Business Accounting and Finance By-Hari Dallakoti

Cost, Volume and Profit Analysis

CVP Analysis Cost-volume-profit (CVP) analysis is the study of the effects of changes of costs and volume on a company’s profits. Cost-volume-profit analysis is important in profit planning. It is also a critical factor in management decisions. The examination of the relationship between costs, volume of production and sales and profit of activity in order to advise to the management about the consequences of various decisions. For example; How many students needed to enrol to break even on delivering a particular course How many tickets does the ANFA needed to sell for a particular match to achieve a desired level of profit What level of sales of a new product are required by a manufacturing company to make it a viable product.

Contd. Cost-volume-profit (CVP) analysis helps to managers to understand the interrelationships among Cost, Volume and Profit by focusing their attention on the interactions among the prices of products, volume of activity, per unit variable costs, total fixed costs, and mix of products sold. It is a vital tool used in many business decisions such as deciding what products to manufacture or sell, what pricing policy to follow, what marketing strategy to employ, and what type of productive facilities to acquire.

Factors that Impact on CPV The level of activity or the volume of sales and/or production The selling price of products The variable costs per units The total fixed costs The mix of products if more than one product is sold

Key Assumptions of CVP Analysis Selling price is constant. Costs are constant i.e. linear. All costs can be classified into fixed and variable. In multiproduct companies, the sales mix is constant. In manufacturing companies, inventories do not change (units produced = units sold).

Use of CVP Analysis to Compute Breakeven point The unique sales level at which a company earns neither a profit nor incurs a loss, is called Breakeven point. What is the break-even point? Revenues Costs = Break-even point

Breakeven Analysis Can be computed by three ways: The equation method The contribution margin method Graphic method

The Equation Method The equation method centers on the contribution approach to the income statement. Particulars Amount (Rs.) Sales Revenues xxxx Less: Variable Costs Contribution Margin Less: Fixed Costs Net Operating Income Or Sales = Variable Costs + Fixed Costs+ Profit Sales = Variable Costs + Fixed Costs + Profit At Break-even point; Profit is Zero Therefore, Break-even equation is; Sales = Variable Costs + Fixed Costs

Example While using PV ratio S & S trading house information Per cycle Percent SPPU Rs.500 100% VCPU Rs.300 60% CM Rs.200 40% Fixed costs = Rs.80,000 Solution: Use our BE Equation; and Let X is BE Point in Cycles While using CMPU While using PV ratio Sales = VC + FC Rs. 500x = Rs. 300x + Rs. 80,000 Rs. 500x- Rs. 300x = Rs. 80,000 Rs. 200x = Rs. 80,000 X = 400 Cycles 1x = 0.6x + Rs. 80,000 1x- 0.6x = Rs. 80,000 0.4x = Rs. 80,000 X = Rs. 200,000

The Unit Contribution Method Is a variation of the equation method. The method may be just a bit more intuitive than the equation method. The approach centers on the idea that each unit sold provides a certain amount of CM that goes toward covering fixed costs. Fixed Costs = BEP in units Unit Contribution Margin* Fixed Costs = BEP in Rupees Contribution Margin ratio** * Unit Contribution Margin or Contribution Margin Per Unit = Selling Price Per Unit – Variable Cost Per Unit ** Contribution Margin Ratio or P/V Ratio = SPPU-VCPU SPPU

Contribution Margin Income Statement ACC 202 8/25/2018 Contribution Margin Income Statement Sales (50,000 units) Rs.1,000,000 Variable costs 600,000 Contribution margin Rs.400,000 Fixed costs 300,000 Income from operations Rs.100,000 The contribution margin is available to cover the fixed costs and income from operations. FIXED COSTS Contribution margin Income from Operations Sales – Variable Cost = Contribution Margin C-V-P Analysis

Contribution Margin Ratio Sales (50,000 units) Rs.1,000,000 Variable costs (600,000) Contribution margin Rs.400,000 Fixed costs (300,000) Income from operations Rs.100,000 100% 60% 40% 30% 10% Contribution margin ratio = Sales – Variable costs Sales Rs.1,000,000 – Rs.600,000 Rs.1,000,000 Contribution margin ratio = Contribution margin ratio = 40%

Expression of Contribution margin 100% 60% 40% 30% 10% Sales (50,000 units) Rs.1,000,000 Variable costs 600,000 Contribution margin Rs.400,000 Fixed costs 300,000 Income from operations Rs.100,000 Rs.20 12 Rs. 8 The contribution margin can be expressed in three ways: 1. Total contribution margin in Rupees. 3. Contribution margin ratio P/V Ratio (percentage). 3. Unit contribution margin (Rupees per unit).

Calculating the Break-even Point In Units Sales (Rs.25 x ? units) Rs. ? Variable costs (Rs.15 x ? units) ? Contribution margin Rs. 90,000 Fixed costs 90,000 Income from operations Rs. 0 Sales (Rs.25 x 9,000) Rs.225,000 Variable costs (Rs.15 x 9,000) 135,000 Contribution margin Rs. 90,000 Fixed costs 90,000 Income from operations Rs. 0 Rs.25 15 Rs.10 Fixed costs Rs.90,000 9,000 units Break-even sales (units) = Rs.10 Unit contribution margin PROOF! At the break-even point, fixed costs and the contribution margin are equal.

Cost-Volume-Profit Chart Rs.500 Rs.450 Rs.400 Rs.350 Rs.300 Rs.250 Rs.200 Rs.150 Rs.100 Rs. 50 Total Sales Sales and Costs (Rs.000) Variable Costs 60% 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) Unit selling price Rs.50 Unit variable cost 30 Unit contribution margin Rs.20 Total fixed costs Rs.100,000

40% 60% Contd. Total Sales Variable Costs Contribution Margin Rs.500 Rs.450 Rs.400 Rs.350 Rs.300 Rs.250 Rs.200 Rs.150 Rs.100 Rs. 50 Total Sales Contribution Margin 40% Sales and Costs (Rs.000) Variable Costs 60% 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) Unit selling price Rs.50 Unit variable cost 30 Unit contribution margin Rs.20 Total fixed costs Rs.100,000 100% 60% 40%

40% Contd. Total Costs Sales and Costs (Rs.000) 100% 60% 40% Rs.500 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) Unit selling price Rs.50 Unit variable cost 30 Unit contribution margin Rs.20 Total fixed costs Rs.100,000 100% 60% 40%

40% Contd. Rs.100,00 Rs.20/unit = 5,000 units Break-Even Point Sales and Costs (Rs.000) 1 2 3 4 5 6 7 8 9 10 Units of Sales (000) Unit selling price Rs.50 Unit variable cost 30 Unit contribution margin Rs.20 Total fixed costs Rs.100,000 100% 60% 40% Rs.100,00 Rs.20/unit = 5,000 units

Contd. Sales and Costs (Rs.000) Operating Profit Area Operating Loss Area Sales and Costs (Rs.000) Units of Sales (000) Unit selling price Rs.50 Unit variable cost 30 Unit contribution margin Rs. 20 Total fixed costs Rs.100,000 100% 60% 40%

Sales Mix Considerations Product Units Weight (W) SPPU VCPU CMPU W × CMPU A B C XX …. .. … TOTAL Weighted Average Contribution Margin (WACMPU) = …. For example; Product Units Weight (W) SPPU VCPU CMPU W × CMPU A B C 100 200 500 100/800=0.125 200/800=0.25 500/800=0.625 10 8 4 6 5 3 1 4×0.125=0.5 3×0.25=0.75 1×0.625=0.625 TOTAL 800 Weighted Average Contribution Margin (WACMPU) =1.875

Contd. Product Units Weight (W) SPPU VCPU CM Ratio W × CM Ratio A B C XX …. .. … TOTAL Weighted Average Contribution Margin Ratio (WACM Ratio) = …. For example; Product Units Weight (W) SPPU VCPU CM Ratio W × CM Ratio A B C 100 200 500 100/800=0.125 200/800=0.25 500/800=0.625 10 8 4 6 5 3 0.400 0.375 0.250 0.4×0.125=0.2065 0.375×0.25=0.094 0.25×0.625=0.175 TOTAL 800 Weighted Average Contribution Margin (WACMPU) =0.4755

Or, 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑀𝑎𝑟𝑔𝑖𝑛 𝑃𝑒𝑟 𝑈𝑛𝑖𝑡 = 𝑇𝑜𝑡𝑎𝑙 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑚𝑎𝑟𝑔𝑖𝑛 𝑇𝑜𝑡𝑎𝑙 𝑠𝑎𝑙𝑒𝑠 𝑢𝑛𝑖𝑡𝑠 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑀𝑎𝑟𝑔𝑖𝑛 Ratio = 𝑇𝑜𝑡𝑎𝑙 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑚𝑎𝑟𝑔𝑖𝑛 𝑇𝑜𝑡𝑎𝑙 𝑠𝑎𝑙𝑒𝑠 𝑟𝑒𝑣𝑒𝑛𝑢𝑒

Example Products A B Sales Rs.90 Rs.140 Variable costs (70) (95) XYZ Company sold 8,000 units of Product A and 2,000 units of Product B during the past year. XYZ Company’s fixed costs are Rs.200,000. Other relevant data are as follows: Sales Rs.90 Rs.140 Variable costs (70) (95) Contribution margin Rs.20 Rs.45 Sales mix 80% 20% Products A B

Sales Mix Consideration Products A B Selling price per unit Rs.90 Rs.140 Variable costs per unit 70 95 Contribution margin Rs.20 Rs.45 Sales mix 80% 20% Weighted average contribution margin Rs.16 Rs.9 Rs.25 Fixed costs, Rs.200,000

Sales Mix Consideration Product A B Contribution margin Rs.16 Rs.9 Rs.25 Break-even Sales Units = 𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑠𝑡𝑠 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑚𝑎𝑟𝑔𝑖𝑛 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 Rs.200,000 Rs.25 = = 8,000 Units

Contd. Rs.25 Product A B Contribution margin Rs.16 Rs.9 A: 8,000 units x Sales Mix (80%) = 6,400 B: 8,000 units x Sales Mix (20%) = 1,600

Explanation Product A Product B Total Break-even point PROOF Sales: 6,400 units x Rs.90 Rs.576,000 0 576,000 1,600 units x Rs.140 0 Rs.224,000 224,000 Total sales Rs.576,000 Rs.224,000 Rs.800,000 Variable costs: 6,400 x Rs.70 Rs.448,000 0 Rs.448,000 1,600 x Rs.95 0 Rs.152,000 Rs.152,000 Total variable costs Rs.448,000 Rs.152,000 Rs.600,000 Contribution margin Rs.128,000 Rs.72,000 Rs.200,000 Fixed costs 200,000 Income from operations Rs.0 Break-even point PROOF

Margin of Safety (MOS) MOS Excess of expected sales over breakeven sales. It is the difference between actual or expected sales and sales at the break-even point. Sales revenue Rs. Current sales revenue Total costs MOS BEP Units

Margin of Safety Ratio Margin Safety Ratio= Actual Sales −Break Even Sales Actual Sales or Total Sales x100 Margin Safety = Rs.2,50,000 −Rs.2,00,000 Rs.2,50,000 x 100 Margin Safety = 20%

Formulae of Cost Volume Profit Analysis 1. Contribution Margin per Unit (CMPU) = Selling Price per unit – Variable cost per unit = Selling Price per unit x PV ratio = Difference in Profit/difference in sales units = Profit/margin of safety units 2. Profit Volume (Contribution margin) Ratio = 1 –CV ratio or = 1- VCPU/SPPU = Difference in Profit/difference in sales revenues = 1- Difference in costs/ difference in sales = Profit/margin of safety rupees 3. Break Even Point (in units) = Fixed cost/CMPU = … units = Fixed cost/PV ratio = ….in Rupees 4. Margin of Safety = Actual Sales – Break Even Sales = Margin of Safety/Actual sales = Profit/CMPU or PV ratio

Contd. 5. Required sales to earn desired profit: Target sales volume to earn profit before tax in rupees = [FC+ before tax target profit]/Contribution margin ratio Target sales volume to earn profit before tax in units = [FC+ before tax target profit]/Contribution margin per unit Target sales volume to earn profit after tax (in rupees) = [FC+{(desired profit after tax) / (1-t)}]/Contribution margin ratio Target sales volume to earn profit after tax (in units) = [FC+{(desired profit after tax) / (1-t)}]/Contribution margin per unit 6. Profit on Sales = Sales – Variable Cost – Fixed Cost = (Sales Rs.  P/V Ratio) – Fixed Cost = (Sales Units  CMPU) – Fixed Cost = Margin of Safety  CMPU 7. Sales to earn equal profit by two alternative =Differences in fixed costs/difference in PV ratio or CMPU

End of the Unit Thank you