Question

A bond has a face value of $1,000, a coupon of 4% paid annually, a maturity of 33 years, and a yield to maturity of 7%. What rate of return will be earned by an investor who purchases the bond for $617.39 and holds it for 1 year if the bond’s yield to maturity at the end of the year is 8%?

The answer -15.82% is being marked as wrong please help!

Answer 1

Rate of return earned by the investor

Current Price of the Bond = $617.39

Price of the Bond in One Year

Face Value = $1,000

Annual Coupon Amount = $40 [$1,000 x 4%]

Yield to Maturity (YTM) of the Bond = 8%

Maturity Years = 32 Years [33 Years – 1 Year]

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

= $40[PVIFA 8%, 32 Years] + $1,000[PVIF 8%, 32 Years]

= [$40 x 11.43500] + [$1,000 x 0.08520]

= $457.40 + $85.20

= $542.60

Rate of return on the Bond

Rate of return on the Bond = [(Coupon Amount + Change in Bond Price) / Current Price of the Bond] x 100

= [{$40 + ($542.60 - $617.39)} / $617.39] x 100

= [($40 - $74.79) / $617.39] x 100

= [-$34.79 / $617.39] x 100

= -5.64% (Negative Return)

“Therefore, the Rate of return earned by the investor is -5.64% (Negative Return)”

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.