Question

You have a bond with a 5% coupon, 10 years to maturity and a Yield to Maturity of 4.75%. What is the dollar value of the bond?

Answer 1

Dollar Value 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 = $1,000

Annual Coupon Amount = $50 [$1,000 x 5%]

Yield to Maturity of the Bond = 4.75%

Maturity Period = 10 Years

The Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $50[PVIFA 4.75%, 10 Years] + $1,000[PVIF 4.75%, 10 Years]

= [$50 x 7.81635] + [$1,000 x 0.62872]

= $390.82 + $628.72

= $1,019.54

“Hence, the Dollar Value of the Bond will be $1,019.54”

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.