Advanced : Scarce capacity and the use of shadow prices Black and Brown are two divisions in a group of companies and both require intermediate products Alpha and Beta which are available from divisions A and B respectively Black and Brown divisions convert the intermediate products into products Blackalls and Brownalls respectively . The market demand for Blackalls and Brownalls considerably exceeds the production possible , because of the limited availability of intermediate products Alpha and Beta No external market exists for Alpha and Beta and no other inte1mediate product market is ava1lable to Black and Brown divisions.

Other data are as follows :

Black division Blackalls: Selling price per unit £45 Processing cost per unit £12 Intermediate products required per unit:

Alpha: 3 units Beta : 2 units Brown diviston Brownalls: Selling price per unit £54 A division Alpha :

Bdivision Beta :

Processing cost per unit £14 Intermediate products reqUired per unit:

Alpha. 2 umts Beta 4 units Variable cost per unit £6 Maximum production capacity 1200 units Variable cost per unit £4 Max1mum produchon capacity 1600 units The solution to a linear programming model of the situation shows that the imputed scarcity value (shadow price) of Alpha and Beta is

£0 .50 and £2 .75 per umt respectively and indicates that the intermediate products be transferred such that 200 units of Blackalls and 300 units of BrownaJis are produced and sold.

Required:

(a) Calculate the contribution earned by the group rt the sales pattern indicated by the linear programming model is implemented. (3 marks)

(b) Where the transfer prices are set on the basis of variable cost plus shadow price, show detailed calculations for

(i) the contribution per unit of intermediate product earned by divisions A and B and

(ii) the contribution per unit of final product earned by Black and Brown divisions . (4 marks)

(c) Comment on the results derived in

(b) and on the possible attitude of management of the various divisions to the proposed transfer pncing and product deployment policy

(6 marks)

(d ) In the followmg year the capacities of divisions A and B have each doubled and the following changes have taken place:

1. Alpha : There IS still no external market for this product, but A division has a large demand for other products which could use the capacity and earn a contribution of 5% over cost. Variable cost per unit for the other products would be the same as for Alpha and such products would use the capacity at the same rate as Alpha.

2. Beta: An intennediate market for th1s product now exists and Beta can be bought and sold in unlimited amounts at

£7.50 per unit. External sales of Beta would incur additional transport costs of SOp per unit which are not incurred in inter-divisional transfers.

The market demand for Blackalls and Brownalls will still exceed the production availability of Alpha and Beta.

(i) Calculate the transfer prices at which Alpha and Beta should now be offered to Black and Brown divisions in order that the transfer policy implemented will lead to the maximization of group profit.

(ii) Detennine the production and sales pattern for Alpha, Beta, Blackalls and Brownalls which will now maximize group contribution and calculate the group contribution thus achieved. It may be assumed that divisions will make decisions consistent with the financial data available.