# How to Calculate Maximum Theoretical Value of a Bond

When you shop for bonds, like any other investment, you want a good price without overpaying. A bond’s maximum theoretical value is the most you can pay for it to earn your desired annual return. A bond typically pays periodic interest and repays its face -- or par -- value when it matures. Because the interest rate and face value are fixed, the price you pay for a bond determines your actual return.

Multiply a bond’s annual coupon rate -- or interest rate - by its par value to determine its annual interest. For example, assume a bond has a 6 percent annual coupon and a \$1,000 par value. Multiply 6 percent, or 0.06, by \$1,000 to get \$60.

Decide the annual return you require to own the bond. This return is typically close to the yield to maturity, or YTM, on similar bonds, which you can find on any financial website that provides bond information. You might require a higher return if you think the bond in question has more risk than others, or a lower return if you think it has less risk. In this example, assume similar bonds have an 8 percent YTM, which you believe is an adequate return for the bond in question.

Plug the information into the formula (C/N)[(1 - ((1 + (R/N))^(-N x T)))/(R/N)] + [F/((1 + (R/N))^(N x T))], in which C represents the annual interest, N represents the number of payments per year, R represents your required return as a decimal, F is the face value and T is the number of years until maturity. In this example, assume the bond pays semiannual interest and matures in 10 years. The formula is (\$60/2)[(1 - ((1 + (0.08/2))^(-2 x 10)))/(0.08/2)] + [\$1,000/((1 + (0.08/2))^(2 x 10))].

Solve the numerator and denominator in the first set of brackets. In this example, divide 0.08 by 2 to get 0.04. Add 0.04 to 1 to get 1.04. Multiply -2 by 10 to get -20. Raise 1.04 to the -20th power to get 0.4564. Subtract 0.4564 from 1 to get 0.5436. This leaves (\$60/2)(0.5436/0.04) + [\$1,000/((1 + (0.08/2))^(2 x 10))].

Solve the first sets of parentheses. In this example, divide \$60 by 2 to get \$30. Divide 0.5436 by 0.04 to get 13.59. Multiply \$30 by 13.59 to get \$407.70. This leaves \$407.70 + [\$1,000/((1 + (0.08/2))^(2 x 10))].

Calculate the numbers in brackets. In this example, divide 0.08 by 2 to get 0.04. Multiply 2 by 10 to get 20. Add 1 to 0.04 and raise your result to the 20th power to get 2.1911. Divide \$1,000 by 2.1911 to get \$456.39. This leaves \$407.70 + \$456.39.

Add the remaining numbers to calculate the bond’s maximum theoretical value. Concluding the example, add \$407.70 and \$456.39 to get \$864.09. This means you could pay up to \$864.09 for the bond to earn an 8 percent annual return.

### Warning

• If you sell a bond before it matures, your actual return might differ from that used to calculate its maximum theoretical value.

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