Question

one year ago you purchased a 30-year 8% annual coupon bond at par. today, you receive the first coupon and sold the bond at a market rate of interest of 6%. what rate of return did you earn?

8%, 19.12%, 6%,22.13%

Answer 1

Current Bond Price

Face Value = $1,000

Annual Coupon Amount = $80 [$1,000 x 8%]

Yield to Maturity (YTM) = 6%

Maturity Period = 30 Years

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

= $80[PVIFA 6%, 30 Years] + $1,000[PVIF 6%, 30 Years]

= [$80 x 13.76483] + [$1,000 x 0.17411]

= $1,101.19 + $174.11

= $1,275.30

Price of the Bond after 1 year

Face Value = $1,000

Annual Coupon Amount = $80 [$1,000 x 8%]

Yield to Maturity (YTM) = 6%

Maturity Period = 29 Years [30 Years – 1 Year]

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

= $80[PVIFA 6%, 29 Years] + $1,000[PVIF 6%, 29 Years]

= [$80 x 13.59072] + [$1,000 x 0.18456]

= $1,087.25 + $184.56

= $1,271.81

Rate of return earned on the Bond

Rate of return = [{Coupon Amount + (1 Year Price – Current Price)} / Current Price] x 100

= [{$80 + ($1,271.81 - $1,275.30} / $1,275.30] x 100

= [($80 - $3.48) / $1,275.30] x 100

= [$76.52 / $1,275.30] x 100

= 6%

“Hence, the Rate of return earned on the Bond would be 6%”

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.