Question

National Corporation has semiannual bonds outstanding with nine years to maturity and the bonds are currently priced at $754.08. If the bonds have a coupon rate of 7.25 percent, then what is t

he after-tax cost of debt for Beckham if its marginal tax rate is 30 percent? Solution

• Number of periods = 9 * 2 = 18

  Coupon = (0.0725 * 1000) / 2 = 36.25

  Yield to maturity = 11.7499%

  Keys to use in a financial calculator: 2nd I/Y 2, FV 1000, PMT 36.25, PV -754.08, N 18, CPT I/Y

  After tax cost of debt = YTM (1 - tax)

  After tax cost of debt = 0.117499 (1 - 0.3)

  After tax cost of debt = 0.0822 or 8.22%

HOW DID THEY FIND THE  Yield to maturity = 11.7499%

HOW CAN I DO THIS PROBLEM BY HAND STEP BY STEP OR BY FINANCE CALCULATOR STEP BY STEP ?? PLEASE HELP

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 7.25% x ½]	PMT	36.25
Market Interest Rate or Yield to maturity on the Bond	1/Y	?
Maturity Period/Time to Maturity [9 Years x 2]	N	18
Bond Price/Current Market Price of the Bond [-$754.08]	PV	-754.08

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) = 5.875%.

The semi-annual Yield to maturity = 5.875%.

Therefore, the annual Yield to Maturity of the Bond = 11.75% [5.875% x 2]

(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 = Annual Yield to maturity on the bond x (1 – Tax Rate)

= 11.75% x (1 – 0.30)

= 11.75% x 0.70

= 8.23%

“Hence, the after-tax cost of debt will be 8.23%”