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 Bond Yields 

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If you have a "business" calculator, it includes a bond Yield-to-Maturity calculation routine. Using the procedure below, you can also use this routine to calculate a bond's Yield-to-Call. Calculating both these yields before you buy a bond verifies the bond specifications you've been given by the seller. Further, you can use these routines to negotiate a better purchase or sale price with your broker, based on these calculations and your knowledge of current market yields. Bond market yields are published in newspapers and on websites.

The Yield-to-Maturity ["YTM"] is a yield that takes account of both the interest payments and the change in the bond's price between the purchase date and the maturity date. It is the best measure of a bond's investment return. To compute the YTM, you need to know four things: (1)  a bond's current price [usually quoted as a percentage of the bond's face value],  (2) it's "coupon" or "face" interest rate, (3) the purchase date, and  (4) the bond's maturity date.

Example: Suppose you buy a $10,000 Face Value bond at a price of 103% with a coupon rate of 5.5% on February 15, 1999 and it matures on October 1, 2016. The bond will cost $10,300 since that's 103% of its face value. With a 5.5% coupon rate, this bond will pay $550 per year in interest, since that's 0.055 times $10,000.

With a typical business calculator, you'd enter 103 as the "Present Value"; enter 5.5 as the "Payment"; enter 2/15/1999 as the "Buy Date"; and enter 10/1/2016 as the "Maturity Date". Putting those numbers into your calculator should give a Yield-to-Maturity of 5.24%. [Try this yourself to verify the data entry procedure!]

The YTM of 5.24% is lower than the coupon rate of 5.5% because you invested $300 more capital than the bond will pay out at its maturity. That $300 -- amortized over your 17.6 year holding period -- will effectively reduce the annual interest yield by 0.26% a year.

Suppose the bond in the Example above is "callable" [that is, redeemable by the issuer before maturity]. Let the "call price" be 101 [again, a percentage of Face Value] and the first call date be October 1, 2009. If the bond is called on the first call date, your holding period will be reduced by 7 years but you'll get a 1% premium over face value for giving back the bond early. The true yield you'll earn each year in this case is designated the Yield-to-Call ["YTC"].

To compute a Yield-to-Call, first calculate an adjustment factor, F:

F = 100  / (Call Price in %)

Then repeat the YTM calculation procedure described above using the following adjusted purchase price and adjusted coupon rate...

Adjusted Purchase Price = F  x  (Bond Purchase Price in %)

Adjusted Coupon Rate = F  x  (Coupon Rate in %)

where: "x" means multiplication.

For the Example numbers of the hypothetical bond given above:

F = 100/101 = 0.990

Adjusted Purchase Price = 0.990  x  103% = 101.98%

Adjusted Coupon Rate = 0.990  x  5.5% = 5.45%

Now, put these Adjusted Price and Rate numbers, the original Purchase Date of 2/15/1999, and the Call Date of 10/1/2009 [the "effective" maturity date] into your calculator's YTM routine. Doing this produces a Yield-to-Call evaluation of 5.20%.

This Yield-to-Call is a little lower than the Yield-to-Maturity because there are only ten years to amortize a $200 reduction [$20 per year] in the bond's value if it's called. If the bond was held to maturity, there'd be 17.6 years to amortize a $300 reduction [$17 per year] in value.

One special case that will simplify your work...  If a"call price" is 100 [or "par"], meaning you'll receive the bond's Face Value on the call date, then the Yield-to-Call calculation is identical to the Yield-to-Maturity calculation for the bond except the Call Date replaces the Maturity Date entry. You don't need to compute the adjustment factor F since a call price of 100 makes F=1.

 

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