Present Value of Bond Calculator
**This is a basic calculator and does not accept commas. When entering values, just enter the numbers.
Present Value of Bond Formula
Present Value of a Bond =
Present Value of Interest Payments + Present Value of Redemption Value
Present Value of Interest Payments + Present Value of Redemption Value
Note:
Present Value of Interest Payments =
I(1-(1+k)-n÷k)
I(1-(1+k)-n÷k)
Present Value of Redemption Value =
Face Value ÷ (1 + k)n
Face Value ÷ (1 + k)n
Where:
k = Current Period Market Rate
n = Number of Compounding Periods
I = Interest Payment per distribution
Present Value of Bond Sample Problem
Calculate Present Value of Interest Payments
Since calculating the present value of a bond is a two-step process, the first thing we're going to calculate is the Present Value of Interest Payments. This requires us to know the interest payment amount, the current period market rate (or discount rate), and the number of periods remaining until the bond matures.
If we assume the bonds face value is $1,000 and it has a coupon rate of 5%, then the bond will receive an annual interest payment of $50. If this particular bond pays interest semi-annually, then the interst payment (I) will be $25 per distribution period. It is important to note that the coupon rate is only used to determine Interst Payments, and it is different from the Current Period Market Rate (k).
Now let's assume the market rate is paying 4% interest semi-annually. Because we are working semi-annually, k will be 4%/2 = 2%; k = 2%.
If the bond has 10 years until it reaches maturity, and since we know it pays semi-annually, then we know n = 20 (10 years x 2 times a year).
Using the formula to calculate Present Value of Interest Payments: $25[1-(1+.02)^-20]/.02 = $408.79
Calculate Present Value of Redemption Value
Continuing with our $1,000 bond from above, assuming it comes due in 10 years (with interest payable semi-annually), and a Current Period Market Rate of 4% (keeping in mind, again, this is paid semi-annually), we would calculate Present Value of Bond Redemption as follows:
PV of Redemption Value = $1,000/(1+.02)^20 = $672.97
Therefore, the Present Value of the Bond = 408.79 + 672.97 = $1,081.76