Question

Ursala, Incorporated, has a target debt-equity ratio of .65. Its WACC is 10.4 percent, and the tax rate is 23 percent. a. If the company’s cost of equity is 14 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 5.8 percent, what is the cost of equity? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

The pretax cost of debt for Ursala, Inc. is approximately 6.74%, while the cost of equity is approximately 19.22%.

Step-by-step explanation:

To calculate the pretax cost of debt, we need to use the formula:

WACC = (E/V) * Ke + (D/V) * Kd * (1 - T)

Given that the target debt-equity ratio is 0.65 and the WACC is 10.4%, we can solve for the pretax cost of debt. Plugging in the values, we have:

10.4% = (1 - 0.65) * 14% + 0.65 * Kd * (1 - 0.23)

Simplifying this equation, we find that the pretax cost of debt is approximately 6.74%.

To calculate the cost of equity when the aftertax cost of debt is 5.8%, we use the same formula as above and solve for Ke:

10.4% = (1 - 0.65) * Ke + 0.65 * 5.8% * (1 - 0.23)

Simplifying the equation, we find that the cost of equity is approximately 19.22%.

Answer 2

To calculate the pretax cost of debt, the WACC formula is rearranged using the debt-equity ratio, tax rate, and cost of equity. For the cost of equity, when the aftertax cost of debt is known, rearrange the WACC formula again to solve for the unknown cost of equity.

Step-by-step explanation:

To answer the question regarding the pretax cost of debt for Ursala, Incorporated, given the target debt-equity ratio, WACC, tax rate, and the cost of equity, we use the Weighted Average Cost of Capital (WACC) formula:
WACC = E/V * Re + D/V * Rd * (1 - Tc)

Here, E represents the market value of the equity, D is the market value of the debt, V is the total value of financing (E + D), Re is the cost of equity, Rd is the pretax cost of debt, and Tc is the tax rate.

From the given target debt-equity ratio (D/E), we can find E/V and D/V as follows:

• E/V = 1 / (1 + D/E)
• D/V = 1 - E/V

By plugging in the given values including the tax rate and rearranging for Rd, we can calculate the pretax cost of debt.

For the second part, to find the cost of equity (Re) when the aftertax cost of debt (Rd * (1 - Tc)) is given, we rearrange the WACC formula once again and solve for Re, using the previously calculated values of E/V and D/V.

Answer to Part A

Given the following:

• Target Debt-Equity Ratio (D/E): 0.65
• WACC: 10.4%
• Tax Rate (Tc): 23%
• Cost of Equity (Re): 14%
  E/V = 1 / (1 + 0.65) = 0.6061
  D/V = 1 - 0.6061 = 0.3939
  Plugging the values into WACC equation:
  10.4% = 0.6061 * 14% + 0.3939 * Rd * (1 - 0.23)
  Solving for Rd gives us the pretax cost of debt.
  

Answer to Part B

If instead the aftertax cost of debt is 5.8%, and using the tax rate:

Rd * (1 - Tc) = 5.8%

From this we can find Rd, and then use WACC formula again to solve for the cost of equity (Re).