Question

Shanken Corp. issued a 20-year, 4.2 percent semiannual bond 3 years ago. The bond currently sells for 89 percent of its face value. The company's tax rate is 22 percent. a. What is the pretax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the aftertax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places.

Answer 1

(a)-Pre-tax cost of debt

• The Company's pre-tax cost of debt is the Yield to maturity (YTM) of the Bond
• The Yield to maturity (YTM) of the Bond is the discount rate at which the Bond’s price equals to the present value of the coupon payments plus the present value of the Face Value/Par Value
• The Yield to maturity of (YTM) of the Bond is the estimated annual rate of return expected by the bondholders for the bond assuming that the they hold the Bonds until it’s maturity period/date.
• The Yield to maturity of (YTM) of the Bond is calculated using financial calculator as follows (Normally, the YTM is calculated either using EXCEL Functions or by using Financial Calculator)

Variables	Financial Calculator Keys	Figure
Par Value/Face Value of the Bond [$1,000]	FV	1,000
Coupon Amount [$1,000 x 4.20% x ½]	PMT	21
Market Interest Rate or Yield to maturity on the Bond	1/Y	?
Maturity Period/Time to Maturity [(20 Years – 3 Years) x 2]	N	34
Bond Price/Current Market Price of the Bond [-$1,000 x 89%]	PV	-890

We need to set the above figures into the financial calculator to find out the Yield to Maturity of the Bond. After entering the above keys in the financial calculator, we get the semi-annual yield to maturity on the bond (1/Y) = 2.59%.

The semi-annual Yield to maturity = 2.59%.

Therefore, the annual Yield to Maturity of the Bond = 5.18% [2.59% x 2]

“Hence, the Company's pre-tax cost of debt will be 5.18%”

(b)-The after-tax cost of debt

The firm’s after-tax cost of debt on the Bond is the after-tax Yield to maturity (YTM)

The After-tax cost of debt = Yield to maturity on the bond x (1 – Tax Rate)

= 5.18% x (1 – 0.22)

= 5.18% x 0.78

= 4.04%

“Hence, the after-tax cost of debt will be 4.04%”