A firm’s cash flows one year from now will be either $2 million if there is a boom or $0.96 million if there is a recession. A boom and a recession are equally likely. A new project is available to the firm: It requires an investment today of $0.4 million and will generate a cash flow one year from now of $0.68 million for sure. The interest rate is 10%.
a. Suppose the firm has no debt. Will the project be taken by the all equity firm?
b. Suppose now that the company has debt in the form of zero coupon bonds that expire in one year. The debt has face value F=$1.6 million.
i. Calculate the value of the firm, the value of debt and the value of equity under a boom and under a recession with and without the project.
ii. Calculate the expected value of equity with and without the project. What is the increase in equity value from taking the project? Is this greater or smaller than the cost of the project? Will the project be taken by the levered firm?