Question

Nesmith Corporation's outstanding bonds have a $1,000 par value, a 9% semiannual coupon, 14 years to maturity, and an 9.5% YTM. What is the bond's price? Round your answer to the nearest cent.

Answer 1

the following is the calculation of bond price:

price = [present value of annuity factor * coupon payment] + [present value factor * face value]

here,

present value of annuity factor = [1-(1+r)^(-n)]/r

here,

r = 9.5% for year =>4.75% for 6 months =>0.0475.

n = 14 years * 2 semi annual periods =>28 periods.

=>[1-(1.0475)^(-28)]/0.0475

=>0.7272988/0.0475

=>15.3115537

coupon payment = $1,000 * 9%*1/2 =>$45.

present value factor = 1 / (1+r)^n

=> 1 /(1.0475)^28

=>0.27270124.

face value =$1,000.

bond price = [15.3115537*$45] + [0.27270124*$1,000]

=>689.019916+272.70124

=>961.72........(rounded to two decimals)

bond's price = $961.72.