$4.$ Bombs$-$Away bonds are currently selling at $$1,200.$ Their face value is $$1,000,$ coupon is $11\%,$ and years left to maturity is $10.$ The bonds are callable in five years, at $109.$

a$)$ What is the yield to maturity?

P $=[$C $/(1+$ YTM$)^$t$]+[$F $/(1+$ YTM$)^$n$]$

$1,200=110/(1+$ YTM$)^1+110/(1+$ YTM$)^2+...+110/(1+$ YTM$)^\{10\}+1,000/(1+$ YTM$)^\{10\}$

YTM $=8\mathrm{.}02\%$

b$)$ What is the yield to call if they are called at first opportunity?

P $=[$C $/(1+$ YTC$)^$t$]+[$Cp $/(1+$ YTC$)^$t$\_$call$]$

$1,200=110/(1+$ YTC$)^1+110/(1+$ YTC$)^2+...+110/(1+$ YTC$)^\{5\}+1,090/(1+$ YTC$)^\{5\}$

YTC $7\mathrm{.}59\%$