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.
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
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