The Corp. has issued 18-year, 8% semi-annual coupon, noncallable bonds at their par value of $1,000 one year ago. Today, the market interest rate on these bonds is 4.5%. What is the current price of the bonds? (Hint: the bonds have 17 years to maturity now).
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 * 8% * 1/2
= $40
Why did we multiply 1/2?
- Since compounding is Semi Annual
Redemption Amount = $1,000
r is the Yield to Maturity (YTM) or market interest rate
Yield for 6 months = 4.5/2
r = 2.25%
n is the remaining maturity
n = 17 * 2
n = 34
(Semi Annual Compounding)
Present Value of Annuity Factor (2.25% ,34) = 23.5868261745
Present Value of Interest Factor (2.25% ,34) = 0.46929641086
Therefore
Bond Price =$40* 23.5868261745 + $1,000 * 0.46929641086
Bond Price =$943.47304698 + $469.29641086
Bond Price = $1412.76945784
[Note if answer requires rounding off to two decimal places]
Bond Price = $1412.77
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