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Bond Valuation

Generally when we talk about bond pricing we also include other fixed income investments.  Thus this section would be more aptly named Stock and Fixed income valuation.  But for tradition we won’t complain 😉

Bond pricing (at the level we will cover it)  is fairly easy.  This is because we assume we know the cash flows.  (Which clearly is not true as issuers default, but for starters we will assume the payments are made as promised in the bond contract (aka the bond covenant as it is often called).

Assuming no default for a moment, bond pricing is almost entirely a function of interest rates.

For a straight coupon bond, break the cash flows into an annuity and a lump sum.   These can be priced separately and then added back together to calculate the total bond value.

Suppose a 5 year bond pays an 6% annual coupon.  This 6% refers to the interest payments and is calculated as a percentage of par.  Unless otherwise stated, assume the principle value is $1000.  Thus each year you would receive 6% of $1000 which is $60.  In addition in the last year you would receive the original $1000 back.  Further assume that the going rate of interest for such a bond is 7%.  You must find the price of the bond The timeline of this would be :  ______________________________
60    60     60      60        60
1000 The PV of the annuity is
$60(PVIFA(7%,5)) = $60*4.1002 = $246.01

(For more on PV of an annuity see: http://www.frickcpa.com/tvom/TVOM_PV_Annuity.asp)



The PV of the principle amount is
$1000/(1.07)5= 712.99


By adding the two together you get $959
Note that it is not coincidence that this bond is selling at a discount (that is below par).  Companies usually try to sell new bonds at par, so if companies are selling new bonds with 7% interest, you would rather buy that than a similarly priced bond with 6% interest.  So to persuade you to buy the lower coupon bond, the price is reduced.
The Wall Street Journal (WSJ) reports bond prices as a % of par.  Hence 102=102% of par which would be $1020 per $1000.  The bond in the above example would be quoted as 95.9.  You should know how to read bond prices.


Types of Bonds
There are many different types of bonds.  This is to meet the needs of both investors and issuers.

Some of the different types are:

Treasury Bonds, US Agency Bonds, Corporate Bonds, Callable bonds, Convertible bonds, Putable bonds, Floating, Fixed, Extendables, Senior Debt, Junior Debt, Mortgage backed, Debenture, Income Bonds, Eurobonds, Zero Coupon, Original Issue Discount Bonds etc.
In addition to all of these types of debt instruments, Preferred Stock is usually included as a fixed income security.   The difference between debt and preferred stock is that failure to pay the dividend does not result in bankruptcy.  It should be noted that often in preferred stock the firm must pay any dividends that are arrears before any common dividend can be paid.  Preferred Stock trades very much like debt instruments.  There is much less of an informational asymmetry and price changes with interest rate changes.

San Francisco: AT&T Park - San Francisco Giant...

San Francisco: AT&T Park – San Francisco Giants Wall of Fame – Bobby Bonds (Photo credit: wallyg)

It should also be noted that many types of engineered securities trade exactly like bonds.  For example many investment banking firms sell Strips.  These are similar to zero coupon bonds.  The Investment bankers merely strip the coupons off of Treasury bonds and sell the two series of cash flows: the coupon payments and the principle amounts. Many other type of securities are in many ways similar to bonds.  For example swaps, IOs, and POs.  These are slightly more complex, but once you have your timeline drawn, they are priced very much like anything else.

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