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An entrepreneur has a new idea for a project that requires an initial investment of £5 million

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An entrepreneur has a new idea for a project that requires an initial investment of £5 million. The project generates a single cash flow a year from now. The size of the cash flow depends on how well the U.K. economy does next year. If the economy does well, which occurs with 50% probability, the project generates a cash flow of £20 million. If the economy performs poorly, the project generates a cash flow of £5.5 million. The risk-free rate in the economy is 10% (investing £1 today in a risk-free bond yields £1.1 in a year for sure). a) (5 marks] The entrepreneur, who has no own funds to invest, approaches a local banker to request financing in the form of debt for the total amount needed for the investment (i.e. £5 million). What is the promised repayment in a year for which the market value of the debt is exactly equal to £5 million? Given such a repayment, what are the payoffs to the entrepreneur in the two possible states? Aside from the risk free bonds, there is another investment opportunity in the economy: a portfolio of risky stocks that yields a 200% return if the economy does well and a -100% return if the economy performs poorly (that is, if you invest £1 in the risky portfolio, it will be worth £3 if the economy does well, and £o if the economy does poorly). b) (12 marks] Still given the debt repayment computed in part a), what is the market value of equity? (hint: you need the find a way to replicate the cash flows.) What is the total value of the firm?
Q1a a) Risk-free rate = 10% Promised repayment in a year for market value of debt equal to 5 million = 5*(1+0.10) = 5.5 million In the two possible scenarios Economy does well (50%) Payoff to entrepreneur = 20 -5.5 = 14.5 million - Economy does poorly (50%) Payoff to entrepreneur = 5.5-5.5 = 0 million