Heather Smith is considering a bond investment in Locklear A

Heather Smith is considering a bond investment in Locklear Airlines. The $1,000 par value bonds have a quoted annual interest rate of 10 percent and the interest is paid semiannually. The yield to maturity on the bonds is 12 percent annual interest. There are 9 years to maturity.    
  
Compute the price of the bonds based on semiannual analysis.

Solution

Price of Bond = Cupon Amount * Present Value of Annuity Factor (r,n) + Redemption Amount * Present Value of Interest Factor (r,n)

Where Cupon Amount = $1,000 * 10% * 1/2

= $50

Why did we multiply 1/2?

- Since compounding is Semi Annual

Redemption Amount = $1,000

r is the Yield to Maturity (YTM)

Yield for 6 months = 12/2

r = 6%

n is the remaining maturity

n = 9*2

n = 18

(Semi Annual Compounding)

Present Value of Annuity Factor (6% ,18) = 10.8276034802

Present Value of Interest Factor (6% ,18) = 0.35034379106

Therefore

Bond Price =$50* 10.8276034802 + $1,000 * 0.35034379106

Bond Price =$541.38017401 + $350.34379106

Bond Price = $891.72396507

Note - For simplicity we can round it up to two decimal places

Bond Price = $891.72

Therefore the bond\'s price is $891.72