Overhead Absorption and a Make-or-Buy Decision Under Capacity Constraint
Halcyon Components makes two products, Alpha and Beta, using a single machine that runs 4,000 hours per year. Alpha uses 2 machine hours per unit and sells for $90 with variable costs of $50. Beta uses 4 machine hours per unit and sells for $160 with variable costs of $100. Annual fixed manufacturing overhead is $240,000 and is absorbed on machine hours at $60 per hour. Current demand is 1,200 units of Alpha and 400 units of Beta, which together require 4,000 hours - exactly full capacity. A customer offers to buy 300 units of a new product, Gamma, at $140 each; Gamma would use 3 machine hours and incur variable costs of $70. The sales manager argues Gamma is profitable because its price exceeds its 'full cost' of $70 variable plus $180 absorbed overhead = $250? No - the sales manager actually says Gamma's contribution of $70 per unit 'covers overhead' and should be accepted. The production manager warns that accepting Gamma means cutting Alpha or Beta output.
1. Determine whether Halcyon should accept the Gamma order, showing the relevant-cost analysis and the opportunity cost of the constrained machine hours.
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Fixed overhead of $240,000 is unavoidable and irrelevant to the decision; the binding constraint is machine hours.
Contribution per machine hour:
- Alpha: ($90 − $50) / 2 = $20 per hour
- Beta: ($160 − $100) / 4 = $15 per hour
- Gamma: ($140 − $70) / 3 = $23.33 per hour
Gamma earns the highest contribution per constrained hour, so on a pure throughput basis it should displace the lowest-ranked product, Beta. Each Gamma unit uses 3 hours, so 300 units need 900 hours. Displacing Beta frees hours at $15 each: 900 × $15 = $13,500 of lost Beta contribution.
Gamma contribution: 300 × $70 = $21,000. Net benefit = $21,000 − $13,500 = $7,500. Accept Gamma, but only by reducing Beta output by 225 units (900/4). The sales manager's 'covers overhead' reasoning is wrong in direction - overhead is not avoided - but the conclusion happens to be right for the wrong reason. Confirm Beta demand can absorb the cut without penalty.
2. The sales manager claims Gamma's $70 contribution 'covers overhead.' Critique this reasoning and explain the correct role of the $60 per hour absorption rate.
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The claim confuses contribution with profit. Contribution is what remains after variable costs to cover fixed costs and generate profit; it does not 'cover overhead' per unit in any decision-relevant sense. Fixed overhead of $240,000 is incurred whether or not Gamma is made, so it is irrelevant to the incremental decision.
The $60 per hour absorption rate is a product-costing device for inventory valuation and pricing guidance. It allocates $240,000 across 4,000 hours. If Gamma is produced, the absorption base changes and the rate per hour on remaining products shifts - a classic death-spiral effect where dropping a product raises the apparent cost of the others. The rate must not be used as a hurdle for incremental orders.
The correct test is contribution per unit of scarce resource. Gamma passes at $23.33 per hour versus Beta's $15. The board should also note that if fixed costs were genuinely avoidable or stepped (e.g., a second machine), the analysis would change and should be re-run.