Final answer:
To calculate the pretax cost of debt for Debbie's Cookies with an ROA of 8.3%, cost of equity of 11.4%, and a debt-equity ratio of 0.83, the weighted average cost of capital formula is used. By rearranging and solving the WACC equation, the pretax cost of debt is determined to be approximately 4.57%.
option a is the correct
Step-by-step explanation:
The question asks how to determine the pretax cost of debt for Debbie's Cookies with given financial metrics. We are given a return on assets (ROA) of 8.3%, a cost of equity of 11.4%, and a debt-equity ratio of 0.83, with instructions to ignore taxes.
To find the pretax cost of debt, we can use the weighted average cost of capital (WACC) formula, which is not provided directly but is implied by the information we have. WACC is a calculation of a firm's cost of capital in which each category of capital is proportionately weighted. Without tax considerations, WACC is given by the formula:
WACC = (E/V) * Re + (D/V) * Rd
Where:
E = Market value of equity
V = Total value of capital (equity + debt)
Re = Cost of equity
D = Market value of debt
Rd = Cost of debt
In this case, the debt-equity ratio (D/E) is 0.83. This can be used to find the proportions of debt and equity in the firm's capital structure. If E is equity and D is debt:
D/E = 0.83
D = 0.83 * E
Thus, E + D = E + 0.83E = 1.83E (This represents the total value of capital, V).
We can plug into the WACC formula using ROA as the overall required return on the firm's assets (since the firm's assets are financed by both debt and equity) and solve for Rd, the cost of debt:
ROA = WACC = (E/V) * Re + (D/V) * Rd
0.083 = (1/1.83) * 0.114 + (0.83/1.83) * Rd
0.083 = 0.0623 + (0.83/1.83) * Rd
Subtracting 0.0623 from both sides to isolate Rd:
0.083 - 0.0623 = (0.83/1.83) * Rd
0.0207 = (0.83/1.83) * Rd
Now, solving for Rd:
Rd = 0.0207 / (0.83/1.83)
Rd = 0.0207 / 0.4536
Rd = 0.04566 or 4.57%
Therefore, the pretax cost of debt for Debbie's Cookies is approximately 4.57%.