Question

A bond that matures in 13 years has a ​$1000 par value. The annual coupon interest rate is 9 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 12 percent. What would be the value of this bond if it paid interest​ annually? What would be the value of this bond if it paid interest​ semiannually?

a.  The value of this bond if it paid interest annually would be ​$ nothing. ​ (Round to the nearest​ cent.)

Answer 1

Face Value of the bond = 41000

Time to maturity = 13 years

Annual coupon rate = 9%

Annual Coupon Payment = Annual coupon rate*Face Value = 9%*1000 = 90

Yield to Maturity = YTM = 12%

Part - 1:Value of the Bond when the interest is paid annually

We will take the annual coupon payment, time to maturity in years and the annual YTM. We can calculate the price of the bond using ba ii plus calculator as shown below:

N = 13

I/Y = 12

PMT = 90

FV = 1000

CPT -> PV [Press CPT and then press PV]

We get, PV = -807.2935475

Answer -> Value of the bond if it paid interest annually = 807.29

Part - 2:Value of the Bond when the interest is paid semiannually

We will take the semiannual coupon payment, time to maturity in semiannual periods and the semiannual YTM. We can calculate the price of the bond using ba ii plus calculator as shown below

Face Value = $1000

Semi-annual coupon payments = Annual coupon payment/2 = 90/2 = $45

Semi-annual YTM = 12%/2 = 6%

Time to maturity in semiannual periods = 13*2 = 26

Value of the bond calculation using ba ii plus calculator:

N = 26

I/Y = 6

PMT = 45

FV = 1000

CPT -> PV [Press CPT and then press PV]

We get, PV = -804.9525072

Answer -> Value of the bond if it paid interests semiannually = 804.95