Question

#23 ch.7: semi-annual bond ; coupon = 7.2; matures=14 yrs; Last Price=108.96What is YTM, CY and effective Yield.

Answer 1

(a)-Yield to maturity of (YTM) of the Bond

• The Yield to maturity of (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 7.20% x ½]	PMT	36
Market Interest Rate or Yield to maturity on the Bond	1/Y	?
Maturity Period/Time to Maturity [14 Years x 2]	N	28
Bond Price [-$1,000 x 108.96%]	PV	-1,089.60

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 (YTM) on the bond = 3.115%.

The semi-annual Yield to maturity = 3.115%.

Therefore, the annual Yield to Maturity of the Bond = 6.23% [3.115% x 2]

“Hence, the Yield to maturity of (YTM) of the Bond will be 6.23%”

(b)-Current Yield on the Bond

Current Yield on the Bond = [Annual Coupon amount / Market Price of the Bond] x 100

= [($1,000 x 7.20%) / ($1,000 x 108.96%)] x 100

= [$72 / $1,089.60] x 100

= 6.61%

(c)-Effective Annual Yield

Number of Compounding per year = 2 (Since, the compounding is done semi-annually)

Therefore, the Effective Annual Yield = [(1 + (YTM/2)]² – 1

= [(1 + (0.0623/2)] ² – 1

= [1 + 0.03115]² – 1

= [1.03115] ² – 1

= 1.063270 - 1

= 0.063270 or

= 6.33% (Rounded to 2 decimal place)

“Hence, the Effective Annual Yield on the Bond will be 6.33%”