When production leans on the cheaper ingredient, the usage variance hides a saving and a loss that only the split can separate.
Split the material usage variance in two. The mix variance is the actual total input re-spread in the standard proportions, minus the actual quantity of each material, valued at standard price; the yield variance is the standard input for the output achieved, minus the actual total input, valued at the standard cost per kilogram of input. In the illustrative blend below, using more of the cheapest ingredient gave a 1,750 favourable mix variance but a 3,250 adverse yield variance, so the substitution lost 1,500.
Worked in full in Cost Accounting by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The split only makes sense where the inputs can replace one another: a feed, a mortar, a chemical batch, a food recipe. When production leans on the cheaper ingredient, the usage variance hides two opposite effects, and a plant manager can point to the favourable half while the adverse half sits in scrap and lost output.
| Material | Standard kg per batch | Standard price | Standard cost | Actual kg used | Actual price |
|---|---|---|---|---|---|
| A, filler | 50 | 2.00 | 100 | 25,500 | 2.10 |
| B, binder | 30 | 3.50 | 105 | 13,800 | 3.40 |
| C, additive | 20 | 6.00 | 120 | 9,700 | 6.00 |
| Total | 100 | 325 | 49,000 |
The standard cost is 3.25 per kg of input and, at a 90 per cent yield, 3.6111 per kg of output. Actual output for the month was 43,200 kg. Price variances are calculated first, on the actual quantities, so that everything below is at standard price; the price and usage mechanics on their own are in how to calculate material price and usage variances.
Standard input = actual output / standard yield = 43,200 / 0.90 = 48,000 kg, split 50/30/20: 24,000 of A, 14,400 of B and 9,600 of C.
Re-spread the 49,000 kg actually used in the standard proportions: 24,500 of A, 14,700 of B and 9,800 of C. This is the hinge: it holds total quantity at actual and changes only the proportions.
Mix variance = (actual total in standard mix − actual quantity) × standard price, per material.
A: (24,500 − 25,500) × 2.00 = 2,000 adverse. B: (14,700 − 13,800) × 3.50 = 3,150 favourable. C: (9,800 − 9,700) × 6.00 = 600 favourable. Total 1,750 favourable.
Yield variance = (standard input for actual output − actual total input) × standard cost per kg of input = (48,000 − 49,000) × 3.25 = 3,250 adverse.
The same figure from the output side: 49,000 kg should have produced 44,100 kg; the plant made 43,200, a shortfall of 900 kg at 3.6111 = 3,250.
Excel, with actual kg in C2:C4, standard shares in D2:D4 and standard prices in E2:E4: mix =SUMPRODUCT((SUM(C2:C4)*D2:D4-C2:C4)*E2:E4); yield =(43200/0.9-SUM(C2:C4))*SUMPRODUCT(D2:D4,E2:E4).
| Material | Mix variance | Yield variance | Usage variance | Price variance |
|---|---|---|---|---|
| A | −2,000 | −1,000 | −3,000 | −2,550 |
| B | 3,150 | −1,050 | 2,100 | 1,380 |
| C | 600 | −1,200 | −600 | 0 |
| Total | 1,750 | −3,250 | −1,500 | −1,170 |
The checks close. Mix plus yield equals usage: 1,750 less 3,250 is 1,500 adverse. Usage plus price equals the total material variance: the standard cost of 43,200 kg of output is 156,000, the actual cost was 158,670, and the 2,670 adverse difference is the 1,500 usage plus the 1,170 price.
The story the split tells is one the usage line alone does not. Production ran filler at 52.0 per cent of input instead of 50, and binder at 28.2 instead of 30. That lowered the standard-price cost of a kilogram of input from 3.25 to 3.2143, worth 1,750 on the month. But the leaner binder content cut yield from 90 per cent to 88.16, and 900 kg of lost output at 3.6111 cost 3,250. The cheaper recipe was the dearer product.
Read the total, not the lines. The per-material mix figures say only which way the proportions moved. Material A shows 2,000 adverse on mix because more of it was used, yet using more of it is precisely what made the mix cheaper. Only the total mix variance carries meaning.
The substitution saves 0.0357 a kilogram of input, so it pays only if the yield it costs is small. At the actual mix the input costs 3.2143 a kg; dividing by the 3.6111 standard cost per kg of output gives a break-even yield of 89.0 per cent. Same 49,000 kg, same mix, different yields:
| Yield | Output, kg | Mix variance | Yield variance | Usage variance |
|---|---|---|---|---|
| 88.0% | 43,120 | 1,750 | −3,539 | −1,789 |
| 88.5% | 43,365 | 1,750 | −2,654 | −904 |
| 89.0% | 43,610 | 1,750 | −1,769 | −19 |
| 89.5% | 43,855 | 1,750 | −885 | 865 |
| 90.0% | 44,100 | 1,750 | 0 | 1,750 |
Each point of yield is worth 1,769 on this volume, more than the whole mix saving. That asymmetry is common: the cheaper ingredient is usually cheaper because it does less work, and the work shows up in yield.
A favourable mix variance is a claim that needs the yield variance beside it before anyone is congratulated. Here the recipe change looked like 1,750 saved and was 1,500 lost, and the test is one number: the break-even yield of 89.0 per cent against the 88.16 actually achieved. How standards like these are built, and what a wrong one does to pricing, is worked through in the free workbook for this case.
The mix variance measures the cost of changing the proportions of inputs, holding total input at actual. The yield variance measures the cost of using more or less total input than the output achieved requires, in the standard proportions. In the illustrative blend, a mix leaning on filler saved 1,750 while the 1,000 kg of extra input it needed cost 3,250 at 3.25 a kg.
Yes, when the cheaper mix lowers yield by more than it saves. In the illustrative case the cheaper recipe cut the cost of a kilogram of input to 3.2143, but yield fell from 90 per cent to 88.16 and the lost output cost 3,250 against a 1,750 saving. Below an 89.0 per cent yield the substitution destroys value.
Multiply actual input by the standard yield to get expected output, subtract actual output, and value the shortfall at the standard cost per kilogram of output. With 49,000 kg of input and a 90 per cent standard yield, expected output is 44,100 kg; the plant made 43,200, and 900 kg at 3.6111 gives the same 3,250 adverse as the input method.
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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