Question

Boulder Furniture has bonds outstanding that mature in 15 years, have a 6 percent coupon, and pay interest annually. These bonds have a face value of $1,000 and a current market price of $1,075. What is the company's aftertax cost of debt if its tax rate is 32 percent?

a. 3.58%
b. 5.53%
c. 5.21%
d. 2.97%

Answer 1

The after-tax cost of debt for Boulder Furniture is calculated by first finding the pre-tax cost of debt and then adjusting for taxes. The pre-tax cost of debt comes out to 5.3%, and after adjusting for a 32% tax rate, the after-tax cost of debt is approximately 3.6%, making the closest answer (a) 3.58%.

Step-by-step explanation:

To calculate the aftertax cost of debt for Boulder Furniture, we first need to find the yield to maturity (YTM) on the bond, which represents the internal rate of return on the bond investment. The formula to calculate the cost of debt before tax is:

C = (I + ((F - P) / N)) / ((F + P) / 2)

Where:
C = cost of debt
I = annual interest payment ($60, which is 6% of $1,000)
F = face value of the bond ($1,000)
P = current price of the bond ($1,075)
N = number of years to maturity (15)

Plugging the numbers into the formula, we get:

C = ($60 + (($1,000 - $1,075) / 15)) / (($1,000 + $1,075) / 2)

C = ($60 - $5) / $1,037.50

C = $55 / $1,037.50

C = 0.053 or 5.3%

This is the cost of debt before taxes. To get the after-tax cost of debt, we multiply the before-tax cost of debt by (1 - tax rate):

Aftertax cost of debt = C x (1 - Tax rate)

Aftertax cost of debt = 0.053 x (1 - 0.32)

Aftertax cost of debt = 0.053 x 0.68

Aftertax cost of debt = 0.036 or 3.6%

Since this is not one of the exact options provided, the closest answer to the actual calculated aftertax cost of debt would be (a) 3.58%.

Answer 2

a. 3.58%

Step-by-step explanation:

First, find the pretax cost of debt ; the YTM.

You can solve this using a financial calculator. Input the following;

Maturity of the bond; N = 15

Face value; FV = 1,000

Price of the bond; PV = -1,075

Recurring annual coupon payments; PMT = (6%) *1000 = 60

Compute Semiannual interest rate; CPT I/Y = 5.264%

Therefore, the pretax cost of debt = 5.264%

Aftertax cost of debt = Pretax cost of debt (1-tax)

= 5.264%(1-0.32)

= 3.58%