A company has no debt. Its cost of capital is 8.7 percent. Suppose the firm converts to a debt-equity ratio of 0.65. The interest rate on the debt is 6.9 percent. What is its new WACC?

Question

BlackTom AI · Accepted Answer

We start by identifying the key relationships in the problem. The company initially has no debt, so its cost of capital equals its cost of equity, which is given as 8.7%. When the firm adopts a debt-to-equity ratio of 0.65, we can derive the corresponding weights of debt and equity in the new capital structure.

First, compute D/E = 0.65. This implies D = 0.65E. The total value V = D + E = 0.65E + E = 1.65E. Therefore, the debt-to-total value and equity-to-total value are:
- D/V = 0.65E / 1.65E = 0.65 / 1.65 ≈ 0.3939 (about 39.39%)
- E/V = E / 1.65E = 1 / 1.65 ≈ 0.6061 (about 60.61%)

With no taxes specified, we use the straightforward weighted average cost of capital formula without tax shields:
WACC = (E/V) * Re + (D/V) * Rd
where Re is the cost of equity (which we know from the all-equity situation), and Rd is the cost of debt.

From the initial condition (no debt), WACC = Re = 8.7%. So Re = 8.7% and Rd = 6.9%.

Plugging the values into the formula:
WACC = (0.6061) * 8.7% + (0.3939) * 6.9%
Compute each term: 0.6061 * 8.7% ≈ 5.2727% and 0.3939 * 6.9% ≈ 2.7183%
Add them: 5.2727% + 2.7183% ≈ 7.9910% ≈ 7.99%

Now compare with the provided options. The calculation yields about 7.99 percent, which corresponds to the option labeled 7.99 percent. The other options can be checked similarly by plugging the same weights and the same Re and Rd values if desired, but their values do not match the computed WACC. For instance, 8.13% would be higher than the weighted contribution from debt, and 8.44% or 8.36% would require a different mix or cost inputs than those given.

In summary, using the debt and equity weights derived from D/E = 0.65 and applying WACC = (E/V)*Re + (D/V)*Rd with Re = 8.7% and Rd = 6.9% yields approximately 7.99%, matching the corresponding option.

A company has no debt. Its cost of capital is 8.7 percent. Suppose the firm converts to a debt-equity ratio of 0.65. The interest rate on the debt is 6.9 percent. What is its new WACC? 单项选择题

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