UAI has two mutually exclusive investment opportunities (projects), R and S, each requiring an investment of $50 million, which it plans to fund with debt. Project S pays off $60 million for certain. Project R has an uncertain outcome: it pays $90 million when the economy is good but only $20 million when the economy is poor.

(i) What is the NPV of each project, assuming that investors are risk neutral, the risk-free rate is zero and that the economy is equally likely to be good or poor.

(ii) Assuming for simplicity that the debt issued will be one period, pure discount debt, compute the face value of the debt that needs to be issued to raise the required investment amount of $50 million, if (a) Lenders believe that the firm will undertake the project S or (b) Lenders believe that the firm will undertake the project R?

(iii) IF the firms management makes its investments decisions in order to maximize the cash flows to equity holders, which project will the firm undertake in practice?

(iv) if lenders are sophisticated, what is the promised payment that the firm has to offer in return for the $50 million in current debt financing?