Analysing the Effect of a Cost-Structure Change on the Break-Even Point

Cost Accounting

Skill: Analyse

Stimulus

Question

(a) Calculate the Break-Even Point (in units) for the Current position.

(b) Analyse the effect of Proposal A and Proposal B on the Break-Even Point, and for each proposal explain the CAUSE of the change.

(c) Proposal B raises fixed cost but lowers variable cost. Explain why its net effect still improves the break-even position.

(d) If sales are expected to be 9,000 units, recommend the best proposal and justify your choice with calculated evidence.

Thinking steps

1. Recall the base formulas: Contribution Margin per unit = Selling Price − Variable Cost, and Break-Even Point (units) = Fixed Cost ÷ Contribution Margin per unit.
2. Compute the current BEP as a benchmark against which to compare both proposals.
3. For each proposal, identify WHICH figure changes (price, variable cost or fixed cost) and recompute the new contribution margin and BEP.
4. Link cause to effect: explain WHY the BEP rises or falls by connecting the change in contribution margin per unit to the number of units needed to cover fixed cost.
5. Compare the net effect: in Proposal B the gain in contribution must be weighed against the rise in fixed cost to see which dominates.
6. Support the decision with quantitative evidence: compute profit and margin of safety at the given sales level to confirm which proposal is best.

Model answer

Formula: Break-Even Point (units) = Fixed Cost ÷ Contribution Margin per unit, where Contribution Margin = Selling Price − Variable Cost.

CURRENT: Contribution margin = RM20 − RM12 = RM8. BEP = RM48,000 ÷ RM8 = 6,000 units.

PROPOSAL A (cut price to RM18): Contribution margin = RM18 − RM12 = RM6. BEP = RM48,000 ÷ RM6 = 8,000 units. EFFECT: BEP RISES by 2,000 units (from 6,000 to 8,000). CAUSE: lowering the selling price shrinks the contribution margin per unit (RM8 → RM6), so each unit covers less of the unchanged fixed cost and the business must sell MORE before breaking even. This proposal WORSENS the position.

PROPOSAL B (automation: fixed cost up to RM55,000, variable cost down to RM10): Contribution margin = RM20 − RM10 = RM10. BEP = RM55,000 ÷ RM10 = 5,500 units. EFFECT: BEP FALLS by 500 units (from 6,000 to 5,500). CAUSE: although fixed cost rises RM7,000, the lower variable cost raises the contribution margin per unit (RM8 → RM10); this rise in contribution more than offsets the higher fixed cost. This proposal IMPROVES the position.

DECISION: Proposal B is better. Supporting evidence (profit at sales of 9,000 units): Current = (9,000 × RM8) − RM48,000 = RM24,000; A = (9,000 × RM6) − RM48,000 = RM6,000; B = (9,000 × RM10) − RM55,000 = RM35,000. B gives the lowest BEP (5,500 units), the highest margin of safety (9,000 − 5,500 = 3,500 units) and the highest profit (RM35,000).