High-low cost estimation with an abnormal repair
Westfield Engineering is preparing next year's flexible budget. The management accountant has six months of production cost data: January 12,000 units, £96,000; February 15,000 units, £111,000; March 9,000 units, £81,000; April 18,000 units, £146,000; May 14,000 units, £106,000; June 16,000 units, £116,000. April included a £20,000 one-off machine repair after a breakdown; without it, cost would have been £126,000. The accountant used the high-low method on the highest and lowest activity months and estimated variable cost of £7.22 per unit and fixed cost of £16,000. The resulting budget for 17,000 units is £138,778. The production manager says the estimate is too high and that the April repair should be ignored. The sales director wants a quick budget because a bank loan application is due. The data was entered manually from job sheets, and one job sheet is missing. The company has never used regression analysis.
1. Evaluate the high-low estimate. Recalculate using the adjusted data and explain the difference.
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The original high-low used the highest activity month, April (18,000 units, £146,000), and the lowest, March (9,000 units, £81,000):
- Variable cost = (£146,000 − £81,000) / (18,000 − 9,000) = £65,000 / 9,000 = £7.22 per unit.
- Fixed cost = £81,000 − (9,000 × £7.22) = £16,000.
- Budget for 17,000 units = £16,000 + (17,000 × £7.22) = £138,778.
The problem is that April includes a £20,000 abnormal repair. High-low uses only two points, so one outlier can distort both the variable rate and the fixed cost. Adjusting April to £126,000 and using June (16,000 units, £116,000) as the highest normal month:
- Variable cost = (£116,000 − £81,000) / (16,000 − 9,000) = £35,000 / 7,000 = £5.00 per unit.
- Fixed cost = £81,000 − (9,000 × £5) = £36,000.
- Budget for 17,000 units = £36,000 + (17,000 × £5) = £121,000.
The adjusted estimate is £17,778 lower. It also fits the normal months: January 12,000 units gives £96,000; February 15,000 gives £111,000; May 14,000 gives £106,000. Those figures are consistent with £5 variable and £36,000 fixed. The original estimate overstates the variable cost and understates the fixed cost, which is dangerous for decisions at different volumes.
2. Advise whether the company should use the adjusted high-low estimate, regression, or another approach for the bank loan budget. Include data quality issues.
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The adjusted high-low estimate of £121,000 is more plausible than £138,778, but it is still based on only two observations. With six months of data and one clear outlier, regression would be better if the company can obtain the missing job sheet and validate the figures. Regression uses all valid observations, provides a measure of fit, and can include a dummy variable for the April repair so that the one-off cost does not distort the normal cost relationship. A simple regression on the five normal months would probably give a variable cost close to £5 and fixed cost close to £36,000, but the small sample means the result should be treated as a range, not a precise number.
Data quality issues must be addressed before the bank submission:
- The data was entered manually, so check for transposition and omission errors against the ledger and job sheets.
- The missing job sheet should be traced or estimated and disclosed.
- Confirm that the activity measure, units, is the main driver; if there are step costs or batch effects, a simple linear estimate may be misleading.
- Separate abnormal items such as the repair from normal operating costs.
- Document the assumptions and provide a sensitivity range, for example £118,000 to £125,000 for 17,000 units.
For a bank loan, transparency is more important than a single precise figure. A well-supported range and an explanation of the one-off repair are more credible than an unexplained high-low result.
3. The production manager argues that the £20,000 repair should be ignored because it is non-recurring. The sales director argues it should be included because it was actually incurred. Discuss the treatment.
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Both managers are partly right, but they are answering different questions. For estimating the normal relationship between activity and cost, the £20,000 repair should be excluded or modelled separately because it is abnormal and non-recurring. Including it in a two-point high-low calculation raises the apparent variable cost from £5.00 to £7.22 and lowers the apparent fixed cost from £36,000 to £16,000. That distorts the flexible budget and could lead to overpricing at high volumes and underpricing at low volumes.
For predicting the actual cash outflow next year, however, the repair cannot simply be assumed away. If the breakdown was a random one-off, it should not be built into the normal cost formula, but the company should still consider a maintenance provision or contingency. If the breakdown was caused by inadequate maintenance, it may recur, and the expected cost of prevention or breakdown should be included. The relevant question is whether the event is truly non-recurring and independent of activity.
The best treatment is to use a dummy variable in regression, or to estimate the normal cost function from the adjusted data and then add a separately justified maintenance provision. The sales director is correct that the cash was spent, but that does not make it part of the normal variable cost. The production manager is correct to exclude it from the cost behaviour estimate, but should not ignore the underlying risk. The bank application should disclose the adjustment and the maintenance policy.