Accounting: The Language of Business (Part 90)

The Big Dream of any entrepreneur really has very little to do with the entrepreneur. If you truly love repairing automobiles, chances are, you'll be a lousy business owner. Likewise, if you are fascinated by debits and credits, the dream of building an accounting firm with you at the helm is probably best left unfulfilled.

Michael Gerber

 Bonds Payable and Investments in Bonds (Part A)

by

Charles Lamson

The prices of bonds are quoted as a percentage of the bonds' face value. Thus, investors could purchase or sell bonds quoted at 116.992 for $1,169.92. likewise, bonds quoted at 109 could be purchased or sold for $1,090.

When all bonds of an issue mature at the same time, they are called term bonds. If the maturities are spread over several dates they are called serial bonds. For example, one tenth of an issue of $1,000,000 bonds, or $100,000, may mature 16 years from the issue date, another $100,000 in the 17th year, and so on until the final $100,000 matures in the 25th year.

Bonds that may be exchanged for other securities, such as common stock, are called convertible bonds. Bonds that a corporation reserves the right to redeem before their maturity are called callable bonds. Bonds issued on the basis of general credit of the corporation are called debenture bonds.

The Present-Value Concept and Bonds Payable

When a corporation issues bonds, the price that buyers are willing to pay for the bonds depends upon the following three factors:

1. The face value amount of the bonds, which is the amount due at the maturity date.

2. The periodic interest to be paid on the bonds.

3. The market rate of interest.

The face amount and the periodic interest to be paid on the bonds are identified in the bond indenture. The periodic interest is expressed as a percentage of the face amount of the bond. This percentage or rate of interest is called the contract rate or coupon rate.

The market or effective rate of interest is determined by transactions between buyers and sellers of similar bonds. The market rate of interest is affected by a variety of factors, including investors' assessment of current economic conditions as well as future expectations.

If the contract rate of interest equals the market rate of interest, the bonds will sell at their face amount. If the market rate is higher than the contract rate, the bonds will sell at a discount, or less than their face amount. Why is this the case? Buyers are not willing to pay the face amount for bonds whose contract rate is lower than the market rate. The discount, in effect, represents the amount necessary to make up for the difference in the market and the contract interest rates. In contrast, if the market rate is lower than the contract rate, the bonds will sell at a premium, or more than their face amount. In this case, buyers are willing to pay more than the face amount for bonds whose contract rate is higher than the market rate.

The face amount of the bonds and the periodic interest on the bonds represent cash to be received by the buyer in the future. The buyer determines how much to pay for the bonds by computing the present value of these future cash receipts, using the market rate of interest. The concept of present value is based on the time value of money.

The time value of money concept recognizes that an amount of cash to be received today is worth more than the same amount of cash to be received in the future. For example, what would you rather have: $100 today or $100 1 year from now? You would rather have the $100 today because it could be invested to earn income. For example, if the $100 could be invested to earn 10% per year, the $100 will accumulate to $110 ($100 + $10 earnings) in one year. In this sense you can think of the $100 in hand today as the present value of $110 to be received a year from today. This present value is Illustrated in the following timeline:

A related concept to present value is future value. In the preceding illustration, the $110 to be received a year from today is the future value of $100 today, assuming an interest rate of 10%.

Present Value of the Face Amount of Bonds

The present value of the the face amount of bonds is the value today of the amount to be received at a future maturity date. For example, assume that you are to receive the face value of a $1,000 bond in one year. If the market rate of interest is 10% the present value of the face value of the $1,000 bond is $909.09 ($1,000 / 1.10).This present value is illustrated in the following timeline:

If you are to receive the face value of a $1,000 bond in two years, with interest of 10% compounded at the end of the first year, the present value is $826.45 ($909.09 / 1.10). Note that the future value of $826.45 in two years, at an interest rate of 10% compounded annually, is $1,000. This present value is illustrated in the following timeline:

 You can determine the present value of the face amount of bonds to be received in the future by a timeline and a series of divisions. In practice, however, it is easier to use a table of present values. The present value of $1 table can be used to find the present-value factor for $1 to be received after a number of periods in the future. The face amount of the bonds is then multiplied by this factor to determine its present value. Exhibit 3 is a partial table of the present value of $1. (To simplify the illustrations, the tables presented in this post are limited to 11 periods for a small number of interest rates, and the amounts are carried to only five decimal places. Computer programs are available for determining present value factors for any number of interest rates, decimal places, or periods. More complete interest tables, including future value tables will be presented in an upcoming post.)

Exhibit 3 indicates that the present value of $1 to be received in two years with a market rate of interest of 10% a year is 0.82645. Multiplying the $1,000 face amount of the bond in the preceding example by 0.82645 yields $826.45

In Exhibit 3, the Periods column represents the number of compounding periods, and the percentage columns represent the compound interest rate per period. For example, 10% for two years compounded annually, as in the preceding example, is 10% for two periods. Likewise, 10% for 2 years compounded semiannually would be 5% (10% per year / 2 semiannual periods) for four periods (2 years * 2 semiannual periods). Similarly, 10% for three years compounded semiannually would be 5% (10% / 2) for six periods (3 years * 2 semiannual periods).

Present Value of the Periodic Bond Interest Payments

The present value of the periodic bond interest payments is the value today of the amount of interest to be received at the end of each interest period. Such a series of equal cash payments at fixed intervals is called an annuity.

The present value of an annuity is the sum of the present values of each cash flow. To illustrate, assume that the $1,000 bond in the preceding example pays interest of 10% annually and that the market rate of interest is also 10%. In addition, assume that the bond matures at the end of 2 years. The present value of the two interest payments of $100 ($1,000 * 10%) is $173.56, as shown in the time line below. It can be determined by using the present value table shown in Exhibit 3. 

Instead of using present value of amount tables, such as Exhibit 3, separate present value tables are normally used for annuities. Exhibit 4 is a partial table of the present value of an annuity of $1 at compound interest. It shows the present value of $1 to be received at the end of each period for various compound rates of interest. For example, the present value of $1,000 to be received at the end of each of the next two years at 10% compound interest per period is $173.55 ($100 * 1.73554). This amount is the same amount that we computed previously, except for rounding.

As noted earlier, the amount buyers are willing to pay for a bond is the sum of the present value of the face value and the periodic interest payments, calculated by using the market rate of interest. In our example, this calculation is as follows:

In this example, the market rate and the contract rate of interest are the same. Thus, the present value is the same as the face value. 

*WARREN, REEVE, & FESS, 2005, ACCOUNTING, 21ST ED., PP. 604-608*

end