Material mix variance: formula and a worked example

Material mix variance measures the cost effect of changing the proportions of materials consumed, holding total input and standard prices constant. It separates a cheaper or more expensive blend from changes in purchase prices and production yield. The check is that mix plus yield equals material usage variance.

The formula and sign convention

Revised standard quantity by material = Total actual input quantity × Standard mix proportion

Material mix variance = Sum of [(Actual quantity − Revised standard quantity) × Standard price]

This article uses actual minus standard: positive cost variances are unfavorable, and negative cost variances are favorable. Some reports reverse the subtraction, so retain the direction labels when comparing workbooks.

The revised quantity answers a precise question: what would the actual total input have cost if its composition had followed the approved recipe? It is different from the standard input allowed for actual finished output. Confusing those quantities turns the mix calculation into a usage calculation.

The OpenStax explanation of materials variances distinguishes quantity variance, valued at standard prices, from price variance. Mix is a further split of that quantity variance. The broader variance analysis guide covers the price and usage bridge; here the question is what happened inside usage.

Start with consumption and the approved recipe

Use production consumption rows, net of material returns, with batch ID, product, material ID, quantity, unit of measure and production date. Join the standard recipe effective for that batch, its standard prices and the actual good output. Retain issue and return identifiers so duplicate movements can be found.

Analyze each product and recipe separately. Aggregating unrelated recipes first can create a mix variance merely because the factory made a different assortment of finished products.

A fictional Ohio compound manufacturer produces 900 lb of good output in one batch. The approved recipe allows the following input for that output. All material quantities use pounds; prices and costs use USD.

Allowed cost is quantity times standard price: 600 × 4 = $2,400 and 400 × 6 = $2,400. Standard yield is 900 / 1,000 = 90.0%. The allowed input already reflects expected process loss; do not add that loss again.

Actual consumption and the cost assigned to that consumption are:

The actual input total is 770 + 330 = 1,100 lb. Actual yield is 900 / 1,100 = 81.8%, rounded to one decimal place. Keep full precision in the workbook; dollar results here are exact to the displayed cent prices.

Rebuild the actual input at standard proportions

Apply the standard blend to the actual 1,100 lb. Base resin's revised quantity is 1,100 × 60% = 660 lb; reinforcing resin's is 1,100 × 40% = 440 lb.

The manufacturer used 110 lb more of the cheaper resin and 110 lb less of the expensive resin. The mix effect is 110 × 4 − 110 × 6 = −$220, favorable.

The quantity differences must sum to zero. Both columns describe the same total input, so any nonzero difference identifies a proportion, unit or missing-row problem.

There is a second proof. Actual input at standard prices costs 770 × 4 + 330 × 6 = $5,060. Revised input costs 660 × 4 + 440 × 6 = $5,280. Their difference is $5,060 − $5,280 = −$220.

This concerns the mix of production inputs. Price-volume-mix analysis addresses the different question of changes in the sales mix.

Reconcile mix to usage and total cost

Yield variance compares revised quantities with the standard quantities allowed for actual output. Usage compares actual quantities directly with those allowed quantities.

Mix plus yield is −220 + 480 = $260 unfavorable usage. The direct check is (770 − 600) × 4 + (330 − 400) × 6 = $260. Never add mix and yield on top of usage; they explain it.

The remaining cost difference comes from prices on consumed quantities:

The complete bridge is −220 mix + 480 yield + 187 price = $447 unfavorable. It equals actual cost less allowed cost: $5,247 − $4,800 = $447. This price bridge uses consumed quantities; a purchasing variance calculated on purchases needs a separate inventory reconciliation.

Where it goes wrong

• Using allowed quantities for the mix baseline. Revised quantities use actual total input. Allowed quantities belong in yield and usage.
• Combining incompatible units. Convert to an approved common basis before calculating proportions.
• Changing standards mid-comparison. Use the recipe and prices effective for the batch, with revisions identified.
• Treating favorable mix as a quality result. Compare it with scrap, rework and finished-product acceptance before changing the recipe.
• Counting usage twice. A cost bridge contains either usage or its mix-and-yield components.

Production owns the consumption explanation; finance owns the standard-cost reconciliation. Quality must approve any recipe change. OpenStax's discussion of variance reporting explains why favorable variances also merit investigation. Use the budget versus actual layout to present the reconciled result alongside other cost movements.

Calculate the mix on your own file in Covirage

Bring your batch consumption, approved mix, standard prices and output file; Covirage maps the columns, and its tools compute and check the supplied comparisons. The external AI model explains the result with every figure traced to its rows. Create a free Covirage account and bring a sample of your own data.

See cost variance analysis for the supporting workflow.