Question

A 25-year, $1,000 par value bond has an 8.5% annual payment coupon. The bond currently sells for $925. If the yield to maturity remains at its current rate, what will the price be 10 years from now?

Answer 1

We will first compute the YTM of the bond

Face value of the bond = $1000

Present value of the bond = $925

Time to maturity = 25 years

Annual coupon rate = 8.5%

Annual coupon payment = Annual coupon rate*Face value = 8.5%*1000 = 85

YTM Calculation

Method 1: YTM calculation using Excel

We can compute the YTM of the bond using the RATEfunction in Excel as shown below:

=RATE(25,85,-925,1000) = 9.281%

Method 2: YTM calculation using ba ii plus calculator

YTM can also be computed using ba ii plus calculator as shown below:

N = 25

PV = -925

PMT = 85

FV = 1000

CPT -> I/Y [Press CPT and then press I/Y]

We get I/Y = 9.280999758

YTM = 9.280999758%

Price calculation 10 years from now

We need to calculate the price of the bond 10 years from now. After 10 years, there will be 15 years to maturity

Face value of the bond = $1000

Time to maturity = 15 years

Annual coupon payment = 85

YTM = 9.280999758%

Method 1: Price calculation using Excel

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

=PV(9.281%,15,85,1000) = -938.08

Method 2: Price calculation using ba ii plus calculator

We can also calculate the price of the bond using ba ii plus calculator

Input following values in ba ii plus calculator

N = 15

I/Y = 9.281

PMT = 85

FV = 1000

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

We get, PV = -938.0768669

Price of the bond 10 years from now = $938.08 (Rounded to the nearest cent)

Answer ($) -> 938.08