Constraint hour, not unit: mix, export order and debottlenecking
Vasudha Speciality Chemicals runs a three-stage continuous plant. Stage B is the constraint: 42,000 machine hours a month after scheduled maintenance. Direct labour and variable overhead are treated as period costs in the company's throughput reporting, and total operating expenses are ₹18.5 crore a month.
| Product X | Product Y | |
|---|---|---|
| Selling price (₹/unit) | 12,000 | 18,000 |
| Material cost (₹/unit) | 4,200 | 7,800 |
| Stage B hours per unit | 1.2 | 2.0 |
| Monthly demand (units) | 30,000 | 25,000 |
Capital of ₹12 crore would release 600 additional Stage B hours a month from month 4, with incremental power and operator costs of ₹1.2 crore a year; the WACC is 12% and the asset life eight years. A new export customer offers ₹14,500 a unit for 5,000 units of variant Z, which needs 1.5 Stage B hours and ₹5,000 of material. Regular customers are on annual contracts with no volume flexibility.
1. Determine the monthly mix that maximises throughput and compute monthly throughput and plant profit. Show why a ranking by contribution per unit gives the wrong answer.
Read the worked answer
Throughput per unit (T) = price − material
X = 12,000 − 4,200 = ₹7,800. Y = 18,000 − 7,800 = ₹10,200.
Throughput per constraint hour
X = 7,800 / 1.2 = ₹6,500. Y = 10,200 / 2.0 = ₹5,100.
Optimal mix. Stage B is a hard ceiling, so every hour must earn the highest throughput it can. Rank by T per Stage B hour: X first.
- X: 30,000 units × 1.2 = 36,000 hours.
- Remaining: 42,000 − 36,000 = 6,000 hours → 3,000 units of Y.
Throughput = 30,000 × 7,800 + 3,000 × 10,200 = ₹23.40 crore + ₹3.06 crore = ₹26.46 crore a month. Plant profit = 26.46 − 18.50 = ₹7.96 crore a month.
Why the per-unit ranking fails. Y has the higher unit throughput (₹10,200 against ₹7,800) and the higher price, so a conventional contribution-per-unit ranking puts Y first. Making Y first means 25,000 × 2.0 = 50,000 hours, which exceeds capacity, so only 21,000 units of Y are made and no X at all: throughput = 21,000 × 10,200 = ₹21.42 crore - ₹5.04 crore a month worse, ₹60 crore a year.
Points to make explicit
- The ₹18.5 crore of operating expenses is irrelevant to the mix; it does not change with the mix, so it cannot change the ranking.
- Labour and variable overhead are not ignored - they sit inside the ₹18.5 crore, and as long as they are genuinely fixed in the short run they do not affect the constrained decision. If overtime or shift premium varies with the mix, it must be added back as a truly variable cost per constraint hour and the ranking re-run.
- The ranking is valid only while Stage B remains the constraint. If the mix shifts so that Stage B is no longer binding, the constraint moves and the analysis restarts.
2. Evaluate the 5,000-unit Z export order. Show the displacement effect of the constraint hours, compute the monthly gain or loss, and derive the minimum acceptable price for this order and for a larger one.
Read the worked answer
Z economics. T = 14,500 − 5,000 = ₹9,500 per unit at 1.5 hours → ₹6,333 per Stage B hour.
Ranking: X ₹6,500 > Z ₹6,333 > Y ₹5,100. Z beats Y but not X, so it should displace Y first and X only where Y's hours run out.
The order needs 5,000 × 1.5 = 7,500 hours. The plant currently runs X 36,000 hours and Y 6,000 hours. Displacement is taken from the bottom of the ranking:
| ₹ crore | |
|---|---|
| Throughput gained on Z (5,000 × 9,500) | 4.750 |
| Throughput lost on Y (3,000 units × 10,200) | (3.060) |
| Throughput lost on X (1,250 units × 7,800) | (0.975) |
| Net monthly gain | 0.715 |
Cross-check by hours: 6,000 hours of Y at ₹5,100 and 1,500 hours of X at ₹6,500 give up ₹4.035 crore; Z earns ₹4.750 crore. Incremental margin ≈ ₹8.6 crore a year.
Accept, subject to: the 5,000 units being genuinely incremental; no contractual penalty for cutting X and Y volumes; Z not becoming a reference price for regular customers; and no incremental fixed cost (dedicated packaging, additional quality testing) that would absorb the ₹71.5 lakh.
Minimum price. The displaced hours average 4.035 crore / 7,500 = ₹5,380 an hour. Z needs 1.5 × 5,380 = ₹8,070 of throughput, so the floor is 5,000 + 8,070 = ₹13,070.
That floor holds only for this order size. Beyond 5,000 units the next hours displaced are X's at ₹6,500, so the marginal floor rises to 5,000 + (1.5 × 6,500) = ₹14,750. Quoting a single floor price for any volume is the classic error: the opportunity cost per constraint hour is a step function, not a constant.
3. Advise the board on the ₹12 crore debottlenecking project. Support your recommendation with a discounted cash flow analysis and set out the conditions you would attach.
Read the worked answer
What the extra hours are worth. 600 hours a month = 7,200 hours a year. The best available use is Y at ₹5,100 per hour: Y demand is 25,000 units against 3,000 currently made, so there is no risk of running out of demand at this scale.
Incremental throughput = 600 × 5,100 = ₹30.6 lakh a month = ₹3.672 crore a year.
| ₹ crore |
|---|
| Incremental throughput p.a. |
| Incremental power and operator cost |
| Net annual cash inflow |
| PV at 12% for 8 years (× 4.968) |
| Capex |
| NPV |
IRR ≈ 12.7%, against a WACC of 12%.
Interpretation. The project clears the hurdle by a fraction of a percentage point. An NPV of ₹28 lakh on ₹12 crore of capital is inside the error bars of any forecast: a 5% capex overrun, a six-month delay, or a 10% shortfall in Y demand turns it negative. The decision is not 'the maths says yes' - the maths says almost.
Conditions I would attach
- Contracted Y volumes covering at least 80% of the incremental output before the purchase order is placed.
- A fixed-price equipment offer; if the supplier will not fix the price, the project fails the test.
- Test cheaper constraint relief first: set-up reduction, smaller batches, debottlenecking of the feeder stages so that Stage B runs without starved hours, and selective overtime at Stage B. Any of these that buys hours at under ₹12 crore/600 hours a month wins by default.
- Re-run the case with the Z order included. If Z is accepted, the marginal hour is worth more than ₹5,100 and the NPV improves materially - the two decisions cannot be evaluated in isolation.
- Check the eight-year life assumption: if the equipment lasts twelve years the NPV roughly doubles, and if the product life is five years it is negative. Match the asset life to the product life, not to the depreciation schedule.
Recommendation. Conditional go. Approve only with contracted demand and a fixed price; otherwise defer and pursue operational relief first.