Advanced : Calculating optimum transfer prices and profits using differential ca lculus Megacorp pic is a divisionalized enterprise. Among its divisions are Chern and Drink . Both of these diVIsions have a wide range of independent activities. One product. Fizz , is made by Chern for Drink. Chern does not have any external customers for the product.

The central management of Megacorp pic delegates all pricing decisions to divisional management, and the pricing of Fizz has been a contentious issue . It has been suggested that Chern should give a transfer price schedule for the supply of Fizz. based on Chern's own production costs, and that all transfers would be made at Chern 's marginal cost. Drink would then order the quantity it requires each month Chern estimates its monthly total costs, TCc. for producing Fizz are as follows :

TCc = £10000 + £5.500c + £0.0020~

where Oc is the quantity of Fizz manufactured .

Drink incurs costs in using Fizz. Its monthly total costs (TC0) in using Fizz, excluding the transfer price, are:

TC 0 = £15 000 + £11 0o + £0.001 Qb where Oo is the quantity of product , each unit of which incorporates one unit of Fizz Dnnk estimates that the demand function for its product incorporating F1zz IS.

P0 = £45 - £0.00080o where Po is the price per unit of the product incorporating Fizz.

Neither division holds any stocks of Fizz .

Requirements

(a) (i) Calculate the quantity of Fizz production which would maximize profits for Megacorp pic;

(ii) calculate the transfer price corresponding to that production if Chern 's marginal cost is adopted for transfer pricing , and show the resulting profits for each division . (6 marks)

(b) (i) Calculate the quantity of F1zz which Drink would take (at Chern 's marginal cost) if it wanted to maximize its own profits;

(ii) calculate the transfer pnce corresponding to that quantity, and show the resulting profits for each division.

(5 marks)

(c) Examme the imp lications for Megacorp pic of the transfer pricmg issues involved 1n reqUirements

(a) and (b)

(6 marks)

(d ) Briefty describe the other main methods of transfer pricing and discuss their limitations.