A firm has access to two mutually exclusive investment projects. Both the projects require an initial investment of $15,000. If project 1 is undertaken, with probability 1/2, it pays off $20,000 or $34,000. Project 2 is considerably riskier and can pay off either $0 or $50,000. Analysts, using data that we do not have access to, have determined that the NPV of Project 1 is $7,500 while that of project 2 is $5,000.

(a) If the firm is all equity financed, which project should it choose? Does your answer depend on the risk-preferences of the equity holders? Why or why not?

(b) Suppose the firm decides to invest $3,000 of the equity holders’ money and goes to a bank to borrow $12,000. The bank does not know of the existence of Project 2. Given the payoff pattern of Project 1, the bank decides to lend the $12,000 to the firm at the risk-free rate of 10%.

(i) What are the expected payoffs to the bank and to the firm’s shareholders if the firm invests in Project 1? What is the increase in the value of equity?

(ii) What are the expected payoffs to the bank and to the firm’s shareholders assuming that the firm invests in Project 2 instead (the bank loan still carries a 10% interest rate)? What is the increase in the value of the equity? [Hint: Use the risk-neutral valuation method to value the equity.]

(iii) In (ii) what promised interest rate would have given the bank a fair return given the risk of Project 2?

(iv) Suppose the bank knows that the firm’s investment alternatives include Project 2. What promised interest rate would the bank charge the firm for the $12,000 loan if it can’t observe in which project the firm actually invests? In which project will the stockholders choose to invest?

(Note: The expected payoffs are not the same thing as value. In particular, the addition of value that gets impounded into the stock price in a well functioning market is the NPV of the new project. You will need to take this distinction into account while calculating risk neutral probabilities to determine equity values when you treat equity as an option.)

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