A bond payable is just a promise to pay a stream of payments over time (the interest component), and a fixed amount at maturity (the face amount). Thus, it is a blend of an annuity (the interest) and lump sum payment (the face). To determine the amount an investor will pay for a bond, therefore, requires some present value computations to determine the current worth of the future payments.

To illustrate, let's assume that Schultz Company issues 5-year, 8% bonds. Bonds frequently have a $1,000 face value, and pay interest every six months. To be realistic, let's hold to these assumptions.

Par scenario Market rate of 8%

If 8% is the market rate of interest for companies like Schultz (i.e., companies having the same perceived integrity and risk), when Schultz issues its 8% bonds, then Schultz's bonds should sell at face value (also known as "par" or "100"). That is to say, investors will pay $1,000 for a bond and get back $40 every six months ($80 per year, or 8% of $1,000). At maturity they will also get their $1,000 investment back. Thus, the return on the investment will equate to 8%.

Premium scenario Market rate of 6%

On the other hand, if the market rate is only 6%, then the Schultz bonds look pretty good because of their higher stated 8% interest rate. This higher rate will induce investors to pay a premium for the Schultz bonds. But, how much more will they pay? The answer to this question is that they will bid up the price to the point that the effective yield (in contrast to the stated rate of interest) drops to only equal the going market rate of 6%. Thus investors will pay more than $1,000 to gain access to the $40 interest payments every six months and the $1,000 payment at maturity. The exact amount they will pay is determined by discounting (i.e., calculating the present value) the stream of payments at the market rate of interest. This calculation is demonstrated below, followed by an additional explanation.

Discount scenario Market rate of 10%

Also, consider the alternative scenario. If the market rate is 10% when the 8% Schultz bonds are issued, then no one would want the 8% bonds unless they can be bought at a discount. How much discount would it take to get you to buy the bonds? The discount would have to be large enough so that the effective yield on the initial investment would be pushed up to 10%. That is to say, your price for the bonds would be low enough so that the $40 periodic payment and the $1,000 at maturity would give you the requisite 10% market rate of return. The exact amount is again determined by discounting (i.e., calculating the present value) the stream of payments at the market rate of interest.

The table below calculates the price under the three different assumed market rate scenarios:

To further explain, the interest amount on the $1,000, 8% bond is $40 every six months. Since the bonds have a 5-year life, there are 10 interest payments (or periods). The periodic interest is an annuity with a 10-period duration, while the maturity value is a lump-sum payment at the end of the tenth period. The 8% market rate of interest equates to a semiannual rate of 4%, the 6% market rate scenario equates to a 3% semiannual rate, and the 10% rate is obviously 5% per semiannual period. The present value factors are taken from the present value tables (annuity and lump-sum, respectively). You should take time to trace the factors to the appropriate tables. The present value factors are multiplied times the payment amounts, and the sum of the present value of the components would equal the price of the bond under each of the three scenarios. Note that the 8% market rate assumption produced a bond priced at $1,000, the 6% assumption produced a bond priced at $1,085.30 (which includes an $85.30 premium), and the 10% assumption produced a bond priced at $922.78 (which includes a $77.22 discount).

These calculations are not only correct theoretically, but you will find that they are very accurate financial tools - reality will emulate theory. But, one point is noteworthy. Bond pricing is frequently done to the nearest 1/32nd. That is, a bond might trade at 103.08. You could easily misinterpret this price as $1,030.80. But, it actually means 103 and 8/32. In dollars, this would come to $1,032.50 ($1,000 X 103.25). So, now you should understand the theory and mechanics of how a bond is priced. It is time to examine the correct accounting.

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