Wednesday, November 4, 2009

Bond Pricing 101

If you're going to learn how to effectively interpret corporate financial statements, it's a good idea to possess at least a cursory understanding of the pricing of long-term non-operating liabilities - also known as bonds.

o start off, you need to know that bond pricing involves two separate interest rates, the Coupon Rate and the Market Rate. The coupon rate, also known as the contract or stated rate, is the interest rate listed in the bond contract, and is used to compute the amount of the cash interest payments that are due periodically from the issuer. The market rate is the interest rate demanded by investors, and is usually referred to as the bond's "yield".

Next, you need to think of a bond in terms of the two distinct cash flows involved; the bond pays periodic, usually semiannual interest payments (interest annuity), as well as the lump sum principal amount (face value) which is returned at maturity.

Moving on, the next distinction which needs to be made is that the price of the bond varies depending upon the relationship between the coupon and the yield. If the two are the same, the bond is priced at what is known as "par". If the market rate is greater than the coupon rate, the bond will be priced at a discount; conversely, if the coupon rate exceeds the market rate, the bond is priced at a premium. I'll start with pricing a bond at par; it's a much simpler process, for reasons I'll touch on a bit later. The assumptions used in this example of pricing a bond at face value are as follows: Face amount of $800,000, annual coupon rate of 6%, semi-annual interest payments, and a 5 year maturity. The first step involves calculating the interest payment, the formula for which is:
est Payment = Face Value X Annual Coupon Rate X Payment Period (time)
= $800,000 X 6% X 6/12
= $24,000
Next you need to calculate the present value of both sets of cash flows. Instead of going into detail on the present value calculation, I'll just direct you to the PV() function in Excel. Present value is built on the concept that $24,000 today is worth less to the investor than $24,000 in three years, simply due to the time value of money. In the current example, it's easy to ascertain that the sum of the bonds interest payments over the five year period is $240,000 ($24,000 X 5 (years) X 2 (payments per year). However, the present value of those five years worth of payments is only $204,724.87. Along th
ose same lines, the present value of (the lump sum principal payment of) $800,000 is only $595,275.13. Now, we sum the present value of the bonds future cash flows:

Present Value of Cash Flows = $595,275.13 + $204,724.87 = $800,000

Well then, this all looks pretty simple: the present value of a par priced bond's future cash flows is in fact the face value of the bond. For bonds sold at a premium or a discount however, the equation shakes up a little differently. For a discount example, let's assume that all of the variables are identical to the par example above, except that the market is demanding an 8% yield. The calculation of
the cash interest payment still uses the coupon rate, so we arrive at an identical $24,000 semi-annual interest obligation for the issuer. The curve ball arrives when calculating the present value of the bond's future cash flows; these cash flows must be discounted using the bond's yield rate of 8%. Therefore, the present value of the discount bond's interest payments is $194,661.50, and the principal payment's present value is $540,451.34. Add them together, and you arrive at $735,112.83. What this means is that the bond issuer will receive $735,112.83 in cash from investors, but will still be required to make $24,000 interest payments (that were calculated using a face value of $800,000). The difference of $64,887.17 (discount balance) shows up on the balance sheet as a contra-liability account which reduces bonds payable in line with the amount of cash actually received by the issuer. The discount balance is then amortized over the life of the bond, and falls into the income statement as successively higher amounts of interest expense (although not an actual cash outlay). The amortization table for this example is below:

As you can see above, the bond discount amount feeds - in entirety - into the income statement throughout the 10 periods, until it is no more. A bond sold at a premium works in the exact inverse way; a premium balance is created on the balance sheet which effectively reduces the issuer's interest expense - by the premium amount - over the life of the bond. Obviously, the issuer would prefer to sell bonds at a premium. Despite the interest expense reduction, a premium usually means that the market judges the firm to be more credit worthy than implied by the coupon rate. Nevertheless, it's important to comb through a corporation's filings to determine the amounts and associated maturities of it's bond liabilities, and be able to understand the income statement ramifications.

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