Sundaram Precision Components - Production Plan Under a Machine-Hour Constraint
Sundaram Precision Components runs a single machining cell with 24,000 machine hours available next quarter; no extra hours can be obtained without leasing a second machine. Three products are made, and demand at current prices is capped:
Product P: price ₹480, variable cost ₹300, 3.0 machine hours, maximum 4,000 units. Product Q: price ₹360, variable cost ₹240, 1.5 machine hours, maximum 6,000 units. Product R: price ₹900, variable cost ₹630, 5.0 machine hours, maximum 1,500 units.
Fixed costs of ₹9,00,000 are incurred each quarter and do not change with the mix. The plant manager has always scheduled production in proportion to planned sales value, and quarterly profit has hovered around ₹6.5 lakh. At the sales conference next week the sales team intends to push Product R, arguing that it carries the highest unit contribution and the highest price. The finance director wants a defensible production plan and a break-even figure to put in front of them.
1. Rank the three products and determine the optimal production plan and quarterly profit. Explain why unit contribution is a misleading ranking measure here.
Read the worked answer
Rank on contribution per machine hour, the scarce resource:
| Product | Contribution per unit | Hours per unit | Contribution per hour | Rank |
|---|---|---|---|---|
| Q | ₹120 | 1.5 | ₹80.00 | 1 |
| P | ₹180 | 3.0 | ₹60.00 | 2 |
| R | ₹270 | 5.0 | ₹54.00 | 3 |
Optimal plan:
- Q: 6,000 units use 9,000 hours, contribution ₹7,20,000.
- P: 4,000 units use 12,000 hours, contribution ₹7,20,000.
- Balance 3,000 hours ÷ 5 = 600 units of R, contribution ₹1,62,000.
Total contribution ₹16,02,000 − fixed cost ₹9,00,000 = profit ₹7,02,000.
Why unit contribution misleads: R earns the most per unit (₹270) but consumes five scarce hours. Each hour given to R earns ₹54; the same hour given to Q earns ₹80. Ranking by unit contribution, or by sales value as the plant manager does, would fill the cell with R (1,500 units = 7,500 hours) and leave only 16,500 hours for Q and P, sacrificing contribution. The correct test is contribution per unit of the limiting factor. Note also that the current practice produces a profit near ₹6.5 lakh, so the re-planning is worth roughly ₹50,000 a quarter before any capital is spent.
2. A lease of a second machine would add 2,000 machine hours for ₹1,20,000 for the quarter. Evaluate the proposal.
Read the worked answer
Identify the best use of the extra hours. Under the recommended plan, Q and P demand are fully satisfied; the only unsatisfied demand is 900 units of R, requiring 4,500 hours. With 2,000 hours the company can produce 400 units of R (2,000 ÷ 5), each earning ₹54 of contribution per hour.
Additional contribution = 2,000 hours × ₹54 = ₹1,08,000. Lease cost = ₹1,20,000. Net effect = −₹12,000 → reject.
The lease is worth taking only if it costs less than ₹1,08,000, i.e. below ₹54 per hour of added capacity.
Two checks before closing the file:
- Demand check: Q and P are already at their demand caps, so no higher-ranked product can absorb the hours.
- Term check: if the lease is for twelve months but only this quarter has been evaluated, the decision should be made on the full term. Future growth in Q demand (₹80 per hour) could justify the lease even though this quarter does not.
Reject now, but keep the quote on file: it becomes viable at a rental of ₹54 per hour or below, or if Q's demand grows by about 1,500 units.
3. Compute the break-even sales value and margin of safety for the recommended plan, and state the main caveat that must accompany the break-even figure.
Read the worked answer
Sales value of the recommended plan:
- Q: 6,000 × ₹360 = ₹21,60,000
- P: 4,000 × ₹480 = ₹19,20,000
- R: 600 × ₹900 = ₹5,40,000
- Total = ₹46,20,000
Contribution ₹16,02,000 ÷ sales ₹46,20,000 = C/S ratio 34.68%.
Break-even sales = ₹9,00,000 ÷ 0.3468 = ₹25,95,529. Margin of safety = ₹46,20,000 − ₹25,95,529 = ₹20,24,471, i.e. 43.8% of planned sales. Sales could fall by almost 44% at this mix before the quarter made a loss.
Caveat: in a multi-product firm the break-even point is not a single number - it moves with the mix. ₹25,95,529 is valid only while the 6,000:4,000:600 mix holds. If customers shift towards R (₹54 per hour) and away from Q (₹80 per hour), the rupee break-even rises even though sales value looks healthier. Present it as "break-even at the planned mix" and add one sensitivity line showing break-even if the sales team's preferred R-heavy mix were adopted - the figure the conference should actually see.