Compare contribution per hour when production time is scarce
Suppose selling one unit of a product generates ¥6,000 in contribution, while another generates ¥4,000. Will producing more of the first product also increase factory profit? If machine capacity is insufficient to produce all the units you could sell, the amount per item alone cannot answer that question. When the ¥6,000 product takes two hours and the ¥4,000 product takes one, their ranking reverses for the same amount of time.
Contribution is selling price less variable costs, which change with sales volume. ACCA explains a method of allocating scarce resources by dividing each product's contribution per unit by the resource needed to make that unit. For a factory short of machine time, the denominator is time on that machine. (Throughput accounting)
Compare contribution per item with contribution per hour of the scarce machine when considering production quantities.
Product A contributes more per item but less per machine hour
The following hypothetical example assumes specific figures and cost behavior. A factory makes products A and B on the same machine and sells everything it produces during the month. All amounts are in Japanese yen, excluding tax. Variable costs include materials and packaging incurred per sale; employees' monthly salaries are included in fixed costs.
| Item being compared | Product A | Product B |
|---|
| Selling price per item | ¥10,000 | ¥6,000 |
| Variable costs per item | ¥4,000 | ¥2,000 |
| Contribution per item | ¥6,000 | ¥4,000 |
| Machine time per item | 2 hours | 1 hour |
| Contribution per machine hour | ¥3,000 | ¥4,000 |
| Maximum units that can be sold this month | 50 | 60 |
A contributes ¥6,000 ÷ 2 = ¥3,000 per machine hour; B contributes ¥4,000 ÷ 1 = ¥4,000. A generates ¥2,000 more per item, while B generates ¥1,000 more per hour.
There are 100 machine hours available this month. Producing 50 units of A and 60 of B would require 50 × 2 + 60 × 1 = 160 hours, so the factory cannot meet both sales limits. Materials, staff, and other processes have sufficient capacity; only this machine's time is scarce.
Assume constant machine time and variable costs per item, with no setup time between products, defective units, or minimum production batches. Everything produced within the sales limits can be sold, and there are no existing delivery commitments or minimum supply requirements.
The product mix changes profit by ¥60,000 within the same 100 hours
Making 50 units of A first consumes all 100 hours, leaving none for B. Total contribution is ¥6,000 × 50 = ¥300,000.
Making 60 units of B first uses 60 hours. The remaining 40 hours allow 20 units of A. Total contribution is ¥4,000 × 60 + ¥6,000 × 20 = ¥360,000.
| Monthly production plan | Make 50 units of A first | Make 60 units of B first |
|---|
| Units of A produced and sold | 50 | 20 |
| Units of B produced and sold | 0 | 60 |
| Total machine time | 100 hours | 100 hours |
| Revenue | ¥500,000 | ¥560,000 |
| Total variable costs | ¥200,000 | ¥200,000 |
| Total contribution | ¥300,000 | ¥360,000 |
| Monthly fixed costs | ¥200,000 | ¥200,000 |
| Profit after fixed costs | ¥100,000 | ¥160,000 |
Assume fixed costs are ¥200,000 under either plan. Profit is therefore ¥100,000 or ¥160,000, giving the plan that produces 60 units of B a ¥60,000 advantage.
The difference comes from making 30 fewer units of A and using the released 60 hours to produce 60 units of B. The factory loses ¥180,000 of contribution from A and gains ¥240,000 from B, a net increase of ¥60,000. It changes the products sold within the same 100 hours without increasing machine operating time.
Production quantities change if only 20 units of B can be sold
A higher contribution per hour does not turn units produced beyond the sales limit into revenue for that month. Now assume that only B's sales limit falls, to 20 units.
Making 20 units of B uses 20 hours, leaving 80 hours for 40 units of A. Contribution is ¥4,000 × 20 + ¥6,000 × 40 = ¥320,000. After ¥200,000 of fixed costs, profit is ¥120,000, compared with ¥160,000 when 60 units of B could be sold.
In practice, distinguish confirmed orders from forecast sales when setting production quantities. If B's sales forecast falls from 60 units to 20, the production plan changes even though its calculated contribution remains ¥4,000 per hour. Completing products does not mean that every unit has been sold and contributed to profit.
If both products also consume time in another process whose staff capacity is insufficient, ranking by this machine alone is insufficient. Calculate both machine hours and staff hours for each production proposal, then compare profit among plans that satisfy both capacity limits. Recalculate quantities for minimum batches and product changeover time as well.
Do not turn monthly salaries into additional variable costs
Changing cost classification changes calculated contribution per hour. In this example, monthly salaries that remain payable at the same amount regardless of this month's production quantities form part of the ¥200,000 in fixed costs. Dividing those salaries by machine hours and also charging them as variable costs per item would deduct the same expense twice.
If a production plan increases overtime payments or outsourcing expenses, include that increase. For example, if the plan producing 60 units of B alone requires ¥70,000 in extra costs, its ¥160,000 profit falls to ¥90,000, below the ¥100,000 from making 50 units of A.
ACCA distinguishes throughput accounting, which subtracts direct material costs from selling price, from contribution calculations, which subtract variable costs. This article uses contribution because it assumes some costs beyond materials also vary with sales volume. (Throughput accounting)
Calculate monthly profit using sales limits and scarce production time
Producing more of A, which has the higher contribution per item, did not increase monthly profit in this capacity-constrained example. Producing 60 units of B and 20 of A generated ¥60,000 more profit than making 50 units of A.
When comparing production plans, calculate total monthly profit for a product mix that fits the scarce machine's capacity and does not exceed sales limits. Contribution per hour helps allocate time; it does not justify omitting sales limits or additional expenses.
If the production plan changes which new orders you accept, publish the products available, order quantity limits, and expected delivery dates on your website. This keeps the quantities and dates communicated to customers consistent with what you plan to produce and sell.
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