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 x 2 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 Σx 2 142 500 Σxy 732 140 We now solve the following simultaneous equations: Σy Na bσx Σxy Σxa bσx 2 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 Subtract equation (2) from equation (3): 735 110 760a 142 500b (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) (b) (c) = 18 1000 0.1520 = 18 0.3499 = 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 = 18 5000 0.1520 = 18 0.274 = 4.9321 minutes Therefore the estimated time taken to produce 5000 units is 24 660 minutes (5000 4.9321 minutes) = 18 6000 0.1520 = 18 0.2665 = 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. Revised learning curve effect: = 18 1000 0.320 = 18 0.1096 = 1.9737 minutes Question 24.26 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. margin a 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, meaningless 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: yx ax b 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: For an output of 14 units: b log 0.8/log 2 0.322 y 14 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: y 50 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: y 30 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. Question 24.27 Note a Fixed 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 estimates and planned labour requirements. If standards are not adjusted, they will cease to represent meaningful targets and lead to the reporting of erroneous 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