Question

Unida Systems has 32 million shares outstanding trading for $ 10 per share. In​ addition, Unida has $ 109 million in outstanding debt. Suppose​ Unida's equity cost of capital is 14 % ​, its debt cost of capital is 8 % ​, and the corporate tax rate is 35 % .

a. What is​ Unida's unlevered cost of​ capital?
b. What is​ Unida's after-tax debt cost of​ capital?
c. What is​ Unida's weighted average cost of​ capital?

Answer 1

a. Unida's unlevered cost of capital is 17.03%. b. Unida's after-tax debt cost of capital is 5.2%. c. Unida's weighted average cost of capital is 17.03%.

Step-by-step explanation:

a. Unida's unlevered cost of capital can be calculated using the formula:

Unlevered Cost of Capital = (Equity Cost of Capital * Proportion of Equity) + (Debt Cost of Capital * Proportion of Debt * (1 - Tax Rate))

In this case, Unida's equity cost of capital is 14%, and there are 32 million shares outstanding trading for $10 per share. Thus, the proportion of equity is 32 million shares * $10 per share / (32 million shares * $10 per share + $109 million debt) = 0.0808. The debt cost of capital is 8%, and the proportion of debt is $109 million / ($32 million shares * $10 per share + $109 million debt) = 0.9192. The tax rate is 35%. So the unlevered cost of capital is (0.14 * 0.0808) + (0.08 * 0.9192 * (1 - 0.35)) = 0.12232 + 0.047984 = 0.170304, or 17.03%.

b. Unida's after-tax debt cost of capital can be calculated by multiplying the debt cost of capital by (1 - Tax Rate). In this case, Unida's debt cost of capital is 8%, and the tax rate is 35%. So the after-tax debt cost of capital is 0.08 * (1 - 0.35) = 0.052, or 5.2%.

c. Unida's weighted average cost of capital (WACC) can be calculated using the formula:

WACC = (Equity Cost of Capital * Proportion of Equity) + (Debt Cost of Capital * Proportion of Debt * (1 - Tax Rate))

Using the values from part (a), the WACC is (0.14 * 0.0808) + (0.08 * 0.9192 * (1 - 0.35)) = 0.170304, or 17.03%.