Question

In: Finance

Last year, Joan purchased a $1,000 face value corporate bond with an 8% annual coupon rate...

Last year, Joan purchased a $1,000 face value corporate bond with an 8% annual coupon rate and a 25-year maturity. At the time of the purchase, it had an expected yield to maturity of 9.62%. If Joan sold the bond today for $1,053.36, what rate of return would she have earned for the past year? Round your answer to two decimal places.

Solutions

Expert Solution

Market Price of the Bond

Face Value = $1,000

Annual Coupon Amount = $980 [$1,000 x 8%]

Yield to Maturity (YTM) = 9.62%

Maturity Years = 25 Years

The Price of the bond = Present Value of the Coupon payments + Present Value of Face Value

= $80[PVIFA 9.62%, 25 Years] + $1,000[PVIF 9.62%, 25 Years]

= [$80 x 9.34889] + [$1,000 x 0.10064]

= $747.91 + $100.64

= $848.55

The Rate of return would she have earned for the past year

Rate of return = [{Coupon Amount + (Selling price of the Bond today - Market Price of the Bond)} / Market Price of the Bond] x 100

= [{$80 + ($1,053.36 - $848.55} / $848.55] x 100

= [($80 - $204.81) / $848.55] x 100

= [$284.81 / $848.55] x 100

= 33.56%

“Therefore, the Rate of return would she have earned for the past year would be 33.56%”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)n} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)n], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond


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