How to Calculate Yield to Maturity for a Callable Bond

Financial newspapers and websites commonly report yield to maturity.

Financial newspapers and websites commonly report yield to maturity.

Yield to maturity, or YTM, is one of the most closely watched figures among bond investors. It represents the annual percentage return you earn if you hold a bond until it matures. However, if you intend to hold a callable bond until it matures, your plans might not play out as expected. An issuer that sells callable bonds has the right to “call,” or buy back, the bonds for a predetermined price before they mature. You can calculate a callable bond’s YTM to estimate its return, but if the issuer calls the bond, your actual return will likely differ.

Find out a callable bond’s price from your broker or from the Financial Industry Regulatory Authority’s website. Assume, for the following example, that a bond’s price is $833.44.

Multiply the bond’s coupon, or interest, rate by its par value to figure the annual coupon payment. In this example, assume the bond has a 5 percent coupon and a $1,000 par value. Multiply 5 percent, or 0.05, by $1,000 to get $50.

Guess the YTM you think the bond might have. When a bond’s price exceeds its par value, its YTM is typically less than its coupon rate. When par value exceeds price, YTM is typically greater than the coupon. Your guess doesn’t need to be exact. Finding YTM is a trial-and-error process. In this example, the bond’s price is less than its par value, so try a 7 percent YTM.

Substitute the information into the formula (C/N)[(1 - ((1 + (Y/N))^(-N x T)))/(Y/N)] + [P/((1 + (Y/N))^(N x T))], in which C is the annual coupon payment, N is the number of payments per year, Y represents your guessed YTM as a decimal, T is the number of years until maturity and P is par value. In this example, assume the bond makes semiannual coupon payments and matures in 20 years. The formula is ($50/2)[(1 - ((1 + (0.07/2))^(-2 x 20)))/(0.07/2)] + [$1,000/((1 + (0.07/2))^(2 x 20))].

Calculate the first half of the formula. In this example, divide 0.07 by 2 to get 0.035. Multiply -2 by 20 to get -40. Add 1 to 0.035, raise the result to the -40th power and subtract that result from 1 to get 0.7474. Divide 0.7474 by 0.035 to get 21.3543. Divide $50 by 2 to get $25. Multiply $25 by 21.3543 to get $533.86. This leaves $533.86 + [$1,000/((1 + (0.07/2))^(2 x 20))].

Solve the rest of the formula. In this example, the formula equals $786.43.

Check your result to see if it equals the bond’s price. If it does, you guessed the correct YTM and no further calculation is required. If not, your guess is incorrect and you must try again. In this example, $786.43 doesn’t equal $833.44, so the number crunching continues.

Guess another YTM and recalculate the formula. Repeat this process until your result equals the bond’s price. If your result is greater than the bond’s price, try a YTM that’s higher than your previous guess. If your result is less than the bond’s price, try a lower YTM. Concluding the example, $786.43 is less than $833.44, so try a YTM that’s less than 7 percent, such as 6.5 percent. Plug 6.5 percent into the formula and solve it to get $833.44. Because this result equals the bond’s price, 6.5 percent is the bond’s YTM.

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