Two formulas that must add back to the total, worked on one month of a moulding line, and the cheaper grade of material that cost more than it saved.
The material price variance is (actual price − standard price) × actual quantity, and the usage variance is (actual quantity − standard quantity for the output achieved) × standard price. The two always add up to actual cost minus standard cost. In the worked month below, buying a cheaper grade saved 4,680 on price and lost 5,040 on usage: the line was 360 worse off than standard, while the purchasing report showed a saving.
Worked in full in Cost Accounting by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Variance analysis exists to put each part of a cost overrun in front of the person who controls it. Price belongs to purchasing, quantity to production. The formulas are designed so that the two never overlap, which is why the order of the terms, and the price used to value the quantity, are not a matter of taste.
| Input | Value |
|---|---|
| Good units produced | 12,000 |
| Standard resin per unit | 2.5 kg |
| Standard price of resin | 4.20 per kg |
| Resin actually used | 31,200 kg |
| Actual price paid | 4.05 per kg |
| Resin purchased in the month | 36,000 kg |
Purchasing switched to a lower grade at 0.15 below standard. Production reports more short shots and regrind losses since the switch.
Step 1: the standard quantity for actual output. Not the budgeted volume, the volume actually produced: 12,000 × 2.5 = 30,000 kg, which at standard price is a standard cost of 126,000. Actual cost is 31,200 × 4.05 = 126,360. The total variance to explain is 360 adverse.
Step 2: split it.
=(B5-B3)*B4, usage =(B4-B1*B2)*B3, with AP in B5, SP in B3, AQ in B4, units in B1 and standard kg in B2The bridge between the two is the middle column every textbook draws: actual quantity at standard price, 31,200 × 4.20 = 131,040. Actual cost to that figure is the price variance; that figure to standard cost is the usage variance.
| AQ × AP | AQ × SP | SQ × SP | |
|---|---|---|---|
| Amount | 126,360 | 131,040 | 126,000 |
| Variance | Price 4,680 F | Usage 5,040 A | |
| Total | 360 A | ||
The line used 1,200 kg, or 4.0 per cent, more resin than standard. The saving on price would have survived an overrun of 0.15 ÷ (4.20 − 0.15) = 3.7 per cent of standard, 1,111 kg; at that point the 0.15 saved on 31,111 kg exactly pays for 1,111 extra kg at 4.20. The lower grade cost more in scrap than it saved at the invoice, and the monthly pack, if it reports the two variances on different pages, credits purchasing with 4,680 and charges production with 5,040 for the same decision.
A favourable price variance next to an adverse usage variance of similar size is the signature of a substituted material. Read the two lines together before rewarding either department.
Labour splits the same way. At a standard of 0.4 hours a unit and 22.00 an hour, the 12,000 units should have taken 4,800 hours costing 105,600. The line used 4,650 hours at 22.80, costing 106,020. The rate variance is 0.80 × 4,650 = 3,720 adverse and the efficiency variance is (4,650 − 4,800) × 22.00 = 3,300 favourable: more experienced operators, paid more, worked faster. Net, 420 adverse, and the four variances together are 780 adverse.
| Discount per kg | Overrun 2% | Overrun 4% | Overrun 6% | Break-even overrun |
|---|---|---|---|---|
| 0.10 | −540 | 1,920 | 4,380 | 2.4% |
| 0.15 | −2,070 | 360 | 2,790 | 3.7% |
| 0.25 | −5,130 | −2,760 | −390 | 6.3% |
The break-even overrun is the discount divided by the standard price less the discount. A material with a high standard price and a thin discount has almost no room for extra scrap: at 0.10 off, an overrun of 2.4 per cent already wipes out the saving.
Valuing the usage variance at actual price. (31,200 − 30,000) × 4.05 = 4,860 instead of 5,040. The 180 difference is the joint effect of paying less on the extra kilograms, a price effect, now hidden in production's line. The convention is AQ for price and SP for usage, so each manager is measured only on what they control.
Using standard quantity in the price variance. (4.05 − 4.20) × 30,000 = 4,500, which leaves 180 of the saving unexplained or pushes it into usage. The kilograms actually bought at the lower price are 31,200, and the variance should say so.
Mixing purchase and usage timing. The month bought 36,000 kg. If raw material is held at standard cost, the price variance is taken at purchase, 0.15 × 36,000 = 5,400 favourable, and the 4,800 kg left in stock sit in the balance sheet at the 4.20 standard, 20,160. Taking the variance at purchase one month and at usage the next double counts or loses part of it. Pick one and keep it.
Variances are only as good as the standard behind them. The free workbook on the Cost Accounting companion page builds a factory's unit costs from their inputs and shows how far the overhead allocation method moves the margin on each product family. For the overhead side of the same standard, see how to calculate activity-based costing per unit.
So that each variance isolates one cause. Valuing the excess quantity at standard price keeps purchasing's price effect out of production's usage effect. In the worked case the 1,200 excess kilograms at the 4.20 standard give 5,040 adverse; valued at the actual 4.05 they would give 4,860, and the 180 difference would be a price effect wrongly credited to production.
On purchase, if raw material stock is held at standard cost, because that isolates the buyer's decision when it is made. Buying 36,000 kg at 0.15 below standard gives a 5,400 favourable variance at purchase, against 4,680 on the 31,200 kg used. Either method works if applied consistently; mixing them double counts or loses part of the variance.
The break-even overrun is the discount per unit divided by the standard price less the discount. A saving of 0.15 a kilogram on a 4.20 standard is cancelled by 3.7 per cent more material, 1,111 kg on a 30,000 kg standard. The line used 4.0 per cent more, so the cheaper grade lost money.
This article is one calculation from Cost Accounting. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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