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CHAPTER 7
Bonds Valuation
CHAPTER ORIENTATION
This chapter introduces the concepts that underlie asset valuation. We are specifically
concerned with bonds. We also look at the concept of the bondholder’s expected rate of
return on an investment.
CHAPTER OUTLINE
I. Types of bonds
A. Debentures: unsecured long-term debt.
B. Subordinated debentures: bonds that have a lower claim on assets in the
event of liquidation than do other senior debtholders.
C. Mortgage bonds: bonds secured by a lien on specific assets of the firm, such
as real estate.
D. Eurobonds: bonds issued in a country different from the one in whose
currency the bond is denominated; for instance, a bond issued in Europe or
Asia that pays interest and principal in U.S. dollars.
E. Zero and low coupon bonds allow the issuing firm to issue bonds at a
substantial discount from their $1,000 face value with a zero or very low
coupon.
1. The disadvantages are, when the bond matures, the issuing firm will
face an extremely large nondeductible cash outflow much greater than
the cash inflow they experienced when the bonds were first issued.
2. Zero and low coupon bonds are not callable and can be retired only at
maturity.
3. On the other hand, annual cash outflows associated with interest
payments do not occur with zero coupon bonds.
F. Junk bonds: bonds rated BB or below.
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II. Terminology and characteristics of bonds
A. A bond is a long-term promissory note that promises to pay the bondholder a
predetermined, fixed amount of interest each year until maturity. At maturity,
the principal will be paid to the bondholder.
B. In the case of a firm’s insolvency, a bondholder has a priority of claim to the
firm’s assets before the preferred and common stockholders. Also,
bondholders must be paid interest due them before dividends can be
distributed to the stockholders.
C. A bond’s par value is the amount that will be repaid by the firm when the
bond matures, usually $1,000.
D. The contractual agreement of the bond specifies a coupon interest rate that is
expressed either as a percent of the par value or as a flat amount of interest
which the borrowing firm promises to pay the bondholder each year. For
example: A $1,000 par value bond specifying a coupon interest rate of 9
percent is equivalent to an annual interest payment of $90.
E. The bond has a maturity date, at which time the borrowing firm is committed
to repay the loan principal.
F. An indenture (or trust deed) is the legal agreement between the firm issuing
the bonds and the bond trustee who represents the bondholders. It provides
the specific terms of the bond agreement such as the rights and
responsibilities of both parties.
G. The current yield on a bond refers to the ratio of annual interest payment to
the bond’s market price.
H. Bond ratings
1. Three primary rating agencies exist—Moody’s, Standard & Poor’s,
and Fitch Investor Services.
2. Bond ratings are simply judgments about the future risk potential of
the bond in question. Bond ratings are extremely important in that a
firm’s bond rating tells much about the cost of funds and the firm’s
access to the debt market.
3. The different ratings and their implications are described.
III. Definitions of value
A. Book value is the value of an asset shown on a firm’s balance sheet which is
determined by its historical cost rather than its current worth.
B. Liquidation value is the amount that could be realized if an asset is sold
individually and not as part of a going concern.
C. Market value is the observed value of an asset in the marketplace where
buyers and sellers negotiate an acceptable price for the asset.
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D. Intrinsic value is the value based upon the expected cash flows from the
investment, the riskiness of the asset, and the investor’s required rate of
return. It is the value in the eyes of the investor and is the same as the present
value of expected future cash flows to be received from the investment.
IV. Valuation: An Overview
A. The value of an asset is a function of three elements:
1. The amount and timing of the asset’s expected cash flows
2. The riskiness of these cash flows
3. The investors’ required rate of return for undertaking the investment
B. Expected cash flows are used in measuring the returns from an investment.
V. Valuation: The Basic Process
The value of an asset is found by computing the present value of all the future cash
flows expected to be received from the asset. Expressed as a general present value
equation, the value of an asset is found as follows:
V =
=+
N
1 t t
t
k) (1
$C
where Ct = the cash flow to be received at time t
V = the intrinsic value or present value of an asset
producing expected future cash flows, Ct, in
years 1 through N
k = the investor’s required rate of return
N = the number of periods
VI. Bond Valuation
A. The value of a bond is simply the present value of the future interest
payments and maturity value discounted at the bondholder’s required rate of
return. This may be expressed as:
Vb =
=+
+
+
N
1 t N
b
t
b
t
)k(1
$M
)k(1
$I
where It = the dollar interest to be received in each
payment
M = the par value of the bond at maturity
kb = the required rate of return for the bondholder
N = the number of periods to maturity
In other words, we are discounting the expected future cash flows to the
present at the appropriate discount rate (required rate of return).
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B. If interest payments are received semiannually (as with most bonds), the
valuation equation becomes:
Vb =
=
+
+
+
2N
1 t 2N
b
t
b
t
2
k
1
$M
2
k
1
2
$I
VII. Bondholder’s Expected Rate of Return (Yield to Maturity)
A. We compute the bondholder’s expected rate of return by finding the discount
rate that gets the present value of the future interest payments and principal
payment just equal to the bond’s current market price.
B. The bondholder’s expected rate of return is also the rate the investor will earn
if the bond is held to maturity, provided, of course, that the company issuing
the bond does not default on the payments.
VIII. Bond Value: Five Important Relationships
A. First relationship
A decrease in interest rates (required rates of return) will cause the value of a
bond to increase; an interest rate increase will cause a decrease in value. The
change in value caused by changing interest rates is called interest rate risk.
B. Second relationship
1. If the bondholder’s required rate of return (current interest rate) equals
the coupon interest rate, the bond will sell at par, or maturity value.
2. If the bondholder’s required rate of return exceeds the bond’s coupon
rate, the bond will sell below par value or at a “discount.”
3. If the bondholder’s required rate of return is less than the bond’s
coupon rate, the bond will sell above par value or at a “premium.”
C. Third relationship
As the maturity date approaches, the market value of a bond approaches its
par value.
1. The premium bond sells for less as maturity approaches.
2. The discount bond sells for more as maturity approaches.
D. Fourth relationship
A bondholder owning a long-term bond is exposed to greater interest rate risk
than when owning a short-term bond.
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E. Fifth relationship
The sensitivity of a bond’s value to changing interest rates depends not only
on the length of time to maturity, but also on the pattern of cash flows
provided by the bond.
1. The duration of a bond is simply a measure of the responsiveness of
its price to a change in interest rates. The greater the relative
percentage change in a bond price in response to a given percentage
change in the interest rate, the longer the duration.
2. Calculating duration
duration =
0
t
b
t
1
P
)k (1
tC
+
=
n
t
where t = the year the cash flow is to be received
N = the number of years to maturity
Ct = the cash flow to be received in year t
kb = the bondholder’s required rate of return
P0 = the bond’s present value
ANSWERS TO
END-OF-CHAPTER QUESTIONS
7-1. Book value is the asset’s historical value and is represented on the balance sheet as
cost minus accumulated depreciation. Liquidation value is the dollar sum that could
be realized if the assets were sold individually and not as part of a going concern.
Market value is the observed value for an asset in the marketplace where buyers and
sellers negotiate a mutually acceptable price. Intrinsic value is the present value of
the asset’s expected future cash flows discounted at an appropriate discount rate.
7-2. The value of a security is equal to the present value of cash flows to be received by
the investor. Hence, the terms value and present value are synonymous.
7-3. The first two factors affecting asset value (the asset characteristics) are the asset’s
expected cash flows and the riskiness of these cash flows. The third consideration is
the investor’s required rate of return. The required rate of return reflects the
investor’s risk-return preference.
7-4. The relationship is inverse. As the required rate of return increases, the value of the
security decreases, and a decrease in the required rate of return results in a price
increase.
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7-5. (a) The par value is the amount stated on the face of the bond. This value does
not change and, therefore, is completely independent of the market value.
However, the market value may change with changing economic conditions
and changes within the firm.
(b) The coupon interest rate is the rate of interest that is contractually specified in
the bond indenture. As such, this rate is constant throughout the life of the
bond. The coupon interest rate indicates to the investor the amount of
interest to be received in each payment period. On the other hand, the
investor’s required rate of return is equivalent to the bond’s current yield to
maturity, which changes with the changing bond’s market price. This rate
may be altered as economic conditions change and/or the investor’s attitude
toward the risk-return trade-off is altered.
7-6. In the case of insolvency, claims of debt holders in general, including bonds, are
honored before those of both common stock and preferred stock. However, different
types of debt may also have a hierarchy among themselves as to the order of their
claim on assets.
Bonds also have a claim on income that comes ahead of common and preferred
stock. If interest on bonds is not paid, the bond trustees can classify the firm
insolvent and force it into bankruptcy. Thus, the bondholder’s claim on income is
more likely to be honored than that of common and preferred stockholders, whose
dividends are paid at the discretion of the firm’s management.
7-7. Ratings involve a judgment about the future risk potential of the bond. Although they
deal with expectations, several historical factors seem to play a significant role in
their determination. Bond ratings are favorably affected by (1) a greater reliance on
equity, and not debt, in financing the firm, (2) profitable operations, (3) a low
variability in past earnings, (4) large firm size, and (5) little use of subordinated debt.
In turn, the rating a bond receives affects the rate of return demanded on the bond by
the investors. The poorer the bond rating, the higher the rate of return demanded in
the capital markets.
For the financial manager, bond ratings are extremely important. They provide an
indicator of default risk that in turn affects the rate of return that must be paid on
borrowed funds.
7-8. The term debentures applies to any unsecured long-term debt. Because these bonds
are unsecured, the earning ability of the issuing corporation is of great concern to the
bondholder. They are also viewed as being more risky than secured bonds and as a
result must provide investors with a higher yield than secured bonds provide. Often
the issuing firm attempts to provide some protection to the holder through the
prohibition of any additional encumbrance of assets. This prohibits the future
issuance of secured long-term debt that would further tie up the firm’s assets and
leave the bondholders less protected. To the issuing firm, the major advantage of
debentures is that no property has to be secured by them. This allows the firm to
issue debt and still preserve some future borrowing power.
A mortgage bond is a bond secured by a lien on real property. Typically, the value of
the real property is greater than that of the mortgage bonds issued. This provides the
mortgage bondholders with a margin of safety in the event the market value of the
secured property declines. In the case of foreclosure, the trustees have the power to
sell the secured property and use the proceeds to pay the bondholders. In the event
that the proceeds from this sale do not cover the bonds, the bondholders become
general creditors, similar to debenture bondholders, for the unpaid portion of the
debt.
7-9. (a) Eurobonds are not so much a different type of security as they are securities,
in this case bonds, issued in a country different from the one in whose
currency the bond is denominated. For example, a bond that is issued in
Europe or in Asia by an American company and that pays interest and
principal to the lender in U.S. dollars would be considered a Eurobond.
Thus, even if the bond is not issued in Europe, it merely needs to be sold in a
country different from the one in whose currency it is denominated to be
considered a Eurobond.
(b) Zero and very low coupon bonds allow the issuing firm to issue bonds at a
substantial discount from their $1,000 face value with a zero or very low
coupon. The investor receives a large part (or all on the zero coupon bond)
of the return from the appreciation of the bond at maturity.
(c) Junk bonds refer to any bond with a rating of BB or below. The major
