Question

The Outlet has a cost of equity of 16.8 percent, a pre-tax cost of debt of 8.1 percent, and a return on assets of 14.5 percent. Ignore taxes. What is the debt-equity ratio?This question has two answers.

1) 0.28
2) 0.36
3) 0.44
4) 0.52
5) 0.57

Answer 1

The calculation of the debt-equity ratio using the given financial metrics results in a negative value, suggesting a possible discrepancy in the question as the cost of equity is higher than the return on assets. A review of the initial data or assumptions may be necessary.

Step-by-step explanation:

The question at hand involves calculating the debt-equity ratio for 'The Outlet' based on the given financial metrics: a cost of equity of 16.8 percent, a pre-tax cost of debt of 8.1 percent, and a return on assets (ROA) of 14.5 percent. We are instructed to ignore taxes. To find the debt-equity ratio, we need to utilize the Modigliani-Miller theorem formula for the cost of capital without taxes:

ROA = (Equity / (Debt + Equity)) * Cost of Equity + (Debt / (Debt + Equity)) * Cost of Debt

Since we are looking for the debt-equity ratio (Debt/Equity), let's rearrange the formula to solve for this:

Debt/Equity = (ROA - Cost of Equity) / (Cost of Equity - Cost of Debt)

Plugging in the values:

Debt/Equity = (0.145 - 0.168) / (0.168 - 0.081)

Debt/Equity = -0.023 / 0.087

Debt/Equity = -0.2644

Given the negative result, this suggests that the question may contain a discrepancy as the cost of equity is higher than the return on assets, which typically would not happen in a stable financial scenario. Hence, we cannot find a positive debt-equity ratio with the given values and we should consider reviewing the initial data or the assumptions made.