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9706 · 2.2.4

Cost-volume-profit analysis — practice questions

Practice and worked examples for 9706 Cost-volume-profit analysis. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

The following information relates to a single product:

Selling price $25 per unit Variable cost $10 per unit Fixed costs $18 000 per month Budgeted sales 1 500 units

Calculate (a) break-even in units, (b) margin of safety in units and %, (c) units required for $12 000 profit.

Show solution outline

(a) Contribution = $25 − $10 = $15 BEP = $18 000 ÷ $15 = 1 200 units

(b) MoS = 1 500 − 1 200 = 300 units MoS% = (300 ÷ 1 500) × 100 = 20%

(c) Required contribution = $18 000 + $12 000 = $30 000 Units = $30 000 ÷ $15 = 2 000 units

Worked example 2

Using the same data, calculate break-even revenue.

Show solution outline

C/S ratio = $15 ÷ $25 = 0.60 (or 60%)

Break-even revenue = $18 000 ÷ 0.60 = $30 000

Check: $30 000 ÷ $25 = 1 200 units ✓

Worked example 3

A company sells two products, X and Y, in a sales mix of 3:2. Fixed costs are $96,000. Product X: Selling Price $50, Variable Cost $20. Product Y: Selling Price $80, Variable Cost $40. Calculate the number of units of each product that must be sold to break even.

Show solution outline

Step 1: Calculate contribution per unit for each product. Product X Contribution = $50 - $20 = $30 Product Y Contribution = $80 - $40 = $40

Step 2: Calculate the weighted average contribution per unit. The sales mix is 3:2, meaning for every 5 units sold, 3 are X and 2 are Y. Sales mix ratio for X = 3/5 = 0.6 Sales mix ratio for Y = 2/5 = 0.4 Weighted Average Contribution = ($30×0.6)+($40×0.4\text{\textdollar}30 \times 0.6) + (\text{\textdollar}40 \times 0.4) = $18 + $16 = $34

Step 3: Calculate the total break-even point in units (of the mix). Total BEP (units) = Total Fixed Costs / Weighted Average Contribution Total BEP (units) = $96,000 / $34 ≈ 2,823.53 units. We round up to 2,824 units as we cannot sell a fraction of a unit to fully cover costs.

Step 4: Apportion the total units to each product based on the sales mix. Units of Product X = 2,824 ×(3/5)=1\times (3/5) = 1,694.4 ≈ 1,695 units Units of Product Y = 2,824 ×(2/5)=1\times (2/5) = 1,129.6 ≈ 1,130 units

(Note: Rounding up is standard practice to ensure fixed costs are fully covered. Selling 1694 units of X and 1129 units of Y would result in a small loss.)

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