Chapter 16: The Valuation of Acquisitions and Mergers

Three companies and projects are described below. Debt is treated as risk-free (beta of debt zero), so the asset beta formula on the formulae sheet reduces to: asset beta = Ve / (Ve + Vd (1 - T)) x equity beta. Every gearing ratio below is debt to equity, at market values. Round asset betas to 2 decimal places before any regearing.

(a) P plc and Q plc. P plc has a gearing ratio (debt to equity) of 0.4 and the beta of its shares is 1.8. Q plc has a gearing ratio of 0.2 and the beta of its shares is 1.5. The rate of corporation tax is 30%. Which company has the more risky business activity?

(b) A plc and B plc. A plc is a company with a gearing ratio (debt to equity) of 0.4. Shares in A plc have a beta of 1.48. They are considering acquiring another company - B plc. Shares in B plc have a beta of 1.8 and B plc has a gearing ratio (debt to equity) of 0.2. A plc is raising more debt in order to partly finance the acquisition of B plc, but their overall gearing ratio is not expected to change substantially. A plc has an after-tax cost of debt of 7%. The market return is 15% and the risk free rate is 8%. Corporation tax is 25%. Calculate the discount rate that should be applied to the free cash flows of B plc in order to arrive at a value of B plc.

(c) X plc and Y plc. X plc is an oil company with a gearing ratio (debt to equity) of 0.4. Shares in X plc have a beta of 1.48. They are considering investing in a new operation to build ships, and have found a quoted shipbuilding company - Y plc. Y plc has a gearing ratio (debt to equity) of 0.2, and shares in Y plc have a beta of 1.8. The market return is 18% and the risk free rate is 8%. Corporation tax is 25%. At what discount rate should X plc appraise the new project if it is to be financed entirely from equity?