Question

A recent project was financed with $90m: $31m in equity capital, $18m in unsecured debt borrowed at 8% from one bank, and the remaining debt from another bank at 9.2%. what is the overall after-tax cost of the debt if the firm's marginal tax rate is 28%?

A. 3.46%
B. 9.37%
C. 5.91%
D. 6.36%

Answer 1

The overall after-tax cost of the debt for the financing of the $90m project, considering the two different interest rates and the firm's marginal tax rate of 28%, is 6.36%.

Step-by-step explanation:

The overall after-tax cost of the debt for the project financed with $90 million is calculated by accounting for the interest expense on the unsecured debt and the debt from the second bank, then adjusting for the effect of the firm's marginal tax rate, which is 28%.

First, let's calculate the annual interest expense on both debts:

• Unsecured debt interest = $18m × 8% = $1.44m
• Remaining debt = $90m - $31m - $18m = $41m
• Remaining debt interest = $41m × 9.2% = $3.772m
• Total interest = $1.44m + $3.772m = $5.212m

Next, we account for the tax shield:

• Tax shield = Total interest × Tax rate = $5.212m × 28% = $1.45936m
• After-tax interest = Total interest - Tax shield = $5.212m - $1.45936m = $3.75264m

Finally, we find the percentage of the after-tax cost of debt to the total debt financed:

• Total debt = $18m + $41m = $59m
• After-tax cost of debt percentage = ($3.75264m / $59m) × 100% = 6.36%

Therefore, the correct answer is D. 6.36%.