Question

Drogo, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 23 years to maturity that is quoted at 97 percent of face value. The issue makes semiannual payments and has an embedded cost of 5 percent annually. What is the company’s pretax cost of debt? If the tax rate is 35 percent, what is the aftertax cost of debt?If the tax rate is 35 percent, what is the aftertax cost of debt?

Answer 1

before taxes 5.23%

after tax: 3.40%

Step-by-step explanation:

The bonds coupon interest rate is not the market rate . If Drogo Inc tries to take debt in the market it will be at a different rate as it is not selling at par.

We should determinate the market rate of the bond.

The bond sales as 97% which means the present value of the coupon payment and maturity discounted at the market rate equal 97% of the face value

We solve for this using excel and get:

Present value of the coupon payments

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 25 (1,000 x 5% / 2 payment per year)

time 46 (23 years x 2 payment)

rate 0.026128

`25 * (1-(1+0.026128)^(-46) )/(0.026128) = PV\\`

PV $664.7027

Present value

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 1,000.00

time 46.00

rate 0.026128

`(1000)/((1 + 0.026128)^(46) ) = PV`

PV 305.30

PV coupon $664.7027 + PV maturity $305.2973 = $970.0000

We know have to multiply this rate by 2 as it is semiannual like the payment:

0.026128 * 2 = 0.0523 = 5.23%

Last we calcualte the after tax cost of debt:

0.0523 (1 - 0.35) = 0.033995‬ = 3.40%