Kelbrook Precision Coatings: high–low analysis across a step cost
Kelbrook Precision Coatings operates a powder-coating plant and quotes for contract work on a machine-hour recovery basis. The management accountant extracted six months of total production overhead, together with machine hours: 2,200 hours £79,600; 2,600 hours £86,800; 2,900 hours £92,200; 3,400 hours £110,200; 3,800 hours £117,400; 4,200 hours £124,600. A second shift supervisor costing £9,000 a month is appointed whenever machine hours exceed 3,000; the appointment is made for whole months and cannot be reversed part-way through a month. Coating powder is bought for each job and charged directly to the contract. Oven depreciation is £6,000 a month on a straight-line basis. A customer has asked for a fixed-price quotation on a contract requiring 500 machine hours in a month when existing work already absorbs 2,600 machine hours. The sales manager proposes to estimate overhead with a single high–low calculation over all six months and to add a 25% mark-up.
1. Calculate the overhead cost function using a single high–low analysis over all six months, and separately using an analysis that respects the step in supervisor cost. Reconcile the two and state which should be used for the quotation, with figures.
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Single high–low (all six months) Variable rate = (£124,600 − £79,600) ÷ (4,200 − 2,200) = £45,000 ÷ 2,000 = £22.50 per machine hour. Fixed element = £79,600 − (2,200 × £22.50) = £30,100.
Analysis by relevant range (the correct approach) Lower band (2,200–2,900 hours, no supervisor): (£92,200 − £79,600) ÷ (2,900 − 2,200) = £12,600 ÷ 700 = £18.00 per hour; fixed = £79,600 − £39,600 = £40,000. Upper band (3,400–4,200 hours, supervisor included): (£124,600 − £110,200) ÷ 800 = £18.00 per hour; fixed = £110,200 − (3,400 × £18) = £49,000 = £40,000 + £9,000 step. The two bands agree on the variable rate, which confirms the result.
Why the single calculation fails. High–low uses only the two extreme points, which sit in different cost structures. Part of the £9,000 step is absorbed into the variable rate (£22.50 vs £18.00) and the fixed element is understated (£30,100 vs £40,000/£49,000). The line fits 2,200 and 4,200 hours but nothing in between: at 3,100 hours it predicts £30,100 + £69,750 = £99,850 against a true £49,000 + £55,800 = £104,800, understating by £4,950.
Recommendation. Use £40,000 + £18/hour for output up to 3,000 hours and £49,000 + £18/hour above it. For 3,100 hours the £9,000 step applies.
2. Advise whether the £9,000 supervisor cost and the £6,000 depreciation are relevant to the 500-hour quotation, calculate the incremental overhead to be recovered, and comment on the 25% mark-up on the high–low estimate.
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Supervisor - relevant, and wholly attributable. Without the contract the month would run at 2,600 hours, below the 3,000-hour threshold. With the contract it runs at 3,100 hours, so the £9,000 appointment is caused entirely by the contract. It is a step (semi-fixed) cost whose relevant range is being crossed: within a band it is fixed, but at the margin it behaves as a lump-sum incremental cost.
Incremental overhead for the contract = £9,000 + (500 × £18) = £18,000. The £40,000 base fixed overhead is incurred whether or not the contract is taken, so it is not incremental - although in the long run prices must recover it.
Depreciation - not relevant to the price decision. It is a committed fixed cost, non-cash, and in substance a sunk cost of an asset already bought. It should not drive a short-term quotation.
The mark-up. The high–low estimate gives 500 × £22.50 = £11,250 of overhead; with a 25% mark-up that recovers £14,062 - about £3,938 below the £18,000 incremental overhead, before any powder or labour is considered. The contract would reduce profit. The mark-up is also arbitrary: it ignores competitor pricing and the value of the capacity. Recommend quoting on incremental cost for the step and hours, recovering depreciation and base fixed costs through the general recovery rate, and testing the resulting price against the market.