Kenny Electric Company's noncallable bonds were issued several years ago and now have 20 years to...

Question:

Kenny Electric Company's noncallable bonds were issued several years ago and now have 20 years to maturity. These bonds have a 9.25% annual coupon, paid semiannually, sells at a price of $1,075, and has a par value of$1,000.

If the firm's tax rate is 25%, what is the component cost of debt for use in the WACC calculation?

Cost of Debt:

The cost of debt refers to the interest cost of debt that the borrower has to pay periodically. The interest cost of debt is not the coupon payment of a bond; rather, it is its yield to maturity, which has to be calculated separately.

The component cost of debt is calculated through the calculation of the yield to maturity of the bonds:

{eq}YTM=\displaystyle\frac{C+\frac{F-P}{nm}}{\frac{F+P}{2}} \times m\\ whereas:\\ C=coupon~rate\\ F=face~value\\ P=bond~price\\ n=number~of~periods~until~maturity\\ m=periodicity\\ {/eq}

Coupons are semi-annual. Therefore,

{eq}\begin{align*} YTM&=\frac{46.25+\frac{1,000-1,075}{20 \times 2}}{\frac{1,000+1,075}{2}} \times 2\\ &=\frac{44.375}{1,037.5} \times 2\\ &=.0428 \times 2\\ &=.0855 \end{align*} {/eq}

The annual yield to maturity of the bond or pretax cost of debt is 8.55%

The after tax cost of debt can be calculated as follows:

{eq}\begin{align*} After~cost~of~debt&=Pretax~cost~of~debt*(1-tax~rate)\\ &=.0855*(1-.25)\\ &=.0855*.75\\ &=.0641 \end{align*} {/eq}

The component after tax cost of debt is 6.41%