Question

A corporate bond has a face value of $10,000, a coupon rate of interest of 8.25% per annum, payable semi-annually, and six and a half years remaining to maturity. The market interest rate for bonds of similar risk and maturity is currently 9.5% per annum, what is the present value of the bond?

Answer 1

Present Value of the Bond

The Present Value of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $10,000

Semi-annual Coupon Amount = $412.50 [$10,000 x 8.25% x ½]

Semi-annual Yield to Maturity = 4.75% [9.50% x ½]

Maturity Period = 13 Years [6.50 Years x 2]

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

= $412.50[PVIFA 4.75%, 13 Years] + $10,000[PVIF 4.75%, 13 Years]

= [$412.50 x 9.536570] + [$10,000 x 0.547013]

= $3,933.83 + $5,470.13

= $9,403.96

“Hence, the Present Value of the Bond will be $9,403.96”

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.