A firm of accountants in Enugu prices an audit on the basis that each audit needs 1 hour of a senior’s time and 4 hours of a junior’s. In practice the team that does the work is mixed differently: more senior hours and fewer junior hours, because two juniors were on leave. The total hours worked may be the same as the standard, but the cost is not.
A single labour efficiency variance would hide the reason.
If a product or service is made by grades of labour that can be substituted for each other, the efficiency variance can be split into a labour mix variance, which shows the effect of using a different combination of grades from the standard. A labour yield variance, which shows the effect of the total hours worked being more or fewer than the standard for the output.
The method is exactly the same as for materials, with hours of each grade in place of kilograms of each material. This topic explains how to calculate them, how they fit with the rate and idle time variances, and how to interpret them. The worked method in the course reading is given for materials, so the labour version here applies the same method to grades of labour.
It builds on the earlier topic on material mix and yield variances. The next topic covers sales mix and quantity variances.
In 30 seconds
The labour efficiency variance for a product made by several grades of labour is the sum of the efficiency variance for each grade: (standard hours for the actual output − actual hours worked) × the grade’s standard rate.
If the grades are substitutable, it splits into:
- the labour mix variance = (hours of each grade in the standard proportions of the actual total hours − actual hours of that grade) × standard rate of that grade, summed
- the total in hours is zero
- the labour yield variance = (standard hours for the actual output − total actual hours worked) × the average standard rate per hour
Mix + yield = labour efficiency variance. The rate variance (hours paid × standard rate against actual cost) and the idle time variance are calculated first and kept separate; efficiency uses hours worked. A mix variance is adverse when more of the dearer grade (or less of the cheaper) is used than the standard mix.
An adverse mix may be justified if the dearer grade works faster or with fewer errors, which would appear as a favourable yield variance. Full marks come from the grade-by-grade table, the check to the efficiency total and a comment on cause.
Mix and yield for labour
When the split is meaningful
Many outputs need more than one grade of labour: skilled, semi-skilled and unskilled workers in a factory, or partner, manager and junior staff in a professional firm. Each grade has a different standard rate. The standard cost card shows the hours of each grade per unit.
If management can vary the proportions, by using more of one grade and less of another, the efficiency variance can be analysed into a mix element and a yield element. If the grades cannot be substituted (a task that only a qualified electrician can do), the split has no meaning. The efficiency variance for each grade is reported on its own.
Efficiency variance by grade
For each grade: standard hours for the actual output (units × standard hours per unit) less actual hours worked, times the grade’s standard rate. Favourable if fewer hours were worked than standard. Add the grades for the total. Rate variance (on hours paid) and idle time are dealt with first, as in the earlier topic.
The mix variance
- Take the total actual hours worked across all grades.
- Share them between the grades in the standard proportions.
- For each grade: standard-mix hours − actual hours worked (positive = fewer hours than the standard mix: favourable). The total in hours is zero.
- Multiply by the grade’s standard rate, and add.
The total is adverse if the actual mix has more of the dearer grades than the standard, favourable if more of the cheaper.
The yield variance
The labour yield variance is (standard hours for the actual output − total actual hours worked) × the average standard rate per hour (the standard labour cost of a unit ÷ standard hours per unit). It shows the effect of the team taking more or fewer total hours than it should have for the output, with the standard mix.
This is the labour equivalent of the materials yield variance, and is sometimes simply called the efficiency element.
Interpreting the variances
- Favourable mix, adverse yield. The cheaper grades were used more, saving rate cost, but the work took more hours in total. Is the saving worth it? It often is not: more total hours may also mean more idle time, more supervision and more errors.
- Adverse mix, favourable yield. More of the dearer, more skilled grade was used and the work was done in fewer hours or with less rework. This can be sound management, for example when a rush order or a difficult job calls for experience.
- Causes. Shortages of staff of a grade (leave, resignations, hiring problems); deliberate substitution to cut costs; training of juniors by seniors; poor planning of work between grades.
- Interrelationships. The labour rate variance, the mix variance and the yield variance may all arise from one decision to change the team. A lower-grade team gives a favourable rate variance (cheaper rates), an adverse yield (slower work) and, when the grades are compared with the standard mix, a favourable mix. They should be looked at together, and any variance reported to the manager who can control it.
- Limits. The split depends on the standard mix being right and on the grades being truly substitutable. A mix that is cheaper per hour but produces lower quality may harm customers, an effect that the variances do not show.
Layouts for labour mix and yield
- Standard hours for actual output, by grade and in total; average standard rate per hour.
- Efficiency by grade: (standard hours − actual hours worked) × standard rate; total.
- Mix: total actual hours × standard proportion; difference from actual; × standard rate; total.
- Yield: (total standard hours − total actual hours) × average standard rate.
- Check: mix + yield = efficiency.
Money is in naira and each answer is rounded once, at the end.
Worked examples
Example 1: three grades. A unit needs 2 hours of skilled labour at ₦900, 3 hours of semi-skilled at ₦500 and 1 hour of unskilled at ₦300 (6 hours, ₦3,600, so ₦600 an hour). In a month 1,000 units were made; hours worked were skilled 1,800, semi-skilled 3,200 and unskilled 1,300 (6,300 hours). Required: the efficiency, mix and yield variances.
- Standard hours for 1,000 units. Skilled 2,000; semi-skilled 3,000; unskilled 1,000; total 6,000.
- Efficiency by grade.
Skilled: 2,000 − 1,800 = 200 F × 900 = ₦180,000 F.
Semi-skilled: 3,000 − 3,200 = 200 A × 500 = ₦100,000 A.
Unskilled: 1,000 − 1,300 = 300 A × 300 = ₦90,000 A.
Total ₦10,000 A. - Mix.
Standard proportions of 6,300 hours: skilled 2/6 × 6,300 = 2,100
semi-skilled 3/6 × 6,300 = 3,150
unskilled 1/6 × 6,300 = 1,050.
Skilled: 2,100 − 1,800 = 300 F × 900 = 270,000 F.
Semi-skilled: 3,150 − 3,200 = 50 A × 500 = 25,000 A.
Unskilled: 1,050 − 1,300 = 250 A × 300 = 75,000 A.
Total ₦170,000 F; hours sum to zero. - Yield.
(6,000 − 6,300) = 300 hours A × ₦600 = ₦180,000 A. - Check.
170,000 F − 180,000 A = 10,000 A, equal to the efficiency total. - Comment. Fewer skilled hours than the standard mix would give looks like a saving of ₦170,000, but 300 more hours were needed in total, costing ₦180,000. The work was done more slowly overall, and the net result is adverse.
Expect variants: a rate variance and idle time given as well, a standard mix of two grades, and a question asking whether a change of team was justified.
Common mistakes
- Using hours paid instead of hours worked for efficiency, mix and yield.
- Using standard hours instead of actual total hours when finding the standard-mix hours.
- Valuing the yield at one grade’s rate instead of the average.
- Splitting when grades are not substitutable.
- Ignoring the interrelationship with rate and quality.
Quick revision
- Efficiency = mix + yield. Mix: actual hours in standard proportions v actual, at each grade’s standard rate. Yield: standard hours v actual total hours, at average standard rate.
- Hours worked, not paid; rate and idle time first.
- Read mix and yield together.
How the marks are earned
- Grade table with correct hours and signs.
- Check to the efficiency variance.
- Comment on cause and whether the change was justified.
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. A labour mix variance is meaningful when:
- Only one grade is used
- Grades of labour can be substituted
- All wages are fixed
- There is idle time
Show the answer
B. Management can vary the proportions.
Question 2. The labour mix variance plus the labour yield variance equals:
- The labour efficiency variance
- The rate variance
- The idle time variance
- The total labour variance
Show the answer
A. Excluding rate and idle time.
Question 3. The mix variance compares actual hours of each grade with:
- Budgeted hours
- Hours paid
- Last year’s hours
- The total actual hours in the standard proportions
Show the answer
D. Valued at each grade’s standard rate.
Question 4. The labour mix variance is valued at the:
- Actual rate
- Selling price
- Standard rate of each grade
- Average actual rate
Show the answer
C. Rates are standard in efficiency variances.
Question 5. The labour yield variance is valued at the:
- Highest standard rate
- Average standard rate per hour
- Lowest rate
- Actual rate
Show the answer
B. Standard labour cost per unit ÷ standard hours per unit.
Question 6. Using more of the higher-paid grade than the standard mix gives:
- An adverse mix variance
- A favourable mix variance
- No mix variance
- A rate variance only
Show the answer
A. The actual mix is dearer than standard.
Question 7. Idle time is:
- Included in hours worked
- Ignored
- Excluded from hours worked and reported separately
- A mix effect
Show the answer
C. Efficiency uses hours worked.
Question 8. The labour rate variance is calculated on:
- Standard hours
- Hours worked
- Budgeted hours
- Hours paid for
Show the answer
D. Separately from mix and yield.
Question 9. A favourable mix variance may be:
- Offset by an adverse yield variance
- Always a gain
- Never explained
- Equal to the rate variance
Show the answer
A. Cheaper staff may take longer.
Question 10. The total of the mix variance in hours is:
- Positive
- Negative
- Zero
- Equal to the yield
Show the answer
C. Hours only move between grades.
Section B style: written questions
Question 11 (10 marks). (a) Explain the labour mix and yield variances. (6 marks) (b) State TWO causes of an adverse mix variance. (2 marks) (c) Explain how they relate to the rate variance. (2 marks)
Question 12 (15 marks). A unit needs 3 hours of senior time at ₦1,000 and 5 hours of junior time at ₦400 (8 hours, ₦5,000). 800 units were made; hours worked were senior 2,300 and junior 4,300.
(a) Calculate the efficiency variance for each grade and in total. (4 marks) (b) Calculate the mix variance. (4 marks) (c) Calculate the yield variance. (3 marks) (d) Comment. (4 marks)
Question 13 (20 marks). A unit needs 1 hour of grade A at ₦800 and 4 hours of grade B at ₦300 (5 hours, ₦2,000). 1,500 units were made; hours worked were A 1,700 and B 5,800.
(a) Explain when mix and yield variances are meaningful. (4 marks) (b) Calculate the efficiency variance by grade and in total. (4 marks) (c) Calculate the mix variance. (4 marks) (d) Calculate the yield variance. (3 marks) (e) Interpret the result and say whether the change of team could be justified. (5 marks)
Model answers
Show the model answer to Question 11
(a) The mix variance shows the cost effect of using a different combination of grades from the standard: actual total hours in standard proportions compared with actual hours by grade, at standard rates (3). The yield variance shows the effect of total hours being different from the standard for the output, valued at the average standard rate (3).
(b) Any two: shortage of a grade; deliberate substitution; training; poor planning (1 each).
(c) A change of team may cause a favourable rate variance (cheaper staff), an adverse yield (slower work) and a mix variance; they should be read together (2).
Show the model answer to Question 12
(a)
- Standard hours: senior 2,400; junior 4,000.
- Senior.
2,400 − 2,300 = 100 F × 1,000 = 100,000 F. - Junior.
4,000 − 4,300 = 300 A × 400 = 120,000 A. - Total ₦20,000 A (4).
(b)
- Total hours 6,600; standard proportions senior 3/8 × 6,600 = 2,475, junior 5/8 × 6,600 = 4,125.
- Senior.
2,475 − 2,300 = 175 F × 1,000 = 175,000 F. - Junior.
4,125 − 4,300 = 175 A × 400 = 70,000 A. - Mix ₦105,000 F (4).
(c)
- Standard hours 6,400; actual 6,600; 200 A × ₦625 = ₦125,000 A.
- Check 105,000 F − 125,000 A = 20,000 A (3).
(d) More senior and fewer junior hours would normally be dearer, but the actual team used more junior hours than the standard mix gives, so the mix is favourable. The total hours were 200 over standard, costing ₦125,000, and the net result is adverse (4).
Show the model answer to Question 13
(a) When the grades can be substituted so that management can vary the proportions; if not, report the efficiency variance by grade (4).
(b)
- Standard hours: A 1,500; B 6,000.
- A: 1,500 − 1,700 = 200 A × 800 = 160,000 A.
- B: 6,000 − 5,800 = 200 F × 300 = 60,000 F.
- Total ₦100,000 A (4).
(c)
- Total hours 7,500; standard mix A 1/5 × 7,500 = 1,500; B 6,000.
- A: 1,500 − 1,700 = 200 A × 800 = 160,000 A.
- B: 6,000 − 5,800 = 200 F × 300 = 60,000 F.
- Mix ₦100,000 A (4).
(d) Standard hours 7,500 = actual 7,500; yield nil (3).
(e) All of the variance is mix: 200 hours of the dearer grade A replaced 200 hours of the cheaper grade B, at a net cost of ₦100,000, and total hours did not change. It could be justified only if grade A’s work brought benefits not measured here, such as higher quality or avoiding rework (5).
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