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\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|}{Item} & \multicolumn{1}{|c|}{Value} \\
\hline Debt Capital & [tex]$\$[/tex] 80,000$ \\
\hline Income before interest and tax & [tex]$\$[/tex] 50,000$ \\
\hline Interest on debt capital & [tex]$5 \%$[/tex] \\
\hline Tax rate & [tex]$40 \%$[/tex] \\
\hline
\end{tabular}

What is the net savings on the interest calculated after tax?
The after-tax cost of debt capital is [tex]$\square$[/tex] percent.



Answer :

GinnyAnswer
To find the net savings on the interest calculated after tax and the after-tax cost of debt capital as a percentage, we need to follow these steps:

1. Calculate the interest on the debt capital:
The interest on the debt capital can be calculated using the given interest rate.
[tex]\[ \text{Interest on debt capital} = \[tex]$80,000 \times 5\% = \$[/tex]80,000 \times 0.05 = \$4,000
\][/tex]

2. Calculate the interest after tax:
Apply the tax rate to the interest to calculate the net savings.
[tex]\[ \text{Interest after tax} = \[tex]$4,000 \times (1 - 0.40) = \$[/tex]4,000 \times 0.60 = \$2,400
\][/tex]
Thus, the net savings on the interest after tax is \$2,400.

3. Calculate the after-tax cost of debt capital as a percentage:
This is found by taking the interest after tax and expressing it as a percentage of the debt capital.
[tex]\[ \text{After-tax cost of debt capital percentage} = \left( \frac{\[tex]$2,400}{\$[/tex]80,000} \right) \times 100 = 3\%
\][/tex]

So, to answer the question:

The net savings on the interest calculated after tax is \$2,400.

The after-tax cost of debt capital is [tex]\( 3 \)[/tex] percent.

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