HMK Enterprises would like to raise $$10\mathrm{.}0$ million to invest in capital expenditures. The company plans to issue $5-$year bonds with a face value of $$1,000$ and a coupon rate of $6\mathrm{.}51\%($annual payments$).$ The following table summarizes the yield to maturity for $5-$year $($annual$-$payment$)$ coupon corporate bonds of various ratings: $.$

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

b$.$ How much of the total principal amount of these bonds must HMK issue to raise $$10\mathrm{.}0$ 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 be the rating of the bonds for them to sell at par?

d$.$ Suppose that when the bonds are issued, the price of each bond is $$959\mathrm{.}55.$ What is the likely rating of the bonds? Are they junk bonds?

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

The price of the bonds will be $\{($Round to the nearest cent.$)$

b$.$ How much of the total principal amount of these bonds must HMK issue to raise $$10\mathrm{.}0$ 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.$)$

The number of bonds to be issued is $($Round up to the nearest integer.$)$

c$.$ What must be the rating of the bonds for them to sell at par? $($Select the best choice below.$)$

A$.$ For the bonds to sell at par, the coupon must equal the yield. Since the coupon is $6\mathrm{.}38\%,$ the yield must also be $6\mathrm{.}38\%,$ or A rated.

B$.$ For the bonds to sell at par, the coupon must equal the yield. Since the coupon is $6\mathrm{.}51\%,$ the yield must also be $6\mathrm{.}51\%,$ or A rated.

C$.$ For the bonds to sell at par, the coupon must equal the yield. Since the coupon is $6\mathrm{.}99\%,$ the yield must also be $6\mathrm{.}99\%,$ or BBB rated.

D$.$ For the bonds to sell at par, the coupon must equal the yield. Since the coupon is $6\mathrm{.}51\%,$ the yield must also be $6\mathrm{.}51\%,$ or BBB rated.

d$.$ Suppose that when the bonds are issued, the price of each bond is $$959\mathrm{.}55.$ What is the likely rating of the bonds? Are they junk bonds? $($Select the best choice below.$)$

A$.$ Given a yield of $7\mathrm{.}51\%,$ it is likely these bonds are rated BB$.$ Yes, BB$-$rated bonds are junk bonds.

B$.$ Given a yield of $7\mathrm{.}51\%,$ it is likely these bonds are rated BB$.$ No$,$ BB$-$rated bonds are not junk bonds.

C$.$ Given a yield of $6\mathrm{.}99\%,$ it is likely these bonds are rated BBB$.$ Yes, BBB$-$rated bonds are junk bonds.

D$.$ Given a yield of $6\mathrm{.}99\%,$ it is likely these bonds are rated BBB$.$ No$,$ BBB$-$rated bonds are not junk bonds.

Data table

$($Click on the following icon in order to copy its contents into a spreadsheet.$)$

$\backslash$table$[[$Rating$,$AAA,AA$,$A$,$BBB$,$BB$],[$YTM$,6\mathrm{.}18\%,6\mathrm{.}38\%,6\mathrm{.}51\%,6\mathrm{.}99\%,7\mathrm{.}51\%$