Question

Ursala, Incorporated, has a target debt-equity ratio of .90. Its WACC is 8.2 percent, and the tax rate is 22 percent. a. If the company's cost of equity is 11 percent, what is its pretax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. If instead you know that the aftertax cost of debt is 6.3 percent, what is the cost of equity?

Answer 1

For part a, the pretax cost of debt is approximately 6.72%. In part b, if the aftertax cost of debt is known to be 6.3%, the cost of equity can be calculated to be approximately 10.14%.

Step-by-step explanation:

To solve part a, we need to determine the pretax cost of debt. Ursala, Incorporated has a target debt-equity ratio of 0.90, a WACC (Weighted Average Cost of Capital) of 8.2%, and a tax rate of 22%. The cost of equity is given as 11%. Using the formula for WACC: WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc), where E is the market value of the equity, D is the market value of the debt, V is the total value (E + D), Re is the cost of equity, Rd is the cost of debt, and Tc is the corporate tax rate, we can solve for Rd.

Since the debt-equity ratio (D/E) is 0.90, we can express D and E as a proportion of V. If E = V, then D = 0.90V. Therefore, E/V = 1/(1+D/E) = 1/(1+0.90) = 1/1.90 ≈ 0.5263 and D/V = D/(D+E) = 0.90/(1+0.90) ≈ 0.4737.

Using these values in the WACC formula: 8.2% = 0.5263 * 11% + 0.4737 * Rd * (1 - 0.22), we can solve for the pretax cost of debt Rd which gives us Rd ≈ 6.72%.

For part b, knowing the aftertax cost of debt is 6.3%, we can reverse-engineer the pretax cost of debt using the formula: Rd = Aftertax Rd / (1 - Tc). Plugging in the values: Rd = 6.3% / (1 - 0.22), we get a pretax Rd of 8.08%. We can then plug this back into the WACC formula and solve for the cost of equity Re which yields Re ≈ 10.14%.