### Learning Objectives

At the end of this section, students should be able to meet the following objectives:

- Identify the characteristics of a zero-coupon bond.
- Explain how interest is earned on a zero-coupon bond.
- Understand the method of arriving at an effective interest rate for a bond.
- Calculate the price of a zero-coupon bond and list the variables that affect this computation.
- Prepare journal entries for a zero-coupon bond using the effective rate method.
- Explain the term “compounding.”
- Describe the theoretical problems associated with the straight-line method and identify the situation in which this method can still be applied.

*Question: A wide array of bonds and other types of financial instruments can be purchased from parties seeking money. A zero-coupon bond is one that is popular because of its ease. The face value of a zero-coupon bond is paid to the investor after a specified period of time but no other cash payment is made. There is no stated cash interest. Money is received when the bond is issued and money is paid at the end of the term but no other payments are ever made*. *Why does any investor choose to purchase a zero-coupon bond if no interest is paid?*

Answer: No investor would buy a note or bond that did not pay interest. That makes no economic sense. Because zero-coupon bonds are widely issued, some form of interest must be included. These bonds are sold at a discount below face value with the difference serving as interest. If a bond is issued for $37,000 and the company eventually repays the face value of $40,000, the additional $3,000 is interest on the debt. That is the charge paid for the use of the money that was borrowed. The price reduction below face value can be so significant that zero-coupon bonds are sometimes referred to as deep discount bonds.

To illustrate, assume that on January 1, Year One, a company offers a $20,000 two-year zero-coupon bond to the public. A single payment of $20,000 will be made to the bondholder on December 31, Year Two. According to the contract, no other cash is to be paid. An investor who wishes to make a 7 percent annual interest rate can mathematically compute the amount to pay to earn exactly that interest. The debtor must then decide whether to accept this offer.

Often, the final exchange price for a bond is the result of a serious negotiation process to determine the interest rate to be earned. As an example, the potential investor might offer an amount that equates to interest at an annual rate of 7 percent. The debtor could then counter by suggesting 5 percent with the two parties finally settling on a price that provides an annual interest rate of 6 percent. In the bond market, interest rates are the subject of intense negotiations. After the effective rate (also called the yield or negotiated rate) has been established by the parties, the actual price of the bond is simply a mathematical computation.

*Question: A $20,000 zero-coupon bond is being issued by a company. According to the indenture, it comes due in exactly two years. The parties have negotiated an annual interest rate to be earned of 6 percent*. *How is the price to be paid for a bond determined after an effective rate of interest has been established?*

Answer: Determination of the price of a bond is a present value computation in the same manner as that demonstrated previously in the coverage of intangible assets. Here, a single cash payment of $20,000 is to be made by the debtor to the bondholder in two years. The parties have negotiated an annual 6 percent effective interest rate. Thus, a portion of the future cash ($20,000) serves as interest at an annual rate of 6 percent for this period of time. In a present value computation, total interest at the designated rate is calculated and subtracted to leave the present value amount. That is the price of the bond, often referred to as the principal. Interest is computed at 6 percent for two years and removed. The remainder is the amount paid for the bond.

#### Present Value of $1

http://www.principlesofaccounting.com/ART/fv.pv.tables/pvof1.htm

The present value of $1 in two years at an annual rate of interest of 6 percent is $0.8900. This can be found by table, by formula, or by use of an Excel spreadsheet^{1}. Because the actual payment is $20,000 and not $1, the present value of the cash flows from this bond (its price) can be found as follows:

present value = future cash payment × $0.8900

present value = $20,000 × $0.8900

present value = $17,800

Bond prices are often stated as a percentage of face value. Thus, this bond is sold to the investor at “89” ($17,800/$20,000), which indicates that the price is 89 percent of the face value. The price is the future cash payments with the negotiated rate of interest removed. If the investor pays $17,800 today and the debtor returns $20,000 in two years, the extra $2,200 is the interest. And, mathematically, that extra $2,200 is exactly equal to interest at 6 percent per year.

The issuance is recorded through the following entry^{2}.