Standard Costing and Variance
Arcada
Veronica Fellman
28 April 2003
Case
The following data relate to actual output, costs and variances for the four-weekly accounting period number 4 of a company that makes only one product. Opening and closing work in progress figures were the same.
Actual production of product Tonne 18 000 units
(£000)
Actual costs incurred
Direct materials purchased and used (150 000 kg) 210
Direct wages for 32 000 hours 136
Variable production overhead 38
Variances:
Direct materials price 15F
Direct materials usage 9A
Direct labour rate 8A
Direct labour efficiency 16F
Variable production overhead expenditure 6A
Variable production overhead efficiency 4F
Variable production overhead varies with labour hours worked. A standard marginal costing system is operated.
You are required to present a standard product cost sheet for one unit of product Tonne.
A = adverse variance (the budget is less than the actual cost) F = flexible variance (the actual cost is less than the budget)
Case Tonne
Standard product cost for one unit of product Tonne £
Direct materials (8 kg (W2) at £ (W1) per kg)
Direct wages (2 hours (W4) at £4 (W3) per hour)
Variable overhead (2 hours (W4) at £1 (W5) per hour)
Total
Workings
W1 Actual quantity of materials purchased at standard price is £225 000 (actual cost plus favourable material price variance). Standard price = £ (£225 000 / 150 000kg)
W2 Material usage variance = 6 000 kg (£9 000 / £ standard price). Therefore standard quantity for actual production = 144 000 kg (150 000 – 6 000 kg). Therefore standard quantity per unit = 8 kg (144 000 kg / 18 000 units).
W3 Actual hours worked at standard rate = £128 000 (£136 000 - £8 000). Therefore standard rate per hour = £4 (£128 000 / 32 000 hours)
W4 Labour efficiency variance = 4 000 hours (£16 000 / £4). Therefore standard hours for actual production = 36 000 hours (32 000 + 4 000). Therefore standard hours per unit = 2 hours (36 000 hours / 18 000 units) Labour efficiency variance = (standard quantity of labour hours for actual production – actual labour hours) x standard wage rate
W5 Actual hours worked at the standard variable overhead rate is £32 000 (£38 000 actual variable overheads less £6 000 favourable expenditure variance). Therefore standard variable overhead rate = £1 (£32 000 / 32 000 hours).
Material mix variance - optional
Example: A company has established the following standard mix for producing 9 litres of product A:
5 litres of material X at £7 per litre, £ 35
3 litres of material Y at £5 per litre, £ 15
2 litres of material Z at £2 per litre, £ 4
£54
A standard loss of 10% of input is expected to occur. Actual input was
53 000 litres of material X at £7 per litre, £ 371 000
28 000 litres of material Y at £ per litre, £ 148 400
19 000 litres of material Z at £ per litre, £ 41 800
£561 200
The total input for the period is 100 000 litres, and, using the standard mix, an input of 50 000 litres of X (5/10 x 100 000), 30 000 litres of Y (3/10 x 100 000) and 20 000 litres of Z (2/10 x 100 000) should have been used. However, 53 000 litres of X, 28 000 litres of Y and 19 000 litres of Z were used. Therefore, 3 000 additional litres of X at a standard price of £7 per litre were substituted for 2 000 litres of Y (at a standard price of £5 per litre) and 1 000 litres of Z (at a standard price of £2 per litre). A material mix variance of £9 000 will therefore be reported. The formula for the material mix variance is as follows:
(Actual quantity in standard mix proportions – actual quantity used) x standard price
If we apply this formula, the calculation is as follows:
Actual usage in standard proportions: £ Actual usage in actual proportions: £
X = 50 000 litres (5/10 x 100 000) at £7 350 000 X = 53 000 litres at £7 371 000
Y = 30 000 litres (3/10 x 100 000) at £5 150 000 Y = 28 000 litres at £5 140 000
Z = 20 000 litres (2/10 x 100 000) at £2 40 000 Z = 19 000 litres at £2 38 000
Total 540 000 549 000
Mix variance = £9 000A
Direct materials yield variance - optional
The yield variance arises because there is a difference between the standard output for a given level of inputs and the actual output attained. In the previous example an input of 100 000 litres should have given an output of 90 000 litres of product A. In fact, 92 700 litres were produced, which means that the output was 2 700 litres greater than standard. This output is valued at the average standard cost per unit of output, which is calculated as follows: Each 10 liters of input is expected to yield 9 litres of output. The standard cost for this output is £54. Therefore the standard cost for one litre of output = £54 x 1/9 = £6
The yield variance will be £6 x 2 700 = £16 200 F. The formula is as follows:
(actual yield – standard yield from actual input of material) x standard cost per unit of output = (92 700 litres – 90 000 litres) x £6.
The material mix variance in the example is £9 000 adverse, while the material yield variance is £16 200 favourable. There was a trade-off in the material mix, which boosted the yield. This trade-off may have arisen because the prices of materials Y and Z have increased whereas the actual price paid for material X is identical with the standard price. The manager of the production process may have responded to the different relative prices by substituting material X (the most expensive material) for materials Y and Z. This substitution process has resulted in an adverse mix variance and a favourable yield variance. Note, however, that actual material cost per unit of output is £ (£561 200 / 92 700 litres) whereas the standard cost per unit is £6 (£54/9 litres). This difference has been partly caused by an adverse material price variance of £12 200.
Materials price, mix and yield variances are inter-related and individual variances should not be interpreted in isolation. Inter-dependencies should be recognized.
Material usage variance - optional
The material usage variance consists of the mix variance and the yield variance. The material usage variance is therefore a favourable variance of £7 200, consisting of an adverse mix variance of £9 000 and a favourable yield variance of £16 200. To calculate the material usage variance, we compare the standard quantity of materials for the actual production with the actual quantity of materials used and multiply by the standard material prices in the normal way. The calculations are as follows:
Standard quality for actual production at standard prices:
Actual production of 92 700 litres requires an input of 103 000 litres (92 700 x 10/9), consisting of £
51 500 litres of X (103 000 x 5/10) at £7 per litre 360 500
30 900 litres of Y (103 000 x 3/10) at £5 per litre 154 500
20 600 litres of Z (103 000 x 2/10) at £2 per litre 41 200
Total 556 200 (i)
Actual quantity at standard prices:
53 000 litres of X at £7 per litre 371 000
28 000 litres of Y at £5 per litre 140 000
19 000 litres of Z at £2 per litre 38 000
Total 549 000 (ii)
Material usage variance (i) – (ii) = £7 200F
Summary of material variances - optional
The total material variance and the price variances are calculated using the approaches described in the previous chapter. The calculations are as follows:
Total material variance:
Standard cost for actual production (92 700 x £6) = £556 200
Actual cost (£561 200)
= £5 000A
Material price variances, (standard price – actual price) x actual quantity:
Material X = (£7 - £7) x 53 000 = 0
Material Y = (£5 - £) x 28 000 = £8 400A
Material Z = (£2 - £) x 19 000 = £3 800A
£12 200A
Recording standard costs in the accounting
Drury, p. 590-596 - optional
Standard costs can be used for planning, control, motivation and decision-making purposes without being entered into the books.
Purchase of materials
Usage of materials
Direct wages
Manufacturing overhead costs incurred
Absorption of manufacturing overheads and recording the variances
Completion of production
Sales
Calculation of profit
Transfer pricing
Anthony and Dearden:
Motivate manager to make sound decisions
Report of reasonable measures of the managerials performance of the division
Divisional autonomy is not undermined.
Intermediate products: goods transferred from the supplying division to the receiving division
Final products: Goods sold be the receiving division to the outside market
In a perfectly competitive market for an intermediate product, the current market price is the most suitable basis for setting the transfer price. Then the supplying division should supply as much as the receiving division requires at the current market price, so long as the incremental cost is lower than the market price. If the supplying division produces more of the intermediate product than the receiving division requires, the excess can be sold to the outside market at the current market price.
Transfer pricing in divisionalized companies
Purchase and sale of intermediate product in the external market
Supplying division
Intermediate external product market
Incremental costs of 1 000 units = £5 000
Market price for 1 000 units = £8 000
Contribution = £3 000
Receiving division
Final product market
Contribution = £6 000
Total company contribution = £9 000
1 000 units purchased at market price = £8 000
Incremental processing costs = £4 000
Sales revenue = £18 000
Supplying division
(b) Purchase and sale of intermediate product internally
Incremental costs of transfer = £5 000
Transfer price = £8 000
Receiving division
Contribution = £3 000 (supplying division)
External market
Transfer price = £8 000 Incremental costs = £4 000
Sales revenue of final product = £18 000
Contribution = £6 000 (receiving division)
Total company contribution = £9 000
Drury, p. 795
Transfer pricing
When there is no market for the intermediate product, economic theory indicates that the theoretically correct transfer price to encourage total organizational optimality is, in the absence of capacity constraints, the marginal cost of producing the intermediate product at theoptimal output level for the company as a whole:
(marginal cost of supplying division) + (marginal cost of receiving division) = (marginal revenue of receiving division)
(marginal cost of supplying division) = (marginal revenue of receiving division) - (marginal cost of receiving division)
= (marginal cost of the supplying division) = (net marginal revenue of the receiving division)
Figure: Allocation of output of supplying division between intermediate and external market.
Output units Marginal cost of supplying division £ Allocation per ranking Marginal revenue/net marg. rev. £
1 19 Intermediate market
2 18 Intermediate market
3 17 Final market
4 15 Intermediate market
5 14 Final market
6 15 Final market
7 16 Intermediate market
8 18 Final market
9 20 Final market
10 23 Intermediate market
11 27 Final market
12 32 No allocation
Transfer pricing
Effect of cost-plus based transfer prices
Supplying division Receiving division
Units produced Variable (marginal) cost, £ Units produced Net marginal revenue, £
1 10 1 20
2 10 2 19
3 10 3 18
4 10 4 17
5 10 5 16
6 10 6 15
7 10 7 14
8 10 8 13
9 10 9 12
10 10 10 11
11 10 11 10
12 10 12 9
Transfers should be at a standard marginal cost and not at actual costs.
Transfer pricing
A
MCS
C
D
P
B
Revenue/cost per unit
Q1 Q2
Output
Intermediate market price
MRS=P
NMR = MRS - MCR
Perfect external market for the intermediate product
Transfer pricing, case
A company has two divisions. The South division manufactures an intermediate product for which there is no intermediate external market. The North division incorporates this intermediate product into a final product, which it sells. One unit of the intermediate product is used in the production of the final product. The expected units of the final product which the North division estimates it can sell at various selling prices are as follows:
Net selling price, £ Quantity sold, units
100 1 000
90 2 000
80 3 000
70 4 000
60 5 000
50 6 000
The costs of each division is as follows: South, £ North, £
Variable cost per unit 11 7
Fixed cost per annum 60 000 90 000
The transfer price is £35 for the intermediate product, and it is determined on a full cost-plus basis. You are required to:
Prepare profit statements for each division and the company as a whole for the various selling prices.
State which price maximizes the profit of the North division and the company as a whole, and comment on why the latter selling price is not selected by the North division.
Transfer pricing, case
The contributions for each division and the company as a whole for the various selling prices are as follows:
The South division:
Output level, units Total revenues, £ Variable costs, £ Total contribution, £ - fixed costs 60 000
1 000 35 000 11 000 24 000 - 36 000
2 000 70 000 22 000 48 000 - 12 000
3 000 105 000 33 000 72 000 12 000
4 000 140 000 44 000 96 000 36 000
5 000 175 000 55 000 120 000 60 000
6 000 210 000 66 000 144 000 84 000
The North division:
Output level, units Total revenues, £ Variable costs, £ Total cost of transfers, £Total contribution, £ (-FC90000)
1 000 100 000 7 000 35 000 58 000 (- 32 000)
2 000 180 000 14 000 70 000 96 000 (6 000)
3 000 240 000 21 000 105 000 114 000 (=£80)(24 000)
4 000 280 000 28 000 140 000 112 000 (22 000)
5 000 300 000 35 000 175 000 90 000 (0)
6 000 300 000 42 000 210 000 48 000 (-42 000)
The whole company:
Output level, units Total revenues, £ Company variable costs, £ Company contribution, £ - fixed costs 150 000
1 000 100 000 18 000 82 000 -68 000
2 000 180 000 36 000 144 000 -6 000
3 000 240 000 54 000 186 000 36 000
4 000 280 000 72 000 208 000 58 000
5 000 300 000 90 000 210 000 (= £60) 60 000
6 000 300 000 108 000 192 000 42 000
