# How to Calculate Maximum Theoretical Value of a Bond

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Bonds offer regular, simple interest coupons payment until the bond matures, at which time the face value of the bond is paid to the investor. Bonds may sell at below face value discounts, or above face value premiums, which are largely dependent on comparable investments. For example, if a bond offered a 5 percent coupon rate, it would have to sell at a discount to compete with a similar investment offering 8 percent. Effectively, the bond would need to offer an 8 percent yield to compete. Using that required yield, you can calculate the maximum theoretical value of a bond.

Add 1 to the required yield rate, in decimal format. If the bond pays semi-annually, divide the required yield rate by the number of payments per year. In the example, if the bond pays twice per year, then divide 8 percent by 2 to get a semi-annual yield of 4 percent, or 0.04. Add 1 to this number to get 1.04.

Raise this value to the power of N, where N is the total number of payments throughout the life of the bond. If the example bond matures in 15 years, there would be 30 payments. Therefore, raise 1.04 to the power of 30 to get a required yield factor of 3.2434.

Divide 1 by this number. In the example, this gives you 0.30832.

Subtract this number from 1. In the example, this leaves 0.69168.

Divide this figure by the semiannual yield rate. In the example, this gives you 17.292.

Multiply this by the coupon payment per period. The coupon payment is the coupon rate times the face value of the bond, divided by the number of payments per year. In the example, 0.05 times a face value of \$1,000 gives you coupon payments of \$50 per year, or \$25 twice per year. Therefore, multiply \$25 times 17.292 to get \$432.30.

Add this number to the face value of the bond, divided by the required yield factor to calculate the maximum theoretical value. In the example, \$1,000 divided by 3.2434 gives you \$308.32. Adding 432.30 gives you a maximum theoretical value of \$740.62.