Cost estimation and cost behaviour

Cost estimation and cost behaviour Question IM 4.1 Question IM 4. Question IM 4.3 Question IM 4.4 Question IM 4.5 Comparison of independent variables for cost estimates Discuss the conditions that should apply if linear regression analysis is to be used to analyse cost behaviour. ACCA Level Management Accounting (a) Briefly discuss the problems that occur in constructing cost estimation equations for estimating costs at different output levels. (7 marks) (b) Describe four different cost estimation methods and for each method discuss the limitations and circumstances in which you would recommend their use. (18 marks) Explain the learning curve and discuss its relevance to setting standards. (5 marks) ACCA Level Management Accounting (a) Comment on factors likely to affect the accuracy of the analysis of costs into fixed and variable components. (b) Explain how the analysis of costs into fixed and variable components is of use in planning, control and decision-making techniques used by the management accountant. (9 marks) (Total 17 marks) ACCA Level Management Accounting Abourne Ltd manufactures a microcomputer for the home use market. The management accountant is considering using regression analysis in the annual estimate of total costs. The following information has been produced for the twelve months ended 31 December: Number of Direct Total Output, employees, labour cost Y X 1 X hours, X 3 Month ( ) (numbers) (numbers) (hours) 1 38 00 300 8 4 480 40 480 30 30 4 700 3 41 400 350 30 4 800 4 51 000 500 3 5 10 5 5 980 530 3 5 150 6 60 380 640 35 5 700 7 70 440 790 41 7 10 8 3 70 50 41 3 00 9 75 800 80 41 7 300 10 71 90 780 39 7 00 11 68 380 750 38 6 400 1 33 500 70 33 3 960 Σ Y= Σ X 1 = Σ X = Σ X 3 = 637 00 6 300 40 65 0 178 COST ESTIMATION AND COST BEHAVIOUR

Additionally: ΣY = 36 614.05 10 6 ΣX1 = 3.858 10 6 ΣX = 14 954 ΣX 3 = 374.43 10 6 ΣX 1 Y = 373.537 4 10 6 ΣX Y =.81 84 10 6 ΣX 3 Y = 369.77 4 10 6 The management accountant wants to select the best independent variable (X 1, X or X 3 ) to help in future forecasts of total production costs using an ordinary leastsquares regression equation. He is also considering the alternatives of using the Hi- Lo and multiple regression equations as the basis for future forecasts. You are required to: (a) Identify which one of the three independent variables (X 1, X or X 3 ) given above is likely to be the least good estimator of total costs (Y). Give your reasons, but do not submit any calculations. (b) Compute separately, for the remaining two independent variables, the values of the two parameters and for each regression line. Calculate the coefficient of determination (R ) for each relationship. (c) State, with reasons, which one of these independent variables should be used to estimate total costs in the future given the results of (b) above. (d) Devise the two equations which could be used, using the Hi-Lo technique, instead of the two regression lines computed in (b) above and comment on the differences found between the two sets of equations. (5 marks) (e) Comment critically on the use of Hi-Lo and ordinary least-squares regression as forecasting and estimating aids using the above results as a basis for discussion. In addition, comment on the advantages and problems of using multiple regression for forecasting and estimating; and state whether, in your opinion, the management accountant should consider using it in the present circumstances. Note: The following formulae can be used to answer the above question. β = xy nxy x nx α = y βx α y+ β xy ny R = y ny α β = y y xy Se n Sβ = Se nx x ICAEW P Management Accounting COST ESTIMATION AND COST BEHAVIOUR 179

Question IM 4.6 Calculation of coefficient of determination A management accountant is analysing data relating to retail sales on behalf of marketing colleagues. The marketing staff believe that the most important influence upon sales is local advertising undertaken by the retail store. The company also advertises by using regional television areas. The company owns more than 100 retail outlets, and the data below relate to a sample of 10 representative outlets. Local Regional advertising by advertising Outlet Monthly the retail store by the company number sales ( 000) ( 000 per month) ( 000 per month) y x 1 x 1 0 6 4 30 8 6 3 40 1 10 4 340 1 16 5 40 18 6 460 8 0 7 50 16 6 8 600 15 30 9 70 14 36 10 800 0 46 The data have been partly analysed and the intermediate results are available below. Σy = 4550 Σy = 451 300 Σx 1 y = 58 040 Σx 1 = 113 Σx 1 = 1 533 Σx y = 11 100 Σx = 1 Σx = 6 10 Σx 1 x = 780 You are required to examine closely, using co-efficients of determination, the assertion that the level of sales varies more with movements in the level of local advertising than with changes in the level of regional company advertising. Note that the co-efficient of determination for y and x 1 may be calculated from r n x y x y = ( n x 1 ( x1 ) ) n y y ( ( ) ) 1 1 CIMA Stage 3 Management Accounting Techniques 180 COST ESTIMATION AND COST BEHAVIOUR

The Crispy Biscuit Company (CBC) has developed a new variety of biscuit which it has successfully test marketed in different parts of the country. It has, therefore, decided to go ahead with full-scale production and is in the process of commissioning a production line located in a hitherto unutilized part of the main factory building. The new line will be capable of producing up to 50 000 packets of new biscuit each week. The factory accountant has produced the following schedule of the expected unit costs of production at various levels of output: Production level (packets per week) (10 000) (0 000) (30 000) (40 000) (50 000) Unit costs (pence) Labour (1) 0.0 15.0 13.3 1.5 1.0 Materials 8.0 8.0 8.0 8.0 8.0 Machine costs () 8.0 5.0 4.0 3.5 3. Total direct costs 36.0 8.0 5.3 4.0 3. Factory overhead (3) 9.0 7.0 6.3 6.0 5.8 Total costs 45.0 35.0 31.6 30.0 9.0 (1) The labour costs represent the cost of the additional labour that would require to be taken on to operate the new line. () Machine costs include running costs, maintenance costs and depreciation. (3) Factory overhead costs are fixed for the factory overall but are allocated to cost centres at 5% of total direct costs. In addition to establishing product acceptability, the test marketing programme also examined the likely consumer response to various selling prices. It concluded that the weekly revenue likely to be generated at various prices was as follows: Retail price Revenue to CBC 0.6 15 190 0.68 14 960 0.78 11 310 0.84 10 500 0.90 10 350 0.98 4 900 The above prices represent the prices at which the product was test marketed, but any price between 0.60 and 0.99 is a possibility. The manufacturer receives 50% of the retail revenue. Requirements (a) Estimate the variable costs of producing the new biscuit, using any simple method (such as the high low method). (b) Using linear regression, estimate the relationship between the price charged by CBC and the expected demand. (c) Using the above estimates, calculate the optimum price and evaluate how sensitive your solution is to changes in this price. (d) Outline the practical problems faced in attempting to derive a unit cost for a new product. (Total 5 marks) ICAEW P Management Accounting The question provided the following formula for answering this question: x x y y n xy x y b = ( )( ) or ( x x) n x ( x) and a = y bx Question IM 4.7 Estimates of sales volume and revenues using regression analysis and calculation of optimum price using differential calculus COST ESTIMATION AND COST BEHAVIOUR 181

Question IM 4.8 Learning curves Question IM 4.9 The application of the learning curve to determine target cash flows Present a table of production times showing the following columns for E. Condon Ltd, which produces up to 16 units while experiencing a 90% learning curve, the first unit requiring 1000 hours of production time: (1) units produced, () total production time (hours), (3) average production time per unit in each successive lot (hours), (4) cumulative average production time per unit (hours), and (5) percentage decline in (4). (10 marks) ICAEW Management Accounting Leano plc is investigating the financial viability of a new product X. Product X is a short life product for which a market has been identified at an agreed design specification. It is not yet clear whether the market life of the product will be six months or 1 months. The following estimated information is available in respect of product X: (i) Sales should be 10 000 units per month in batches of 100 units on a just-in-time production basis. An average selling price of 100 per batch of 100 units is expected for a six month life cycle and 1050 per batch of 100 units for a 1 month life cycle. (ii) An 80% learning curve will apply in months 1 to 7 (inclusive), after which a steady state production time requirement will apply, with labour time per batch stabilising at that of the final batch in month 7. Reductions in the labour requirement will be achieved through natural labour turnover. The labour requirement for the first batch in month 1 will be 500 hours at 5 per hour. (iii) Variable overhead is estimated at per labour hour. (iv) Direct material input will be 500 per batch of product X for the first 00 batches. The next 00 batches are expected to cost 90% of the initial batch cost. All batches thereafter will cost 90% of the batch cost for each of the second 00 batches. (v) Product X will incur directly attributable fixed costs of 15 000 per month. (vi) The initial investment for the new product will be 75 000 with no residual value irrespective of the life of the product. A target cash inflow required over the life of the product must be sufficient to provide for: (a) the initial investment plus 33 1 / 3 % thereof for a six month life cycle, or (b) the initial investment plus 50% thereof for a 1 month life cycle. Note: learning curve formula: y=ax b where y = average cost per batch where a = cost of initial batch where x = total number of batches where b = learning factor (= 0.319 for 80% learning rate) Required: (a) Prepare detailed calculations to show whether product X will provide the target cash inflow over six months and/or 1 months. (17 marks) (b) Calculate the initial batch labour hours at which the cash inflow achieved will be exactly equal to the target figure where a six month life cycle applies. It has been determined that the maximum labour and variable overhead cost at which the target return will be achieved is 59 000. All other variables remain as in part (a). (c) Prepare a report to management which: (i) explains why the product X proposal is an example of a target costing/pricing situation; (ii) suggests specific actions which may be considered to improve the return on investment where a six month product cycle is forecast; 18 COST ESTIMATION AND COST BEHAVIOUR

(iii) comments on possible factors which could reduce the rate of return and which must, therefore, be avoided. (Total 35 marks) ACCA Paper 9 Information for Control and Decision Making Limitation plc commenced the manufacture and sale of a new product in the fourth quarter of 000. In order to facilitate the budgeting process for quarters 1 and of 001, the following information has been collected: (i) Forecast production/sales (batches of product): quarter 4, 000 30 batches quarter 1, 001 45 batches quarter, 001 45 batches (ii) It is estimated that direct labour is subject to a learning curve effect of 90%. The labour cost of batch 1 of quarter 4, 000 was 600 (at 5 per hour). The labour output rates from the commencement of production of the product, after adjusting for learning effects, are as follows: Question IM 4.10 Application of learning curve to determine the incremental costs for different production batches Total produced (batches) Overall average time per batch (hours) 15 79.51 30 71.56 45 67.8 60 64.40 75 6.5 90 60.55 105 59.15 10 57.96 Labour hours worked and paid for will be adjusted to eliminate spare capacity during each quarter. All time will be paid for at 5 per hour. (iii) Direct material is used at the rate of 00 units per batch of product for the first 0 batches of quarter 4, 000. Units of material used per batch will fall by % of the original level for each 0 batches thereafter as the learning curve effect improves the efficiency with which the material is used. All material will be bought at 1.80 per unit during 001. Delivery of the total material requirement for a quarter will be made on day one of the quarter. Stock will be held in storage capacity hired at a cost of 0.30 per quarter per unit held in stock. Material will be used at an even rate throughout each quarter. (iv) Variable overhead is estimated at 150% of direct labour cost during 001. (v) All units produced will be sold in the quarter of production at 100 per batch. Required: (a) Calculate the labour hours requirement for the second batch and the sum of the labour hours for the third and fourth batches produced in quarter 4, 000. (b) Prepare a budget for each of quarters 1 and, 001 showing the contribution earned from the product. Show all relevant workings. (14 marks) (c) The supplier of the raw material has offered to deliver on a just-in-time basis in return for a price increase to 1.90 per unit in quarter 1, 001 and per unit thereafter. (i) Use information for quarters 1 and, 001 to determine whether the offer should be accepted on financial grounds. (ii) Comment on other factors which should be considered before a final decision is reached. COST ESTIMATION AND COST BEHAVIOUR 183

(d) Limitation plc wish to prepare a quotation for 1 batches of the product to be produced at the start of quarter 3, 001. Explain how the learning curve formula y=ax b may be used in the calculation of the labour cost of the quotation. Your answer should identify each of the variables y, a, x and b. No calculations are required. (5 marks) (Total 30 marks) ACCA Level Cost and Management Accounting II 184 COST ESTIMATION AND COST BEHAVIOUR