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Ouestion 4Samuel King Limited, an all equity firm, has expected earnings before interest and taxes ofGHC6million a year. Samuel King's tax rate is 25%, and the market value is V = E = GHC20million. The firm has a beta of 1.50, and the risk-free rate is 5%. The expected market returnIS 15%. The Senior Management at Samuel King Ltd 1s considering the use of debt. The debtwould be issued and used to buy back the company's own shares, in order to keep the size ofthe firm constant. The default free rate of interest on debt is 7%. Since interest expense is taxdeductible, the value of Samuel King would tend to increase as debt is added to the capitalstructure. but there would be an offset in the form of the increasing cost of gearing orbankruptcy. It is estimated that the present value of any gearing or bankruptcy cost that wouldbe incurred by Samuel King is GHC15 million and the probability of gearing or bankruptcywill rise with the level of debt according to the following schedule:Value of Debt (GHC)Probability of Failure (%)3,000,0005,000,0007.000,000259.000.00011.000.00014,000,0005015.000.000A0Required:Calculate the cost of equity using the CAPM, when debt is GHC7,000,000 and whendebt is GHC14,000,000.(6 marks)Calculate the cost of capital using the WACC when debt is GHC7,000,000 and whendebt is GHC14,000,000.6 marks)Using the adjusted present value (APV), calculate the optimal capital structure whengearing or bankruptcy costs are considered.(12 marks)State the value of Samuel King at this optimal capital structure.(1 mark)(Total = 25 marks)
Ouestion 4
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 1s 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 (%)
3,000,000
5,000,000
7.000,000
25
9.000.000
11.000.000
14,000,000
50
15.000.000
A0
Required:
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)
Using the adjusted present value (APV), calculate the optimal capital structure when
gearing or bankruptcy costs are considered.
(12 marks)
State the value of Samuel King at this optimal capital structure.
(1 mark)
(Total = 25 marks)
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