Last year Janet purchased a $1,000 face value corporate bond with an 9% annual coupon rate and a 25-year maturity. At the time of the purchase, it had an expected yield to maturity of 13.45%. If Janet sold the bond today for $1,108.92, what rate of return would she have earned for the past year? Do not round intermediate calculations. Round your answer to two decimal places.
Answer:
Calculation of purchase price:
Face value = $1,000
Annual coupon rate = 9%
Annual coupon = 9% * $1,000
Annual coupon = $90
Annual YTM = 13.45%
Time to maturity = 25 years
Purchase price = $90 * PVIFA(13.45%, 25) + $1,000 * PVIF(13.45%,
25)
Purchase price = $90 * (1 - (1/1.1345)^25) / 0.1345 + $1,000 /
1.1345^25
Purchase price = $683.25
Calculation of rate of return earned:
Purchase price = $683.25
Coupon received = $90.00
Selling price = $1,108.92
Rate of return = (Selling price + Coupon received - Purchase
price) / Purchase price
Rate of return = ($1,108.92 + $90.00 - $683.25) / $683.25
Rate of return = $515.67 / $683.25
Rate of return = 0.7547 or 75.47%
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