Grain, Spoilage and a Trainee's Shortcut
A trader buys 240 kg of grain at ₹42 per kg and pays a single freight charge of ₹1,008 for the consignment. On arrival 4% of the purchased weight has spoiled and cannot be sold; the remainder is sold loose, priced per kg. The trader fixes the selling price before the consignment is sold and wants the price to guarantee a stated return on everything he has spent, including freight. He also wants a floor figure, so that he knows at a glance when a quoted price would leave him at a loss. A trainee, asked for a quick estimate, offers: 'Take ₹42, add 20% profit and then 4% for the spoilage - about ₹52.42 per kg will do it.'
1. Compute the selling price per kg that gives exactly 20% profit on total cost, and compute the break-even price per kg.
Read the worked answer
Total outlay = purchase + freight = (240 × 42) + 1,008 = 10,080 + 1,008 = ₹11,088.
Sellable weight = 240 × 0.96 = 230.4 kg. Spoilage reduces the weight that carries the freight, which is why the cost per sellable kg is not ₹42 but 11,088 ÷ 230.4 = ₹48.125.
For 20% profit: required revenue = 11,088 × 1.20 = ₹13,305.60.
Price = 13,305.60 ÷ 230.4 = ₹57.75 per kg (check: 230.4 × 57.75 = 13,305.60).
The break-even price is exactly the cost per sellable kg: ₹48.125, i.e. about ₹48.13. Below that figure every kilogram sold deepens the loss; the 20%-profit price sits ₹9.625 above the floor.
2. The trainee's ₹52.42 is not the right answer. Identify each distinct error and state what his price actually delivers.
Read the worked answer
Two separate errors, plus one omission.
- Spoilage is treated as a markup instead of a divisor. Multiplying by 1.04 assumes 104 kg are sold for every 100 kg bought. In fact only 96 kg are sold, so cost per sellable kg must be divided by 0.96, not multiplied by 1.04. The two give 43.75 vs 43.68 per kg - close, but systematically wrong in the same direction every time it is used.
- Freight is ignored. ₹1,008 over 230.4 sellable kg adds ₹4.375 per kg, about 9% of the purchase price - larger than the spoilage adjustment he did make.
- The order of operations is also wrong: profit must be calculated on total cost including freight, applied after the weight has been reduced.
What his price delivers: revenue = 230.4 × 52.42 = ₹12,077.57; profit = 12,077.57 − 11,088 = ₹989.57, i.e. about 8.9% on cost - less than half the 20% he believes he has built in.
3. A colleague says the target should be 'a price that makes the profit percentage equal the spoilage percentage'. What price satisfies that, and why is the target a bad decision rule?
Read the worked answer
Equal percentages means a return of 4% on outlay: revenue = 11,088 × 1.04 = ₹11,531.52; price = 11,531.52 ÷ 230.4 = ₹50.05 per kg.
The arithmetic is fine; the rule is not. Tying the required return to a physical loss figure makes the price drift with an accident of handling rather than with the trader's cost of capital or the market. A batch with 10% spoilage would demand a higher price exactly when the produce is worse and buyers will pay less, and a batch with zero spoilage would demand almost nothing above the floor. Spoilage belongs in the cost base - it already pushes the break-even from ₹42 to ₹48.125 - not in the margin target. The margin should be set by the return the business needs, and then the price checked against what the market will bear.