Question

To calculate the after-tax cost of debt, multiply the before-tax cost of debt by   .

Perpetualcold Refrigeration Company (PRC) can borrow funds at an interest rate of 11.10% for a period of four years. Its marginal federal-plus-state tax rate is 25%. PRC’s after-tax cost of debt is     (rounded to two decimal places).

At the present time, Perpetualcold Refrigeration Company (PRC) has 15-year noncallable bonds with a face value of $1,000 that are outstanding. These bonds have a current market price of $1,136.50 per bond, carry a coupon rate of 12%, and distribute annual coupon payments. The company incurs a federal-plus-state tax rate of 25%. If PRC 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.)

7.64%

6.11%

6.88%

9.17%

Answer 1

Perpetualcold Refrigeration Company (PRC) can borrow funds at an interest rate of 11.10% for a period of four years. Its marginal federal-plus-state tax rate is 25%. PRC’s after-tax cost of debt is  

After tax cost of debt = before tax cost of debt * ( 1 - tax rate)

Here,

before tax cost of debt = 11.10%

tax rate = 25% = 0.25

After tax cost of debt = 11.10 * ( 1 - 0.25 )

After tax cost of debt = 11.10 * 0.75 = 8.33%

At the present time, Perpetualcold Refrigeration Company (PRC) has 15-year noncallable bonds with a face value of $1,000 that are outstanding. These bonds have a current market price of $1,136.50 per bond, carry a coupon rate of 12%, and distribute annual coupon payments. The company incurs a federal-plus-state tax rate of 25%. If PRC wants to issue new debt, what would be a reasonable estimate for its after-tax cost of debt (rounded to two decimal places)?

Cost of debt = yield to maturity (YTM)

The formula for YTM

YTM = (C+ ((P-M) / n)) / ((p+m) / 2)

Here,

C (coupon interest) = Coupon rate * Par value = 12% * $1000 = $120

P (Par Value or face value ) = $1000

M (Market Price or current price ) = $1,136.50

n (years to maturity) = 15 years

By applying values into the formula we get,

YTM = ($120 + ( ($1000 - $1136.50 ) / 15 ) ) / ( ($1000 + $ 1136.50 ) / 2)

YTM = ($120 + - 9.10 ) / 1068.25

YTM = 110.9 / 1068.25

YTM = 0.1038   = 10.38%

So the cost of debt before tax = 10.38%

After tax cost of debt = 10.38 - 25% = 7.79%

In the answer 7.64% is the answer. The reason for miss matching is 7.64% is calculated on using YTM calculator. If can’t get through this process.