The Tuck Shop Order: Discount, Breakage and Break-Even
Neo runs the tuck shop at a junior secondary school in Palapye. She buys exercise books in sealed packs of 24 for P18.60 per pack and sells them singly at P1.25. Her supplier charges a flat P120 delivery fee on every order, whatever its size, and offers 5% off the pack price when a single order reaches 60 packs or more.
Experience shows that about 4 in every 100 books arrive damaged or get spoiled on the shelf and cannot be sold. Neo expects to sell roughly 900 books next term and has nowhere to store a large surplus.
She is deciding between ordering 40 packs now and ordering 60 packs to claim the discount. Last term she ordered 40 packs, paid the delivery fee, sold out in week six and turned away customers, so she is tempted by the bigger order - but the school bursar has warned her that the tuck shop account must not make a loss.
1. For an order of 40 packs, calculate the total cost, the number of books Neo can actually sell, her revenue if every sellable book is sold at P1.25, and her percentage profit on total cost (to 1 decimal place).
Read the worked answer
Costs. 40 packs × 24 = 960 books. Goods: 40 × P18.60 = P744.00. Add the delivery fee of P120.00 (it is charged per order, not per pack): total cost = P864.00.
Sellable books. 4% are lost: 960 × 0.04 = 38.4, so about 39 books are spoilt. 960 × 0.96 = 921.6, and Neo cannot sell two-thirds of a book, so she can sell 921 books.
Revenue and profit. 921 × P1.25 = P1,151.25. Profit = 1151.25 − 864.00 = P287.25.
Percentage profit. 287.25 ÷ 864.00 × 100 = 33.2% (1 d.p.).
Judgement point. A candidate who divides by P744 gets 54.9% and overstates the business by more than twenty percentage points: the delivery fee is 16% of the goods cost and must be carried by the same 921 books. The breakage rate matters too - pricing as if all 960 books sell would overstate profit by 39 × P1.25 = P48.75.
2. Calculate the number of books Neo must sell to cover the full cost of a 60-pack order, and use that figure, together with her expected sales, to advise her on which order to place.
Read the worked answer
Cost of 60 packs. 60 × P18.60 = P1,116.00. The 5% discount applies to the pack price: 1116 × 0.95 = P1,060.20. Add delivery: 1060.20 + 120 = P1,180.20.
Break-even sales. 1180.20 ÷ 1.25 = 944.16, so she must sell 945 books (944 books raise P1,180.00, which is P0.20 short).
Compare with demand. Expected sales are about 900, which is 45 books below break-even. At 900 sales the revenue is 900 × 1.25 = P1,125.00, giving a loss of P55.20 - a direct breach of the bursar's rule - and leaves about 1,382 − 900 = 482 books in stock (the order yields 1440 × 0.96 = 1,382 sellable books).
Is the discount worth it? The discount saves only 1,116 × 0.05 = P55.80, while committing an extra P255.00 of stock (20 extra packs at the discounted price) that has no proven buyer.
Advice. Place the 40-pack order. The 60-pack order only makes sense if Neo has a firm second buyer (another school, a stationery retailer) for at least 945 books, or secure storage and confirmed demand next term. Optimism about last term's sell-out is not evidence that demand reaches 945.
3. Neo decides to keep the 40-pack order. What is the largest percentage discount she can offer on the P1.25 selling price and still make a 20% profit on total cost?
Read the worked answer
Target revenue. Total cost is P864.00. A 20% profit means revenue = 864 × 1.20 = P1,036.80.
Price per book. She can sell 921 books, so the price must be at least 1036.80 ÷ 921 = P1.1257 per book.
Discount. The reduction from P1.25 is 1.25 − 1.1257 = P0.1243, so the maximum discount is 0.1243 ÷ 1.25 = 0.0994, i.e. 9.9%.
Judgement. Rounded to a shop-friendly figure, a 9% discount (price P1.1375, revenue P1,047.64, profit P183.64 = 21.3%) is safe. A round 10% discount gives P1.125 per book, revenue of P1,036.13 and a profit of P172.13 - 19.9%, just below the target. Advertising "10% off" and then discovering the target is missed is exactly the kind of rounding trap this question tests; the discount must be rounded down, not to the nearest whole percent.