In: Finance
A bond has a 10-year maturity, an 4% annual coupon rate, with quarterly coupons paid, and a par value of $1,000. The annual discount rate is 8%. What should be the bond’s price?
Price of the Bond
The Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value
Face Value of the bond = $5,000
Quarterly Coupon Amount = $10 [$1,000 x 4% x ¼]
Quarterly Yield to Maturity = 2% [4% x ¼]
Maturity Period = 40 Years [10 Years x 4 Quarters]
The Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value
= $10[PVIFA 2%, 40 Years] + $1,000[PVIF 2%, 40 Years]
= [$10 x 27.35548] + [$1,000 x 0.45289]
= $273.56 + $452.89
= $726.45
“Therefore, the Price of the Bond = $726.45”
NOTE
-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)n} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.
--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)n], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.