Cost-Volume-Profit Analysis

Cost-Volume-Profit Analysis

Syllabus tag: KASNEB CPA | Intermediate Level | CA25 Management Accounting | Topic 4 Cost-Volume-Profit Analysis

Lesson objectives

By the end of this topic, you will be able to:

• Compute contribution per unit and the contribution to sales ratio
• Compute the break-even point in units and in sales value
• Compute the volume needed for a target profit
• Compute and interpret the margin of safety
• Compute operating gearing and explain what it says about risk
• State the assumptions on which all of this rests

Why this matters

Cost Classification separated fixed from variable. This topic uses that split to answer the question every manager asks: how much must we sell before we stop losing money?

One company throughout

Chui Manufacturers: selling price KES 400 per unit, variable cost KES 240 per unit, fixed costs KES 4,800,000 a year. Current sales are 50,000 units.

Words to know

• Contribution — selling price less variable cost. What each unit contributes towards fixed costs and then towards profit.
• C/S ratio — contribution as a percentage of selling price.
• Break-even point — the volume at which profit is exactly nil.
• Margin of safety — how far sales can fall before reaching break-even.
• Operating gearing — how sensitive profit is to a change in sales.

Contribution

Contribution per unit = Selling price − Variable cost

= 400 − 240 = KES 160

C/S ratio = 160 / 400 = 40%

Contribution is not profit. It is what is left after variable costs and before fixed costs. Until fixed costs are covered, every shilling of contribution is reducing a loss rather than creating a profit.

Break-even point

BEP in units = Fixed costs / Contribution per unit

= 4,800,000 / 160 = 30,000 units

BEP in sales value = Fixed costs / C/S ratio

= 4,800,000 / 0.40 = KES 12,000,000

which is the same thing: 30,000 units at 400 each.

Target profit

Units = (Fixed costs + Target profit) / Contribution per unit

For a target profit of KES 2,400,000:

= (4,800,000 + 2,400,000) / 160 = 45,000 units

The target profit simply joins the fixed costs. Nothing else changes, because each unit still contributes the same 160.

Margin of safety

Margin of safety = Current sales − Break-even sales

= 50,000 − 30,000 = 20,000 units, or 20,000 / 50,000 = 40%

Sales could fall by 40% before the company reaches break-even. A margin of safety of 5% and one of 40% describe very different businesses, even where both are currently profitable.

Profit at current volume = (50,000 × 160) − 4,800,000 = KES 3,200,000

:::checkpoint Two companies both earn a profit of KES 3,200,000. One has a margin of safety of 40%, the other 6%. Both face a recession in which industry sales fall 15%. Describe what happens to each, and say which board should be more worried. :::

Operating gearing

Operating gearing = Contribution / Profit

= 8,000,000 / 3,200,000 = 2.5 times

This says a 1% change in sales produces a 2.5% change in profit. High operating gearing comes from a cost structure heavy in fixed costs: profits rise sharply when volume grows and collapse just as sharply when it falls.

A company choosing to automate is choosing higher operating gearing — and choosing to be more fragile in a downturn.

The assumptions

CVP is a straight-line model of a world that is not straight. It assumes:

• Selling price stays constant however much is sold
• Variable cost per unit stays constant at every volume
• Fixed costs stay fixed across the whole range considered
• The sales mix does not change
• Everything produced is sold, so inventory does not move

In practice, selling more usually means discounting, and buying more usually means bulk discounts. Neither is captured. CVP is a good approximation within the relevant range and an unreliable one outside it.

:::checkpoint A manager uses CVP to argue that selling 300,000 units would produce a profit of KES 43,200,000, ten times the current level. Name two assumptions that are almost certainly broken at that volume. :::