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Suppose Luther Industries is considering divesting one of its product lines.The product line is expected to generate free cash flows of $2 million per year,growing at a rate of 3% per year.Luther has an equity cost of capital of 10%,a debt cost of capital of 7%,a corporate tax rate of 21%,and a debt-equity ratio of 2.This product line is of average risk and Luther plans to maintain a constant debt-equity ratio.
-Luther's unlevered cost of capital is closest to:
A)8.0%.
B)8.5%.
C)9.0%.
D)6.4%.

Question

Quizplus · Accepted Answer

We are asked to find the unlevered cost of capital (also known as the weighted average cost of capital or WACC) of Luther Industries. The formula for WACC is:

WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc)

Where:
E = market value of equity
D = market value of debt
V = E + D
Re = cost of equity
Rd = cost of debt
Tc = corporate tax rate

We are given the following information:

- Equity cost of capital (Re) = 10%
- Debt cost of capital (Rd) = 7%
- Corporate tax rate (Tc) = 21%
- Debt-equity ratio = 2

To find the unlevered cost of capital, we need to assume that Luther has no debt. This means that D = 0, and V = E.

We can rearrange the WACC formula to solve for the unlevered cost of capital (Re):

Re = WACC / (E/V)

where WACC = (E/V) * Re

Plugging in the given values, we get:

WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc)
WACC = (E/E) * 10% + (0/1) * 7% * (1 - 21%)
WACC = 10% - 0%
WACC = 10%

Therefore, Re = WACC / (E/V) = 10% / (E/E) = 10%.

However, this is the levered cost of equity, which takes into account the fact that Luther has debt. To find the unlevered cost of equity, we need to "unlever" the levered cost of equity, by removing the effects of debt. We can do this using the following formula:

Reu = Re - (D/E) * (Re - Rd) * (1 - Tc)

where Reu = unlevered cost of equity.

Plugging in the given values, we get:

Reu = 10% - (2/3) * (10% - 7%) * (1 - 21%)
Reu = 8.0%

Therefore, the answer is A) 8.0%.

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