b$.$ What is the internal rate of return of your investment?

$13.$ Consider the following bonds:

$\backslash$table$[[$Bond$,$Coupon Rate $($annual payments$),$Maturity $($years$)],[$A$,0\%,16],[$B$,0\%,12],[$C$,2\%,16],[$D$,7\%,12]]$

a$.$ What is the percentage change in the price of each bond if its yield to maturity falls from $7\%$ to $6\%?$

b$.$ Which of the bonds A$-$D is most sensitive to a $1\%$ drop in interest rates from $7\%$ to $6\%$ and why? Which bond is least sensitive$?$ Provide an intuitive explanation for your answer.

Problems

$233$

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$14.$ Suppose you purchase a $30-$year, zero$-$coupon bond with a yield to maturity of $4\%.$ You hold the bond for five years before selling it$.$

a$.$ If the bond's yield to maturity is $4\%$ when you sell it$,$ what is the internal rate of return of your investment?

b$.$ If the bond's yield to maturity is $5\%$ when you sell it$,$ what is the internal rate of return of your investment?

c$.$ If the bond's yield to maturity is $3\%$ when you sell it$,$ what is the internal rate of return of your investment?

d$.$ Even if a bond has no chance of default, is your investment risk free if you plan to sell it before it matures? Explain.

$15.$ Suppose you purchase a $30-$year Treasury bond with a $6\%$ annual coupon, initially trading at par. In $10$ years' time, the bond's yield to maturity has risen to $7\%($EAR$).$

a$.$ If you sell the bond now, what internal rate of return will you have earned on your investment in the bond?

b$.$ If instead you hold the bond to maturity, what internal rate of return will you earn on your investment in the bond?

c$.$ Is comparing the IRRs in $($a$)$ versus $($b$)$ a useful way to evaluate the decision to sell the bond? Explain.

$16.$ Suppose the current yield on a one$-$year, zero$-$coupon bond is $4\%,$ while the yield on a five$-$year, zero$-$coupon bond is $5\%.$ Neither bond has any risk of default. Suppose you plan to invest for one year. You will earn more over the year by investing in the five$-$year bond as long as its yield does not rise above what level?

The Yield Curve and Bond Arbitrage

For Problems $17-22,$ assume zero$-$coupon yields on default$-$free securities are as summarized in the following table:

$\backslash$table$[[$Maturity $($years$),1,2,3,4,5],[$Zero$-$coupon YTM$,4\mathrm{.}6\%,5\mathrm{.}0\%,5\mathrm{.}4\%,5\mathrm{.}8\%,6\mathrm{.}1\%$