Two Storage Offers for 8,000 Bags of Paddy
A co-operative marketing society holds 8,000 bags of paddy (50 kg each) and must keep them in a hired godown for a period that is still uncertain - the mill has indicated anything between three and five months. Two offers are on the table.
Offer A (public warehouse tariff): ₹27 per bag per quarter, or part of a quarter, payable in advance. No other charge; the society supplies its own dunnage.
Offer B (private warehouse): ₹8 per bag per month, billed for the exact number of months, plus a one-time charge of ₹40,000 for dunnage and initial disinfection.
The society's accountant has already entered Offer A in the books on the principle that 'a quarterly rate always beats a monthly rate'. The financing bank insists only that the stock be held in a licensed warehouse and has no preference between the two. Neither offer includes insurance; the society's own policy covers the stock at either site. Nothing in either offer changes with volume.
1. Compute the total cost under both offers for a storage period of exactly 3 months and exactly 4 months, and say which offer should be chosen in each case.
Read the worked answer
Offer A is charged per bag per quarter with any part quarter counted as a full quarter.
- 3 months = 1 quarter: 8,000 × ₹27 = ₹2,16,000
- 4 months = 2 quarters: 8,000 × ₹54 = ₹4,32,000
Offer B is ₹8 per bag-month plus ₹40,000 once.
- 3 months: (8,000 × 8 × 3) + 40,000 = 1,92,000 + 40,000 = ₹2,32,000
- 4 months: (8,000 × 8 × 4) + 40,000 = 2,56,000 + 40,000 = ₹2,96,000
Decision:
- At 3 months, A is cheaper by ₹2,32,000 − ₹2,16,000 = ₹16,000.
- At 4 months, B is cheaper by ₹4,32,000 − ₹2,96,000 = ₹1,36,000.
The single extra month costs ₹2,16,000 under A but only ₹64,000 under B. That ₹1.52 lakh gap is not a price difference in any normal sense - it is the part-quarter rule working exactly as written. Any decision therefore hinges on the storage period, which is precisely the item the mill has left uncertain.
2. Month by month, for which storage durations does Offer A actually cost less? Generalise what the part-quarter rule does to the comparison.
Read the worked answer
Monthly totals (A is charged for whole quarters):
| Months | Offer A | Offer B | Cheaper |
|---|---|---|---|
| 1 | 2,16,000 | 1,04,000 | B |
| 2 | 2,16,000 | 1,68,000 | B |
| 3 | 2,16,000 | 2,32,000 | A |
| 4 | 4,32,000 | 2,96,000 | B |
| 5 | 4,32,000 | 3,60,000 | B |
| 6 | 4,32,000 | 4,24,000 | B |
| 7–9 | 6,48,000 | 4.88–6.16 lakh | B |
| 10–12 | 8,64,000 | up to 8,08,000 | B |
Offer A wins only at exactly 3 months, and only by ₹16,000 - under 7% of the difference that appears one month later.
Generalisation: A's cost is a step function that jumps by one full quarter on day 1 of months 4, 7 and 10, while B's cost rises smoothly by ₹64,000 a month. The two cross wherever a quarter boundary is just being reached. So the accountant's maxim is not wrong in direction - ₹27 per quarter is cheaper than ₹24 per quarter equivalent - but it is dominated in practice by the ₹40,000 fixed charge at short durations and by the step jump at every part-quarter.
The defensible instruction to the mill is: contract for a fixed 3-month term under A and extend only by a fresh negotiation, never by drifting into month 4.
3. The bank releases finance for only 5,000 bags. Recompute at 3 and at 4 months, and find the volume at which each offer breaks even at each duration.
Read the worked answer
At 5,000 bags:
- 3 months - A: 5,000 × 27 = ₹1,35,000; B: (5,000 × 8 × 3) + 40,000 = 1,20,000 + 40,000 = ₹1,60,000 → A cheaper by ₹25,000.
- 4 months - A: 5,000 × 54 = ₹2,70,000; B: (5,000 × 8 × 4) + 40,000 = 1,60,000 + 40,000 = ₹2,00,000 → B cheaper by ₹70,000.
The ranking at these two durations is unchanged, but the margin at 3 months widens, because the ₹40,000 fixed charge is now spread over fewer bags.
Break-even volumes (let n = number of bags):
- 3 months: 27n = 24n + 40,000 → 3n = 40,000 → n ≈ 13,333 bags. A is cheaper for any volume below about 13,300 bags.
- 4 months: 54n = 32n + 40,000 → 22n = 40,000 → n ≈ 1,818 bags. A is cheaper only for volumes below about 1,800 bags.
The lesson is that the part-quarter step dominates volume. At 4 months the per-bag penalty under A is ₹22, so even a small consignment crosses over quickly; at 3 months the only thing separating the offers is B's fixed charge, so volume decides. A single 'rate per bag' comparison, without the duration and the fixed charge, cannot answer the question.