Basic bond valuation Complex Systems has an outstanding issue of $$1,000-$par$-$value bonds with a $13\%$ coupon interest rate. The issue pays interest annually and has $16$ years remaining to its maturity date.

a$.$ If bonds of similar risk are currently earning a rate of return of $12\%,$ how much should the Complex Systems bond sell for today?

b$.$ Describe the two possible reasons why the rate on similar$-$risk bonds is below the coupon interest rate on the Complex Systems bond.

c$.$ If the required return is $13\%$ instead, what would the current value of Complex Systems' bond be$?$ Contrast this finding with your findings in part a and discuss.

a$.$ If bonds of similar risk are currently earning a rate of return of $12\%,$ the Complex Systems bond should sell today for $$.($Round to the nearest cent.$)$