Problem $14-31($Algo$)$

A newly issued bond pays its coupons once annually. Its coupon rate is $4\%,$ its maturity is $20$ years, and its yield to maturity is $11\mathrm{.}5\%.$

Required:

a$.$ Find the holding$-$period return for a $1-$year investment period if the bond is selling at a yield to maturity of $10\%$ by the end of the year.

b$.$ If you sell the bond after one year, what taxes will you owe if the tax rate on interest income is $40\%$ and the tax rate on capital gains income is $30\%?$ The bond is subject to original$-$issue discount tax treatment.

c$.$ What is the after$-$tax holding$-$period return on the bond?

d$.$ Find the realized compound yield before taxes for a $2-$year holding period, assuming that $($i$)$ you sell the bond after two years, $($ii$)$ the bond yield is $10\%$ at the end of the second year, and $($iii$)$ the coupon can be reinvested for one year at a $3\%$ interest rate.

e$.$ Use the tax rates in part $($b$)$ to compute the after$-$tax $2-$year realized compound yield. Remember to take account of OID tax rules.