To understand the solution, let’s break it down step-by-step:
1. Calculating the interest on debt capital:
- The debt capital is [tex]$80,000.
- The interest rate on the debt capital is 5%.
- Therefore, the interest amount is calculated as:
\[
\text{Interest} = \text{Debt Capital} \times \text{Interest Rate} = 80,000 \times 0.05 = \$[/tex]4,000
\]
2. Calculating the tax savings on the interest:
- The tax rate is 40%.
- Therefore, the tax savings due to the interest expense (because interest expense reduces taxable income) is:
[tex]\[
\text{Tax Savings} = \text{Interest} \times \text{Tax Rate} = 4,000 \times 0.40 = \$1,600
\][/tex]
3. Calculating the after-tax cost of debt capital:
- The after-tax cost of debt capital is the interest paid minus the tax savings:
[tex]\[
\text{After-Tax Cost} = \text{Interest} - \text{Tax Savings} = 4,000 - 1,600 = \$2,400
\][/tex]
4. Calculating the after-tax cost as a percentage of the interest:
- To find the percentage, the after-tax cost is divided by the total interest and then multiplied by 100:
[tex]\[
\text{After-Tax Cost Percentage} = \left( \frac{\text{After-Tax Cost}}{\text{Interest}} \right) \times 100 = \left( \frac{2,400}{4,000} \right) \times 100 = 60\%
\][/tex]
Summary of the results:
- The interest on debt capital is [tex]$4,000.
- The tax savings on this interest is $[/tex]1,600.
- The after-tax cost of debt capital is [tex]$2,400.
- The after-tax cost of debt capital as a percentage of the interest is 60%.
Thus, to fill in the final blanks:
- The net savings on the interest calculated after tax is $[/tex]1,600.
- The after-tax cost of debt capital is 60 percent.
