MERTON enterprises has bonds on the market making annual pay

MERTON enterprises has bonds on the market making annual payments with sixteen yyears to maturity. currently selling for $957. at this price the bond yields 9%. what must the coupon rate be?

Solution

hope you are referring to yield to maturity (9.0%)

he coupon rate for this bond is 8.55 assuming that the par value is $1000

the formula for yield of maturity is as

c(1+r)^-1 + c(1+r)^-2 + ....... + c(1+r)^-y + B(1+r)^-y = P

where c= annual coupon payment (in $ , not a percent)

y= number of years to maturity

B = Par value

P =purchase price.

so the equation is

the coupo payment is $90 (that\'s 95 of $1000) so the equation satisfy

90(1+r)^-1 + 90(1+r)^-2 +90(1+r)^-3 +........90(1+r)^-15 +90(1+r)^-16 +1000(1+r)^-16 = 957

by using the calculator we can get

finally curreny yield =9.404

yield of maturity =9.534