Top-Down, Inc. ﬁnances its operations using $1.50 of debt for every $2 of common stock. The pre- tax cost of debt is 7.5 percent, the cost of equity is 11 percent, and the tax rate is 34 percent.
Currently, the ﬁrm is considering a small project that it considers to be equally as risky as the overall
ﬁrm) The project has an initial cash outlay of $18,500 and is expected to have a single cash inﬂow
Of $25,000 at the end of year two. What is the net present value of this project?

Question

Quizplus · Accepted Answer

First, we need to calculate the cost of capital for the project using the weighted average cost of capital (WACC) formula:

WACC = (E/V) x Re + (D/V) x Rd x (1 - T)
where:
E = market value of equity
D = market value of debt
V = E + D
Re = cost of equity
Rd = cost of debt
T = tax rate

Given:
E/V = 2/5
D/V = 3/5
Re = 11%
Rd = 7.5%
T = 34%

The market value of equity can be calculated by multiplying the number of shares by the market price per share. Since this information is not given, we cannot calculate E or D directly. However, we can use the debt-to-equity ratio to assume that the market value of debt is $1.50 for every $2 of equity. Therefore, we can assume that the market value of equity is 2/5 of the total capital and the market value of debt is 3/5 of the total capital.

Assuming a total capital of $100:
Equity = $40
Debt = $60

Using the WACC formula:
WACC = (2/5) x 11% + (3/5) x 7.5% x (1 - 34%) = 8.36%

Now we can use the net present value (NPV) formula to calculate the NPV of the project:
NPV = -initial outlay + (cash inflow / (1 + WACC)^t)
where:
t = year of cash flow

NPV = -$18,500 + ($25,000 / (1 + 8.36%)^2) = $2,773

Therefore, the net present value of the project is $2,773. Option (C) is the correct answer.