Question

A bond has a face value of $1,000, a coupon rate of 8%, and a yield to maturity of 9.5%. If the bond matures in 8 years, what is the price of the bond? (Assume coupons are paid annually.)

Answer 1

Current Market Price of the Bond

The Market 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 = $1,000

Annual Coupon Amount = $80 [$1,000 x 8%]

Annual Yield to Maturity = 9.50%

Maturity Period = 8 Years

Therefore, the Market Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $80[PVIFA 9.50%, 8 Years] + $1,000[PVIF 9.50%, 8 Years]

= [$80 x 5.43344] + [$1,000 x 0.48382]

= $434.68 + $483.82

= $918.50

“Therefore, the Price of the Bond will be $918.50”

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.