Yield to Call and Yield to Maturity
Source: Encyclopedia of Banking & Finance (9h Edition) by Charles J Woelfel
(We recommend this as work of authority and you can order it here)

YIELD TO CALL

The discount rate that equates the present value of the guaranteed cash flow (interest plus call price) if the bond is called.

YIELD TO MATURITY

Because bonds and other obligations are contractual in nature, specifying promise to pay principal at fixed future date and interest annually in the meantime, yield to maturity is the proper calculation of annual return, because it involves determination of the income elements as both the annual interest income and either accretion (appreciation per year on straight-line basis from discount cost price to full par at maturity, over remaining maturity) or amortization (depreciation per year on straight-line basis from premium cost price down to full par at maturity, over remaining maturity).  In mere current return on bonds, properly used for income bonds (those whose interest payment is contingent upon earnings, and is not fixed at precise rate as fixed charge) and sometimes for bonds subject to great uncertainty of continuation of nominally fixed interest, the only income element figured is the year’s annual interest projected or expected.

As an alternative to yield to maturity, it may be appropriate to calculate yield to first call date, especially in the case of U.S. government bonds, because the U.S. Treasury has been quite consistent in exercising the call feature at the first call date if the issue can be refunded at a lower interest rate.

Yield to maturity may be precisely determined mathematically, but the computation may be complex and time-consuming, and so bond yield tables, in a wide range of coupon rates, maturities, and prices, are available from publishers.  These are a great convenience in determining, with a minimum of necessary interpolation, the precise yields resulting from the interplay of the above variables.

In the absence of a convenient bond yield table, the formula for approximate yield to maturity on a bond is basically the following:  (1) take annual interest payment, plus accretion (discount, or aggregate dollar difference between cost price and full maturity value of the bond, divided by remaining maturity) or minus amortization (premium, or aggregate dollar difference between cost price and full maturity value of the bond, divided by remaining maturity); (2) divide by a simple average of cost price and full maturity value.  Thus, if a bond is bought at 80 ($800 per $1,000 bond) pays 4% interest annually, and has 10 years’ remaining maturity at the time of purchase, the approximate yield to maturity is 6.67% (interest of $40 annually, plus annual accretion of $20, divided by average principal of $900).

BIBLIOGRAPHY

FINANCIAL PUBLISHING Co. Comprehensive Bond Values Tables.
SCHAEFER, S.M. “The problem with Redemption Yields.”  Financial Analysts Journal, July/August, 1977.  

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