The City of Springfield is renewing its water treatment facility. The new facility costs

more than what their budget allows so the mayor decides to issue a $20-$year bond to finance the

project. Each bond has a face value of $$1,000$ and it promises a coupon rate of $3\mathrm{.}90\%,$ which will

be paid semi$-$annually. The City of Springfield had a credit rating of A$+$ at that time.

a$.$Calculate the price of this bond if its initial Yield to Maturity $($YTM$)$ was $5\mathrm{.}28\%$ pa$.$

b$.$Let$$s assume you bought this bond on the date of issue. Right after receiving the tenth

coupon payment, you decided to sell the bond. Exactly on that date, the credit rating of the City

of Springfield was upgraded to AA$-,$ which reduced the bond$$s YTM by $60$ basis points $(=0\mathrm{.}6\%).$ If

you did not reinvest your coupon payments, what is your holding period return $($HPR$)?$

c$.$Let$$s assume that the scenario in part a continues. If your holding period return $($HPR$)$

after five years is $40\mathrm{.}00\%$ and you did not reinvest your coupon payments, what is the YTM at

the selling time?