 60 150 200 150 100

4,438 5,938

Required (d) (e)

If Amit Amit wants wants the AASS AASS to to break-e break-even ven in in the first first year year,, compute compute the brea breakeve keven n (i) in units (number of cars) and (ii) in amount for all the three services offered? If Amit Amit wants wants to earn earn a mont monthly hly surpl surplus us of Rs Rs 10,00 10,000, 0, what what would would be be the answ answer  er  to (i) and (ii)?

Thandak Desert Coolers

Mr Coolguy of ‘Thandak’ desert coolers enjoys a monopoly in his local market catering to around 10,000 customers every year. His friend Mr Imandar Singh of  ‘Zordar’ pumps supplies him good quality pumps at very reasonable rates (Rs 400 per   pump). The year year 2003 2003 was not not a good good year year for Mr. Mr. Coolguy. Coolguy. He lost his his good good friend Mr Imandar in a road accident. He also lost most of the savings in share market scam. The sun God did not bless him with a hot summer and the sales were expected to fall by 20 per cent. To make the matter worse, the new head of ‘Zordar’ pumps, Mr  Opportunist Singh increased the price of pumps by 30 per cent. Mr Coolguy asked his chief accounting, Mr Calculator Singh, to show the current financial data and the projected financial data if the supply from Zordar pumps were to  be maintained. maintained. Mr. Calculator Calculator Singh Singh came came out out with the the following following reports. reports.

Cost Data The cost data is divided into two parts: fixed cost and variable cost. The fixed and the variable components components of the mixed mixed costs are separated. The variable costs are divided into three major categories: direct material cost, direct labour costs and the variable overhead. The division of all the cost data is tabulated, for 10,000 units as well as 8,000 units, as follows: (I) Scenario (10,000 units)

 Item

Labour Steel sheets Electricity Depreciation Pumps (@ 400 per unit) Khus Tubes Wires Fan Telephone Rent (office) Office expenses Bank charges Insurance Repair and maintenance Recruitment Travel Conveyance Post, courier and parcel Miscellaneous Total

Present

Fixed cost 

Variable cost and expenses Variable Dire Direct ct mat mater eria iall Direc Directt labo labour  ur  overheads Rs 12,10,000 Rs 20,00,000 Rs 60,00,000 35,000 Rs 1,00,000 15,06,620 40,00,000 9,00,000 5,00,000 50,000 14,50,000 4,580 4,60,000 1,20,000 22,000 3,46,000 18,000 35,000 25,000 2,40,000 64,000 3,80,000 16,800 1,90,000 7,000 1,70,000 1,50,000 30,00,000 129,00,000 20,00,000 21,00,000

(II) units)

Future Scenario If Pumps Are Bought From Zordar Pumps (8,000

 Item

Labour Steel sheets Electricity Depreciation Pumps (@ 520 per unit) Khus Tubes Wires Fan Telephone Rent (office) Office expenses Bank charges Insurance Repair and maintenance Recruitment Travel Conveyance Post, courier and parcel Miscellaneous Total

Fixed cost 

Variable cost and expenses  Direct material  material  Direct labour  Variable overheads Rs 12,10,000 Rs 16,00,000 Rs 48,00,000 35,000 Rs 80,000 15,06,620 41,60,000 7,20,000 4,00,000 40,000 11,60,000 4,580 3,68,000 1,20,000 22,000 3,46,000 18,000 35,000 25,000 2,76,800 51,200 3,04,000 16,800 1,52,000 7,000 1,36,000 1,20,000 30,00,000 112,80,000 16,00,000 18,34,000

(III) Comparative Analysis of Both Scenarios  Item 10,000 10,000 units Sales revenue @ Rs 2,500 per unit Rs 250,00,000 Less: Variable costs Direct material 129,00,000 Direct labour 20,00,000 Variable overhead 21,00,000 Total contribution 80,00,000 Less: Total fixed costs 30,00,000 Operating profits 50,00,000

8,000 units Rs 200,00,000 112,80,000 16,00,000 18,34,000 52,86,000 30,00,000 22,86,000

After going through the report Mr Coolguy realized that his profits would drop by Rs 27.14 lakh if he continued continued to purchase pumps and sales drop to 8,000 units. units. Since there were no other pump manufacturers in the market, the only alternative for Mr Coolguy was to manufacture the pumps indigenously. But he had lost most of his money and for  manufacturing pumps he needed to expand his factory and purchase a new machinery (overall Rs 5 lakh more was needed). needed). Raw material for pumps would would be needed which would cost Rs 300 per unit. Additional labour would be required to make the pumps, thus increasing the labour costs to Rs 250 per unit. The making of pumps would also draw more electricity etc. thereby increasing the variable overhead costs. The banks were not willing to finance him. Mr Lalchi Singh, the loan shark, saw opportunity to

make money and offered to loan money to Mr Coolguy for a period of one year at the rate of more than 20 per cent, the loan to be paid in two installments of Rs 3 lakh each, the first one is to be made in the first six months and the second installment at the end of the year. The interest would be paid at the end of the year. If Mr Coolguy Coolguy fails to  pay back back the interest interest and the principal principal on on the due due date, Mr Mr Lalchi would be entitled entitled to auction off the factory and get back his sum. Mr Coolguy now now has to decide whether to accept the offer or not. Mr Coolguy asked Mr Calculator to find out the implications of the above mentioned factors on the profit and whether he would be able to satisfy Mr Lalchi’s conditions. Mr  Calculator came out with the following reports: (IV)

Cost if Loan Is Taken For Production of Pumps

 Item

Fixed cost 

Labour Steel sheets Electricity Depreciation Khus Tubes Wires Fan Telephone Rent (office) Office expenses Bank charges Insurance Repair and maintenance Recruitment Travel Conveyance Post, courier and parcel Machinery Miscellaneous Pump shaft Pump wires Pump cylinder Lubrication and insulation Total (V)

Variable cost and expenses Dire Direct ct mat mater eria iall Dire Direct ct lab labou our  r  Variable overheads Rs 12,10,000 Rs 20,00,000 Rs 48,00,000 35,000 Rs 360,000 15,06,620 7,20,000 4,00,000 40,000 11,60,000 4,580 3,68,000 1,20,000 22,000 3,46,000 18,000 35,000 25,000 2,76,800 51,200 3,04,000 16,800 1,52,000 7,000 1,36,000 5,00,000 1,20,000 800,000 400,000 10,00,000 200,000 3500,000 95,20,000 20,00,000 21,14,000

Projected Profit When Pumps Are Produced

Sales revenue @ Rs 2,500 per unit (8,000 units) Less: Variable costs Direct material Direct labour Variable overhead

Rs 200,00,000 95,20,000 20,00,000 21,14,000

Total contribution Less: Fixed costs Operating profits Less: Interest + Principal EBT Contribution per unit = Rs 63,66,000/ 8,000 = Rs 795.75 BEP (units) = Total fixed cost/contribution margin per unit = Rs 41,00,000/795.75 = 5152 units.

63,66,000 35,00,000 28,66,000 6,00,000 22,20,00

Attributing no fixed cost in the first six months so as to pay the first instalment comfortably:  Number  Number of units units to be be sold in the first six months

= Rs 300,000/contribution margin per  unit = Rs 300,000/Rs 795.75 = 377 units = Rs 38,00,000/Rs 795.75 = 4,775 units

 Number  Number of units units to be be sold in the next next six months Attributing half the fixed costs in the first six months:  Number  Number of units units to be be sold in the first six = Rs 20,50,000/Rs 795.75 = 2,576 units months  Number  Number of units units to be be sold in the next next six = Rs 20,50,000/Rs 795.75 = 2,576 units months Mr Calculator’s Inference:

Manufacturing pumps indigenously would eat away the profits by another Rs 66,000. There is also an inherent risk of default of the first instalment to Mr Lalchi as it would not be possible possible to sell even 377 units in the off season. There is no reason why Mr Coolguy should go ahead with the idea of indigenous pumps. After seeing the income statement and break-even analysis, Mr Coolguy decided not to take the loan but since his son, Mr Cooldude (doing MBA from IIT Delhi) had come home for a few days. He though it wise wise to take his opinion too. Cooldude came up with a radically different opinion. He suggested that since the the machinery was meant for long-term use, it would not be prudent to charge its cost in the current year itself. It would be be better to amortise the cost over a period of five years. He suggested to amortise Rs 1 lakh per year (assuming no sale value at the end of 5 years). This gave gave a different picture altogether. (VI) Cost Estimate (Revised)

 Item

Labour Steel sheets Electricity Depreciation

Fixed cost 

Variable cost and expenses  Direct material material Direct labour labour Variable Variable overheads Rs 12,10,000 Rs 20,00,000 Rs 48,00,000 35,000 Rs 360,000 15,06,620

Khus Tubes Wires Fan Telephone Rent (office) Office expenses Bank charges Insurance Repair and maintenance Recruitment Travel Conveyance Post, courier and parcel Miscellaneous Depreciation on machinery Interest Pump shaft Pump wires Pump cylinder Lubrication and insulation Total

(VII) Sales revenue @ Rs 2,500 per unit Less: Variable costs Direct material Direct labour Variable overhead Total contribution Less: Fixed costs EBIT

7,20,000 4,00,000 40,000 11,60,000 4,580 1,20,000 22,000 18,000 35,000 25,000

3,68,000 3,46,000

2,76,800 51,200 3,04,000 1,52,000 1,36,000 1,20,000

16,800 7,000 100,000 1,00,000

32,00,000

800,000 400,000 10,00,000 200,000 95,20,000

20,00,000

21,14,000

Projected Profit (Revised)

Rs 200,00,000 96,00,000 20,00,000 20,34,000 63,66,000 32,00,000 31,66,000

Cooldude then explained his father that charging the entire cost of the machine in the current year leads to the reduction in profits of the current year. Such purchases (capital expenditures) should be amortised over a period of time. Besides, payment of  loan is not an expense. It is expense only to the extent of interest paid. Thus, what seemed to be a decrease in profit by Rs 66,000 was actually an increase by Rs 8,80,000. At this juncture, Mr Coolguy became very enthusiastic about taking the loan. Cooldude then warned his father that Mr. Lalchi might have set up a trap for him as it was the  beginning  beginning of of February. February. Generally, Generally, desert desert coolers coolers are not bought bought in these months. months. It would be difficult to sell even a modest target of 377 units (not taking the fixed costs into account in the first six months) in these months. However, by offering heavy offseason discount (up to 20 per cent) the sales can be pushed up significantly. Proper  advertising should be done so as to inform the people that the discount would be available only for a short-term. As Thandak has a monopoly in the region, the people would like to cash on this opportunity, and the sales would go go up. The discount should

 be discontinued discontinued as soon as the cash cash position position (with (with respect to to the first payment payment of  instalment) is reached.  New selling selling price price = Rs 2,000 2,000 Revise contribution per unit = Rs 295.75 Rs 300,000/Rs 295.75 = 1,014 units. As soon as 1,014 units are sold the discount should be discontinued. (VIII) Projected Profits With Change in Selling Price Total contribution = 1,014* Rs 295.75 + (8000 – 1014)* Rs 795.75 Rs 58,59,000 Less: Fixed costs 32,00,000 EBIT 26,59,000

Thus, the proposition of Mr Lalchi is not devoid of connivance. In order to pay the first instament of Rs 3 laks to Mr Lalchi, Mr Coolguy would have to forego a substantial  profit.