How to Calculate for a Callable Bond

by C. Taylor

The option to call a bond allows the issuer to buy back a bond before its normal maturity date. This can be exercised if interest rates are low, and the bond can be reissued at a lower coupon rate. The price of a bond depends on the annual yield rate. For example, if you receive 5 percent from another investment without incurring additional risk, then it would be disadvantageous to invest in a bond offering a lower yield than 5 percent. For callable bonds, the yield-to-call rate represents the yield rate offered if the issuing company exercises its right to buy back the bond.

Divide the required yield-to-call rate by the number of payments per year. For example, if you wanted a 5 percent yield-to-call rate on a callable bond, which makes coupon payments twice per year, you would divide 0.05 by 2 to get 0.025. This is the periodic yield.

Add 1 to the periodic yield. In the example, 1 plus 0.025 gives you 1.025.

Raise this figure to the number of periods before the bond is callable. In the example, if the bond is callable at the end of the second year, you would raise 1.025 to the power of 4, because there are four semiannual payments in those two years. This gives you 1.1038. Remember this number as you will use it again later.

Divide 1 by the figure from Step 3, and subtract the quotient from 1. In the example, 1 divided by 1.1038 gives you 0.90595. Subtracting this figure from 1 gives you 0.094049.

Multiply this figure by the annual coupon payments. The annual coupon payments are calculated by multiplying the coupon rate by the face value of the bond. Bonds typically have face values of \$100. If the example \$100 bond offered a 4 percent coupon rate, then you would multiply 0.04 by \$100 to calculate annual coupon payments of \$4. Multiplying \$4 by 0.094049 gives you 0.3762.

Divide this figure by the annual yield-to-call rate. In the example, dividing \$0.3762 by 0.05 gives you 7.52. Note that this calculation uses the annual rate, rather than the periodic rate used previously.

Add the callable price, divided by the figure you calculated in Step 3. The callable price can be the face value of the bond, or a premium amount offered for the callable option. In the example, if the issuing company was to buy back the bond for \$105, instead of the normal \$100 buyback amount at maturity, then you would divide \$105 by 1.1038 to get 95.13. Adding this figure to 7.52 gives you a callable bond price of \$102.65. This means you could purchase the bond for \$2.65 more than its face value and still obtain a yield-to-call of 5 percent.