Question

Last year, Joan purchased a $1,000 face value corporate bond with an 9% annual coupon rate and a 20-year maturity. At the time of the purchase, it had an expected yield to maturity of 11.5%. If Joan sold the bond today for $1,105.62, what rate of return would she have earned for the past year? Round your answer to two decimal places.

Answer 1

Calculation of purchase price:

Face value = $1,000

Annual coupon rate = 9.00%
Annual coupon = 9.00% * $1,000
Annual coupon = $90

Time to Maturity = 20 years
Annual YTM = 11.50%

Purchase price = $90 * PVIFA(11.50%, 20) + $1,000 * PVIF(11.50%, 20)
Purchase price = $90 * (1 - (1/1.1150)^20) / 0.1150 + $1,000 / 1.1150^20
Purchase price = $807.25

Rate of return earned = (Selling price + Coupon received - Purchase price) / Purchase price
Rate of return earned = ($1,105.62 + $90.00 - $807.25) / $807.25
Rate of return earned = 0.4811 or 48.11%

So, Joan earned a return of 48.11% during last year.