A cement plant in Ewekoro blends limestone, clay and iron ore in fixed proportions. The standard blend of 10 kilograms of input makes one unit of output. In one month the operators use more clay and less iron ore than the standard recipe, because iron ore was short and clay was cheaper.
The usual usage variance for each material shows a mix of adverse and favourable figures, and the production manager asks which part of the total is due to choosing a different blend and which part to the blend turning out more or less output than it should. The answer is the mix variance and the yield variance, which together make up the total material usage variance.
This topic explains when the split is meaningful, how to calculate the mix variance in kilograms and in naira, the two ways of calculating the yield variance, the quicker line-by-line method, and the factors management must consider before changing a mix. It builds on the earlier topic on basic variances: material, labour and idle time. The next topic covers labour mix and yield variances.
In 30 seconds
Where a product uses two or more substitutable materials, the usage variance can be split.
The mix variance shows the effect of using a different proportion of materials from the standard mix: take the total actual input, share it in the standard proportions, compare each material’s standard-mix quantity with the quantity actually used, and value the difference at standard price; the total mix variance in quantity is always zero, and in money it is favourable if the actual mix is cheaper than standard.
The yield variance shows the effect of the total input giving more or less output than standard: (standard input for the actual output − actual total input) × standard cost per kg of input, or equivalently (actual output − output the actual input should give) × standard cost per unit of output.
Mix + yield = total usage variance. The line-by-line method:
- actual quantity in actual mix at standard prices
- actual quantity in standard mix at standard prices (the difference is mix)
- standard quantity in standard mix (the difference is yield)
The split is useful only if management can vary the mix. Before changing the mix, weigh cost (a favourable mix variance may be offset by an adverse yield), quality and customer acceptance.
Full marks come from correct standard-mix quantities, correct signs and a check to the usage total.
Mix and yield: the idea
Usage variances by material, and when to split
When a product has several direct materials, the total usage variance can be found as the sum of the usage variance of each: for each material, (standard quantity for the actual output − actual quantity used) × standard price. Some will be favourable and some adverse, and they are netted off.
If the materials are substitutable, so that less of one can be offset by more of another, the usage variance can be analysed further into a mix variance and a yield variance. The split is meaningful only when the proportions can be varied and so are under management control.
A car maker cannot make up for a missing engine with extra tyres; a blend of chemicals, a flour mix or a feed formula can be varied.
The mix variance
The mix variance measures how much of the usage variance is due to the actual combination of materials being cheaper or dearer than the standard combination. To calculate it:
- Take the total quantity of all materials actually used.
- Share it between the materials in the standard proportions (the standard mix): this gives the quantity of each that would have been used if the actual total had been in the standard mix.
- For each material, standard-mix quantity − actual quantity. A positive figure means less was used than the standard mix would give (favourable in quantity). The total across materials is always zero.
- Multiply each by the standard price per unit of that material.
- Add. The total is favourable if the actual mix is cheaper than the standard mix, adverse if dearer.
The yield variance
The yield variance measures the effect of the total input giving more or less output than the standard. It can be calculated in two equivalent ways.
Based on output: the actual input should have produced a certain output at standard (for example 10 kg of input should give 1 unit, so 4,150 kg should give 415 units); the difference from actual output, in units, is valued at the standard cost of a unit of output.
Based on input: the actual output should have used a certain input (400 units × 10 kg = 4,000 kg); the difference from the actual input, in kg, is valued at the standard cost per kg of input (standard cost of one unit ÷ standard kg of input). Both give the same money value.
An adverse yield means that more input was needed than standard for the output, because of waste, poorer materials or a poor mix.
Mix + yield = total usage variance. This is the check.
The line-by-line method and when to change the mix
The line-by-line method changes one element at a time. Start with actual quantities in the actual mix at standard prices. Next, actual total quantity in the standard mix at standard prices: the difference from the first line is the mix variance. Last, standard quantity for the actual output in the standard mix at standard prices: the difference from the second line is the yield variance.
Because the standard mix has a constant average cost per kg, the second and third lines can be found quickly as total kg × standard cost per kg of input (the third is also actual output × standard cost per unit).
Factors to consider when changing the mix. Splitting the usage variance is worth doing only if management control the proportions. Management will look for the optimum mix, and should weigh:
- Cost. The cheapest mix is not necessarily the most cost-effective. A favourable mix variance is often offset by an adverse yield variance, and the total cost per unit may rise.
- Quality. A cheaper mix may reduce quality; customers may not pay the same price, and sales returns and loss of repeat business may follow.
- Availability and technical limits. Some materials may be short; process or safety rules may limit the range of mixes.
- Waste and reliability of the process. A change in mix may change the output obtained from the input.
The mix and yield variances therefore have to be read together, never separately: a favourable mix variance with a larger adverse yield variance is a warning that the cheaper blend is costing more in output than it saves in materials.
Layouts for mix and yield variances
- Standard input per unit and standard cost per kg of input (cost of a unit ÷ kg of input).
- Usage variance by material (standard quantity for actual output − actual) × standard price, and total.
- Mix: total actual input × standard proportion for each material; difference from actual; × standard price; total.
- Yield: (standard input for actual output − total actual input) × standard cost per kg.
- Check: mix + yield = usage total.
Money is in naira and each answer is rounded once, at the end.
Worked examples
Example 1: mix and yield. The standard for one unit is 10 kg of input: 2 kg of A at ₦60, 3 kg of B at ₦100 and 5 kg of C at ₦30, so the standard cost of a unit is 120 + 300 + 150 = ₦570 and of a kilogram of input ₦57. Actual output is 400 units, using 900 kg of A, 1,150 kg of B and 2,100 kg of C (4,150 kg). Required: the usage, mix and yield variances.
- Standard quantities for 400 units. A 800, B 1,200, C 2,000 (4,000 kg).
- Usage by material.
A: 800 − 900 = 100 A × 60 = 6,000 A.
B: 1,200 − 1,150 = 50 F × 100 = 5,000 F.
C: 2,000 − 2,100 = 100 A × 30 = 3,000 A.
Total ₦4,000 A. - Mix.
Standard mix of 4,150 kg: A 20% = 830
B 30% = 1,245
C 50% = 2,075.
A: 830 − 900 = 70 A × 60 = 4,200 A.
B: 1,245 − 1,150 = 95 F × 100 = 9,500 F.
C: 2,075 − 2,100 = 25 A × 30 = 750 A.
Total ₦4,550 F (the quantities add to zero).
The actual blend used more of the cheap C and less of the dear B. - Yield.
Standard input for 400 units 4,000 kg; actual 4,150; 150 kg A × ₦57 = ₦8,550 A.
By output: 4,150 kg should give 415 units; actual 400; 15 units A × 570 = 8,550 A. - Check.
4,550 F − 8,550 A = 4,000 A, equal to the total usage variance. - Line by line.
Actual quantities at standard prices: 54,000 + 115,000 + 63,000 = 232,000.
Actual total in standard mix: 4,150 × 57 = 236,550
difference = 4,550 F (mix).
Standard for actual output: 4,000 × 57 = 228,000; difference 8,550 A (yield). - Comment. The cheaper blend saved ₦4,550 in materials, but the process then yielded 15 units fewer than the input should have, costing ₦8,550. The change of mix has lost money overall.
Expect variants: a standard loss built into the mix, a requirement to calculate only the mix, or a question that asks for the yield variance by both methods and a discussion of the cause.
Common mistakes
- Using standard quantities for the actual output instead of the actual total input when finding the mix.
- Valuing at actual price. Mix and yield use standard prices.
- Mix quantities that do not add to zero.
- Wrong sign. A mix that is cheaper than standard is favourable.
- Splitting the usage variance when the materials cannot be substituted.
- Reading the mix variance alone without the yield.
Quick revision
- Mix = actual input in standard mix v actual use, at standard price. Yield = standard input for actual output v actual input, at standard cost per kg.
- Mix + yield = usage. Total mix in kg = zero.
- Only when substitutable. Weigh cost and quality before changing the mix.
How the marks are earned
- Standard-mix quantities and signs.
- Both variances with a check.
- Comment on cost and quality.
Practice questions
These are original questions, written in the style of the Skills examination. Work each one before you open the answer.
Recall check: multiple choice
Question 1. Mix and yield variances are meaningful only when the materials are:
- Substitutable, so that the mix can be varied
- Always identical
- Fixed in price
- Imported
Show the answer
A. Otherwise nobody controls the proportions.
Question 2. The mix variance plus the yield variance equals:
- The price variance
- The sales variance
- Zero
- The total material usage variance
Show the answer
D. They split the usage variance.
Question 3. The total mix variance in quantity is:
- Positive
- Negative
- Always zero
- The yield
Show the answer
C. The same total is shared in different proportions.
Question 4. The mix variance compares actual use with the quantities in:
- Last year’s mix
- The standard mix applied to the actual total input
- The budget
- The cheapest mix
Show the answer
B. It is valued at standard prices.
Question 5. A favourable mix variance means the actual mix was:
- Cheaper than the standard mix
- Dearer than the standard mix
- Equal to it
- Unrelated to cost
Show the answer
A. More of the cheaper materials were used.
Question 6. The yield variance compares:
- Price with usage
- Budgeted with actual sales
- Actual output with the output the actual input should have given
- Two mixes
Show the answer
C. Or, equivalently, actual input with the standard input for actual output.
Question 7. The yield variance is valued at the:
- Actual price
- Selling price
- Average price
- Standard cost of input or output
Show the answer
D. Both methods give the same value.
Question 8. A cheaper mix may:
- Always raise profit
- Lower quality and cause an adverse yield
- Remove all variances
- Raise the selling price
Show the answer
B. A favourable mix may be offset by an adverse yield.
Question 9. The standard cost per kg of input equals:
- The standard cost of a unit ÷ the standard kg of input per unit
- The actual price
- The yield
- The mix
Show the answer
A. It is the average cost of the standard mix.
Question 10. In the line-by-line method, the difference between actual quantity in the actual mix and in the standard mix, at standard prices, is the:
- Yield variance
- Price variance
- Mix variance
- Rate variance
Show the answer
C. The next line gives the yield.
Section B style: written questions
Question 11 (10 marks). (a) Explain when the usage variance should be split into mix and yield. (3 marks) (b) Explain the mix variance and the yield variance. (4 marks) (c) State TWO factors to consider before changing a mix. (3 marks)
Question 12 (15 marks). A unit uses 4 litres of X at ₦200 and 6 litres of Y at ₦300 (10 litres, ₦2,600). In a month 500 units were made, using 2,300 litres of X and 2,900 litres of Y.
(a) Calculate the usage variance for each material and in total. (4 marks) (b) Calculate the mix variance. (4 marks) (c) Calculate the yield variance by both methods. (4 marks) (d) Comment on the result. (3 marks)
Question 13 (20 marks). A unit uses 5 kg of P at ₦40 and 5 kg of Q at ₦60 (10 kg, ₦500). In a month 600 units were made, using 3,300 kg of P and 3,000 kg of Q.
(a) Calculate the usage variance of each material and in total. (5 marks) (b) Calculate the mix variance. (4 marks) (c) Calculate the yield variance. (3 marks) (d) Present the mix and yield variances in the line-by-line layout. (4 marks) (e) Discuss factors to consider when changing a mix. (4 marks)
Model answers
Show the model answer to Question 11
(a) When the product has two or more materials that can be substituted, so that the proportions can be varied by management (3).
(b) Mix: the effect of using a different combination from the standard, found by comparing actual use with the actual total in standard proportions, at standard prices. Yield: the effect of the total input giving more or less output than standard, valued at the standard cost of input or output (4).
(c) Any two: cost; quality and customer acceptance; availability; process limits (3).
Show the model answer to Question 12
(a)
- Standard quantities: X 2,000, Y 3,000.
- X: 2,000 − 2,300 = 300 A × 200 = 60,000 A.
- Y: 3,000 − 2,900 = 100 F × 300 = 30,000 F.
- Total ₦30,000 A (4).
(b)
- Actual input 5,200 litres.
- Standard mix.
X 40% = 2,080 - Y 60% = 3,120.
- X: 2,080 − 2,300 = 220 A × 200 = 44,000 A.
- Y: 3,120 − 2,900 = 220 F × 300 = 66,000 F.
- Mix ₦22,000 F (4).
(c)
- Standard input 5,000 litres; actual 5,200; 200 A × ₦260 = ₦52,000 A.
- By output.
5,200 litres should give 520 units; actual 500; 20 A × 2,600 = 52,000 A (4).
(d)
- Check.
22,000 F − 52,000 A = 30,000 A. - The cheaper blend (more X, less Y) saved ₦22,000 but the yield fell, costing ₦52,000, so the change of mix was uneconomic and the process should be investigated (3).
Show the model answer to Question 13
(a) Standard quantities: P 3,000, Q 3,000. P: 3,000 − 3,300 = 300 A × 40 = 12,000 A. Q: nil. Total ₦12,000 A (5).
(b)
- Actual input 6,300 kg; standard mix 50:50 gives 3,150 each.
- P: 3,150 − 3,300 = 150 A × 40 = 6,000 A.
- Q: 3,150 − 3,000 = 150 F × 60 = 9,000 F.
- Mix ₦3,000 F (4).
(c)
- Standard input 6,000 kg; actual 6,300; 300 A × ₦50 = ₦15,000 A.
- Check 3,000 F − 15,000 A = 12,000 A (3).
(d)
- Actual in actual mix at standard.
3,300 × 40 + 3,000 × 60 = 132,000 + 180,000 = 312,000. - Actual in standard mix.
6,300 × 50 = 315,000 (mix 3,000 F). - Standard for actual output.
6,000 × 50 = 300,000 (yield 15,000 A) (4).
(e) Cost: a favourable mix may be offset by an adverse yield; quality and customer acceptance; availability of materials; process limits (4).
Pathfinder on Material mix and yield variances
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
Price, mix, yield, sales price, market size and share variances; strategy in a declining market.
Revise first: Layouts for mix and yield variances
Source: ICAN Pathfinder, Performance Management. Diets covered: March/July Diet, 2020 to May Diet, 2026. All 13 diets in the Pathfinder are mapped.
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