Advanced: Estimates of sales volume and revenues using regression analysis and calculation of optimum price using differential calculus (See note on page 984)

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 50000 packets of new biscuit each week.

The factory accountant has produced the follow¬ ing schedule of the expected unit costs of produc¬ tion at various levels of output:

(1) The labour costs represent the cost of the additional labour that would require to be taken on to operate the new line.
(2) Machine costs include running costs, main¬ tenance costs and depreciation.
(3) Factory overhead costs are fixed for the factory overall but are allocated to cost centres at 25% 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:

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). (3 marks)

(b) Using linear regression, estimate the relation¬
ship between the price charged by CBC and the expected demand. (6 marks)

(c) Using the above estimates, calculate the opti¬ mum price and evaluate how sensitive your solution is to changes in this price. (8 marks)

(d) Outline the practical problems faced in attempting to derive a unit cost for a new product. (8 marks)
(Total 25 marks) ICAEW P2 Management Accounting

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Unit costs (pence) Production level (packets per week) (10 000) (20 000) (30 000) (40 000) (50 000) Labour (1) 20.0 15.0 13.3 12.5 12.0 Materials 8.0 8.0 8.0 8.0 8.0 Machine costs 8.0 5.0 4.0 3.5 3.2 (2) Total direct costs 36.0 28.0 25.3 24.0 23.2 Factory overhead 9.0 7.0 6.3 6.0 5.8 (3) Total costs 45.0 35.0 31.6 30.0 29.0