Cost-Volume-Profit (CVP) Analysis

Profit planning is a function of : the selling price of a unit of product, the variable cost of making and selling the product, the volume of product units sold, and in the case of multi-product companies, sales mix and finally total product cost.

The cost-volume-profit (CVP) analysis is a : management accounting tool to show the relationship between these ingredients of profit planning The entire gamut of profit planning is associated with CVP inter-relationships. A widely –used technique to study CVP 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 Point (BEP) may be defined as a point at which the firm`s total revenues are equal to total costs, yielding zero income. This is a no-profit, no-loss point.

Break even analysis, as a technique,seeks to provide answers to the following questions: What sales volume is necessary to produce an X amount of operating profit ? What will be the operating profit or loss at X sales volume? What profit will result from an X per cent increase in sales volume? What additional sales volume is required to make good an X percent reduction in selling prices so as to maintain the current profit level? What will be the effect on operating profit if the company's fixed cost have increased ? What sales volume is needed to achieve the budgeted profit?

BREAK EVEN ANALYSIS A BEP analysis shows the relationship between the costs and profits with sales volume. The sales volume which equates total revenue with related costs and results in neither profit or loss is called Break Even Volume or Point (BEP).

The BEP can be determined by two methods : I Algebraic Methods : (a) Contribution margin Approach (b) Equation Technique II Graphic Presentation : (a) Break Even Chart (b) Profit Volume Graph

I Algebraic Methods : (a)Contribution margin Approach ILLUSTRATION 1 : How many ice-creams having a unit variable cost of Rs.2 and a selling price of Rs.3, must a vendor sell in a fair to recover the Rs.800 fees paid by him for getting the stall and additional cost of Rs.400 to set up the stall.

BEP (units) = Fixed Cost / Contribution Margin per unit BEP (units) = (Entry Fee + Stall Expense) / (Sales Price – Unit Variable Cost) = ( ) / ( 3 - 2) = 1,200 units BEP (amount) = Fixed Cost / Profit Volume Ratio (P/V ratio) = 1,200 / = Rs.3,600

P/V Ratio = Contribution Margin per unit / Selling Price per unit = Re.1 / Rs. 3 = O.3333 or % Variable Cost to Volume Ratio ( V/V ratio) = 1- P/V ratio = = or % V/V ratio = Variable Cost / Sales Revenue = Rs.2 / Rs. 3 = 66.67% Therefore P/V ratio (+) V/V ratio = 100% i.e. 1

Margin of Safety Ratio (M/S Ratio) = (ASR – BESR) / ASR where, ASR = actual sales revenue BESR = break even sales revenue If the actual sale in this case is 2,000 units ( Rs. 6,000), then M/S ratio = (6, ,600) / 6,000 = 40 %

Profit = [ Margin of safety (amount)] * P/V ratio = [ Rs.2,400 ] * = Rs.800 Profit = [ Margin of Safety (units) ] * Contribution Margin per unit = [ 800 units ] * Re.1 = Rs.800

Illustration 2: Sales = 4,000 Rs 10 per unit Break-even point = 1,500 units Fixed Cost = Rs 3,000 What is the amount of (a) variable cost (b) profit ?

Solution : BEP (in units) = FC/ Contribution per unit 1,500 = 3,000 / C C = 3,000/1,500 = Rs 2 (a) Variable Cost = Selling Price –Contribution = 10 – 2 = Rs 8 per unit Contribution at sales of 4,000 units is Rs 8,000 (b) Profit = Contribution – FC = 8,000 – 3,000 = Rs 5,000

Illustration 3: Selling Price = Rs 150 per unit Variable cost = Rs 90 per unit Fixed Cost = Rs 6,00,000 What is the break even point ? What is the selling price per unit if break – even point is 12,000 units ?

Solution : Break even point = FC/ Contribution per unit = 6,00,000 / = 10,000 units When BEP is at 12,000 the contribution will be : 12,000 = 6,00,000/ C C = 6,00,000/ 12,000 = Rs 50 per unit C= S-V 50=S-90 S=90+50 = Rs 140 per unit

ILLUSTRATION 4: During the current year, Superhouse Ltd. showed a profit of Rs.1,80,000 on sale of Rs. 30,00,000. The variable expenses were Rs. 21,00,000. You are required to work out : a) The break even sales at present b) The break even sale if variable cost increases by 5 per cent. c) The break even sale to maintain the profit as at present, if the selling price is reduced by 5 per cent.

Solution: Sale = VC + FC + Profit 30,00,000 = 21,00,000 + FC + 1,80,000 Therefore, FC = Sales - [ VC + Profit ] = 30,00,000 - [ 21,00, ,80,000 ] = Rs. 7,20,000

a) BEP = FC / PV ratio PV ratio = Contribution / Sales = Sales – Variable Cost / Sales = [30,00,000 – 21,00,000] / 30,00,000 = 9,00,000 / 30,00,000 = 0.30 BEP = 7,20,000 / 0.30 = Rs.24,00,000

b) Revised BEP = FC / New PV ratio New PV Ratio = [ Sales – (Variable Cost + 5 %) ] / Sales New PV Ratio = [ 30,00,000 – 22,05,000 ] / 30,00,000 = 7,95,000 / 30,00,000 = Revised BEP = 7,20,000 / = Rs. 27,16,981

c) If sale is reduced by 5 % = 30,00,000 [ ] = 30,00,000 [ 0.95 ] = Rs. 28,50,000 New PV ratio = [ 28,50,000 – 21,00,000 ] / 28,50,000 = 7,50,000 / 28,50,000 = Desired Volume of Sales = [ FC + Desired Profit] / New PV ratio = [7,20, ,80,000 ] / = Rs. 34,19,973

Algebraic Methods : (b) Equation Technique Based on the income equation : Sales Revenue – Total Costs = Net Profit Breaking up total costs into fixed and variable, Sales Revenue – Fixed Costs – Variable Cost = Net Profit Sales Revenue = Fixed Costs + Variable Cost + Net Profit

If S is the number of units required to be sold to break even ; SP is sales revenue ; VC is variable cost per unit and FC is fixed cost, then SP (S) = FC + VC (S) + NI As Net Income is suppose to be Zero at BEP point, therefore SP (S) = FC + VC (S) + Zero SP (S) – VC (S) = FC S (SP-VC) = FC S = FC / (SP-VC)

ILLUSTRATION 5 : X Ltd., a multi product company, furnishes you the following data relating to the current year: Assuming that there is no change in price and variables cost and that the fixed expenses are incurred equally in the two half-year periods, Calculate for the year : a) Profit Volume Ratio b) Fixed Expense c) Break Even sales d) Percentage of Margin of Safety First Half of the Year Second Half of the Year SalesRs. 45,000Rs. 50,000 Total costs 40,000 43,000

Solution : Sales revenue (-) Total cost = Net profit Rs. 45,000(-) Rs.40,000 = Rs. 5,000 ( Ist half) Rs. 50,000(-) Rs.43,000 = Rs. 7,000 ( 2nd half) On a differential basis : ∆ Sales Revenue ( Rs.5,000) minus ∆ Total Cost ( Rs.3,000) = ∆ Total Profit ( Rs. 2,000) As we know that only variable cost changes with a change in the sales volume, hence change in total cost is equivalent to VC ( Rs.3,000). Thus, the additional sales of Rs. 5,000 has earned a contribution margin of Rs. 2,000 [ Rs.5,000 (S) – Rs. 3,000 (VC) ]

a)Profit Volume Ratio = Contribution Margin / Additional Sales = Rs. 2,000 / Rs. 5,000 = 40 % or 0.40 Therefore V/V ratio = = 60% or 0.60 b) Fixed Expense : Sales Revenue = Fixed Costs + Variable Cost + Net Profit Fixed Cost = Sales Revenue – [ VC + NP ] = Rs. 95,000 – ( 95,000 * 0.60) + Rs. 12,000 ] = Rs. 95,000 – Rs.69,000 = Rs. 26,000

c) Break Even Sales: FC / P/V ratio = 26,000 / 0.40 = Rs. 65,000 d) Percentage of Margin of Safety M/S ratio = [Rs.95,000 (-) Rs. 65,000] / Rs.95,000 = %

Limitations: Difficult to separate cost into fixed and variable, some cost are of mixed nature Not correct to assume that fixed cost remain unchanged over the entire range of volume Assumption of constant selling price and variable cost is not valid Difficult to use BEP analysis for a multi-product firm BEP is a short –run concept and has limited use in the long run planning

OPERATING LEVERAGE AND RISK Leverage is a relative change in profits due to a change in sales. A high degree of leverage implies that a large change in profits occurs due to a relatively small change in sales. Two types : Financial Leverage : borrowed funds Operating Leverage : use of fixed cost in operation of business

A firm will have no operating leverage if its ratio of fixed cost to total cost is nil. For such a firm, a given change in sales would produce same percentage change in the operating profit. Or EBIT. If a firm has fixed costs, it would have operating leverage : A) higher operating leverage if the total cost have higher percentage of fixed costs. B) operating leverage increases with fixed cost. C) operating profit of a highly leveraged (operating) firm would increase at a faster rate for any given increase in sales. D) if sales fall, the firm with a high operating leverage would suffer more loss than the firm with no or low operating leverage.

Airline Industry: high fixed cost –profit is highly sensitive to the number of passengers carried. Retail Firm: very high variable cost and negligible fixed cost. Profit fluctuation occurring due to high fixed costs are referred to as operating risk.

Degree of Operating Leverage is the % change in operating profits resulting from a % change in sales. DOL = % change in operating profit/ % change in sales DOL= ∆EBIT/ EBIT / ∆Sales/ Sales here EBIT = operating profit DOL= Q (s-v) / Q (s-v) – F Where Q = qty of output S= selling price V=variable cost

Illustration: Let us suppose that two firms X and Y manufacture same product. Selling price is Rs 8 per unit for both the firms. Fixed cost for X and Y respectively are Rs 80,000 and Rs 2,00,000, while the variable cost per unit is respectively Rs 6 and Rs 4. Cal the DOL for firm Y if its sales increases from 70,000 units to 80,000units.

W/N1: EBIT at 70,000 sales : Sales(-) FC(-) VC 5,60,000(-)2,00,000(-)2,80,000= 80,000 EBIT at 80,000 sales : 6,40,000(-)2,00,000(-)3,20,000=1,20,000 Solution: DOL= 1,20,000-80,000/80,000 / 6,40,000-5,60,000/ 5,60,000 DOL= 40,000/80,000 / 80,000 /5,60,000 = 3.50 i.e. 350% It indicates that if sales increase by 100%, operating profit will increase by 350%.

DOL= Q (s-v) / Q (s-v) – F =70,000 (8-4) / 70,000(8-4)-2,00,000 = 2,80,000/80,000 = 3.5

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