Question

Last year Janet purchased a $1,000 face value corporate bond with an 7% annual coupon rate and a 15-year maturity. At the time of the purchase, it had an expected yield to maturity of 7.42%. if janet sold the bond today for $991.19, what rate of return would she have earned for the past year? round your answer to two decimal places.

Answer 1

Bond's Purchase Value = PV of Coupon Payment + PV of Maturity Value

= [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

= [{7%*$1,000} * {(1 - (1 + 0.0742)^-(15)) / (0.0742)}] + [$1,000 / {1 + (0.0742)}^(15)]

= [$70 * {0.6582 / 0.0742}] + [$1,000 / 2.9260]

= [$70 * 8.8711] + $341.76

= $620.98 + $341.76 = $962.74

Rate of Return earned = [Sale Price - Purchase Price + Coupon Interest] / Purchase Price

= [$991.19 - $962.74 + $70] / $962.74

= $98.45 / $962.74 = 0.1023, or 10.23%