Question

if i have a 9​-year bond that's paying me interest of $28.10 ​semiannually, has a face value of $1,000​,and is selling for $843.43. What would its annual coupon rate and yield to​ maturity be?

Answer 1

(a)-Annual coupon rate of the Bond

Annual coupon rate of the Bond = [Annual coupon amount / Face Value] x 100

= [($28.10 x 2) / $1,000] x 100

= [$56.20 / $1,000] x 100

= 5.62%

(b)-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 5.62% x ½]	PMT	28.30
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 [-$843.43]	PV	-843.43

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) = 4.05%

The semi-annual Yield to maturity = 4.05%.

Therefore, the annual Yield to Maturity of the Bond = 8.10% [4.05% x 2]

“Hence, the annual Yield to maturity (YTM) of the Bond will be 8.10%”