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Bonds and other securities


One of the major applications of the theory of interest is in the determination of prices and values for bonds and other securities, such as preferred stock and common stock. This chapter is mainly concerned with bonds, although brief consideration is given to preferred and common stock in Sections 7.2, 7.10, and 7.11.

There are three main questions which Chapter 7 considers:

1. Given the desired yield rate of an investor, what price should be paid for a given security?

2. Given the purchase price of a security, what is the resulting yield rate to an investor?

3. What is the value of a security on a given date after it has been purchased?

It should be noted that no new basic principles are introduced in this chapter. However, several new terms and formulas are introduced to efficiently handle financial calculations involving these types of securities. 7.2 TYPES OF SECURITIES

Section 7.2 considers three common types of securities which have evolved in the financial markets. This section should not be considered as a complete discussion of these securities, since only a very brief description is presented. For a more complete discussion die reader is encouraged to refer to any of several standard textbooks on finance or securities.

In recent years there has been a proliferation of more exotic financial instruments. These are not discussed at this stage, since it is important to deal

I the basics first. However, these newer financial instruments are discussed I Section 8.8.

The three main categories of securities which will be discussed in this apter are: (1) bonds, (2) preferred stock, and (3) common stock.

% A bond is an interest-bearing security which promises to pay a stated It (or amounts) of money at some future date (or dates). It is a formal tertificate of indebtedness issued by a borrower, usually for some round figure ch as $1000 or $5000. Bonds are commonly issued by corporations and vernmental units as a means of raising capital. Bonds are generally redeemed at the end of a fixed period of time. This period of time is called the term of the bond. The end of the term of a is called the maturity date. On occasion, bonds with an infinite term are 1, e.g. the British consols. Such bonds are called perpetuals. Also bonds ay be issued with a term which varies at the discretion of the borrower. Such bond is termed a callable bond and is discussed in Section 7.7. Any date rior to, or including, the maturity date on which a bond may be redeemed is a redemption date.

r; Bonds may be classified in several different ways. One such classification is the distinction between accumulation bonds and boruls with coupons. The :upons are periodic payments made by the issuer of the bond prior to its Iredemption. An accumulation bond is one in which the redemption price Includes the original loan plus all accumulated interest. The Series E Savings is issued by the United States Treasury are a traditional example of this type of bond. More recently, so-called zero coupon bonds have become very popular Ijrith investors. However, most bonds have coupons payable periodically, and feis will be assumed unless stated otherwise. This chapter will largely be nfined to this latter type of bond, since accumulation or zero coupon bonds can easily be handled with elementary compound interest methods already scussed in earlier chapters.

t;, A second classification is the distinction between registered bonds and \ unregistered bonds. A registered bond is one in which the lender is listed in the records of the borrower. If the lender decides to sell the bond, the change of ownership must be reported to the borrower. The periodic coupon payments are paid by the borrower to the owners of record on each coupon payment date. An unregistered bond is one in which the lender is not listed in the records of the borrower. Since the bond belongs to whomever has legal possession of it, an unregistered bond is often called a bearer bond. Unregistered bonds are almost always issued with coupons attached. The coupons can be detached by

the holder of the bond and cashed. Such a bond is often called a coupon bond 1 for this reason.

A third classification is made according to the type of security behind the bond. A mortgage bond is a bond secured by a mortgage on real property, debenture bond is one secured only by the general credit of the borrower. Variations within these two major classifications exist. In general, mortgage bonds possess a higher degree of security than debenture bonds, since the lenders can foreclose on the collateral in the event of the default of a mortgage bond.

A type of bond with a high degree of risk to the lender is the income bond or adjustment bond. Under this type of bond, the periodic coupons are paid; only if the borrower has earned sufficient income to pay them. Income bonds were once fairly common, but they have largely disappeared in recent years.

The more modern version of a high-risk bond is often called a "junk" bond. Such bonds are issued by corporations, typically in connection with corporate i mergers, acquisitions, or other takeovers. They have a significantly higher risk of default in payments than corporate bonds in general. Accordingly, they must! pay commensurately higher rates of interest to the lender for assuming this risk. \ Such bonds are sometimes characterized as below investment grade. The phrase "investment grade" refers to a schedule of quality rankings for various bonds provided by certain rating organizations. Financial calculations involving the risk of default will not be covered in this chapter, but will be addressed m Section 9.5.

A type of bond which is somewhat of a hybrid is a convertible bond. This, type of bond can be converted into the common stock of the issuing co oratio ; at some future date under certain conditions, at the option of the owner of the bond. Convertible bonds are generally debenture bonds. Such bonds offer an investor a choice between continuing the security as a bond or switching it into common stock, depending upon the performance of the 11 in the future.

A borrower in need of a large amount of funds can issue bonds with a common maturity date. However, a large volume of indebtedness falling due at one time can present problems in redeeming or refinancing the debt. For this reason, some borrowers will divide a large issue of bonds so that individual bonds will have a series of staggered redemption dates. These types of bonds are called serial bonds and will be analyzed fiirther in Section 7.8. An alternative approach is for the lenders to require the establishment of a sinking fund to build up the amount necessary to repay the indebtedness for a large issue of bonds.

The United States Treasury issues indebtedness with a wide range of jnaturities. Long-term debt of seven or more years duration is issued in the form of Treasury bonds. Short-term debt is issued in the form of Treasury bills, often called "T-bills." These are issued on a discount basis for maturities of 13, 26, or 52 weeks, and were discussed briefly in Section 2.8. Debt of an IK intermediate duration, i.e. one to seven years, is typically issued in the form of %%easury notes. Although called "notes," these securities are mathematically equivalent to bonds; the term is just shorter. Calculations involving Treasury 1- bills have some significant differences from those on longer-term Treasury I securities. These differences are explored in Example 7.2.

ferred stock

ppL Preferred stock is a type of security which provides a fixed rate of return Isimilar to bonds. However, it differs from a bond in that it is an ownership rity rather than a debt security, i.e. the owner of preferred stock is part pTOwner of the issuing co oration, while the bond owner is a creditor of the b oration. In general, preferred stock has no maturity date, although on ccasion preferred stock with a redemption provision is issued. The periodic ayment on preferred stock is usually called a dividend, since it is being paid I an owner.

> In terms of the degree of security, preferred stock ranks behind bonds and other debt instruments, since all payments on indebtedness must be made before I the preferred stock receives a dividend. However, preferred stock ranks ahead of common stock in the degree of security involved, since preferred stock Idividends must be paid before common stock dividends can be paid. I To increase the degree of security behind preferred stock, some co o ations ve issued cumulative preferred stock. This type of preferred stock has the eature that any dividends which the co oration is not able to pay are carried prward to fiiture years when they presumably will be paid. For example, if a poration has preferred stock on which it is paying a $5 dividend per share I-J can make only a $3 payment in one year, the $2 balance is carried forward (perhaps without interest) to future years. All arrears on preferred stock must be paid before any dividends on common stock can be paid.

Some preferred stocks receive a share of earnings over and above die I regular dividend if earnings are at a sufficient level. This type of preferred I stock is called participating preferred stock, since it participates in the earnings with the common stock. Participating preferred stock is relatively uncommon

at the present time.

Some preferred stock has a convertible privilege similar to convertible bonds and is called convertible preferred stock. Owners of this type of preferred stock

have the option to convert their preferred stock to common stock under certain conditions.

Common stock

Common stock is a type of ownership security, as is preferred stock. However, it does not earn a fixed dividend rate as preferred stock does. Common stock dividends are paid only after interest payments on all bonds and other debt and dividends on preferred stock are paid. The dividend rate is completely flexible and can be set by the corporations board of directors at its discretion.

Since the dividend rates on common stocks are variable, the prices of common stocks tend to be much more volatile than either bonds or preferred stocks. However, all residual profits after dividends to the preferred stockholders belong to the common stockholders. j

Example 7.1 A zero coupon bond will pay $1000 at the end of 10 years] and is currently selling for $400. Find the yield rate convertible semiannually ] that would be eamed by a purchaser.

Let J be die yield rate per half-year. The equation of value is

400(1 + = 1000

(1 -(- f) = 2.5

which gives J = .0469. Thus, die yield rate convertible semiannually is equal to ] 2(.0469) = .0938, or 9.38%.

Example 7.2 A 13-week Treasury bill matures for $10,000 and is bougM\ at discount to yield 7.5%. Find the price which should be paid.

As noted in Section 2.8, T-bill yields are computed as rates of discount rather dian] rates of interest. These yields are computed on a simple discount basis, which, in effect, f results in a rate of discount convertible at die same fiuency as die term of die T-bill. j Also, it is necessary to know die basis for measuring time periods as described in Section] 2.3. The basis typically used for T-bills is acmal/360. On tfus basis die price would be 1


91 360


= $9810.42.

It should be noted that the basis for determining time periods for longer-term Treasury j securities is actual/actual radier dian acmal/360.


As mentioned in Section 7.1, one of the three primary questions under j consideration in this chapter is the determination of a purchase price which will

produce a given yield rate to an investor. This section considers this question for bonds.

The following assumptions are made:

1. All obligations will be paid by the bond issuer on the specified dates of payment. Market prices of bonds will vary depending upon the probability of default in payments, but we will ignore any possibility of default in this chapter. Financial calculations reflecting the probability of default will be discussed in Section 9.5.

2. The bond has a fixed maturity date. Bonds witii no maturity date are mathematically equivalent to preferred stock and are considered in Section 7.10. Callable bonds with optional redemption dates are considered in

Section 7.7.

3. The price of the bond is desired immediately after an coupon payment date. , The price of a bond between two coupon payment dates is considered in i Section 7.5.

The following symbols will be used in connection with bonds in this and [succeeding sections:

the price of a bond.

the par value face amount of a bond. This value is printed on the front of the bond and is often the amount payable at the maturity date. Its sole purpose is to define the series of payments to be made by the borrower. It is not a measure of the price or the value of a bond prior to maturity. It is customary to quote bond prices in terms of a par value of $100, even though bonds are rarely issued in such small denominations, and this will be assumed unless stated otherwise, the redemption value of a bond, i.e. the amount of money paid at a redemption date to the holder of the bond. Often is equal to F; for example, the common case of a bond redeemed at its maturity date for its par value. It is possible for to differ from F in the following cases: (1) a bond which maftires for an amount not equal to its par value, or (2) a bond which has a redemption date prior to the maturity date on which the bond is redeemed for an amount not equal to its par value. It will be assumed that a bond is redeemable at par unless stated otherwise. The reader should note that the symbol was also used in Section 5.5 to represent the total net amount of principal contributed in determining the yield rate on an investment liind. the coupon rate of a bond, i.e. the rate per coupon payment period used in determining the amount of the coupon. The most common frequency

In r

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