Final answer:
The return on equity for Titan Express, after considering the debt to equity ratio, interest rate, return on ungeared equity, and income tax rate, is approximately 11.18%, which is closest to option (d) 11.52%.
Step-by-step explanation:
Calculation of Return on Equity (ROE) for Titan Express
The question involves calculating the return on equity (ROE) for Titan Express, considering its debt to equity ratio, the interest rate on its debt, the rate of return on ungeared equity, and the applicable income tax rate. The debt to equity ratio is 0.60, the interest rate on debt is 9%, and the return on ungeared equity is 14%, with an income tax rate of 28%.
First, we need to adjust the interest rate for the effect of taxes, since interest expenses are tax-deductible. The after-tax cost of debt is calculated as the interest rate times (1 - tax rate), which in this case is 9% × (1 - 0.28) = 6.48%.
With the debt to equity ratio, we can deduce the proportion of financing that comes from debt and equity. For every $1 of equity, there is $0.60 of debt. So, the total financing is $1 of equity plus $0.60 of debt, which sums up to $1.60 of total financing.
Now we can calculate the weighted return by combining the after-tax cost of debt and the return on ungeared equity considering their respective weights in the financing structure:
- Weight of equity = $1 / $1.60 = 0.625
- Weight of debt = $0.60 / $1.60 = 0.375
- Total return = (Weight of equity × Return on ungeared equity) + (Weight of debt × After-tax cost of debt)
- Total return = (0.625 × 14%) + (0.375 × 6.48%)
- Total return = 8.75% + 2.43%
- Total return = 11.18%
After considering both the equity and debt financing components, the return on equity for Titan Express is approximately 11.18%, which best corresponds to option (d) 11.52% when rounding to the nearest hundredth.