At the present time, Water and Power Company (WPC) has 10-year noncallable bonds with a face value of $1,000 that are outstanding. These bonds have a current market price of $1,495.56 per bond, carry a coupon rate of 10%, and distribute annual coupon payments. The company incurs a federal-plus-state tax rate of 25%. If WPC wants to issue new debt, what would be a reasonable estimate for its after-tax cost of debt (rounded to two decimal places)? (Note: Round your YTM rate to two decimal place.) a. 3.53%
b. 3.38%
c. 2.35%
d. 2.94%

d. 2.94%

Explanation:

First, Calculate the Yield to maturity of the bond using the following formula

Use the following formula to calculate the YTM

P = [ C x ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Where

F = Face value = $1,000

P = Price = $1,495.56

C = Coupon payment = Face value x Coupon rate = $1,000 x 10% = $100

n = numbers of periods = Numbers of years to maturity = 10 years

r = YTM = ?

Placing values in the formula

$1,495.56 = [ $100 x ( 1 - ( 1 + r )^-10 ) / r ] + [ $1,000 / ( 1 + r )^10 ]

r = 3.916%

Now calculate the after-tax cost of debt

After-tax cost of debt = YTM x ( 1 - Tax rate )

After-tax cost of debt = 3.916% x ( 1 - 25% )

After-tax cost of debt = 2.937%

After-tax cost of debt = 2.94%

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