COST-VOLUME-PROFIT ANALYSIS: D8 • • • • • Key ratios/formulae: Breakeven Units = FC/Contribution per unit Breakeven Value Target Profit (F and V) Profit/Volume Ratio % Margin of Safety • • • • • • • Key assumptions: All other variables remain constant Single product or constant sales mix TC & TR are linear functions of output Profits calculated on a VC basis Analysis applied to relevant range only Costs can be accurately divided in F and V elements S/T horizon only The relevant range of activity Accountant’s fixed cost function 1. Within the short term the firm anticipates that it will operate between output levels Q2 and Q3 and commits itself to fixed costs of 0A. 2. Costs are fixed in the short term, but can be changed in the longer term. CVP analysis: non-graphical computations Example 8.1 Fixed costs per annum R60 000 Unit selling price R20 Unit variable cost R10 Relevant range 4 000 - 12 000 tickets 1. Break-even point Net profit = Total revenue – total costs NP = px – (a + bx) BEP 0 = or 1. Break-even point = Fixed costs Contribution per unit = or 1. What if units unknown? R60 000/R10 = 6 000 units CVP analysis: non-graphical computations cont If unit fixed costs and revenues are not given, the breakeven point (expressed in sales values) can be calculated as follows: Total fixed costs x Total sales Total contribution Profit volume ratio = Contribution x 100 Sales revenue Percentage margin of safety = Expected sales - Break-even sales Expected sales CVP analysis: non-graphical computations cont 2a. Units to be sold to obtain a R30 000 profit: Fixed costs + desired profit = R90 000/R10 = 9 000 units Contribution per unit 2b. Units to be sold to obtain a profit = 20% of sales Fixed costs_______________ = R60 000/R6 = 10 000 units Contribution per unit – desired profit CVP analysis: non-graphical computations cont 3. NP if 8000 tickets are sold Breakeven = Incremental units = x contribution per unit = 6000 units Proof: R20 x 8000 units – (R10 x 8000 units + R60K) What if a further 1000 units are sold? CVP analysis: non-graphical computations cont 4. SP to get NP of R30K on x = 8000 units R30K = 8000P – (R10 x 8000+ R60K) 5. Advertising increases by R8K, what increase in sales volume is required? Other key ratios/formulae: Percentage margin of safety = Expected sales - Break-even sales Expected sales How far above BE am I? Interpretation? The Profit-Volume Ratio FC / Contribution per unit = What proportion of sales = contribution If sales increases by R10K, R20K from BE how much will NP change? R60K x = R60K = R70K x = R60K = R80K x = R60K = R200K x = R60K = The variable cost ratio What proportion of sales = variable costs Sensitivity analysis Assume directors unhappy with forecast performance. Two alternatives proposed: (a) Reduce selling price by 10% Increase advertising by R2 000 Sales tickets expected to increase to 9000 from 7000 (b) No change to selling price Increase advertising by R2 000 Offer ticket agents a 5% commission per ticket sold Sales tickets expected to increase to 10000 from 7000 • For each alternative, calculate net profit, break-even point and MOS %. Break-even chart for 8.1 Contribution chart for 8.1 Profit volume graph for 8.1 Multi-product breakeven analysis Example Unit contribution Product D R150 Product S R90 Budgeted sales mix 2/3 1/3 Actual sales mix 1/2 1/2 Fixed costs are R117 000 + 39 000 = R156 000 Budgeted BEP = R156 000 /R130 (a) = 1 200 units Actual BEP = R156 000 /R120 (b) = 1 300 units a: (2/3xR150)+(1/3xR90) = R130 b: (1/2xR150)+(1/2%x90) = R120 Multi-product breakeven D S Sales/unit R300 R200 Less: VC/unit R150 R110 = Contribution/unit R150 R90 Specific FC R90K R27K = Product breakeven 600 units 300 units If we sell exactly these units, our loss = Any units sold above product breakeven, offset the loss incurred by common (unavoidable FC) Having sold 600 D and 600 S, our loss = R12K In a sales mix, BEP is a unique number. If the mix changes, the BEP changes!