Question

An investor is considering purchasing a bond with a 7.83 percent coupon interest​ rate, a par value of $1,000, and a market price of $870.83. The bond will mature in nine years. Based on this​ information, answer the following​ questions:

a. What is the​ bond's current​ yield?

b. What is the​ bond's approximate yield to​ maturity?

c. What is the​ bond's yield to maturity using a financial​ calculator?

​Note: Assume coupon payments are paid annually

a. The​ bond's current yield is 8.99%. (Round to two decimal​ places.)

b. The​ bond's approximate yield to maturity is _______​%.(Round to two decimal​ places.)

Answer 1

(a)-Bond's Current Yield

Bond’s Current Yield = [Annual Coupon Amount / Bond’s Price] x 100

= [($1,000 x 7.83%) / $870.83] x 100

= [$78.30 / $870.83] x 100

= 8.99%

‘The Bond's Current Yield will be 8.99%”

(b)-The Bond's approximate yield to maturity

Here, we’ve Par Value = $1,000

Annual Coupon Amount = $78.30 [$1,000 x 7.83%]

Bond Price = $870.83

Maturity Years = 9 Years

Therefore, the Bond’s Approximate Yield to Maturity [YTM] = Coupon Amount + [ (Face Value – Bond Price) / Maturity Years] / [(Face Value + Bond Price)/2]

= $78.30 + [($1,000 - $870.83) / 9] / [($1,000 + $87083) / 2]

= [$78.30 + ($129.17 / 9)] / [$1,870.83 / 2]

= [$78.30 + $14.35] / $935.42

= $92.65 / $935.42

= 0.0990 or

= 9.90%

“Hence, the Bond’s Approximate Yield to Maturity will be 9.90%”

(c)-Yield to maturity (YTM) of the Bond using the financial calculator

• 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 7.83%]	PMT	78.30
Market Interest Rate or Yield to maturity on the Bond	1/Y	?
Maturity Period/Time to Maturity [9 Years]	N	9
Bond Price/Current Market Price of the Bond [-$870.83]	PV	-870.83

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 annual yield to maturity on the bond (1/Y) = 10.08%.

“Hence, the Yield to maturity (YTM) of the Bond using the financial calculator will be 10.08%”