For this quiz, you may work in groups. A group consists of three or fewer students. Each group must hand in a single set of answers. The same grade will be assigned to each member of the group. The quizzes must be handed in by 1:15 on Thursday April 16.
For this question, adopt all of the perfect market assumptions of Modigliani and Miller other than
the assumption of a zero corporate tax rate. Here, the corporate tax rate is τ.
A profitable firm has a potential new project. The project requires a year-zero investment of
$100MM. The project will generate expected future pre-tax EBIT of $15MM per year forever,
beginning in year one.
For the moment, assume that the initial investment is treated by the firm as an expense. If the
firm adopts the project, this expense will reduce the firm’s year-zero EBIT, and therefore reduce
the firm’s year-zero tax payment. The firm currently has profits of more than $100MM a year,
so the year-zero profit of the firm will be positive even if the firm adopts the project. If the firm
chooses to adopt the project, the firm must come up with $100MM(1 – τ) in new cash at time
zero. The remaining cash will come from the reduction in the firm’s year-zero taxes of
For simplicity, assume that the project’s future pre-tax cash flows are identical to EBIT. For
example, there are no changes in net working capital and no depreciation.
The discount rate of the unlevered project is 10%. The risk-free rate is 5%.
1. (5 pts) Assume the firm issues no debt. For a corporate tax rate of ??, what is the NPV of the project? Show your work.
2. (3 pts) Again assume the firm issues no debt. Does the corporate tax rate affect the firm’s decision of whether to do the project? Explain. 3. (10 pts) Just for this question, alter an assumption. (We go back to the original assumptions after Question
3.) The initial $100MM in investment is not an expense that
immediately lowers the firm’s profit in year zero. Instead, it is an asset that depreciates
over time. The firm will use a twenty-year life of the asset, thus depreciation is $5MM
per year for twenty years, beginning in year one. Continue to assume the firm issues no
debt. Re-calculate the NPV of the project as a function of the corporate tax rate τ. For