Special order with a binding machine-hour constraint
Kalahari Components (Pty) Ltd makes two components, Alpha and Beta, using the same milling machine. Monthly capacity is 10,000 machine hours. Budgeted data for the coming month: Alpha sells for R180, with variable material R60, variable labour R30, variable overhead R20, and 2 machine hours per unit; demand is 2,500 units. Beta sells for R240, with variable material R70, variable labour R40, variable overhead R30, and 3 machine hours per unit; demand is 2,000 units. Total fixed manufacturing overhead is R420,000 per month and is absorbed on machine hours. A new customer offers a one-off order for 800 units of a modified Alpha (Alpha-X) at R150 each. Alpha-X requires 3 machine hours per unit, variable material R50, variable labour R30, variable overhead R20, and a special mould costing R45,000 with no other use. The sales director wants to accept because the price exceeds the absorption cost of Alpha. The production manager says capacity is already tight.
1. Calculate the contribution per machine hour for Alpha and Beta and determine the optimal product mix and total contribution for the coming month, before considering the special order.
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Contribution per unit and per machine hour:
| Alpha | Beta | |
|---|---|---|
| Selling price | 180 | 240 |
| Variable costs | 60 + 30 + 20 = 110 | 70 + 40 + 30 = 140 |
| Contribution per unit | 70 | 100 |
| Machine hours per unit | 2 | 3 |
| Contribution per machine hour | 35.00 | 33.33 |
| Monthly demand | 2,500 units | 2,000 units |
| Hours needed for full demand | 5,000 | 6,000 |
Alpha earns the higher contribution per constrained machine hour, so rank Alpha first. Produce 2,500 Alpha (5,000 hours). Remaining capacity = 5,000 hours, which supports 5,000/3 = 1,666.67 Beta units. In whole units, produce 1,666 Beta and leave 2 hours idle.
Total contribution = 2,500 × R70 + 1,666 × R100 = R175,000 + R166,600 = R341,600 (or R341,667 if fractional units are allowed). Fixed overhead of R420,000 is irrelevant to the mix because it does not change with the product choice.
The sales director's absorption-cost reasoning is misleading. Fixed overhead absorption is R420,000/10,000 = R42 per machine hour. Alpha absorption cost is R110 + 2 × R42 = R194, which exceeds its R180 price, and Beta absorption cost is R140 + 3 × R42 = R266, which exceeds R240. Both products appear to make losses, yet both generate positive contribution. Absorption costing distorts the short-term decision.
2. Evaluate the special order. Calculate the relevant cash flows, including opportunity cost, and recommend whether to accept.
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Incremental cash flows of Alpha-X:
| Item | Calculation | Amount |
|---|---|---|
| Incremental revenue | 800 × R150 | 120,000 |
| Variable costs | 800 × (50 + 30 + 20) | (80,000) |
| Contribution before mould | 40,000 | |
| Special mould | one-off, no other use | (45,000) |
| Net before opportunity cost | (5,000) |
Capacity and opportunity cost. The order needs 800 × 3 = 2,400 machine hours. There is no idle capacity, so production must be displaced. Since Alpha earns R35 per hour and Beta R33.33, displace Beta. Each Beta uses 3 hours, so 2,400 hours displaces 800 Beta units. Lost contribution = 800 × R100 = R80,000.
Net relevant effect = R40,000 − R45,000 − R80,000 = −R85,000. Reject the order. Displacing Alpha would be worse: 2,400/2 = 1,200 Alpha units × R70 = R84,000 lost contribution, giving −R89,000. The R150 price exceeds the variable cost of R100 and even the absorption cost of Alpha is not the right benchmark. The order destroys value because the mould cost and the lost Beta contribution exceed the contribution earned.
3. Discuss qualitative factors and any conditions under which your recommendation would change.
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Qualitative factors include the strategic value of entering a new customer relationship, the possibility of repeat orders at higher prices, the precedent set for existing customers, workforce morale and overtime fatigue, quality risk from a modified product, and delivery reliability for existing customers. A one-off low price can erode pricing discipline if other customers learn of it.
The recommendation would change if the mould can be reused, sold, or charged to another job, because the R45,000 would then be an asset or a shared cost rather than a one-off relevant cost. It would also change if the order can be scheduled in otherwise idle time, for example if Beta demand falls or if overtime can create extra capacity at an incremental cost below the contribution per hour. If the customer offers a longer-term contract with future prices that recover the mould and the opportunity cost, the total package may be positive. Management should also check whether the order uses a different machine or can be outsourced. On the stated facts, the order should be rejected.