Question

A bond has a $1,000 par value, 15 years to maturity, and an 8% annual coupon and sells for $1,080. What is its yield to maturity (YTM)? Round your answer to two decimal places. % Assume that the yield to maturity remains constant for the next three years. What will the price be 3 years from today? Do not round intermediate calculations. Round your answer to the nearest cent. $

Answer 1

Compute the annual interest, using the equation as shown below:

Annual interest = Face value*Rate of interest

                          = $1,000*8%

                          = $80

Hence, the annual interest is $80.

Compute the annual yield to maturity (YTM), using the equation as shown below:

Annual YTM = [Annual interest + {(Redemption value – Net proceeds)/ Maturity period}]/ {(Redemption value + Net proceeds)/2}

                       = [$80 + {($1,000 – $1,080)/ 15}]/ {($1,000 + $1,080)/2}

                      = ($80 - $5.3333333333)/ $1,040

                      = 7.18%

Hence, the annual YTM is 7.18%.

Compute the present value annuity factor (PVIFA), using the equation as shown below:

PVIFA = {1 – (1 + Rate)-Number of periods}/ Rate

                   = {1 – (1 + 0.0718)-12}/ 7.18%

             = 7.86704774692

Hence, the present value annuity factor is 7.86704774692.

Compute the present value factor (PVIF), using the equation as shown below:

PVIF factor = 1/ (1 + Discount rate)Time period

                    = 1/ (1 + 0.0718)12

                    = 1/ 2.29807941449

                    = 0.43514597176

Hence, PVIF is 0.43514597176.

Compute the bond price after 3 years from now, using the equation as shown below:

Bond price = (Annual interest*PVIFA) + (Face value*PVIF)

                   = ($80*7.86704774692) + ($1,000*0.43514597176)

                   = $1,064.50979151

Hence, the bond price is $1,064.51.