Question

The outcome can be either good or bad. The probability that the good outcome realizes is 50%. The cash flow is shown in the above table. Given the riskiness of the business, investors require a 15% risk premium over the risk-free rate of 5%. To answer this, make appropriate assumptions. In answering the following questions, show detailed steps and discuss your results.

Q4. Suppose that you are an entrepreneur with the following business opportunity Year 0 Year 1 Cash flow Investment Good Bad Cash flow £500 £1000 £800 The outcome can be either good or bad. The probability that the good outcome realizes is 50%. The cash flow is shown in the above table. Given the riskiness of the business, investors require a 15% risk premium over the risk-free rate of 5%. To answer this, make appropriate assumptions. In answering the following questions, show detailed steps and discuss your results (a) What is the value of the unlevered equity in this business? What is the entrepreneurial profit? [25 marks] (b) What is the value of levered equity when debt is £100? What is the cost of levered equity in this case? [25 marks) (c) Using the above example, discuss and explain how an Increase in leverage increases the risk to the shareholders. Explain how it affects the share price. [50 marks] [Turn over] Page 3 of 4

Answer 1

Cash flow after year Good Bad 1000 Boo os. 05 discounting rate: 5% +15% - 20% ruf (201, 1) = 0.833 rv of cathinflow after 1 year = 90080133 Net = 7497 Present Value - Present value of inflows- = 749.7-500 = 349.7 / 350 (a) value of unlevered equity = Dividend Eament - the be 400 = 0.8] - 400 500 0.80 Entrepreneurial profit is 900 - 500 = 400 (b) Let a on debt be 5% (crisk free rate) Interest - 5% of 100 Earning after Interest - 400-5 =395 value of levered Equity = EAI -2 395 - Ke= 395 = 0.98775 0.9875 400 clost of Levered Equity

c) As the debt proportion rises in the capital structure, it raises the risk for the equity holders. Because equity holders have the last claim to the earnings and capital payback at the time of liquidation, so as the debt increases their risk tends to rise as well. Due to the increase in risk, the cost of equity(Ke) also rises.

The debt increase can affect or may not affect the share price. If the cost of equity is rising enough to offset the effect of higher EPS as happened in this case then share price would not change. But if the cost of equity is not rising substantially to offset the effect of higher EPS then it would lead to a higher share price.