Choosing Between a Price Cut, an Export Order and a Cheaper Input
A packaging unit in Guntur prints cartons. Monthly fixed costs are ₹48,000, variable cost is ₹35 per carton, and the selling price is ₹75. Current sales are 2,000 cartons a month, and the plant can produce at most 3,000 cartons a month; anything beyond that would need a second shift, which the owner has ruled out. The owner is considering three proposals. P: cut the price by 10%, which the sales team expects to raise volume by 25%. Q: accept a one-year export order of 1,200 cartons a month at ₹56 per carton, with no effect on existing domestic sales; the plant can supply only up to its spare capacity. R: switch to a cheaper board that lowers variable cost by ₹5 per carton but adds ₹6,000 a month to fixed costs, with volume unchanged at 2,000. The owner wants the highest monthly profit and will not accept any plan that lowers current profit.
1. Compute the monthly profit under the current operation and under each of P, Q and R, then rank them.
Read the worked answer
Current contribution per carton = 75 − 35 = ₹40.
| Plan | Contribution per carton | Volume | Total contribution | Fixed cost | Profit |
|---|---|---|---|---|---|
| Current | ₹40 | 2,000 | ₹80,000 | ₹48,000 | ₹32,000 |
| P | ₹32.50 (67.50 − 35) | 2,500 | ₹81,250 | ₹48,000 | ₹33,250 |
| Q | ₹21 (56 − 35) | 2,000 + 1,000 (capacity, not 1,200) | ₹80,000 + ₹21,000 | ₹48,000 | ₹53,000 |
| R | ₹45 (75 − 30) | 2,000 | ₹90,000 | ₹54,000 | ₹36,000 |
Ranking: Q (₹53,000) > R (₹36,000) > P (₹33,250) > current (₹32,000).
The two traps are (a) taking Q's 1,200 units at face value - spare capacity is only 1,000, so the order must be trimmed; and (b) assuming a 10% price cut is aggressive. It is the weakest option here because the contribution falls to ₹32.50 while volume rises only 25%.
2. The export buyer can commit to only a small trial quantity in the first month. At what trial quantity does Q stop beating R?
Read the worked answer
Keep the domestic business fixed: it earns ₹32,000 either way, so the comparison reduces to the incremental profit each plan adds.
- Plan R adds ₹4,000 over the current position (₹36,000 − ₹32,000).
- Each export carton in plan Q adds ₹21 (₹56 − ₹35), since fixed costs do not change.
Q is better than R when 21n > 4,000, i.e. n > 190.48. Since cartons are whole units, the trial must be at least 191 cartons.
Sanity check: 190 × 21 = ₹3,990, so total profit would be ₹35,990 - ₹10 below R. At 191 units the total is ₹36,011, just ahead.
Two qualifications matter for the decision. First, R's ₹4,000 gain assumes the cheaper board does not raise rejection rates; a defect rate above roughly 2% would erase it. Second, the comparison treats R and Q as mutually exclusive, which they are not - the unit could switch board and take a trial order, in which case each export carton adds ₹26 and the cut-off falls to 154 units.
3. How much can the sales team's 25% volume forecast for P be wrong before P becomes no better than doing nothing?
Read the worked answer
Under P the price is ₹67.50, so contribution is ₹32.50 per carton. To match the current profit of ₹32,000:
32.50 × v − 48,000 ≥ 32,000 32.50v ≥ 80,000 v ≥ 2,461.54, so 2,462 cartons.
The forecast is 2,500 cartons (2,000 × 1.25). The safety margin is therefore only 2,500 − 2,462 = 38 cartons, about 1.5% of forecast volume. Put differently, volume growth of 23.1% is enough to break even against today, not the 25% claimed.
That margin is far too thin to act on. A price cut also invites the domestic buyers to expect the lower price permanently, while 2,462 cartons still sit below the 3,000-carton ceiling - so P does not even use the plant's spare capacity. The honest conclusion is that P is nearly profit-neutral whatever the forecast error, and the owner should not spend managerial effort or price reputation on a plan whose best case adds ₹1,250 a month.