Question

Compute Bond Price Compute the price of a 8.0 percent coupon bond with 15 years left to maturity and a market interest rate of 7.0 percent. (Assume interest payments are semi-annual.) Is this a discount or premium bond?

Answer 1

Current Price of the Bond

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

Par Value of the bond = $1,000

Semi-annual Coupon Amount = $40 [$1,000 x 80% x ½]

Semi-annual Yield to Maturity = 3.50% [7% x ½]

Maturity Period = 30 Years [15 Years x 2]

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

= $40[PVIFA 3.50%, 30 Years] + $1,000[PVIF 3.50%, 30 Years]

= [$40 x 18.39205] + [$1,000 x 0.35628]

= $735.68 + $356.28

= $1,091.96

“Hence, the Current Price of the Bond will be $1,091.96”

This is a “PREMIUM BOND”, since the Current Price of the Bond ($1,091.96) is greater than the Par Value of the Bond ($1,000)

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.