Question $2.$

You just bought a newly issued bond which has a face value of $$1,000$ and pays its coupon once

annually. Its coupon rate is $6\%,$ maturity is $20$ years and the yield to maturity for the bond is

currently $9\%.$

a$.$ Do you expect the bond price to change in the future when the yield stays at $9\%?$

Why or why not? Explain. $($No computations are required to answer this part of

the question.$)$

$(3$ marks$)$

b$.$ Calculate what the bond price would be in one year if its yield to maturity stays

at $9\%.$

$(3$ marks$)$

c$.$ Find the before$-$tax holding$-$period return for a one$-$year investment period if the

bond sells at a yield to maturity of $7\%$ by the end of the year $($year $1).$

$(3$ marks$)$

d$.$ When the ordinary income tax rate is higher than the capital gains tax rate, tax

authorities typically tax anticipated price appreciations from bonds at the

ordinary income rate in order to prevent tax aversion with discount bonds.

Suppose that from the total dollar return in part c$),$ the coupon payment and the

difference between the hypothetical prices in part $b)$ and the purchase price are

taxed at the ordinary income tax rate, $40\%.$ The rest of the dollar return is

considered capital gains $($due to unanticipated change in yield$-$to$-$maturity from

$9\%$ to $7\%)$ taxed at $30\%.$ In other words, coupon payments and the anticipated

price appreciation are taxed at the ordinary income tax rate and the rest at the

lower capital gains rate. Using your answers in part b$)$ and c$),$ calculate the after$-$

tax holding period return over one year if the yield to maturity is $7\%$ at the end

of the year.

$(5$ marks$)$

e$.$ Find the realized compound yield before taxes for a two$-$year holding period,

assuming that $1)$ investor who bought the newly issued bond now will sell the

bond in two years, ii$)$ bond's yield$-$to$-$maturity will be $7\%$ at the end of the

second year, and iii$)$ the coupon in year $1$ will be reinvested for one year at a $3\%$

interest rate. Ignore taxes.

$(4$ marks$)$