The numbers. Current: contribution = 25−15 = 10;break−even=80,000 ÷ 10=8,000units;marginofsafety=10,000−8,000=2,000units;profit=(10 × 10,000) − 80,000=∗∗20,000**. After the price cut: contribution = 22−15 = 7;break−even=80,000 ÷ 7=11,429units(roundedup);marginofsafetyattheforecast14,000=14,000−11,429=2,571units;profit=(7 × 14,000) − 80,000=98,000 − 80,000=∗∗18,000**.
Analysis. The price cut is a trade-off. It raises the break-even point sharply (8,000 → 11,429 units) because each unit now contributes only 7insteadof10, so the retailer must sell far more just to avoid a loss. On the forecast of 14,000 units, profit actually falls by 2,000(from20,000 to 18,000)—theextra4,000unitsofsalesdonotfullyoffsetthe3 lost contribution on every unit. The margin of safety does improve slightly in absolute units (2,000 → 2,571), but as a proportion of a much larger required output the position is riskier.
Evaluation and judgement. On these figures the retailer should not cut the price: it lowers profit and lifts break-even, increasing risk. The cut would only be worthwhile if sales rose even further than forecast — profit would match the current $20,000 only at (80,000 + 20,000) ÷ 7 ≈ 14,286 units, and beat it beyond that. Crucially, the whole case depends on the forecast of 14,000 units, which break-even simply assumes will be achieved; if demand is less price-elastic than hoped, the retailer ends up with lower price, lower contribution AND lower volume. Recommendation: keep the current price unless there is robust evidence (e.g. reliable market research) that demand will exceed ~14,300 units; break-even usefully quantifies the risk here but its reliance on an unproven sales forecast and constant costs means it should support, not dictate, the pricing decision.