$q,($p$.287)$ Bond value and changing required returns Midland Utilities has a bond issue outstanding that will mature to its $$1,000$ par value in $12$ years. The bond has a coupon rate of $11\%$ and pays interest annually.

a$.$ Find the value of the bond if the required return is $(1)11\%,(2)15\%,$ and $(3)8\%.$

b$.$ Plot your findings in part a on a set of "required return $(x-$axis$)-$market value of bond $($y$-$axis$)"$ axes.

c$.$ Use your findings in parts a and $b$ to discuss the relationship between the coupon rate on a bond and the required return and the market value of the bond relative to its par value.

d$.$ What two possible reasons could cause the required return to differ from the coupon rate?