334_resource_2. cvp analysis

8/6/2019 334_resource_2. CVP Analysis

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Cost management-final course 1

2. Cost Volume Profit Analysis ( C.V.P. )

Learning Objective

We already know the basic definition & application of P/V ratio, BEP & BEScomputation, application of MOS, etc. Here we are discussing some advancemethods of CVP

1. How to compute BE, Margin of safety , Req. sale volume, etc2. Computation BE with step fixed cost3. BE under DCF technique4. BE in Process costing5. Be with Opportunity cost6. Potential BE7. BE Under multi product with common fixed cost8. BE for perishable product

9. Application of indifference point

Introduction:

Under Marginal costing the product price is determined on the basis of Variable cost of theproduct. Such price is selected for the purpose of penetration pricing where the minimum saleprice = variable cost. As the sale price is very low management is always anxious about therecovery of fixed overhead. So they want to calculate the volume of sales at which fixed cost willbe recovered , profit will arise & the safety margin of the organization , as well as different short-term decision are to be taken by the management.

Marginal costing is not a distinct method of costing like job costing, process costing, operatingcosting, etc. but a special technique used for marginal decision making. Marginal costing is usedto provide a basis for the interpretation of cost data to measure the profitability of differentproducts, processes and cost centre in the course of decision making. It can, therefore, be usedin conjunction with the different methods of costing such as job costing, process costing, etc., oreven with other technique such as standard costing or budgetary control.

In marginal costing, cost ascertainment in made on the basis of the nature of cost. It givesconsideration to behaviour of costs. In other words, the technique has developed from aparticular concept and expression of the nature and behaviour of costs and their effect upon theprofitability of an undertaking.

Cost-Volume profit analysis:

Cost-volume-profit analysis (as the name suggests) is the analysis of three variable viz., cost,volume and profit. Such an analysis explores the relationship existing amongst costs, revenue,activity levels and the resulting profit. It aims at measuring variations of cost with volume. In theprofit planning of a business, cost-volume-profit (C-V-P) relationship is the most significantfactor.

The CVP analysis is an extension of marginal costing. It makes use of principles of marginalcosting. It is an important tool of planning. It is quite useful in making short run decisions.

For this purpose we apply the concept of Marginal Costing. Following definitions are required forthis purpose


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1. Profit Statement Under Marginal Costing

Statement of ProfitRs. Rs.

Revenue/Sales xxx

Less: Variable cost of productionMaterial xxLabour xxD. Expenses xxVariable overhead __xx

XxAdd: Opening Finished goods (at MC) xxLess: Closing Finished goods (at MC) __xx

Variable cost of goods sold xxx

Add: Variable Selling overhead Variable cost of sales

Contribution xx

Less: All types of Fixed cost _xx( Committed, Discretionary steps ) xx

2. Sales - Variable Cost = Contribution = Fixed Cost + Profit

3. P/V ratio (or C/S ratio) = Contribution Sales= Contribution per unit Selling price per unit= Change in Contribution Change in Sales= Profit Margin of Safety

4. Profit = (Sales P/V ratio) - Fixed Cost = P/V ratio Margin of Safety sales(Rs.)= Contribution p.u. Margin of safety ( in units)

5. Break-even Point

a. Break Even point (in units) = Fixed Cost Contribution per unitb. Break Even Sales ( in sales value ) = Fixed Cost P/V ratioc. with semi - variable cost : apply the concept of apparent BEP

d. Composite BEP i.e. more than one product with common fixed costs

(i) With out limiting factor ( non- attributable to a single product )

BEP in units = Fixed cost Average contribution p.u.( when sales mix in units are given )

BEP in Rs. = Fixed cost composite p\v ratio( when sales mix in rupee are given )

where composite p\v ratio = [ Sales Mix P\V Ratio ](ii) With limiting factor ( attributable to a single product )


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Find contribution per limiting factor & give rank . Find totalcontribution from 1st rank product . Calculate the amount of fixedcost still to recover. Whether it can be recovered by 2nd rank productor not ?

(iii) For Perishable product apply the same concept in case of openingstock with different variable cost.

e. BEP in case of process costing is expressed in terms of total raw material input

f. In capital budgeting , BEP is that sales volume where discounted Cash in flow = discounted Cash out flow. In case of perpetuity , the financing charge p.a.= CIFpa

g. Potential BE : On the basis of sales out of current period production only.

h. Multiple BE : Different BE due to change in sales price, variable costs & fixed

costs for different production level.

i. Cash BEP = Cash fixed cost contribution p.u. So do not consider the sunk cost. j. BEP for decision making purpose : Accept that proposal where BEP is lowest

provided the profit can not be calculated.

We already know the basic definition & application of P/V ratio, BEP & BES computation,application of MOS. Here we are discussing some advance methods of CVP i.e. mainly fromRule 5c

Problem 1From the under mentioned figures calculate:(i) P/V ratio and the total fixed expense;(ii) Profit or loss arising from the sales of Rs. 12,000;(iii) Sales required to earn a profit of Rs. 2,000;(iv) Sales required to break-even.

Sales profitRs. Rs.

First period 14,433 385Second period 18,203 1,139

Solution(i) P/V ratio and total fixed expenses

First SecondPeriod period increase

Rs. Rs. Rs.Sales 14,433 18,203 3,770Less: profit ___385 _1,139 __754Total costs 14,048 17,064 3,016

Assuming the variable unit cost per unit and fixed expenses to be the same and that the prices

are stable in both the period, the increase in total cost of Rs. 3,016 consists of variable costsonly. For an increase in the sales of Rs. 3,770 the variable cost is Rs. 3,016. Hence P/v ratio is


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100770,3.

016,3.770,3.x

Rs

RsRs = 20%

Taking the figures relating to period 1.Rs.

Gross margin (Rs. 14,433 20%) 2,887Less: Profit for period 1 __385Fixed expenses 2,502

(ii) Profit or loss on sales of Rs. 12,000Rs.

Gross margin on this sale (Rs. 12,000 20%) 2,400Less: Fixed expenses 2,502Loss __102

(iii) Sales required to earn a profit of Rs. 2,000.Contribution required = fixed expenses + profit

= Rs. 2,502 + Rs. 2,000= Rs. 4,502

The sales, should produce a gross margin of Rs. 4,502

Hence, sales value = 10020

502,4.x

Rs

= Rs. 22,510

(iv) Sales required to break-even:At BEP gross margin is equal to fixed expensesSo, gross margin required = Rs. 2,502

Sales required = ----------------------- = 10020

502,2.x

Rs

______________

Problem 2Paramount Food products is a new entrant in the market for chocolates. It has introduced a newproduct Sweetee. This is a small rectangular chocolate bar. The bars are wrapped inaluminum foil and packed in attractive cartons containing 50 bars. A carton is, therefore,

considered the basic sales unit. Although management had made detailed estimates of costsand volumes prior to undertaking this venture, new projects based on actual cost experience arenow required.

Income statements for the last two quarters are each thought to be representative of the costsand productive efficiency we can expect in the next few quarters. There were virtually noinventories on hand at the end of each quarter. The income statements reveal the following:

First Quarter Second Quarter Sales Rs. Rs.

50,000 Rs. 24 12,00,000 16,80,000

70,000 Rs. 24 cost of Goods sold ___7,00,000 __8,80,000Gross Margin 5,00,000 8,00,000Selling and Administration __6,50,000 __6,90,000Net income (loss) before taxes (1,50,000) 1,10,000Tax (negative) ___(60,000) ___44,000

Rs. 2,502P/V ratio


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Net income (Loss) __(90,000) __66,000

The firms overall marginal and average income tax rate is 40%. This 40% figures has beenused to estimate the tax liability arising from the chocolate operations.Required:(a) Management would like to know the break even point in terms of quarterly carton sales

for the chocolates.(b) Management estimates that there is an investment of Rs. 30,00,000 in this product line.

What quarterly carton sales and total revenue are required in each quarter to earn an after tax return of 20% per annum on investment?

(c) The firms marketing people predict that if the selling price is reduced by Rs. 1.50 percarton (Re. 0.03 off per chocolate bar) and a Rs. 1,50,000 advertising campaign amongschool children is mounted, sales will increase by 20% over the second quarter sales.

SolutionBasic calculations(a) Variance Mfg. Cost per carton = Change in cost/ change in output

=000,50000,70000,00,7000,80,8

= 1,80,000 20,000 = Rs. 9 per carton

(b) Fixed Mfg. Cost = Fixed manufacturing cost + Variable manufacturingcost

cost of goods sold = Rs. 7,00,000 Rs. 4,50,000= Rs. 2,50,000

(c) Variable selling & Admn. costper carton = Change in cost/ change in output

= 000,50000,70

000,50,6000,90,6

= Rs. 40,000 /Rs. 20,000 = Rs. 2 per carton

(d) Fixed selling and Admn. cost = 6,50,000 1,00,000 = Rs. 5,50,000

(e) Total Fixed costs = Rs. 2,50,000 + Rs. 5,50,000 = Rs. 8,00,000

(f) Quarterly Break even point(in cartons) = Fixed costs/ contribution per carton

= 8,00,000 /13 = 61,539 cartons

(b) Desired annual return after tax = Rs. 6,00,000

(ii) Desired quarterly return after tax = 6,00,000 /4 = Rs. 1,50,000

(iii) Desired quarterly return before tax

(Tax rate 40%) = 000,50,2.60

100000,50,1.Rs

xRs=

Quarterly sales for Desired returnIn cartons = -----------------------------------------

= cartons769,8013

000,50,2000,00,8=

+

Quarterly sales revenue = 80,769 Rs. 24 = Rs. 19,38,456

(c) New selling price per carton = Rs. 24 Rs. 1.50 = Rs. 22.50New contribution per unit = Rs. 22.50 Rs. 13 = Rs. 11.50

Fixed Costs + Desired ReturnContribution per carton


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New sales: 70,000 + 14,000 = 84,000 cartons

Total new contribution = 84,000 Rs. 11.50 = Rs. 9,66,000Less: Fixed costs (8,00,000 + 1,50,000) Rs. 9,50,000

Rs. 16,0000Less: Tax (40%) ____6,400Net income after tax ____9,600

The firm made a net income after tax of Rs. 66,000 at a selling price of Rs. 24. The reduction inselling price increases in sales volume but decreases the net income after tax to Rs. 9,600.Hence, the plant to reduce the selling price should not be implemented by the management.

_____________

Problem 3 : BE with linear semi-variable cost

Bottom line ltd.. manufactures pressure cookers the selling price of which is Rs. 300/- per unit.Currently the Capacity utilisation is 60% with a sales turnover of Rs 18 lakhs. The Cc. proposesto reduce the selling price by 20% but desires to maintain the same profit position by increasing

the output. Assuming that the increased output could be made and sold, determine the level atwhich the Co. should operate, to achieve the desired objective.The following further data are available :i) Variable cost per unit Rs. 60/-.ii) Semi-variable cost (including a variable element of Rs. 10/- per unit) Rs. 1,80,000.iii)Fixed cost Rs.3,00,000 will remain same up to 80% level. Beyond this an additional amount of

Rs. 60,000 will be incurred.

SolutionPresent ProposedRs./unit Rs. /unit

Selling price/unit 300 240

Less: Variable cost/unit- Variable 60 60- Semi variable _10 _70 10 _70

(a) Contribution 230 170

(b) Fixed cost: (up to 80%)Fixed cost 3,00,000Fixed cost in semi variable 1,20,000

4,20,000

(c) Sales volume 6,000 units

Profit = 6,000 230 4,20,000= Rs. 9,60,000

Required contribution at present is 13,80,000.

Required sales = (13,80,000 170) = 8,117 = 81.18%

But as it is 80%.Additional fixed cost = 60,000

Required contribution (Revised) = Rs. 14,40,000

Required sales = 14,40,000 170 = 8471 = 84.71%


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BE in case of combination of business

Step-1:Calculate the sales, variable cost, contribution, Fixed cost and profit of the existingcompanies at 100% capacity from the given data.

Step-2:Find the above items for the new companies by adding the results of the existing company(Prepare one chart for above two steps)

Step-3:Find the P/V ratio of the new Co. and give answer of the corresponding question.

Problem 4:

I co. & II co. have decided to merge into one company. The operating details of two companiesare as follows:Company I Company II

Percentage of capacity utilisation 90 60Sales (Rs.) 5,40,00,000 3,00,00,000Variable costs (Rs.) 3,96,00,000 2,25,00,000Fixed costs (Rs.) 80,00,000 50,00,000

Assuming that these two companies merge into one, determinea. The break-even sales of the merged company :b. The turnover of the merged company required to earn a profit of Rs. 75,00,000, andc. The percentage increase in selling price necessary to sustain an increase in fixed overheads

by 5% when the merged company is working at a capacity to earn a profit of Rs. 75,00,000.

Solution(a) Old Company New Co.

Co1 Co2 Co3Capacity utilization 100% 100% 100%

Rs. Rs. Rs.Sales 600 L 500 L 1,100 LLess: Variable cost 400 L 375 L 815 LContribution 160 L 125 L 285 LFixed cost 80 L 50 L 130 L

Profit 80 L 75 L 155 LP/V ratio (Contr. Sales) 26.67% 25% 25.91%

(a) BES of merger Co. = (Fixed cost PV ratio) = 130 25.91% = 5,017,3,678

(b) Contribution at 80% = 285 80% = 228 LLess: Fixed cost _130 LProfit 98 L

Profitability = 100%80100,1

98x

x

L= 11.14%

(b) Rs.Required profit 75,00,000Add: Fixed cost 1,30,00,000Contribution 2,05,00,000


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Required (2,05,00,000 25.91%) = 7,91,20,031 or 791.20 lakhs

Capacity utilization = (791.2 11,00,00,000) = 71.93%

(c) Increase in Fixed cost = 5% of 1,30,00,000 (130 lakhs)= 6.5 lakhs

Now the present capacity, sale volume 4 profits will remain same at 71.93%.

Increase in fixed cost = Increase in sales price= Rs. 6,50,000

% increase in sales = (6,50,000 7,91,20,031) 100 = 0.82%

Multi product BES with the help of profit graph

Profit graph

Profit graph is a special type of break even chart which shows the profit or loss at differentlevels of output.

In the following example:OA = Total fixed expenses C = Break even point

YB

Profit

0 cLoss

xSales

A

F

Single product profit graph

The profit or loss can be calculated by using following

When sales are at zero, the total loss is equal to fixed expenses which is equal to OF. The lossdiminishes as the output increases , the break even point will occur first and then the firm startsearning profits as the output increases beyond the break even point.

When more than one products ( say 3 products A, B &C) are manufactured, the Profit graph canbe so drawn as to show the cumulative effects of the profit and losses. It helps to identify multiproduct BES & BEP as shown below


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Y C

Profit Line of each product

BProfit

O XBEP Sales value

A

Average Profit LineF

Y

Multi product profit graph

.

To draw the above diagram , following steps are required --

Step-1: Compute P/V ratio for each product & give rank.

Step-2: Calculate cumulative sales & cumulative profit on the basis of the above ranking.

Step-3: Identify the points on the basis of cumulative sales (x) & cumulative profit (y). Jointhe points with same line and identify the specific BES.

Step-4: Join the start & end point with a single straight line to find arrange Break evensales

Problem 5The following are the cost and the sales data manufacturer selling three products X, Y and Z.

Product Selling price p.u. Variable cost p.u. % of Sales (Rs.)Rs. Rs.

X 400 325 20Y 500 350 40Z 850 740 40

Capacity of the manufacturer : Rs. 80 lakhs sales volume. Annual fixed cost : Rs. 5,50,000.i) Find the break-even point in rupees.ii) Calculate his profit or loss at 90% of capacity.

SolutionNote-1: computation of ranks

(a) (b) a-b = c (c) (a) 100

Product Sales/unit VC/unit contribution PV ratio RankX 400 325 75 18.35 IIY 500 350 150 30 IZ 850 740 110 12.94 III


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Note 2; Calculation of cumulative sales & Profit

Rank Product Sales Sales Contribution Contribution profitRs. Rs. Rs. Rs. Rs.

I Y 80 L 40% 32 L 9.6 9.6 4.132 L

II X 80L 20% 48L 3 12.6 7.1III Z 32 L 80 L 4.14 16.74 11.24

Average PV ratio = 0.2 18.75% +0.4 30% +0.4 12.94= 20.926%

BES = Fixed cost Avg. P/V ratio = 5.5 Lakhs 20.926% = 26,28,309

Problem 6

(a) Calcutta Company Ltd. manufactures and sells four types of products under thebrand names, ACE, UTILITY, LUXURY and SUPREME. The sales mix in valuecomprise of:

Brand PercentageAce 33.3333%Utility 41.6667%Luxury 16.6667%Supreme __8.3333%

__100%

The total budgeted Sales (100%) are Rs. 6,00,000 per month. The operating costsare :

ACE 60% of selling price UTILITY 68% of selling priceLUXURY 80% of selling price SUPREME 40% of selling price.

The fixed costs are Rs. 1,59,000 per month. Calculate the break-even point for theproducts on an overall basis.

b) It has been proposed to change the sales mix as follows, the total sales per monthremaining Rs. 6,00,000 :

Brand PercentageACE 25%

UTILITY 40%LUXURY 30%SUPREME ____5%

__100%

Assuming that this proposal is implemented, calculate the new break-even point.

Solution(a) Computation of the break even point on Overall Basis

ACE UTILITY LUXURY SUPREME TotalSales Mix 33-1/3% 41-2/3% 16-2/3% 8-1/3% 100%

Rs. Rs. Rs. Rs. Rs.

Sales 2,00,000 2,50,000 1,00,000 50,000 6,00,000Less: Variable cost (operating)1,20,000 1,70,000 __80,000 __20,000 3,90,000Contribution 80,000 80,000 20,000 30,000 2,10,000

Contribution


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Overall P/V ratio = 100Sales

Rs. 2,10,000

= 100Rs. 6,00,000

= 35%

Break-even Point (Sales Value)

Total Fixed costs= -----------------

Composite P/V ratio

Rs. 1,59,000=

35%

= Rs. 4,54,286

(b) Computation of New Break-even PointACE UTILITY LUXURY SUPREME Total

Sales Mix 25% 40% 30% 5% 100%Rs. Rs. Rs. Rs. Rs.

Sales mix 1,50,000 2,40,000 1,80,000 30,000 6,00,000Less Variable costs 90,000 1,63,200 1,44,000 12,000 4,90,000

----Contribution 60,000 76,800 36,000 18,000 1,90,800

Rs. 1,90,800New P/V Ratio = 100 = 31.8%

Rs. 6,00,000

Net Break-even point (Sales value)

Rs. 1,59,000= = Rs. 5,00,000

31.7%_______________

Problem 7Major Ltd. manufactures a single product X whose selling price is Rs. 40 per unit and the variablecost is Rs. 16 p.u. If the Fixed Costs for this year are Rs. 4,80,000 and the annual sales are at50% margin of safety, calculate the rate of net return on sales, assuming an income tax level of40%.

For the next year, it is proposed to add another product line Y whose selling price would be Rs.50 per unit and the variable cost Rs. 10 per unit. The total fixed costs are estimated atRs.6,66,600 . The sales mix of X : Y would be 7: 3 . At what level of sales next year, would theco. break even? Give separately for both X and Y the break even sales in rupees and quantities.

Solution(a) Product X Rs. p.u.

Sales 40Less: Variable cost _16Contribution 24

P/V ratio = {(Contribution/u Selling price/unit) 100} = ({24 40) 100} = 60%


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BES = 4,80,000 60% = Rs. 8,00,000

Actual sales = 16,00,000 ( there is 50% margin of sales)BES +MOS = Actual Sales

Profit = P/V ratio MOS (is Rs.)

= 60% 8,00,000 = 4,80,000

Net return on sales = {4,80,000 16,00,000 100 (1-0.4)} = 18%Margin of safety = 50% of sales

PAT Sales = (MOS Sales) P/V ratio (1-t)= 50% of 60% (1-0.4) = 18%

(b) Y XRs. p.u. Rs. p.u.

Selling price/unit 50 40Less: Variable cost/unit _10 _16

Contribution per unit 40 24P/V ratio 80% 60%

Case-I:Sales mix in Rupee terms

Avg. P/V ratio = 66% (7/10 60% +3/10 80%)BES = 6,66,600 66% = Rs. 10,10,000

BES RS. BEP (in units)

X 70,7,000 40= 17,675

Y 30,3,000 50 =_6,06010,10,000 23,735

Case-II:Sales mix in units 7 : 3

Average contribution = {(7 24 +3 40) 10} =28.8

BEP = 6,66,600 28.8 = 23,147

BES SalesX (7/10) 16,203 64,8,120Y (3/10) _6,944 34,7,200

23,146 99,5,320

Missing Figure problems:

Problem 8A single product company furnishes the following data :

Year 1. Year 2Sales Rs.24,00,000 ?PV ratio 33 1/3% 30%Margin of safety 25% 40%

While there was no change in the volume of sales in year 2, the selling price was reduced.Calculate the sales, fixed costs and profit for year 2.


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Solution Year 1 Year 2Rs. Rs.

(a) Sales 24,00,000 22,85,715(b) Variable cost [a (1-P/V)] 16,00,000 16,00,000(c) Contribution 8,00,000 6,85,715(d) Fixed cost (Bal fig.) 6,00,000 4,11,425

Profit 2,00,000 2,74,286

= Sales MOS% PV 22,85,715 30% 40%

= 24,00,000 25% 33% = 2,74,286= 2,00,000

In year 2Variable cost Sales = 70%

16,00,000 Sales = 70%

Sales = 22,85,715.

Problem 9Titan Engineering is operating at 70% capacity and presents the following information:

Break even point Rs. 20 croresP/V ratio 40 per centMargin of safety Rs. 50 crores

Titan management has decided to increase production to 95% capacity level with the followingmodifications:

(i) The selling price will be reduced by 8 per cent.

(ii) The variable cost will be reduced by 5 per cent on sales.(iii) The fixed cost will increase by RS. 20 crores, including depreciation on additions, but

excluding interest on additional capital.(iv) Additional capital of Rs. 50 crores will be needed for capital expenditure and working

capital.

Required:(a) Indicate the sales figure, with the working, that will be needed to earn Rs. 10 crores over

and above the represent profit and also meet 20% interest on the additional capital.

(b) What will be the revised:

(i) Break even point; (ii) P/V ratio; and (iii) Margin of safety? (CA final, Nov. 1991)

Solution

Statement of revised profit & salePresent Change Proposed

Rs. (cr.) (Rs. in lakhs)

(a) BES 200 (f b) 244.44

(b) MOS __50 (g d) 66.67(c) Total sales 250 311.11(d) P/V ratio ( Note1 ) 40% 45%

(e) Variable cost Sales 60% reduce 55%

5% of sales(f) Fixed cost (a d) 80 200 Cr. +10 Cr. 110 G

(50 cr. 20%)

(g) Profit (b d) Rs. 20 cr. 10 cr. 30 cr.


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Working note - 1

Total sales = Break even sales + Margin of safety= Rs. 200 crores + Rs. 50 croes = Rs. 250 crores.

P/V ratio = 40% of sales

Variable cost ( Present) = 60% of sales( Pro[osed) = 55% of sales

Revised P/V ratio = ( 40 + 5 ) % = 45% of sales

Effect of opportunity cost in break even analysis

When for a new proposal/alternative use current income will be lost or additional cost is to be

incurred then these are known as opportunity cost of the new proposal. In other word theminimum price for the new proposal = variable cost of the alternative + lost income under presentsituation +discretionary fixed cost (if any).The Lost income is generally loss of contribution.

Problem 10A newspaper presently sales 1,00,000 copies of its morning daily. It wants to publish eveningdaily. Particulars are :

Actual for Morning Estimates for Evening

Sale price Rs.2 per paper Re.0.50 per paper Variable cost Rs.1.20 per paper Re.0.22 per paper

Fixed cost Rs.2.4 lakhs per week Rs.10,000 per week

Sale of morning daily will fall @ 1 copy for-every 10 copies sold of evening daily. Calculatebreak-even sales for evening daily per week. What should the minimum price for evening daily.

SolutionSales price 2.00Less: Variable cost 1.20Contribution 0.80

Sales of morning daily fall @ 1 company for 10 copies sold in the evening.

Contribution lost per copy of evening sales = (0.8 10) = 0.08

Revised Variable cost for evening paper = 22+0.08 = 0.3/paperRevised contribution = (0.5-0.3) = 0.2/paper.

PV ratio = Contribution/paper Sales/paper = (0.2 0.5) 100 = 40%

Fixed cost P/V ratioBES = 10,000 40% = Rs. 25,000

OrMorning daily contribution/unit = 0.8

For evening daily:Selling price/unit 0.5Variable cost/unit 0.22


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Opportunity cost (8 10) 0.08Contribution 0.2

PV ratio 40%Fixed cost 10,000

BES = (10,000

40%) = Rs. 25,000

Minimum price = Variable cost/unit +Opportunity cost + Fixed cost= (0.22+0.08) p.u. +Fixed cost 10,000 = 30 P. per unit + 10,000 (Fixed cost).

_____________

Break Even Analysis in Step Fixed Cost situation

Due to presence of step cost more than one BEP can arise as shown below

Rs. RevenueSlab 4

BEP 2

BEP-1 Slab 3

Slab 2

Slab 1

Sales volume (in units)

So in the above diagram the revenue line may cut the total cost line more than once. This isknown as Multiple BEP situation, as 1st BEP, 2nd BEP etc. For this purpose we prepare BEstatement as below.

Problem 10Variable cost/unit = Rs 30Fixed cost = Rs. 3,000

Step fixed cost = Rs. 1,000 for every 50 units or part there ofSelling price p.u. = Rs. 95Find a BE statement & find BEP

SolutionBreak-even statement

(a) Step/slab 1 2 3 4 5(b) Prod. range 0-50 51-100 101-150 151-200 201-250(c) Fixed cost (Rs.) 3,000 3,000 3,000 3,000 3,000(d) Slab fixed cost (Rs.) 1,000 2,000 3,000 4,000 5,000(e) Total fixed cost (c+ d) 4,000 5,000 6,000 7,000 8,000(f) Contribution p/u 65 65 65 65 65

(SP-Vc p.u.)(g) BEP (e/f) 62 77 93 108 123

Nature of BEP Fict. Real Fict. Fict. Fict.


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Production range in 0-50 but BEP in 62. Iit is a fictitious situation as BEP is outside the range.When the amount of fixed cost is very high then we have to find the 1st slab no. where rev& total cost line will intersect. Otherwise we can solve it by statement method as a trial-error method.

Steps to be followed to find the 1st slab no .1. Prepare an algebraic equation in the concept of BE and find the value of x.

2. find slab no where Slab no. or step no. = value of x from above step by units per slab.3. now identify total fixed cost

4. BEP = Total fixed cost Contribution per unit

Problem 11Fixed cost = Rs. 3,000Step fixed cost = Rs. 1,000 for every 50 units or part there ofContribution p.u. = Rs. 57

Find BEP

SolutionLet X is the product volume which indicate slab in which 1st BE occurs

So, total contribution = fixed cost + step or slab fixed cost

57x = 3,000+ {(1,000 50)x}57x = 3,000 +20x37 x = 3,000x = 81.08

Slab no/step no = (81.08 50/slab) = 1.62 i.e. 2nd slab.

Total fixed cost 3,000+2 1,000 = Rs. 5,000

Hence BEP = 5,000 57 = 87.71 i.e. 88 units

So, we can apply this technique for any amount of fixed cost and once we get the 1st break eventhen we prepare the BE statement identify the real and fictitious BEP.

Problem 12Now assume fixed cost is Rs. 30,00,000.Step cost 1,000 per 50 units.

Contribution p.u. is Rs. 57.Prepare a break even statement.

Solution

57x = 30,00,000 + {(1,000 50)x}37x = 30,00,000x = 81,081.08

Slab no = (81,081.08 50 units/slab) = 1,621.62 i.e. 1,622 slab.

Fixed cost = 30,00,000 +1,622 1,000= 46,22,000

BEP = (Total fixed cost Contribution/unit) = 46,22,000 57 = 81,088 units


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BE statement(a) Step/slab 1,621 1,622 1,623 1,624 1,625(b) Prod. range 81,001-81,050 81,051-81,100 81,101-81,150 81,151-81,200 81,201-81,250(c) Fixed cost (Rs. in lakhs) 30 30 30 30 30(d) step fixed cost (Rs.) 16.21 16.22 16.23 16.24 16.25(e) Total fixed cost (c+ d) 46.21 46.22 46.23 46.24 46.25(f) Contribution p/u 57 57 57 57

(SP-Vc/u)(g) BEP (e/f) 81,071 81,088 81,106 81,123 81,141Nature of BEP Fict. Real Real Fict. Fict.

Problem 13If required profit is Rs. 5,00,000 in the last case ( Problem 12, ) find the required sales volume.

Let volume = x for required profit.

Total contribution = Total Fixed cost + req. profit

57x = 30,00,000+ {(1,000 50)x} +5,00,00037x = 35,00,000x = 94,594.59

Step no. = (94,594.59 50) = 1,892

Fixed cost = 30,00,000+ 1,892 1,000= 48,92,000

Add: Profit = 5,00,000

Contribution = 53,92,000

Required sales = 53,92,000 57 = 94,597 units.

Problem 14Kalyan University conducts a special course on Computer Application for a month duringsummer. For this purpose, it invites applications from graduates. An entrance test is given to thecandidates and based on the same, a final selection of a hundred candidates is made. TheEntrance Test consists of four objective type examinations and is spread over four days, oneexamination per day. Each candidate is charged a fee of Rs. 500 for taking up the entrance test.

The following data was gathered for the past tow years.Statement of Net Revenue from the Entrance Test For the Course of Computer Application

2004 2005Gross Revenue (Fees Collected) Rs. 10,00,000 Rs. 15,00,000Costs: Valuation 4,00,000 6,00,000

Question Booklets 2,00,000 3,00,000Hall Rent at Rs. 20,000 per day 80,000 80,000Salary 60,000 60,000Supervision Charges (one supervisor for every100 candidates at the Rate of Rs. 500 per day) 40,000 60,000General Administration Expenses 60,000 _60,000

Total Cost 8,40,000 11,60,000Net Revenue 1,60,000 3,40,000

You are required to compute:(a) The budgeted net revenue if 4,000 candidates take up the entrance test in 2006.


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(b) The break-even number of candidates.(c) The number of candidates to be enrolled if the net income desired is Rs. 20,000

Solution(a) Budgeted net revenue statement for 4,000 candidates in 06

Gross revenue (Fees collected) (4,000 500) 20,00,000Costs: Valuation 8,00,000

Question booklets 4,00,000Hall rent @ Rs. 20,000/day 80,000Salary 60,000Supervision charges 80,000

(500 40 4)General Admn. Exp. 60,000 14,80,000

Net revenue _5,20,000

(b) Total contribution = 20,00,000 12,80,000 = Rs. 7,20,000

Contribution per candidate = 7,20,000 4,000 = Rs. 180

BEP (in units) = (F.C. Contribution per unit) = 2,00,000 180 = 1,112 units.

For BEP

(500-300)x = 2,00,000 +{(2,000 100) x}

Slab no. = 1,112 100 = 12th slab

Fixed cost = 2,00,000+ 12 2,000= 2,24,000

BEP = 2,24,000 200 = 1,120 candidates

(c) Revised income = 20,000 200x = 2,00,000 + (2,000 100) +20,000x = 1,233

Slab no = 1,233 100 = 13th slab.

Total fixed cost = 2,20,000 + 13 2,000= 2,46,000

Resale = 2,46,000 200 = 1,230 candidates.

Problem 15

Satish Enterprises are leading exporters of Kids Toys. J. Ltd. of U.S.A. have approached SatishEnterprises for exporting a special named Jumping Monkey. The order will be valid for nextthree years at 3,000 toys per month. The export price of the toy will be $4.

Cost data per toy is as follows:Rs.

Materials 60Labour 25Variable overheads 20Primary packing of the toy 15

The toys will be packed in lots of 50 each. For this purpose a special box, which will contain the50 toys will have to be purchased, cost being Rs. 400 per box.

Satish Enterprises will also have to import a special machine for making the toys. The cost of themachine is Rs. 24,00,000 and duty thereon will be at 12%. The machine will have an effective


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life of 3 years and depreciation is to be charged on straight-line method. Apart from depreciation,annual fixed overheads is estimated at Rs. 4,00,000 for the first year with 6% increase in thesecond year. Fixed overheads are incurred uniformly over the year.

Assuming the average conversion rate to be Rs. 50 per $, you are required to:

(i) Prepare monthly and yearly profitability statements for the first year and second yearassuming the production at 3,000 toys per month.

(ii) Compute a monthly and yearly break-even units in respect of the first year.

(iii) In what contingency can there be a second break-even point for the month and for the yearas a whole?

(iv) Have you any comments to offer on the above?

Solution(i) Profit Statement of Satish Enterprise for first and second year on monthly and yearly basisFirst year Second year

Monthly Yearly Monthly YearlyRs. Rs. Rs. Rs.

Sales revenue (A): 600 7,200 600 7,200

(3,000 units Rs. 200)Material cost 180 2,160 180 2,160

(3,000 units Rs. 60)Labour cost 75 900 75 900

(3,000 units Rs. 25)Variable overheads 60 720 60 720

(3,000 units Rs. 20)Primary packing cost 45 540 45 540

(3,000 units Rs. 15)Boxes costs 24 288 24 288

units

units

50

000,3 Rs. 400

Total fixed overhead 108 1,296 110 1,320

(Refer to working note 1)

months

Rs

12

296,1.

months

Rs

12

320,1.

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

Working note:1. Fixed overhead: First year: (Rs.) Second year: (Rs.)

Depreciation 8,96,000 8,96,000

+

years

dutyRsRs

3

000,88,2.000,00,24.

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


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(ii) Statement of monthly break-even units of the first yearLevels-no. of units 1351-1,400 1401-1,450 1,451-1,500 1501 1550(Refer to working note) Rs. Rs. Rs. Rs.Fixed costs: (A)Total fixed overheads p.m. 1,08,000 1,08,000 1,08,000 1,08,000(Refer to working note)

Semi-variable costs:(Special boxes cost) (B) 11,200 11,600 12,000 12,400

(28 boxes (29 boxes (30 boxes (31 boxesRs. 400) Rs. 400) Rs. 400) Rs. 400)

Total fixed & semi-variable 1,19,200 1,19,600 1,20,000 1,20,400Cost: (A +B)

Break-even level of units: 1,490 1,495 1,500 1,505(Total fixed & semi variable cost/

Contribution per unit) (Rs. 1,19,200/ (1,19,600/ (1,20,000/ (1,20,400/Rs. 80) Rs. 80) Rs. 80) Rs. 80)

The first and second break-even level of units viz. 1,490 and 1,495 units falls outside the rangeof 1,351 1,400 and 1,401 1,450 units respectively. Here a monthly break-even level of units is1,500 units which lies in the range of 1,451 1,500 units.

Statement of yearly break-even points of the first yearLevels-no. of units 17851-17900 17901-17950 17951-18000 18001-18050

Rs. Rs. Rs. Rs.

Fixed costs: (A) 12,96,000 12,96,000 12,96,000 12,96,000

Semi-variable costs: 1,43,200 1,43,600 1,44,000 1,44,400(Special boxes cost) : (B) (358 boxes (359 boxes (360 boxes (361 boxes

400) 400) 400) 400)Total fixed & semi-variableCosts: (A +B) 14,39,200 14,39,600 14,40,000 14,40,400Break-even level units: 17,990 17,995 18,000 18,005

(14,39,200/ (14,39,600/ (14,40,000/ (14,40,000/Rs. 80) Rs. 80) Rs, 80) Rs. 80)

Here the break-even level of units (on yearly basis) is 18,000 units, which lies in the range of17951-18,000 units as well. The other two figures do not lie in the respective range, so they are

rejected.

Working Notes:Rs.

1. Fixed overheads in the first year 12,96,000Fixed overhead per month 1,08,000Contribution per unit (S.P. per unit V.C. per unit)(Rs. 200 Rs. 120) 80

Hence the break-even no. of units will be above 1,350 units

80.

000,108.

Rs

Rs

2. If the no. of toys goes beyond 1,500 number, one more box will be required to accommodate

each 50 additional units of toys. In that case the additional cost of a box will be Rs. 400/-.This amount can be recovered by the additional contribution of 5 toys. Hence, the secondbreak-even point in such a contingency is 1,505 toys. (Refer to 1(b) (ii) last column of firststatement).


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If the number of toys goes beyond 18,000 number, one more box will be required. Theadditional cost of this box will be Rs. 400; which can be recovered by the additionalcontribution of 5 toys. Hence the second break-even point is 18,005 toys (Refer to 1(b) (ii)last column of 2nd statement).

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

_________________

Problem 16 ( with opp. cost & sunk cost )

You have been approached by a friend who is seeking your advice as to whether he should giveup his job as an engineer, with a current salary of Rs. 15,000 per month and go into business onhis own, assembling and selling a component which he has invented. He can procure the partsrequired to manufacture the component from a supplier.

It is very difficult to forecast the sales potential of the component, but after some research, yourfriend has estimated the sales as follows:

(i) Between 600 to 900 components per month at a selling price of Rs. 250 per component.(ii) Between 901 to 1,250 components per month at a selling price of Rs. 220 components for

the entire lot.

The costs of the parts required would be Rs. 140 for each completed component. However ifmore than 1,000 components are produced in each month, a discount of 5% would be receivedfrom the supplier of parts on all purchases.

Assembly costs would be Rs. 60,000 per month up to 750 components. Beyond this level of

activity assembly costs would increase to Rs. 70,000 per month.

Your friend has already spent Rs. 30,000 on development, which he would written-off over thefirst five years of the venture.

Required:(i) Calculate for each of the possible sales levels at which your friend could expect to benefit by

going into the venture on his own.

(ii) Calculate the break-even point of the venture for each of the selling price.

(iii) Advise your friend as to the viability of the venture.

Solution

Working note-1: identification of range of production

(a) Selling price/unit Rs 250 220Volume 600-900 901-1,250

(b) Variable cost/unit Rs 140 133Volume 600-1,000 1,001-1,250

(c) Fixed cost Rs 75,000 85,000(60,000+15,000) 600-750 1,001-1,250


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Statement of Break even(a) Prod. range/unit 600-750 751-900 901-1,000 1,001-1,250

Rs. Rs. Rs. Rs.(b) Selling price/unit 250 250 220 200(c) Less: VC/unit 140 140 140 133(d) Contribution/unit 110 110 80 87(e) Fixed cost 75,000 85,000 85,000 85,000(f) BEP 682 773 1,063 978

Nature of BEP Real Real Fictitious. Fictitious.

Max Profit (110 750-75,000) 7,500 14,000 -- 23,750

The product should be launched and production volume should set at 1,250 units. This type ofBEP is called cash BEP as the non cash items are already eliminated.

Note ; Rs. 30,000 spent on development--- sunk costCurrent salary of Rs. 15,000 opp. cost

Problem 17Navbharat Commerce college, Bombay has six sections of B. Com, and two sections of M. Comwith 40 and 30 students per section respectively. The college plans one day pleasure trip aroundthe city for the students once in an academic session during winter break to visits part, Zoo,planetarium and aquarium.

A transporter used to provide the required number of buses at a flat rate of Rs. 700 per bus forthe aforesaid purpose. In addition, a special permit fee of Rs. 50 per bus is required to bedeposited with city Municipal Corporation. Each bus is 52 setters. Two seats are reserved for

teachers who accompany in each bus. Each teacher is paid daily allowance of Rs. 100 for theday. No other costs in respect of teachers are relevant to the trip.

The approved caterers of the college supply breakfast, lunch and afternoon tea respectively atRs. 7, Rs. 30 and Rs. 3 per student.

No entrance fee is charged at the park. Entrance fees come to Rs. 5 per student both for the zooand the aquarium. As regards planetarium the authorities charges block entrance fees as underfor group of students of educational institutions depending upon the number of students is group:No. of students in a group Block entrance fee

Rs.

Up to 100 200101 200 300201 & above 450

Cost of prizes to be awarded to the winners in different games being arranged in the parkdepend up on the strength of students in a trip. Cost of prizes to be distributed are:Number of students in a trip cost of Prizes

Rs.Up to 50 90051-125 1,050126 150 1,200151 200 1,300201 250 1,400251 & above 1,500


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To meet the above costs the college collects Rs. 65 from each student who wish to join the trip.The college releases subsidy of Rs. 10 per student in the trip towards it.

You are required to:(a) Prepare a tabulated Statement showing total costs at the levels of 60, 120, 180, 240 and 300

students indicating each item of cost.

(a) Compute average cost per student at each of the above levels.

(b) Calculate the number of students to break even for the trip as the college suffered loss duringthe previous year despite 72% of the students having joined the trip.

Solution(a) Statement showing total costs indicating each item of cost

No. of students 60 120 180 240 300Rs. Rs. Rs. Rs. Rs.

Variable costs:Breakfast 420 840 1,260 1,680 2,100Lunch 1,800 3,600 5,400 7,200 9,000Tea 180 360 540 720 900Entrance fee for Zoo & aquarium 300 600 900 1,200 1,500Total: (A) 2,700 5,400 8,100 10,800 13,500Semi variable costs:Rent of buses 1,400 2,100 2,800 3,500 4,200(Ref. To working note 1)Special permit fee 100 150 200 250 300(Ref. To working note 2)Daily allowance paid to teachers 400 600 800 1,000 1,200

(Ref. To working note 3)Block entrance fee 200 300 300 450 450(Ref. To given table)Cost of prizes 1,050 1,050 1,300 1,400 1,500(Ref. To given table) ________ Total: (B) ____3,150 4,200 5,400 6,600 7,650Grand Total : (A) + (B) ____5,850 9,600 13,500 17,400 21,150

(b) Average cost per student at each of the above levelsNo. of students: (A) 60 120 180 240 300Total costs (Rs.) : (B) 5,850 9,600 13,500 17,400 21,150[Refer to (a) part]

Average cost (Rs.): (B)/(A) 97.50 80 75 72.50 70.50

(c) Statement showing number of students to break-evenNo. of students in the trip 51-100 101-125 126-150 151-200 201-250 251-300No. of buses 2 3 3 4 5 6Semi-variable costsBus rent (Rs.) 1,400 2,100 2,100 2,800 3,500 4,200Permit fee (Rs.) 100 150 150 200 250 300Block entrance fee (Rs.) 200 300 300 300 450 450Daily allowancePaid to teachers (Rs.) 400 600 600 800 1,000 1,200Cost of prizes ___1,050 1,050 1,200 1,300 1,400 1,500Total cost (Rs.) 3,150 4,200 4,350 5,400 6,600 7,650No. of students to break-even: 105 140 145 180 220 255(Total semi-variable cost/ (3,150/ (4,200/ (4,350/ (5,400/ (6,600/ (7,650/contribution per student) 30) 30) 30) 30) 30) 30)


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(Refer to working note 4)

As the figure of 105 and 140 students fall outside the limits (No. of students in the trip.), thereforethere are four break-even points in this case viz., 145, 180, 220 and 255 students. The collegeauthorities should keep these figures in mind while hiring 3, 4, 5 and 6 buses respectively toavoid losses.

The college incurred loss during the previous year as they hired 5 buses and 72% of totalstudents (216 out of 300 students) joined the trip. The break-even in case college authoritieshires 5 buses for the trip comes to 220 students.

Working notes:1. No. of buses required and rent of buses @ Rs. 700/- per bus

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

2. Special permit fee:

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

3. Allowance paid to teachers (Rs.) 400 600 800 1,000 1,200

(No. of buses Rs. 200)

4. Contribution per student towards semi-variable costs Rs.Collection from each student 65Subsidy provided by the college _10

75Less: Variable cost per student _45

Contribution per student _30

BEP in process costing .

In this case the BEP is computed on the basis on input in process 1

Problem 18In an oil-mill three processes are required to convert the raw material to chaff , oil & meal. In thefirst process (cleaning) the chaff is separated. In the second process (pressing) oil and cakes areproduced.

The oil is transferred to finished stock and the cake is transferred to third process(grinding)where it is dried and ground into meal. For an input of 1000 kg. raw material, output are450 litres of oil, 50 kg. chaff and 400 kg. meals.

Raw materials purchase prices is Rs. 12 per kg. The Selling price of oil is Rs. 80 per litre. Sellingprices of the chaff and meals are Rs. 20 and Rs. 200 per kg. respectively.The processing costs are as follows :-

Variable costs Total fixed costs per monthRs.

Process A Rs. 10,000 per 1,000 kg. 1,32,000Process B Rs. 25,000 per 1,000 kg. cleaned material

transferred to this process 3,00,000Process C Rs. 32,000 per 1,000 kg. of meal 4,00,000

There is no opening and closing stocks in any process. How many kg. of raw material input permonth must be processed in order to break-even ?


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Solution 950 kg. CakeRaw Material1,000 kg.

Chaff sold @ Rs. 20/kg. Oil sold @ Rs. 80/litre meal sold @ 200/kg.50 chaff 450 liter 400 kg.

Contribution statementRevenue:

P1 i.e. chaff (50 20) 1,000

P2 i.e. oil (450 80) 36,000P3 meal (400 200) 8,00,000 1,17,000

Les Variable costP1 10,000

P2 {(25,000 1000) 950} 23,750

P3 {(32,000 1,000) 400} 12,800Raw material 11,550 58,100

Contribution 58,900

Contribution per unit of raw material = Rs 58.90So BE input 8,32,000 58.9 = 14,125.63 kg

Break-even point following DCF technique

Case-1:

At break even ( Life of project should be known)

Discounted cash outflow = Discounted cash inflow.Or Investment of Y0 = [(Sp/u- VC/u) no of units Fixed cost (only cash nature)]If the sales volume, VC/u & Fixed cost are equal p.a. then--

investment at Y0 = [(SP-VC) units Fixed cost] Annuity value.

No. of units at BE = [ (Inv. at y0 Annuity value)+Fixed cost] Contribution per unit.Case-2:

When life of the project is unknown (not given in the problems). Then apply the concept ofperpetuity. I.e.

Cash inflow p.a. must equal to financial charges to break even.

Investment at y0 Rate of return = (SP - VC) units Fixed cost (cash)No of units at BE = -----------------------------------------------------------------------

Note: Investment at y0 = Total investment at Y0 + interest on investment paid duringconstruction period.

P1 P3 FGP2

Investment at y0 rate of return +Fixed costContribution per unit


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Problem 19The investment for a project is Rs. 20 cr. The sale price p.u. Rs.400 & variable cost is Rs.240.the fixed cost p.a. is Rs. 23,00,000. The required rate of return is 12%.

Find BEP for an life of 6 yrs.

If the project building period is 2 years with 60% of capital will be invested in 1st year, what is theproject BEP production & sale volume?

Solution(a) Investment = Rs. 20 crores

Rs.Selling price/units 400Variable cost/unit 240Contribution p.u. 160

Fixed cost = 23 lakhs; Life 6 years; Rate of return = 12%

BEP = {(20 cr. 4.114)+ 23 lakhs} 160 = 3,18,408 units

(b) All cash flow are occur at the end of the year (assumption of DCF technique)

Interest at y0 = 20 Cr. +12 Cr. 12%= Rs. 21.44 Cr.

BEP = {(21.44 cr. 4.1114)+ 23 lakhs)} 160= 3,40, 299 units

Problem 20A public company responsible for the supply of domestic gas has been approached by several

prospective customers in a rural area adjacent to a high-pressure main. As a condition of itslicense to operate as a utility, the company is obliged to respond positively to current needsprovided the financial viability of the company is not put at risk. New customers are charged Rs.250 each for connection to the system.

Once a meter is installed, a standing charge of Rs.10 per quarter is billed. Charges for gas arelevied at Rs.400 per 1,000 metered units.A postal survey of the area containing, according to the rating authority, 5,000 domestic units,elicited a 40% response rate. 95% of those who responded confirmed that they wished tobecome gas users and expressed their willingness to pay the connection charge.

Although it is recognized that a small percentage of those willing to pay for connection may notactually choose to use gas, it is expected that the average household will burn 50 metered unitsper month. There will be some seasonal differences.

The companys marginal cost of capital is 17% pa and supplies of bulk gas cost the companyRs.0.065 per metered unit. Wastage of 15% has to be allowed for determine what the maximumcapital project cost can be to allow the company to provide the service required.

SolutionNote-1:

No. of customer 5,000 40% 95% = 1,900

Note-2:

Consumption of gas1,900 50 12 mt. = 11,40,000 mt.

Gas supply 11,40,000 (100 85) = 13,41,176 mt


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Note-3:

Cash inflow:

One time (y0) = 250 1,900 4,75,000

Cash p.a. (in last year) Rs.Rent 1,900 4 10/Q 76,000

Consumption charge 11,40,000 0.4 4,56,0005,32,000

Less: Cost of company (13,41,176 0.065) 87,176Cash inflow P.a. 4,44,824

By following the concept of perpetuity

(Investment-4,75,000) 17% = 4,44,824

Investment Rs. 30,91,612

BEP for a perishable product

1st Calculate the contribution from the sale of opening stock then compare it with the fixedcost.If the fixed cost is not yet recovered then it will recovered from current year production &sales.

Problem 21A Company produces formulations having a shelf life of one year. The company has an opening

stock of 15,000 boxes on 1/1/2006 and expects to produce 75,000 boxes as was in the justended year of 2005. Expected Sale would be 78,000 boxes. Costing department has workedout escalation in cost by 25% on variable cost and 12% on fixed cost for the year 2006.

Fixed costs are estimated at Rs.16,80,000. New price for 2006 is Rs.70/- per box while the saleprice in 2005 was Rs. 60. Variable cost of the opening stock is Rs. 20 per box.

Find actual BEP.

SolutionLast year Current year

2005 2006

Opening stock -- 15,000Production 75,000 75,000Sales -- 78,000Closing stock 15,000 12,000

Rs. Rs.Sales price/unit 60 70Less: Variable cost/unit _20 __25Contribution 40 45

Fixed cost (16,80,000 112) 100 16,80,000= 15,00,000

Contribution from the sale of opening stock (70-20) = Rs. 50 In 2006


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RsFixed cost 16,80,000Less: Contribution from opening stock sales _7,50,000Rest. Fix 9,30,000

Required production & sales = 9,30,000 45 = 20,667 units

BEP (Actual) = 15,000 +20,667 = 35,667 units.

Potential Break-even point

When Break even is expressed only out of current year production or sales then it isknown as potential Break even. In this case sale of opening stock should not be consider

BEP = -----------------------------------------------------------------------------

Step-1: Calculate potential sale value of current year production i.e. if current yearproduction is fully sold out then what should be the revenue generation.

Step-1: Potential sales = (Sales COGS) COP Less: Variable cost of production & sale Potential contribution

Calculate PV ratio= potential contribution potential Sale

Potential BES = total fixed cost PV ratioProblem 23

N.R.I Ltd. produces an unique product, the potential demand for which would diminish with anyprolonged period of business recession. A review of the price product over the past six monthshas become necessary in order to determine future market strategy. A cost and profit statementhas been prepared for this purpose.

You are required to calculate the Break even point for total sales, actual and potential. Whyshould the above procedure be adopted instead of the usual way of finding the B. E. Point ?

Cost and Profit statement for the six months January - June 2007Rs. Rs.

Net Sales 24,50,000Stock 1st January 2004 4,00,000Direct Labour 8,95,000Direct Material 7,45,800Indirect expenses :

Variable 2,38,700Fixed 3,58,000

26,37,500Less stock 30th June 2005 8,00,000Cost of Goods Sold 18,37,500

Gross profit 6,12,500Selling & Distribution Expenses :

Variable 1,00,000Fixed 2,00,000 3,00,000

Fixed cost of current yearsContribution p.u. in current year production & sales


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Profit before Tax 3,12,500Tax provision 1,26,200Net Profit for 6 months 1,86,300

Increase in stock should be assumed as potential sales within the period.

SolutionCost of production = (8,95,000+7,45,800 +2,38,700 + 3,58,000)

= Rs. 22,37,500

Potential sales = {(Sales COGS) COP} Rs.

= (24,50,000 18,37,500) 22,37,500 = 29,83,334Less: Total variable cost (8,95,000+7,45,800 +2,38,700) (-) 18,79,500

Less: Selling & distribution overhead {(1,00,000 24,50,000) 29,83,334} (-) 1,21,769Contribution 9,82,065

Potential P/V ratio = {(9,82,065 29,83,334) 100} = 32.92%

Potential BES = Fixed cost P/V ratio = 5,58,000 32.92%= Rs.1,69,5,019

Cost Indifference Points BEP on basis of costs only

Where there are difference production facility available for a single job we always select thatproduction facility where the total cost is minimized.

Indifference production volume = change in fixed cost save in variable cost p.u.

Problem 24

Machine x Machine yVariable cost/unit Rs 40 35Fixed cost Rs. 10,000 12,500

Rs Total Cost of xP

Total Cost y12,500

10,000

unitsindifference production volume

At P, TCx = Tcy

40q +10,000 = 35q +12,500

Where q is the required volume

q = (2,500 5) = (Charge in Fixed cost gain in variable cost) = 500 units


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Problem 25M companys services department is evaluating new copying machines to replace the firmscurrent copier, which is worn out. The analysis of alternative machines has been narrowed tothree and the estimated costs of operating them are shown below:

________ Cost per 100 copiesMachine A Machine B Machine C

Rs. Rs. Rs.Materials costs 60 40 20Labour cost 80 30 20Annual Lease cost 30,000 58,000 1,00,000

Required:(i) Compute the cost indifference points for the three alternatives.(ii) What do the cost indifference points suggest as a course of action in this regard?(iii) If the management expects to need 87,000 copies next year, which copier would be most

economical?

Solution(i) Computation of cost indifference points for the three alternatives:

Cost indifference point for two machines viz.

A & B = ---------------------------------------------

=)3040.()8060.(

000,30.000,58.

++RsRs

RsRs

=)100(70.

000,28.

copiesperunitofRs

Rs

Cost indifference point for two machines viz.

B & C =)2020.()3040.(

000,58.000,00,1.

++RsRs

RsRs

=)100(30.

000,42.

copiesperunitofRs

Rs

= 1,400 Nos. (Multiple of 100 copies)

C & A = )2020.()8060.(

000,30.000,00,1.

++

RsRs

RsRs

=)100(100.

000,70.

copiesperunitofRs

Rs

= 700 nos. (Multiple of 100 copies)

(ii) From the above computations, it is clear that at activity level below the indifference point thealternative (machine) with lower fixed cost and higher variable costs should be used. In case theactivity level exceeds the indifference point, a machine with lower variable cost per unit (or highercontribution per unit) and higher fixed cost, is more profitable to operate. At the activity levelequal to the indifference point both machines are on equal footing.

Hence, from the above we conclude as follows:From 0 to 400 Nos. (multiple of 100 copies) use machine AFrom 400 to 1,400 Nos. (Multiple of 100 copies) use machine B

Difference in fixed costDifference in variable cost per unit


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Above 1,400 Nos. (multiple of 100 copies) use Machine C.

(iii) if the management needs 87,000 copies next year, i.e., 870 Nos. (Multiple of 100 copies) it isclear that machine B would be most economical.

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Problem 26Standard Pumps Ltd. is manufacturing Petrol and Diesel operated pumps . The company wantsto have a customer survey before marketing the pumps . You are asked to workout theeconomics of choice between the two types of pumps . The company provides you the followingdata .

Petrol Operated Pump X Diesel Operated Pump YSelling Price Rs. 80,000 1,24,000Cost of fuel per Liter Rs. 40.00 25.00Operating Hours per Liter 20.00 40.00

Using above data answer following questions :-----

a. How many hours the pumps should run so that the customer willing to buy is indifferent inchoice between X and Y ? Assume that fuel cost has linear function with respect to time .

b. Assuming the price of X remains unchanged , and the customer wants to run the pumpfor 12,800 hours , how much he will be willing to pay for Y ?

c. If Standard Pump Ltd. offers to convert a Petrol operated Pump to Diesel operated oneafter 18,000 hrs. of operation of the former , how much customer will be willing to pay forthis modification of the pump?

d. If there is a saving of Rs.33,500 in operating cost of Y over its life , how many hours thecustomer should expect to run the pumps so as to be indifferent in choice ?

e. If there is a restriction on the fuel supply to the extent of 750 litres for both Petrol andDiesel , what will be customers preference either for Petrol operated or Diesel operatedone ?

f. Do you suggest any other point that should be considered for choice between alternativesapart from above ?

Solution ; ( TC = total cost )(a)

Petrol: X Diesel: Y Gain

Purchase price Rs. 80,000 1,24,000 ( 44,000)Fuel cost Rs./lt. Rs. 40 25Hr./lt. 20 40

Fuel cost/hr. Rs. 40 20 =2 25 40 = 0.625 1.375

In. pt = 44,000 1.375 = 32,000 hrs

(b) X YPurchase price 80,000 1,24,000Fuel cost Rs./lt. 40 25

Hrs. 1,28,000 12,800Purchase 1,44,000 ?

Indifference point = 12,800

TCx =TCy at 12,800


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80,000 +2 12,800 = PP of Y + 0.625 12,800Purchase Price of Y = Rs. 97,600

(c) Pump x is already purchased so, the customers expectation to run the pump at most 3,200 hrs.Pumps has already run for 18,000 hrs. following this conversion, the user has a gain of at the rate

of 1.375 for 14,000 hrs. of rest life. Maximum opportunity gain.

14,000 1.375 = 19,250.

Hence, maximum discretionary cost for conversion = Rs. 19,250.

(d) Saving of Rs. 33,500 of yTCx TCy = 33,500

Or, Indifference point 32,000 hrs. & then y have again of Rs. 1.375/hr.

Hrs. to run = 33,500 1.375 = 24,363.6 above 32,000 hrs.

Required hrs. = 32,000 +24,363.6 = 56,363.6 hrs.

(e) If a problem of fuel indifference, so we have to calculate cost/hr. as at same volume of fuel, pumpwill run for difference hour.

X y

(a) Fuel 750 lt. 750 lt.(b) Cost/lt. Rs. 40 25(c) Fuel cost Rs. 30,000 18,750(d) purchase price Rs. 80,000 1,24,000

(e) Total cost Rs. 1,10,000 1,42,750(f) Hrs. 750 20 =15,000 750 40 = 30,000

Cost/hr. Rs. 7.33 4.75

So, y is to two selected.

(f) Other points is to be considered.(a) Availability of spare parts & AMC.(b) Resale value(c) Life of the assets(d) Prestige value or esteem value

(e) Pollution factor

Points to remember before examination

1. Analysis the problem very carefully2. analysis of given data into its fixed & variable component3. application of proper BE rule

334_resource_2. cvp analysis

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