Cost estimation and cost behaviour
Solutions to Chapter 24 questions
Question 24.25 (a) The first stage is to convert all costs to a 2002 basis. The calculations are as follows:
1998 1999 2000 2001
(£000) (£000) (£000) (£000)
Raw materials
Skilled labour 242(1.2)4 344(1.2)3 461(1.2)2 477(1.2)
Unskilled labour
Factory overheads 168(1.15)3(1.2) 206(1.15)2(1.2) 246(1.15)(1.2) 265(1.2)
Power 25(1.1)(1.25)3 33(1.25)3 47(1.25)2 44(1.25)
Raw materials
Skilled labour 500.94 595.12 663.84 572.4
Unskilled labour
Factory overheads 306.432 326.304 339.48 318
Power 53.625 64.35 73.32 55
Total (2002 prices) 861 000 986 000 1 077 000 945 000
Output (units) 160 000 190 000 220 000 180 000
The equation Υ a bx is calculated from the above schedule of total production
costs (2002 prices) and output. The calculations are as follows:
Output Total cost
in units (000) (£000)
x y x2 xy
160 861 25 600 137 760
190 986 36 100 187 340
220 1077 48 400 236 940
180 945 32 400 170 100
––– –––– ––––––– –––––––
Σx 750 Σy 3869 Σx2 142 500 Σxy 732 140
––– –––– ––––––– –––––––
We now solve the following simultaneous equations:
Σy Na bΣx
Σxy Σxa bΣx2
Therefore
3869 4a 750b (1)
732 140 750a 142 500b (2)
Multiply equation (1) by 190 (142 500/750) and equation (2) by 1. Then equation (1)
becomes
735 110 760a 142 500b (3)
Subtract equation (2) from equation (3):
2970 = 10a
a 297
192 COST ESTIMATION AND COST BEHAVIOUR
Substitute for a in equation (1):
3869 4 x 297 750b
2681 750b
b 3.57
The relationship between total production costs and volume for 2002 is:
y £297 000 3.57x
where y total production costs (at 2002 price) and x output level.
(b) See pages 1047–1051 in Chapter 24 for the answer to this question.
(c) General company overheads will still continue whether or not product LT is
produced. Therefore the output of LT will not affect general production
overheads. Consequently, the regression equation should not be calculated from
cost data that includes general company overheads. General company overheads
will not increase with increments in output of product LT. Hence short-term
decisions and cost control should focus on those costs that are relevant to
production of LTs. Common and unavoidable general fixed costs are not relevant
to the production of LT, and should not be included in the regression equation.
(a) Question 24.26
Y1000 = 18 × 1000 – 0.1520
Y1000 = 18 × 0.3499
Y1000 = 6.2990 minutes
The cumulative average time taken to produce 1000 units is 6.2990 minutes and
the time taken to produce a total of 1000 units will therefore be 629.9 minutes
(i.e. 104.98 hours).
(£)
Standard cost of 1000 units:
Materials (£28/0.95 × 1000) 29 474
Processing cost (104.98 hours at £25) 2625
––––––
32 099
––––––
(b)
Y5000 = 18 × 5000 – 0.1520
Y5000 = 18 × 0.274
Y5000 = 4.9321 minutes
Therefore the estimated time taken to produce 5000 units is 24 660 minutes
(5000 × 4.9321 minutes)
Y6000 = 18 × 6000 – 0.1520
Y6000 = 18 × 0.2665
Y6000 = 4.7973 minutes
Therefore the estimated time taken to produce 6000 units is 28 784 minutes
(6000 × 4.7973 minutes) so the 1000 units has taken an additional 68.73 hours
(28 784 minutes – 24 660 minutes) giving a standard variable processing cost of
£1718 (68.73 hours × £25). Adding the direct material cost of £29 474 gives a
total standard variable cost of £31 192.
(c) Revised learning curve effect:
Y1000 = 18 × 1000 – 0.320
Y1000 = 18 × 0.1096
Y1000 = 1.9737 minutes
COST ESTIMATION AND COST BEHAVIOUR 193
The estimated total time to produce 1000 units in April is 32.89 hours (1973.7
minutes/60) giving a total standard variable processing cost of £822 (32.89 hours ×
£25). The standard direct material cost will remain unchanged at £29 474 giving a
total standard cost of £30 296.
Original budgeted profit
(£)
Sales 60 000
Variable costs 32 099
––––––
Contribution 27 901
Fixed costs 20 000
––––––
Profit 7 901
––––––
Actual profit
(£) (£)
Sales (900 × £62) 55 800
Production costs: Direct materials 31 870
Variable processing 1 070
Fixed costs 24 840
––––––
57 780
Closing stock (100 units at revised standard cost of
£30.296 per unit) 3 030 54 750
–––––– ––––––
Profit 1 050
––––––
Variance calculations
Processing usage/efficiency variance (original standard of £2625 –
revised standard of £822) £1803F
Selling price variance (£62 actual price – £60 budgeted price) ×
900 units £1800F
Sales volume (900 actual volume – 1000 budgeted volume) × revised
stand. contrib. margina £2970A
Direct material cost (standard cost of 1000 × £29.474 – Actual cost
of £31 870) £2396A
Variable processing expenditure (Flexed budget of 2425 minutes ×
£25/60 – actual cost) £60A
Variable processing efficiency (1.9737 minutes revised standard ×
1000 units – actual time of 2 425 minutes) × stand. rate (£25 per hour) £188A
Fixed cost expenditure (Budgeted cost of £20 000 – Actual cost of
£24 840) £4840A
–––––––
Total variances £6851A
–––––––
Notes
a revised standard contribution margin = £60 selling price – revised variable cost
(£29.474 + £822/1000) = £29.704
Reconciliation statement
Original budgeted profit £7901
Less net variances as shown above £6851A
Actual profit £1050
(d) If budgets and standards are set without considering the learning effect, mean-
ingless standards are likely to be set that are easy to attain. Therefore favourable
variances would be reported that are not due to operational efficiency. Where
learning effects are expected, management should create an environment where
improvements are expected.
194 COST ESTIMATION AND COST BEHAVIOUR
(a) (i) The learning curve is expressed as: Question 24.27
yx axb
The exponent b is defined as the ratio of the logarithm of the learning curve
improvement rate divided by the logarithm of 2. For an 80% learning curve:
b log 0.8/log 2 0.322
For an output of 14 units:
y14 40 14 0.322 17.1 hours per unit
Time taken for 14 units 14 17.1 239.4 hrs
Actual hours 240
It would therefore appear that an 80% learning effect is a reasonable
assumption.
(ii) For an output of 50 units:
y50 40 50 0.322 11.35 hours per unit
Hours required for 50 units: 50 11.35 = 567.5 hrs
For an output of 30 units:
y30 40 30 0.322 13.38 hours per unit
Hours required for 30 units 30 13.38 401.4 hours
The time required for the additional 20 units 166.1 hours (567.5 401.4)
(iii) Estimated cost for an order of 30 units
(£)
Direct materials (30 £30) 900.00
Direct labour (401.4 hrs £6) 2408.40
Variable overhead (401.4 hrs £0.50) 200.70
Fixed overhead (401.4 £5)a 2007.00
–––––––
5516.10
–––––––
The above product cost has been calculated on an absorption costing basis in
accordance with the current standard absorption costing system.
Note
aFixed
overhead for the period £6000
Direct labour hours for the period 1200 (75% 40 hrs 10 employees
4 weeks)
Fixed overhead hourly rate £5 (£6000/1200)
Where the learning effect is present, unit product costs and labour hours will
not be constant per unit of output. Significant variations in product costs and
labour hours per unit of output are likely to occur at lower output levels. It is
therefore necessary to estimate the extent of the learning effect for standard
settings, budgeting and selling price quotations. Failure to take into account
the presence of the learning effect can result in significant errors in cost esti-
mates and planned labour requirements. If standards are not adjusted, they
will cease to represent meaningful targets and lead to the reporting of erro-
neous favourable variances.
(b) The statement refers to the fact that, with modern technology, there is a dramatic
decrease in the direct labour content of most goods and services. Recent studies
suggest that direct labour represents less than 10% of manufacturing cost and that
COST ESTIMATION AND COST BEHAVIOUR 195
overheads are more closely related to machine hours than direct labour hours.
With modern technology, output tends to be determined by machine speeds
rather than changes in labour efficiency. Consequently, the presence of the
learning effect as workers become more familiar with new operating procedures
is of considerably less importance.
The question implies that the learning curve is being replaced by an experience
curve. The experience curve relates to the fact that output and efficiency are
determined by manufacturing technologists such as engineers and production
planners. As these groups of individuals gain experience from a range of
applications of the new technology, efficiency improves and costs are minimized.
It is therefore claimed that the experience curve has replaced the learning curve.
However, the experience curve is extremely difficult to determine, and its impact
is likely to take place over a much longer time period. It is therefore extremely
difficult to capture the ‘experience effect’ within short-term standard setting,
budgeting and cost estimation activities.
196 COST ESTIMATION AND COST BEHAVIOUR