Canteen Sandwich Pricing with Discounts, VAT, and Wastage
A school canteen is reviewing the price of its pre-packed sandwiches. The supplier’s list price is €2.40 per sandwich. The canteen receives a 15% trade discount, and a further 5% early-settlement discount is applied to the net amount. VAT is charged at 19% on the discounted price, but the school can recover all VAT. Kitchen checks show that 8% of sandwiches are unsold and discarded. The current selling price is €2.20, and the business manager wants a gross margin of 30% of the selling price. The wastage figure is an estimate and could be anywhere from 6% to 10%. The canteen sells about 180 sandwiches per day. A parent has complained that €2.20 is too high. Before changing the menu, the manager asks for a cost calculation.
1. Calculate the effective cost per saleable sandwich. State clearly the order in which the trade discount, early-settlement discount, VAT recovery, and wastage are applied.
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Apply the trade discount first: €2.40 × 0.85 = €2.04. The early-settlement discount applies to the net amount: €2.04 × 0.95 = €1.938. VAT at 19% is added on the invoice (€1.938 × 1.19 = €2.30622), but because the school recovers VAT, the relevant cost is €1.938. Wastage means only 92% of purchased sandwiches are saleable, so cost per saleable unit = €1.938 / 0.92 = €2.1065, about €2.11. The two discounts are multiplicative, not additive; treating 15% + 5% as 20% would wrongly give €1.92 before wastage.
2. Find the selling price needed for a 30% gross margin on selling price. Is €2.20 acceptable?
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For a margin on selling price, price = cost / (1 − 0.30). Using the unrounded cost: €2.1065 / 0.70 = €3.009, so about €3.01. At €2.20 the margin is (2.20 − 2.1065) / 2.20 = 0.0425, or 4.3%, far below 30%. Even if cost is rounded to €2.11, the margin is (2.20 − 2.11) / 2.20 = 4.1%. So €2.20 is not acceptable if the 30% target is binding; it would need a price near €3.01, or a subsidy or portion change.
3. If wastage falls to 5%, recompute the effective cost and the required price. Comment on the sensitivity of the decision to the wastage estimate.
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Cost per saleable sandwich = €1.938 / 0.95 = €2.040. Required price = €2.040 / 0.70 = €2.914, about €2.91. A 3-percentage-point improvement in wastage lowers the required price by about €0.09–€0.10. The 30% target is sensitive to wastage, so before setting the menu price the manager should measure wastage more precisely or use a pricing rule that is not tied to a single wastage estimate.