Bond problems and glossary links are at the bottom of these notes.
DEFINITION:
A bond is a commitment by
the issuer to pay a fixed rate of interest for a pre-determined
period of time. By selling bonds, the issuing company has raised
spending power by borrowing. This is called Debt Financing.
BOND TERMS
The following is a [very crude] example of a corporate bond.
The left side of the bond is called the bond's principal.
The $1000 is the bond's PAR value or the FACE
amount. When the bond is first issued, it is sold for $1,000. Bond
holders are loaning the issuing corporation $1,000 in exchange for 30 years of
interest. At the end of the term [when the bond matures] the
bondholder's $1,000 is returned.
The issuing corporation's name is listed on the face of the bond. In
our example case, the issuer is AT&T.
8% in our example is the coupon rate. That is the rate
of interest (as an annual rate) promised by the issuing corporation for the
use of your money. You are paid 8% of $1,000 per year for as many years
as you own this bond. The payments are made semi-annually. We will
be glad to know that their is no fancy math necessary to make these
calculations. Interest is paid on a simple interest basis.
8% of $1,000 = $80, which will be paid in two $40 installments.
The date listed on the bond's face is the maturity date.
Typically 30 years, this is the date that the bondholder is paid $1,000 and
the date that the bond dissolves. The debt is paid, this bond issue is
over!
The dashed lines toward the bottom of the bond's principal represent the
indenture, where the terms and conditions of the bond issue are
listed. The indenture could be short or 100 pages long, we will see what
special circumstances a corporation could include in the indenture as our
study of bonds progress.
The squares to the right of the principal are the bond's coupons.
Principal Bond's coupons. In a 30-year bond, there are 60 coupons
$1000
☺
AT & T
8%
1/1/33
----------------
Indenture
---------------
$40
1/1/33
$40
7/1/03
$40
1/1/04
$40
7/1/04
As attractive as the above drawing is, I thought to look up an actual bond
principal, notice that the coupons are NOT attached.
BOND YIELDS
this is how bond holders calculate returns on their
investments
COUPON RATE/YIELD
Stated on the face of the
bond. Technically, the coupon rate is derived by dividing the
annual income by the par value.
CURRENT YIELD
Annual interest income /
Price. Once the bond is issued and is the secondary market
(has begun trading), an investor may pay a price for the bond
different from par. In this case, the annual income
divided by the price paid, will give the investor a more
accurate yield than the coupon yield. The coupon yield will
equal the current yield if the bond can be purchased at par.
YIELD TO MATURITY
The promised compounded rate of return an
investor will receive from a bond purchased at the current market
price and held to maturity. It captures the coupon interest to be
received on the bond as well as any capital gains or losses
realized by purchasing at a discount or premium.
YTM = {Annual Interest+[(Face Value @ Maturity-Price)/# yrs to
maturity]} / [(face value @ maturity + price)/2]
REALIZED COMPOUNDED YIELD: The YTM calculation assumes that the
investor reinvests all coupons received from a bond at a rate
equal to the computed YTM, thereby earning interest-on-interest
over the life of the bond.
PROMISED YIELD: The YTM is referred to as Promised because
investors will only earn that rate if the bond is held to maturity
and coupon payments are reinvested at the YTM.
The risk that the investor faces with the YTM calculation is
REINVESTMENT risk. The possibility that the coupons CANNOT
be reinvested at that YTM.
The Yield-to-Call
calculation is identical to the Yield-to-maturity with logical
substitutions of elements. The number of years to maturity in the
YTM formula is replaced with the number of years to call.
The Face Value @ Maturity is replaced with the Call Price.
These are usually the same, BUT the company may pay a different
price from par when the bond is called. Sometimes referred
to as a guilt coupon, the firm may add one coupon to the price on
the call date, compensating investors (in some way) for calling
the bond before maturity.
BOND VALUATION
Bond valuation is the process of calculating
the intrinsic value of the bond given changes in market
interest rates. This process describes interest rate
risk.
For example, we have an 8%, $1,000, 30 year
bond, paying $40 semi-annual coupons.
We know that the bond cost $1,000 new, when issued. It
costs $1,000 because that is the face value, it also costs
$1,000 because that is the present value of its parts.
If we calculate the present value of the bond's principal (a
single sum) and added it to the present value of the coupons
(an annuity), we would have $1,000.
$1000 * ( 1+ .08/2)-60
= $95.06
$40 * [1- ( 1+ .08/2)-60 ] / (.08/2) = $904.94
TOTAL
= $1000
The biggest risk of bond ownership is interest rate
risk. We know that interest rates and bond
prices are inversely related. When interest rates
increase, bond prices decrease and vice-versa.
Given our sample bond, let's say that interest rates
increase from 8% to 9%. We know that the price of our
bond will decrease, but how much? Bond valuation will
determine the new price of the bond given this change in the
market. The process is the same, we have to take the
present value of the bond's principal and add it to the
present value of the coupons using the current interest
rate of 9%.
$1000 * ( 1+ .09/2)-60 = $71.28
$40 * [1- ( 1+ .09/2)-60 ] / (.09/2) = $825.52
TOTAL = $896.80
The same process would be used for decreasing interest
rates.
