A firm has expected free cash flow for the coming year of $15 million. There are no taxes. The risk-free rate is 4%, the firm's unlevered (asset) beta is 1 and the market risk premium is 6%. Its free cash flows are expected to grow forever at 5%. [You can use the CAPM to calculate the expected return: r = r_f + beta * market risk premium.]

a) A firm has excess cash of $100 million and zero debt and considers using this to fund an additional investment project which will either have a payoff in one year of $200 million with probability 0.75 or $50 million with probability 0.25. What is the NPV of the investment? What is the total present value of the firm if it undertakes the investment? Assume the cost of capital of the new project is the same as that of assets in place.

b) The firm undertakes the investment in part (a) and also issues debt (perpetuity) with a face value of $400 million and uses the proceeds to pay a dividend to its shareholders maturing at the same date as the project payoff is realized. If the beta of the debt is 0.2, what is the maximum dividend it can pay? Explain. (Assume for this and later parts that its assets in place can be sold for their present value.)