Coastal Components: Overhead Behaviour and a One-Off Tender
Coastal Components Ltd manufactures seawater pumps in a single plant. The management accountant is rebuilding the overhead cost model before a one-off tender. Six recent months of machine hours and electricity cost are: 6,200 hours/£18,400; 5,400/£17,150; 7,800/£21,100; 8,600/£22,600; 9,200/£23,800; 7,000/£19,600. Production supervision costs £34,000 per supervisor per year; one supervisor covers up to 8,000 machine hours in a month and a second is required above that level. Plant depreciation is £96,000 per year on a straight-line basis and cannot be avoided. Research and development is budgeted at £150,000 per year and is reviewed annually. Normal monthly activity is 7,600 machine hours. A customer has requested a one-off order that would add 1,700 machine hours in a single month, taking the plant to 9,300 hours; no other overheads would change. The commercial director proposes pricing the order using the plant-wide absorption rate of £41 per machine hour.
1. Classify each of the four overhead costs by behaviour and estimate the electricity cost function using the high-low method.
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Classification
- Electricity - semi-variable: a standing charge plus a variable element driven by machine hours.
- Supervision - step-fixed: one supervisor to 8,000 hours, two above that, so the cost is fixed within each step but jumps at the boundary.
- Depreciation - committed fixed: straight-line, unavoidable, unrelated to activity in the short term.
- R&D - discretionary fixed: fixed within the annual budget but capable of being changed by management decision.
High-low estimate
Variable rate = (23,800 − 17,150) ÷ (9,200 − 5,400) = 6,650 ÷ 3,800 = £1.75 per machine hour.
Fixed element = 23,800 − (1.75 × 9,200) = 23,800 − 16,100 = £7,700 per month.
Check at the low point: 17,150 − (1.75 × 5,400) = 17,150 − 9,450 = £7,700. The function fits both chosen points exactly, but it says nothing about the other four months.
Caution: the high-low method uses only two observations, so an unusual month can distort the line. More importantly, the linear electricity function and the step in supervision mean there is no single overhead rate that is valid across the whole 5,400–9,300 hour range. The apparent linearity of electricity should be checked against the intermediate points before it is used for pricing.
2. Calculate the incremental overhead cost of the one-off order and explain why it differs from the figure produced by the £41 absorption rate.
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Incremental overhead
Electricity: 1,700 hours × £1.75 = £2,975.
Supervision: normal load is 7,600 hours (one supervisor); the order takes activity to 9,300 hours, which crosses the 8,000-hour step, so a second supervisor is needed. The step is a commitment of £34,000 a year. If the company must appoint on an annual contract, the full £34,000 is the incremental cost caused by the order. If a temporary supervisor can be engaged for one month, the relevant amount is closer to £34,000 ÷ 12 = £2,833 plus agency premium. Total incremental overhead is therefore £36,975 (annual appointment) or about £5,808 (one-month appointment).
Depreciation and R&D do not change, so they are not relevant.
Comparison with absorption
At £41 per machine hour, the order would carry 1,700 × £41 = £69,700 of overhead, overstating the incremental cost by roughly £32,700 (or £63,900 if supervision is temporary). The absorption rate recovers committed fixed costs and the R&D budget, both of which are already covered by normal production. It is an average, not a marginal, cost.
Implication: a bid built on £41 per hour may be uncompetitive, while a bid below £36,975 would leave Coastal worse off. The floor is the incremental cost; the actual price should sit between that floor and what the market will bear, with a risk margin for the supervision commitment.
3. Advise the commercial director on how absorption rates and cost behaviour estimates should be used in tender pricing, and on the risks of the current approach.
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Absorption rates serve stock valuation and long-run, repeat pricing, where all costs must be recovered across a normal volume. They are a poor basis for a one-off order that uses otherwise idle capacity, because they load the order with fixed costs that will be incurred regardless.
The director should use a two-tier approach: an incremental cost floor for short-term capacity-filling work, and a full-cost-plus target for recurring business that will eventually require new capacity. Where an order triggers a step - here, the second supervisor - the step must be recovered explicitly by that order or the company loses money even though the price exceeds variable cost.
The current approach carries three risks. First, the £41 rate is an average across a volume range in which supervision is a step, so it is wrong either side of the 8,000-hour boundary. Second, the high-low electricity function rests on two data points and could misstate the variable rate. Third, pricing at full absorption on marginal work invites undercutting by competitors who price on contribution, while pricing below incremental cost destroys value. The accountant should also test whether the 1,700 hours can physically be delivered in the month alongside normal work, and should re-estimate the cost function with all six observations or a regression before the tender price is fixed.