ADVANCED: A firm has $100 in cash and debt of $80. Assume that the time value of money is zero. A novel project comes along that costs

$60 and that will either deliver $0 or x with equal probabilities.

(a) What is the value of debt and equity without the project?

(b) What is the x value above which the project would be positive NPV? Call this xh.

(c) What is the x value above which the shareholders want the firm to take the project? Call this xl.

(d) Divide the possible regions into those below xl, those between xl and xh, and those above xh. More specifically, pick xl − $10, (xl + xh)/2, and xh + 10 as your returns in the good state. In these three cases:

1. If the debt can convert into 80%

of the post-conversion equity, what would the debt and equity be worth?

Would existing equity want to take the project?

2. If the debt can convert into 0% of the post-conversion equity (i.e., if it is not convertible), what would the debt and equity be worth?Would existing equity want to take the project?

3. If the debt can convert into 40%

of the post-conversion equity, what would the debt and equity be worth?

Would existing equity want to take the project?

(e) What conversion rate would you recommend to maximize the value of the firm today?