Two Promotional Schemes and a Price Ceiling
A wholesaler buys a kitchen appliance at ₹200 per unit and incurs fixed monthly costs of ₹24,000 - rent, salaries and utilities - that do not vary with the number of units sold. For the coming month the wholesaler expects to sell 500 units and must choose one of two promotional schemes. Scheme A: mark the unit price up by 60 per cent over cost, then offer a 20 per cent discount on the marked price. Scheme B: mark up by 40 per cent, offer a 5 per cent discount on the marked price, and give away a free accessory with every unit sold; the accessory costs the wholesaler ₹18 and has no resale value to the customer. A competitor sells a comparable appliance at ₹250 per unit, and the wholesaler has promised not to price above that level. The sales team prefers Scheme B because its marked price looks lower, and argues that the free accessory will build goodwill at little cost.
1. Compute the per-unit profit and the monthly profit for each scheme at the expected volume of 500 units, and identify which scheme the wholesaler should choose.
Read the worked answer
Scheme A: marked price = 200 × 1.60 = ₹320. Selling price after the 20 per cent discount = 320 × 0.80 = ₹256. Profit per unit = 256 − 200 = ₹56. Total contribution = 500 × 56 = ₹28,000. Monthly profit after fixed costs = 28,000 − 24,000 = ₹4,000.
Scheme B: marked price = 200 × 1.40 = ₹280. Selling price after the 5 per cent discount = 280 × 0.95 = ₹266. The free accessory costs ₹18, which must be deducted before profit is measured: 266 − 18 = ₹248 realised per unit. Profit per unit = 248 − 200 = ₹48. Total contribution = 500 × 48 = ₹24,000. Monthly profit = 24,000 − 24,000 = ₹0.
Scheme A is better by ₹8 per unit, or ₹4,000 for the month. The sales team's reasoning is the trap here: a lower marked price and a "free" gift feel attractive, but the gift is a real cost, and Scheme B exactly breaks even at the expected volume. Scheme A leaves a cushion for any shortfall in sales.
2. The manager insists the selling price must not exceed the competitor's ₹250 and wants at least ₹30 profit per unit. What discount range in each scheme satisfies both conditions?
Read the worked answer
Scheme A: profit of ₹30 means a selling price of ₹230 (200 + 30). Against a marked price of ₹320, that is a discount of (320 − 230)/320 = 28.125 per cent. The ceiling of ₹250 implies a discount of (320 − 250)/320 = 21.875 per cent. So Scheme A works anywhere between 21.875 per cent and 28.125 per cent discount - a usable band of 6.25 percentage points.
Scheme B: profit of ₹30 requires 200 + 18 + 30 = ₹248 as the selling price, since the accessory must be paid for. Against a marked price of ₹280, that is a discount of (280 − 248)/280 = 11.43 per cent. At the ₹250 ceiling the discount is (280 − 250)/280 = 10.71 per cent, giving a profit of 250 − 18 − 200 = ₹32.
So Scheme B satisfies both conditions only within 10.71 to 11.43 per cent - a band of less than one percentage point. Both schemes are workable, but Scheme A gives the manager far more room to adjust without breaking either constraint.
3. At what sales volume does each scheme break even, and what does the comparison mean for the risk the wholesaler is carrying?
Read the worked answer
Break-even volume = fixed costs ÷ profit per unit.
Scheme A: 24,000 ÷ 56 = 428.57, so 429 units. Scheme B: 24,000 ÷ 48 = 500 units.
The expected volume is exactly 500 units. Scheme B therefore breaks even only if the forecast is met in full; a single unit less and the month is loss-making. Scheme A breaks even at 429 units, roughly 14 per cent below forecast, so it absorbs a meaningful shortfall before losses begin. In risk terms, Scheme A has a margin of safety of about 71 units, while Scheme B has none.
The comparison also matters because the forecast is a single point estimate. If sales land at 450 units, Scheme A earns 450 × 56 − 24,000 = ₹1,200, while Scheme B loses 450 × 48 − 24,000 = ₹2,400. Unless the accessory demonstrably raises volume above 500 units - and nothing in the brief shows that - Scheme B is the riskier choice for an identical product.