HMK Enterprises would like to raise $$14$ million to invest in capital expenditures. The company

plans to issue five$-$year bonds with a face value of $$1000$ and a coupon rate of $4\%($annual pay$-$

ments$).$ The following table summarizes the yield to maturity for five$-$year $($annual$-$pay$)$ coupon

corporate bonds of various ratings:

Rating AAA AA A BBB BB

YTM $3\mathrm{.}7\%3\mathrm{.}9\%4\%4\mathrm{.}7\%5\mathrm{.}1\%$

a$.$ Assuming the bonds will be rated AA$,$ what will the price of the bonds be$?$

b$.$ How much total principal amount of these bonds must HMK issue to raise $$14$ million

today, assuming the bonds are AA rated? $($Because HMK cannot issue a fraction of a bond,

assume that all fractions are rounded to the nearest whole number.$)$

c$.$ What must the rating of the bonds be for them to sell at par?

d$.$ Suppose that when the bonds are issued, the price of each bond is $$952\mathrm{.}51.$ What is the likely

rating of the bonds? Are they junk bonds?