# National Bank just issued a new 10-year, non-callable bond at par. This bond requires a coupon...

National Bank just issued a new 10-year, non-callable bond at par. This bond requires a coupon rate of 7% with semiannual payments and has a par value of $1,000. The tax rate is 39%. What is the after-tax cost of debt? The after-tax cost of debt for National Bank is _____% (Round to two decimal places.) ## Cost of Debt: Cost of debt is the interest rate that a company will pay on its debt obligations. It is a part of capital structure of the company along with cost of equity. ## Answer and Explanation: Par value of Bond is$1,000 on which interest rate paid is 7%

{eq}\begin{align*} {\rm\text{that is }} &= 1000 \times 7\% \\ &= \70 \end{align*} {/eq} On this interest expense income tax will not be paid as interest on bond is treated as deduction from this taxable income of bank will get reduced by70

{eq}\begin{align*} {\rm\text{So, tax savings of bank is}} &= {\rm\text{Taxrate}} \times \$70\\ &= 39\% \times \$ 70\\ &= \27.3 \end{align*} {/eq} {eq}\begin{align*} {\rm\text{After tax cost of debt}} &= \dfrac{{{\rm\text{Interest rate}} - {\rm\text{Tax savings}}}}{{{\rm\text{Par value of bond}}}} \times 100\\ &= \dfrac{{\ 70 - 27.3}}{{\\$ 1000}} \times 100\\ &= 4.27\% \end{align*} {/eq}

Pretax cost of debt will be equal to coupon rate that is 7 % because it is cost for the company as company has to pay 7% interest to the bondholder

{eq}\begin{align*} {\rm\text{Therefore after - tax cost of debt}} &= {\rm\text{Pretax cost of debt}}\left( {100 - {\rm\text{Taxrate}}} \right)\\ &= 7\% \left( {100 - 39\% } \right)\\ &= 4.27\% \end{align*} {/eq} 