You have a 5-year investment holding horizon, would like to earn a 4% annual compound return each year, and you have a choice between two bonds.
Find (a) the Price, (b) Duration, and (c) Modified Duration for each bond, and answer the questions below:
$\bullet$Bond 1 has a 4% annual coupon rate, $1000 maturity value, n = 5 years, YTM = 4% (pays a $40 annual coupon at the end of each year for each of the 5 years and $1,000 maturity payment at the end of year 5).
$\bullet$Bond 2 is a zero coupon bond with a $1000 maturity value, and n = 5 years; YTM= 4%. (pays no coupons; only a $1,000 maturity payment at the end of year 5)

Question

Quizplus · Accepted Answer

The Answer is a. Price Bond 1 ___$1,000__ Price Bond 2 __ $821.93____
b. Duration Bond 1 ___4.63_______ Duration Bond 2 ___5______
c. Modified Duration Bond 1 __4.45 __ Modified Duration Bond 2 ___4.81_____
Price Bond 1 = $40 (PVIFA 4%, 5) + $1000 (PVIF 4%, 5)
= $40(4.4518) + $1000(.82193) = $178.07 + $821.93 = $1,000
(sells at Par Value since CR = YTM rate).

\begin{array}{l} ext { Duration Calculation: }\\begin{array} { l c c c c } ext { Year } & { ext { CF } } & ext { PVIF } & ext { PVCF } & ext { WtedPVCF } \1 & \$ 40 & .96154 & \$ 38.46 & \$ 38.46 \2 & \$ 40 & .92456 & \$ 36.98 & \$ 73.96 \3 & \$ 40 & .88900 & \$ 35.56 & \$ 106.68 \4 & \$ 40 & .85480 & \$ 34.19 & \$ 136.77 \5 & \$ 1,040 & .82193 & \$ 854.81 & \$ 4274.03 \& ext { Totals } & & \$ 1,000 & \$ 4629.91\end{array}\end{array}

Duration = $4629.91/$1,000 = 4.63
Modified Duration = 4.63/1.04 = 4.45
Price Bond 2 = $1000/(1.04)^5 = $1000(.82193) = $821.93
Duration for Zero Coupon Bond 2 = Its Maturity = 5 years
Modified Duration Bond 2 = 5/1.04 = 4.81

You Have a 5-Year Investment Holding Horizon, Would Like to Earn