Advanced: Regression analysis and an analysis of costs where unit variable cost is not constant (See note on page 984)

Babel Ltd produces a single product. The com¬ pany’s directors want to explore new markets, and they require an accurate analysis of the firm’s cost structure for both forecasting and pricing purposes. An attempt to provide this analysis from the aggregation of individual costs has produced a poor correspondence between actual and predicted costs. You are an accountant employed by Babel Ltd, and you have been asked to provide a statis¬ tical approach to the problem.

The financial director has given you the follow¬ ing data:

You obtain the following further information:
(1) The costs from which the averages have been computed consist of the firm’s entire costs for the relevant month.
(2) Fixed costs can be assumed to be unaffected by seasonal factors except for winter heating. In January and February a supplementary heating system was employed; this cost £10000 per month to operate.
You are asked to transform the original data in any way which may be necessary. Work to the nearest £100 for total costs and to the nearest £0.1 Op for unit cost calculations.
Requirements.

(a) Estimate Babel Ltd’s normal fixed and vari¬ able cost of production using linear regres¬ sion, showing full workings. (7 marks)

(b) Draw a graph of Babel Ltd’s costs versus output to provide a better analysis of costs than the regression estimates in part (a), estimate the point at which variable costs change and estimate the linear cost relation¬ ships over the relevant ranges. (5 marks)

(c) Use your answer from part

(b) to provide an analysis of costs from January to June, set out in spreadsheet format (i.e. rows and columns). Divide the rows into relevant cost categories to explain observed costs, and treat any re¬ sidual amounts as unexplained differences.
(6 marks)

(d) Discuss the difficulties which may be encoun¬
tered in preparing and using statistical cost estimation in practice. (7 marks)
(Total 25 marks) ICAEW P2 Management Accounting

Transcribed Image Text:

Month Output (000 units) Average unit cost () January 9 12.8 February 14 13.0 March 11 11.4 April 8 12.0 May 6 13.0 June 12 11.7