Lancelot plc is a diversified company with three operating divisions – North, South and West. The operating characteristics of North are 50 per cent more risky than South, while West is 25 per cent less risky than South. In terms of financial valuation, South is thought to have a market value twice that of North, which has the same market value as West. Lancelot is all-equity-financed with a Beta of 1.06. The overall return on the FT All-Share Index is 25 per cent, with a standard deviation of 16 per cent.

Recently, South has been under-performing and Lancelot’s management plan to sell it and use the entire proceeds to purchase East Ltd, an unquoted company. East is all-equity-finan1ced, and Lancelot’s financial strategists reckon that, while East is operating in broadly similar markets and industries to South, East has a revenue sensitivity of 1.4 times that of South, and an operating gearing ratio of 1.6 compared to the current operating gearing in South of 2.0.

Assume no synergistic benefits from the divestment and acquisition. You may ignore taxation.

Required

(a) Calculate the asset Betas for the North, South and West divisions of Lancelot. Specify any assumptions that you make.

(b) Calculate the asset Beta for East.

(c) Calculate the asset Beta for Lancelot after the divestment and acquisition.

(d) What discount rate should be applied to any new investment projects in East division?

(e) Indicate the problems in obtaining a ‘tailor-made’ project discount rate such as that calculated in section (d).