Three investors invest in the same $10-$year $8\%$ annual coupon bond. They bought the bond at the same

price $($$$85\mathrm{.}5030$ for a par value of $$100)$ and at the same time. A is a buy$-$and$-$hold investor $($hold till

maturity$),$ B will sell the bond after four years, and C will sell the bond after seven years.

$1.$ What is the yield to maturity of this bond at the time of purchase?

$2.$ After the bond is purchased by the three investors and before the first coupon is received, interest

rate drops to $9\mathrm{.}4\%.$ Calculate:

i$.$ What is the change in IOI for each investor? $($Hint: Find the difference between the IOI

under the original YTM and the IOI under the new yield$).$

ii$.$ What is the capital gain$/$loss for each investor? $($Hint: capital gain$/$loss$=$ price at sale or maturity

$$ pricecarrying. Carrying value is the hypothetic price of the bond if the bond$$s yield remains

at the initial yield to maturity.$)$

iii. What is net gain or loss for each investor after the interest rate change?

$3.$ What is the Macaulay duration of this bond?

$4.$ For each of these three investors, find their respective duration gap. $($Hint: Duration gap$=$Macaulay

duration $$ investor horizon$).$

$5.$ Use the answers from $2-4$ to discuss how the interest rate change has influenced the value of the

investors$$ investment and why? $($Hint: Consider that when duration gap is positive $($negative$),$ the bond$$s Macaulay

duration is greater $($less$)$ than the investor$$s investment horizon, which means the investor faces

greater market price risk than reinvestment risk $($reinvestment risk than market price risk$)$