# How to Calculate a Bond Buy Back

by C. Taylor

Callable bonds allow issuing companies to buy back a bond before maturity, usually at a premium of the face value. The company may opt to buy back bonds when interest rates fall, so they can reissue the bond at lower rates. Put bonds allows investors to force the issuing company to buy back bonds before maturity. The price for this option is generally lower interest rates over the course of the bond's life, so bond buy back is equal to its face value. However, for bonds that pay all accrued interest at buy back, the buy back amount will be the sum of the face value plus all interest.

Ask your investment broker for the bond's face value, interest rate and buy back premium.

Calculate the buy back multiplier. For callable bonds, this will be the buy back premium percentage divided by 100. As an example, if the buy back premium was 105 percent, the multiplier would be 1.05. For cumulative put bonds, the multiplier is 1 plus the periodic interest rate, in decimal form, raised to the power of the number of periods into the bond's life. As an example, for a bond with a 5 percent interest rate, compounded annually, in year five, the multiplier is calculated as 1.05 raised to the 5th power, or 1.27628. If the bond compounded twice per year, the period interest would be the annual rate divided by 2, or 0.025, and be 10 periods into the bond's term. Therefore, the multiplier would be 1.025 raised to the 10th power, or 1.28008.

Multiply the bond's face value by the multiplier. In the examples, a \$1,000 callable bond would have a buy back of \$1,050, and a \$1,000 cumulative put bond would have a buy back of \$1,276.28, or \$1,280.08 if compounded twice per year.