The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


6.2 Bonds


Back in Chapter 1, we discussed promissory notes. Recall that a promissory note is simply
a written agreement between a borrower and a lender, specifying the terms of a loan. The
notes that we discussed in Chapter 1 were fairly simple ones; a borrower borrows some
amount of money and then repays the entire loan together with (simple) interest at the
maturity date. We have seen many variations on this theme: the simple discount notes of
Chapter 2, loans made at compound interest in Chapter 3, and the loans that we analyzed
as annuities in Chapters 4 and 5. In this section, we will take a look at another, much more
complex, generalization of the idea of a promissory note.
Speaking generally, a bond can be thought of as a type of promissory note. A bond is
also a written agreement between a borrower and a lender, specifying the terms of the
loan. The term bond is more commonly used when the borrower makes periodic interest
payments to the lender, instead of repaying the entire principal and interest all at once at
maturity (though there are exceptions to this, as we will see). Also, while simple interest
or simple discount promissory notes tend to be fairly short term loans, bonds often extend
for longer terms.

The Language of Bonds


Before proceeding any further, we need to define certain terms that are commonly used
with bonds.
The issuer of the bond is the entity that creates the bond as a means to borrow funds. Put
more simply, the issuer is the borrower. While a bond could theoretically be issued by just
about any individual, business, or other organization, bonds are most commonly issued by
large companies or federal, state, or local governments or agencies. When a bond is first sold,
its buyer pays the issuer some amount of money in exchange for the bond. More simply put,
the initial buyer of a bond is the lender. The original buyer of a bond may sell it to someone
else, just as we saw with promissory notes in Chapter 2.
The issuer of the bond is obligated to make certain payments to its owner. The par value
of a bond is the amount that will be paid to the bond’s owner at maturity. This can also be
called the face value of the bond. The most common par value for a bond is $1,000, though
other amounts could be used. However, if the amount that the issuer needs to borrow is
large, rather than create higher par value bonds, the issuer may just issue however many
bonds are necessary to raise the needed amount.
A bond is said to be redeemed when the borrower pays the bond’s owner its par value.
For this reason, the par value is also sometimes referred to as the redemption value. Normal-
ly, redemption occurs at the bond’s maturity date, though some bonds include a provision
that the debt can be paid off early, possibly at either the issuer or the owner’s option. When a
bond is redeemed early, we say it is called; bonds that may be called are said to be callable.
We will not consider callable bonds in this section, other than mentioning their existence.
The coupon rate is the interest rate for the bond’s periodic interest payments, as a per-
cent of par value. This name may seem strange; we usually think of “coupons” as clippings
from the Sunday paper to save 50 cents on peanut butter. The reason for this term is that
there are two types of bonds: registered bonds and coupon bonds.
The fact that bonds can be bought and sold poses a challenge for a bond’s issuer: if the
bond is sold, how does the issuer know to whom the interest payments should be made?
With a registered bond, the owner is recorded by the issuer and interest payments are sent
to this registered owner. If that type of bond is sold, the issuer must be notified. This solves
the problem of where to send the payments, but it creates the burden of reporting and keep-
ing track of every sale. With a coupon bond, there are actual coupons attached to the bond,
which the owner clips off and submits when interest payments are due. The issuer sends the
interest to whoever submits the coupon for payment. The term “coupon rate” comes from
this situation (even though the term is used even for registered bonds).

6.2 Bonds 263
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