A firm has expected before-tax earnings of $100 million a year forever, starting next year. It is financed with 30% debt at an expected interest rate of 6% a year and 70% equity with an
Expected cost of 11% a year. If the firm is in the 35% tax bracket, what is its NPV?

Question

Quizplus · Accepted Answer

To calculate the NPV, we need to discount the expected earnings using the weighted average cost of capital (WACC). The WACC is calculated as:
WACC = (0.3 * 0.06 * (1 - 0.35)) + (0.7 * 0.11) = 0.0935 or 9.35%
The perpetual earnings of $100 million can be capitalized using the Gordon growth model:
V = (E / r - g)
where V is the present value of earnings, E is the expected earnings, r is the discount rate (9.35%), and g is the expected growth rate of earnings (assuming it is zero in perpetuity).
V = (100 / 0.0935)
V = $1,070.59 million
The value of debt is assumed to be equal to its face value. Therefore, the value of the equity is:
Equity value = Total firm value – Value of debt
Equity value = $1,070.59 – (0.3 x $100)
Equity value = $1,040.59 million
The NPV is the value of equity minus the initial investment of $0.
NPV = $1,040.59 - $0
NPV = $732.81 million
Therefore, the answer is C.

A Firm Has Expected Before-Tax Earnings of $100 Million a Year