Question

A bond that matures in 18 years has a ​$1,000 par value. The annual coupon interest rate is 14 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 15 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?

Answer 1

Part-1: Interest paid annually

Face value = $1000

Annual coupon rate = 14%

Annual coupon payment = Annual coupon rate*Face value = 14%*1000 = 140

Time to maturity in years = 18 years

YTM = 15%

Method1: Bond's price calculation using ba ii plus calculator

Input the following values in ba ii plus calculator

N = 18

I/Y = 15

PMT = 140

FV = 1000

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

we get, PV = -938.7203413

Price of the bond with annual coupons ($) = 938.72 (Rounded to nearest cent)

Method 2: Bond's price calculation using Excel

We can calculate the price of the bond using the PV function in Excel as shown below:

=PV(15%,18,140,1000) = -938.72

Price of the bond with annual coupons ($) = 938.72

Part -2: Interest paid semiannually

Here we will consider semiannual coupon payments, semiannual YTM and semiannual periods to maturity

Face value of the bond = $1000

Semi-annual coupon payment = Annual coupon payment/2 = 140/2 = 70

Semi-annual number of periods = 18*2 = 36

Semi-annual YTM = 15%/2 = 7.5

Method 1: Bond's price calculation using ba ii plus calculator

Input the following values in ba ii plus calculator

N = 36

I/Y = 7.5

PMT = 70

FV = 1000

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

We get, PV = -938.2673888

Bond's price with semi-annual coupons ($) = 938.27 (Rounded to nearest cent)

Method 2: Bond's price calculation using the PV function in Excel

We can calculate the price of the bond using the PV function in Excel as shown below:

=PV(7.5%,36,70,1000) = -938.27

Bond's price with semi-annual coupon payments ($) = 938.27

Answers

Bond's price if interest paid annually ($) = 938.2

Bond's price if interest paid semiannually ($) = 938.27