# How to Calculate the Beginning Values of Bonds

by Bryan Keythman

The beginning value, or present value, of a bond is equal to the sum of the present value of its cash flows, which are its interest payments. You can use the bond price formula to calculate the present value of a bond. This is the price investors would be willing to pay for the bond based on current interest rates or yields on similar bonds, which cause a bond’s price to fluctuate. Rising interest rates cause a bond’s price to decrease. Falling interest rates cause a bond’s price to rise.

1. Determine a bond’s annual interest payment, the number of years until its maturity, the bond’s face value and the current yield on similar bonds, which you can find on any financial website that provides bond information. For example, assume a bond pays \$100 in annual interest, has five years until its maturity and has a \$1,000 face value, which is the value it pays at maturity. Also assume similar bonds have a current yield of 8 percent.

2. Substitute the values into the bond price formula: C[(1 - ((1 + R)^(-T)))/R] + [F/((1 + R)^T)]. In the formula, C represents the annual interest payment, R represents the current yield on similar bonds, F represents the bond’s face value and T represents the number of years until maturity. In this example, substitute the values to get \$100[(1 - ((1 + 0.08)^(-5)))/0.08] + [\$1,000/((1 + 0.08)^5)].

3. Calculate the numbers in parentheses in the first set of brackets. In this example, add 1 to 0.08 to get 1.08. Raise 1.08 to an exponent of -5 to get 0.681. Subtract 0.681 from 1 to get 0.319. This leaves \$100(0.319/0.08) + [\$1,000/((1 + 0.08)^5)].

4. Divide the remaining numbers in the first set of parentheses. Then multiply your result by the annual interest payment. In this example, divide 0.319 by 0.08 to get 3.9875. Multiply 3.9875 by \$100 to get \$398.75. This leaves \$398.75 + [\$1,000/((1 + 0.08)^5)].

5. Solve the numbers in the remaining set of brackets. In this example, add 1 to 0.08 to get 1.08. Raise 1.08 to the 5th power to get 1.469. Divide \$1,000 by 1.469 to get \$680.74. This leaves \$398.75 + \$680.74.

6. Add the remaining numbers to calculate the beginning value of the bond. Concluding the example, add \$398.75 and \$680.74 to get a beginning bond value of \$1,079.49.

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