ACCA Applied Skills · Performance Management

Material mix and yield variances: formula sheet

Full chapter guide

Key formulas

Total material usage variance: Σ (standard quantity for actual output − actual quantity used) × standard price per unit; Work out each material separately and add. Positive is favourable, negative is adverse.
Material mix variance: Σ (actual total input in standard mix − actual quantity of each input) × standard price per unit; Actual total input is the sum of all inputs actually used. Share it in the standard proportions.
Material yield variance: (standard total input for actual output − actual total input) × standard average cost per unit of input; Standard average cost per unit of input = standard cost of one batch of inputs ÷ total input units in the batch.
Reconciliation: Mix variance + yield variance = total material usage variance; Use this to check your work. Use it also as a shortcut to find one variance from the other two.
Standard input for actual output: Actual output × (standard input in batch ÷ standard output in batch); This gives the total input the standard allows for the actual output.
Material mix variance (per material): (Actual total input × standard mix % − actual quantity used) × standard price per unit; Positive result is favourable. Negative result is adverse.
Actual input in standard mix: Total actual input of all materials × (standard quantity of that material ÷ total standard input per batch); Use the standard proportions from the cost card. Total input is the sum of all materials actually used.
Total mix variance (cost approach): Standard cost of actual input in standard mix − standard cost of actual input in actual mix; Gives the same total as adding the individual material variances. Use it as a check.
Average standard price per unit of input: Standard cost of one standard batch ÷ total standard input quantity of that batch; Useful for the yield variance and for checking your work.
Sum of quantity differences: Σ (standard-mix quantity − actual quantity) = 0; If your quantity differences do not add up to zero, you have made an error.
Standard input for actual output: Actual output × (standard input ÷ standard output); This is the input allowed for what you actually produced. Use the standard loss or yield rate.
Material yield variance (input basis): (Standard input for actual output − Actual total input) × Standard average cost per unit of input; Positive means favourable. Negative means adverse.
Material yield variance (output basis): (Actual output − Standard output from actual input) × Standard cost per unit of output; Gives the same answer as the input basis. Use it as a check.
Standard average cost per unit of input: Total standard cost of standard mix ÷ Total standard input units; Use standard prices only. Never use actual prices.
Link to usage variance: Material usage variance = Material mix variance + Material yield variance; Use this to check your working. Price variance is separate.
Reconciliation rule: Material mix variance + Material yield variance = Material usage variance; Holds when all three use standard prices and the same actual and standard quantities. Use it as a check.
Material usage variance (each material): (Standard quantity for actual output − Actual quantity used) × Standard price; Standard quantity is the standard input for actual output, not the budgeted output.
Material mix variance (each material): (Actual total input in standard mix − Actual input of that material) × Standard price; Actual total input is the sum of all materials actually used. Share it out in standard proportions.
Material yield variance: (Standard total input for actual output − Actual total input) × Average standard cost per unit of input; Average standard cost per unit of input = standard cost of one batch ÷ total input in the batch.
Standard input for actual output: Actual output ÷ (Standard output ÷ Standard input); This allows for the normal loss in the standard.
Material price variance: (Standard price − Actual price) × Actual quantity purchased or used; Kept apart from usage, mix and yield. Use the quantity your question bases price on.
Material mix variance: (Actual total input quantity in standard mix − Actual quantity used) × Standard price per unit, for each material; Positive means favourable. Sum across materials for the total. Applies when materials can be substituted.
Material yield variance: (Actual total input − Standard input for actual output) × Standard average cost per unit of input; Equivalent to (Actual output − Standard output from actual input) × Standard cost per unit of output. Adverse when you used more input than standard allowed.
Link to usage variance: Mix variance + Yield variance = Total material usage variance; Use this as a check on your workings. Keep the sign of each variance (F or A).
Is a mix change worthwhile?: Cost per unit of good output = Cost per unit of input mix ÷ Yield from the mix; Compare the old and new mix. Then consider quality and sales effects that are not in the figures.

Quick revision

Mix and yield variances together make up the material usage variance.
Mix variance: actual input in actual mix versus actual input in standard mix, at standard cost.
Yield variance: actual input in standard mix versus standard input for actual output, at standard cost.
Total input quantity is the same in the first two lines of the mix calculation.
Mix variance is zero if actual materials are used in the standard proportions.
Cheaper materials in the mix often give a favourable mix variance but may hurt yield.
Check the sum of mix and yield against the usage variance every time.
Favourable means lower cost than standard; adverse means higher.
Use standard prices, not actual prices, in mix and yield variances.
Comment on causes, links between variances and action, not only on the figure.
Objective test answers are all or nothing, so check the sign and the units.

Common mistakes

Using actual prices instead of standard prices in mix and yield variances. Fix: Mix, yield and usage variances are quantity variances. Always value them at standard price.
Calculating the yield variance using the standard price of one material instead of the average standard cost per unit of input. Fix: Divide the standard cost of one batch by the total input units in the batch. Use that figure.
Using standard quantity for actual output instead of actual total input in standard mix Fix: For the mix variance, always start from total actual input. Only the yield variance deals with how much input the output should have needed.
Valuing the difference at actual price Fix: All mix variances are valued at standard price. Actual prices belong in the price variance.
Using actual input as the base and forgetting the standard loss. Fix: Always convert actual output to standard input first, using the standard input ÷ standard output ratio.
Valuing the variance at the standard price of one material. Fix: Yield looks at total input. Use the weighted standard average cost per unit of input.
Using budgeted output instead of actual output to find the standard quantity. Fix: Always scale the standard to actual output first. Standard input = actual output ÷ output per unit of input.
Applying the yield variance to actual output or using the price of a single material. Fix: Use the average standard cost per unit of input (batch cost ÷ total input) for yield. Do not use output cost unless the question defines yield in output terms.
Commenting on mix alone and calling a favourable mix variance good. Fix: Always look at yield and the net usage variance. Ask what the cheaper mix did to output and quality.
Using actual prices instead of standard prices in the calculation. Fix: Mix and yield are quantity variances, so use standard prices only.

Exam tips

In objective test cases, mix and yield questions are often short. Write the standard batch and the average cost per unit on your rough paper first, so you can reuse them for every question in the case.
Check the output is stated in the same units as the standard. If the standard shows a loss, you must use the standard output, not the total input, to scale up.
In a written question, show a clear table with standard quantity, actual quantity, and actual in standard mix. Marks are given for method even if one figure is wrong.
Always add a short comment. Say what the variance shows and whether the two variances offset each other, for example a cheaper blend that causes more waste.
Remember that mix + yield = usage. Use it as a fast check before you move on.
Show the actual-input-in-standard-mix column clearly. In Section C, marks are often given for the method even if a number slips.
Always check that the quantity differences sum to zero before valuing them.
State F or A against every figure, and give a one-line meaning, such as more of the expensive material was used.