Question 4 Tax Rf Samuel King Limited, an all equity firm, has expected earnings before interest and taxes of GHC6million a year. Samuel King's tax rate is 25%, and the market value is V-E-GHC20 million. The firm has a beta of 1.50, and the risk-free rate is 5%. The expected market return is 15%. The Senior Management at Samuel King Ltd is considering the use of debt. The debt would be issued and used to buy back the company's own shares, in order to keep the size of the firm constant. The default free rate of interest on debt is 7%. Since interest expense is tax deductible, the value of Samuel King would tend to increase as debt is added to the capital structure, but there would be an offset in the form of the increasing cost of gearing or bankruptcy. It is estimated that the present value of any gearing or bankruptcy cost that would be incurred by Samuel King is GHC15 million and the probability of gearing or bankruptcy will rise with the level of debt according to the following schedule: Value of Debt (GHC) Probability of Failure (%) EM SM 3,000,000 10 5,000,000 15 3mm 7,000,000 25 11m 9,000,000 35 The 1:1,000,000 40 6 14,000,000 50 (4 SM 15,000,000 60 Required: a) b) Calculate the cost of equity using the CAPM, when debt is GHC7,000,000 and when debt is GHC14,000,000. (6 marks) Calculate the cost of capital using the WACC when debt is GHC7,000,000 and when debt is GHC14,000,000. 6 marks) c) Using the adjusted present value (APV), calculate the optimal capital structure when gearing or bankruptcy costs are considered. (12 marks). (d) State the value of Samuel King at this optimal capital structure. (I mark). (Total 25 marks)