Question

You are recruited by the founder of a start-up company to advise her on the optimal capital structure for her company. The sole project of the company will require an initial outlay (at date 0) of £150,000, and is expected to generate a single cash flow in one year (at date 1). The project cash flow at date 1 will take one of two equally likely values depending on the state of the economy: if the economy is strong, then the cash flow will be high at £300,000; in a weak economy the cash flow will be only £140,000. Based on evidence of companies with comparable projects, the project's cost of capital has been estimated as 10% per annum. The rate of return on effectively risk-free treasury securities is expected to remain constant over the project life at 5% per annum.

a) Suppose the entrepreneur finances the project using only equity (zero debt). Assuming that the company operates in perfect capital markets, calculate the market value of (unlevered) equity at date 0.

b) Now suppose that instead of using all-equity financing as in part a), the entrepreneur finances £50,000 of the initial project outlay using debt and the rest using equity. The company promises to repay the debt along with a single interest payment of £2,500 at date 1, and the company can borrow the £50,000 of debt at a cost of debt capital of 5% per annum. Assuming that the company operates in perfect capital markets, calculate the current market value at date 0 of the ‘levered equity’ of this company.

Answer 1

a) As state of economy is equally likely . Therefore, probability of both states (strong economy and weak economy) would be 50%

Hence, cashflow at date 1 = (50%* 300000)+( 50%* 140000) = ₤220000

As, financing here is unlevered , we consider cost of capital for discounting purpose,

Market value of equity = 220000(1.10)-1= ₤200000

b) If financing is levered then , cost of capital = weighted average cost of capital = [( rate of debt * debt taken)+( cost of equity * funds from equity)]/ Total financing

[(50000*5%)+(100000*10%)]/150000 = 8.33%

Because he has promised to return the debt amount along with interest of ₤2500 at date 1 , we reduce that from cashflow of ₤ 220000

Hence,Market value when financing is levered = (220000-50000-2500) * (1.0833)-1= ₤154620.142