Slide 1 7-1Cash Flows for Stockholders• If you o.docx

7-1
Cash Flows for Stockholders
• If you own a share of stock, you can receive
cash in two ways
the market or back to the company
• As with bonds, the price of the stock is the
present value of these expected cash flows
In this module, we turn to the other major source of financing
for corporations, common and preferred stock.
The goal of financial management is to maximize stock prices,
so an understanding of what determines
share values is obviously a key concern. The dividends
currently being paid are one of the primary factors

we look at when we attempt to value common stocks. This
module explores dividends, stock values, and
the connection between the two.
A share of common stock is more difficult to value in practice
than a bond, for at least three reasons.
First, with common stock, not even the promised cash flows are
known in advance.
Second, the life of the investment is essentially forever, since
common stock has no maturity.
Third, there is no way to easily observe the rate of return that
the market requires.
However, we can come up with the present value of the future
cash flows for a share of stock making some
assumptions.
Slide 2

7-2
One Period Example
• Suppose you are thinking of purchasing the
stock of Moore Oil, Inc.
– You expect it to pay a $2 dividend in one year
– You believe you can sell the stock for $14 at that
time.
– You require a return of 20% on investments of this
risk
– What is the maximum you would be willing to
pay?
Slide 3
7-3
One Period Example
• D1 = $2 dividend expected in one year
• R = 20%

• P1 = $14
• CF1 = $2 + $14 = $16
• Compute the PV of the expected cash flows
33.13$
20.1
)142(
P
0
Note, the calculation can also be done as:
FV = 14; PMT = 2; I/Y = 20; N = 1; CPT PV = -13.33
Slide 4
7-4
Two Period Example

• What if you decide to hold the stock for two years?
– In addition to the dividend in one year, you expect a
dividend of $2.10 in two years and a stock price of
$14.70 at the end of year 2.
– Now how much would you be willing to pay?
33.13$
)20.1(
)70.1410.2(
20.1
2
P
20
Calculator: CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1;
NPV; I =
20; CPT NPV = 13.33
We can use uneven cash flow keys.

7-5
Three Period Example
• What if you decide to hold the stock for three
years?
– In addition to the dividends at the end of years 1 and 2,
you expect to receive a dividend of $2.205 at the end of
year 3 and the stock price is expected to be $15.435.
– Now how much would you be willing to pay?
33.13$
)20.1(
)435.15205.2(
)20.1(
10.2
20.1
2
P
320

Calcultator: CF0 = 0; C01 = 2; F01 = 1; C02 = 2.10; F02 = 1;
C03 = 17.64;
F03 = 1; NPV; I = 20; CPT NPV = 13.33
Slide 6
7-6
Developing The Model
• You could continue to push back the year in
which you will sell the stock
• You would find that the price of the stock is
really just the present value of all expected
future dividends
• So, how can we estimate all future dividend
payments?

In equilibrium, the required return, R, is the same as the
“expected return.”
Slide 7
7-7
Stock Value = PV of Dividends
P0 =
^
(1+R)1 (1+R)2 (1+R)3 (1+R)∞
D1 D2 D3 D∞
+ + +…+
1t
t

t
0
)R1(
D
P̂
How can we estimate all future dividend
payments?
Slide 8
7-8
Estimating Dividends
Special Cases
• Constant dividend/Zero growth
– Firm will pay a constant dividend forever
– Like preferred stock
– Price is computed using the perpetuity formula
• Constant dividend growth/Goldon growth

– Firm will increase the dividend by a constant percent
every period (growing perpetuity model)
• Supernormal growth/Nonconstant growth
– Dividend growth is not consistent initially, but settles
down to constant growth eventually (Multistage model)
Three special cases of assumptions for estimating dividends
allow us to value common stock.
dollar amount) and is valued like a
perpetuity.
frequently used assumption. It describes a
constant dividend growth percent.
company experiencing abnormal growth
currently but expected to stabilize to a constant growth situation
in the future.
Slide 9

7-9
Zero Growth
• Dividends expected at regular intervals
forever = perpetuity
P0 = D / R
• Suppose stock is expected to pay a $0.50
dividend every quarter and the required
return is 10% with quarterly compounding.
What is the price?
20$
4
10.
50.0
0
If dividends are paid quarterly, then the discount rate must be a
quarterly rate.
Zero-growth – implies that D1 = D2 = D3 … = D

Since the cash flow is always the same, the PV is that for a
perpetuity:
P0 = D ⁄ R
Example: Suppose a stock is expected to pay a $2 dividend each
period, forever, and the required return is
10%. What is the stock worth?
P0 = 2 ⁄ .1 = $20
Slide 10
7-10
Constant Growth Stock
D1 = D0(1+g)
1
D2 = D0(1+g)
2
Dt = D0(1+g)

t
One whose dividends are expected to
grow forever at a constant rate, g.
D0 = Dividend JUST PAID
D1 to Dt = Expected dividends
Slide 11
7-11
Projected Dividends
• D0 = $2.00 and constant g = 6%
• D1 = D0(1+g) = 2(1.06) = $2.12
• D2 = D1(1+g) = 2.12(1.06) = $2.2472
• D3 = D2(1+g) = 2.2472(1.06) = $2.3820

7-12
Dividend Growth Model
“Gordon Growth Model”
t
t
R
gD
R
gD
R
gD
R
gD
P
)1(
)1(

...
)1(
)1(
)1(
)1(
)1(
)1(
0
3
3
0
2
2
00
0

1
1
2
2
00
)1(
)1(
...
)1(
)1(
)1(
)1(
1
)1(
)1(
t
t

t
t
R
g
DP
g
gR
)1(
)1(
1
)1(
)1()1(
00
Now multiply both sides by (1+R)/(1+g):
Subtract the first equation from the second and you get:
The term 1 – (1+g)t/(1+R)t goes to one as t approaches infinity,
assuming R > g.

If we solve for P
0
, we get the dividend growth model.
Given our basic PV definition and using some advanced
mathematics, we can derive the Dividend
Growth Model, also known as the Gordon Growth Model for the
academic who did extensive work in this
area.
Slide 13
7-13
P0 =
^ D0(1+g)
R - g
=
D1

R - g
1t
t
t
00
)R1(
)g1(
DP̂
“Gordon Growth Model”
Constant growth – Dividends are expected to grow at a constant
percentage rate each period. D1 =
D0(1+g); D2 = D1(1+g); in general Dt = D0(1+g)
t Note that this is really just a future value.
Example: If the current dividend is $2 and the expected growth
rate is 5%, what is D1? D5?

D1 = 2(1+.05) = $2.10
D5 = 2(1+.05)
5 = $2.55
An amount that grows at a constant rate forever is called a
growing perpetuity. The present value of all
expected future dividends under this scenario can be expressed
as follows:
P0 = D1 ⁄ (R − g)and more generally,
Pt = Dt+1 ⁄ (R − g)
“g” is the growth rate in dividends; the subscripts denote the
period in which the dividend is paid. This is
the formula for a growing perpetuity.
Slide 14
7-14

DGM – Example 1
• Suppose TB Pirates, Inc. is expected to pay a $2
dividend in one year. If the dividend is expected to
grow at 5% per year and the required return is 20%,
what is the price?
– D1 = $2.00
– g = 5%
– r = 20%
33.13$
05.20.
00.2
P
gR
D
P
0
1
0

We are finding a present value, so the dividend needed is the
one that will be paid NEXT period, not the
one that has already been paid.
Slide 15
7-15
DGM – Example 2
• Suppose Big D, Inc. just paid a dividend of $.50. It is
expected to increase its dividend by 2% per year. If
the market requires a return of 15% on assets of this
risk, how much should the stock be selling for?
• D0= $0.50
• g = 2%

• R = 15%
92.3$
02.15.
)02.1(50.0
P
gR
)g1(D
P
0
0
0

7-16
Stock Price Sensitivity to Dividend
Growth, g
0
50
100
150
200
250
0 0.05 0.1 0.15 0.2
Growth Rate
S
to
c
k
P
r
ic
e

D1 = $2; R = 20%
As the growth rate approaches the required return, the stock
price increases dramatically. From the DGM
formula, as g → R, the denominator → 0.
Slide 17
7-17
Stock Price Sensitivity to Required
Return, R
0
50
100
150
200
250
0 0.05 0.1 0.15 0.2 0.25 0.3

Required Return
S
to
c
k
P
r
ic
e
D1 = $2; g = 5%
As the required return approaches (is decreased leftward
toward) the growth rate, the price increases
dramatically. This graph is a mirror image of the previous one.
Slide 18
7-18
Gordon Growth Company - I

• Gordon Growth Company is expected to pay a
dividend of $4 next period and dividends are
expected to grow at 6% per year. The required
return is 16%.
• What is the current price?
40$
06.16.
00.4
P
gR
D
P
0
1
0
Remember that we already have the dividend expected next
year, so we don’t multiply the dividend by

1+g.
Slide 19
7-19
Gordon Growth Company - II
• What is the price expected to be in year 4?
50.50$
06.16.
)06.1(00.4
P
)g1(DD
g-R
D
gR
)g1(D
P

4
4
4
15
54
4
The dividend in the numerator is always for one period later
than the price we are computing. This is
because we are computing a Present Value, so we have to start
with a future cash flow.
We know the dividend in one year is expected to be $4 and it

will grow at 6% per year for four more years.
So, D5 = 4(1.06)(1.06)(1.06)(1.06) = 4(1.06)
4
Slide 20
7-20
Gordon Growth Company - II
• What is the implied return given the
change in price during the four year
period?
50.50 = 40(1+return)4; return = 6%
4 N; -40 PV; 50.50 FV; 0 PMT; CPT I/Y = 6%
Slide 21

7-21
Constant Growth Model Conditions
1. Dividend expected to grow at g forever
2. Stock price expected to grow at g forever
3. Expected dividend yield is constant
4. Expected capital gains yield is constant and
equal to g
5. Expected total return, R, must be > g
6. Expected total return (R):
= expected dividend yield (DY)
+ expected growth rate (g)
= dividend yield + g
“How can g ever be assumed to be constant?”
The answer lies in the competitive equilibrium model of
classical macroeconomics. Since g represents not
only the growth rate in dividends but also in earnings and sales,
assuming no change in the firm’s cost
structure, we are simply assuming that the product market that
the firm operates in “settles down” to a

steady state in which competing firms earn sufficient returns to
remain in business, but not large enough
to attract outside capital. From a more practical standpoint,
firms will often attempt to manage their
dividend policy so that there is a reasonably constant growth in
dividends.
“Why do we assume that R > g?”
At least two answers are possible. First, R may be less than g in
the short-run. The supernormal growth
problem is an example of this situation. Second, in equilibrium,
high returns on investment will attract
capital, which, in the absence of technological change, will
ensure that in succeeding periods, higher
returns cannot be earned without taking greater risk. But, taking
greater risk will increase R, so g cannot
be increased without raising R.
Note that, from the equation itself, we can see that the growth
rate must be less than the required return
else the denominator will be negative leading to a negative—
and impossible—stock price

7-22
Nonconstant Growth
• Suppose a firm is expected to increase dividends by
20% in one year and by 15% in two years.
• After that, dividends will increase at a rate of 5% per
year indefinitely.
• If the last dividend was $1 and the required return is
20%, what is the price of the stock?
• Remember that we have to find the PV of all
expected future dividends.
This situation is quite common, especially among younger,
startup companies that may experience a high
growth

7-23
R1
D
. . .
R1
D
R1
D
R1
D

P̂
3
3
2
2
1
1
0
Nonconstant + Constant
growth
gR
D
P̂ 1t
t
Basic PV of all Future Dividends Formula

7-24
2
2
2
1
1
0
)R1(
P
R1
D
R1
D
P̂

gR
D
P
then 2,t after constant g If
)R1(
D
P Because
3
2
3t
t
t
2

Nonconstant + Constant growth
Slide 25
7-25
0 1 2 3R = 20%
= P0
g = 20% g = 15% g = 5%
D0 = 1.00 D1 D2 D3
D3P2 =
^
R – g
Nonconstant growth followed
by constant growth:

7-26
Nonconstant Growth –
Solution
• Compute the dividends until growth levels off
$1.449
• Find the expected future price at the beginning of
the constant growth period:

– g) = 1.449 / (.2 - .05) = 9.66
• Find the present value of the expected future cash
flows
2 + (9.66) / (1.2)2 = 8.67
Calculator: CF0 = 0; C01 = 1.20; F01 = 1; C02 = 11.04 (=1.38 +
9.66); F02 =
1; NPV; I = 20; CPT NPV = 8.67
P2 is the value, at year 2, of all expected dividends year 3 on.
The final step is exactly the same as the 2-period example at the
beginning of the chapter. We can look at
it as if we buy the stock today and receive the $1.20 dividend in
1 year, receive the $1.38 dividend in 2

years and then immediately sell it for $9.66.
Slide 27
7-27
0
1.0000
0.9583
6.7083
1 2 3R = 20%
8.6667 = P0

g = 20% g = 15% g = 5%
D0 = 1.00 1.20 1.38 1.449
$1.449
P2 =
^
0.20 – 0.05
= $9.66
Nonconstant growth followed
by constant growth:
Slide 28
7-28

Quick Quiz: Part 1
• What is the value of a stock that is expected to pay
a constant dividend of $2 per year if the required
return is 15%?
• What if the company starts increasing dividends by
3% per year beginning with the next dividend? The
required return remains at 15%.
33.13$
15.
00.2
P
0
17.17$

03.15.
)03.1(00.2
P
0
Slide 29
7-29
Finding the Required Return
Example

• A firm’s stock is selling for $10.50. They
just paid a $1 dividend and dividends
are expected to grow at 5% per year.
• What is the required return?
Slide 30
7-30
Using the DGM to Find R
Start with the DGM:

g
P
D
g
P
g)1(D
R
g-R
D
g - R
g)1(D
P
0
1
0

0
10
0
Rearrange and solve for R:
Rearrange P0 = D1 ⁄ (R − g) to find R:
R = (D1 ⁄ P0 ) + g

Dividend yield = D1 ⁄ P0
Capital gains yield = g, and
R = Dividend yield + Capital gains yield
Slide 31
7-31
Finding the Required Return
Example
• P0 = $10.50
• D0 = $1

• g = 5% per year
• What is the dividend
yield?
1(1.05) / 10.50 = 10%
• What is the capital gains
yield?
g = 5%
Dividend Capital Gains
Yield Yield
%1505.
10.50
1.00(1.05)
R
g
P
D

7-32
Stock Valuation Using Multiples
• For stocks that don’t pay dividends (or have erratic
dividend growth rates), we can value them using the
price-earnings (PE) ratio and/or the price-sales ratio:
(multiply a benchmark PE ratio by earnings per share (EPS) to
come up
with a stock price)
Price at time t = Pt
= Benchmark PE ratio X Earnings per sharet

Price at time t = Pt
= Benchmark price-sales ratio X Sales per sharet
• The price-sales ratio can be especially useful when earnings
are
negative.
How to find PE?
Benchmark PE come from similar companies (Industry average)
or from a firm’s historical values.
The price-sales ratio is often used to value newer companies
that do not pay dividends and are not yet
profitable (meaning that earnings are negative).

7-33
Stock Valuation Using Multiples
Example
• Suppose we are trying to value the company Inactivision,
a video game developer that does not pay dividends. If
the appropriate industry PE for this type of company is
20 and you predict earnings to be $2.50 per share for the
coming year, then the forecasted stock price for a year
from now, or target price, is the following:
Target price = 20 x $2.50 = $50

7-34
Table 7.1
Slide 35
7-35
Features of Common Stock
• Voting Rights
– Stockholders elect directors

– Cumulative voting vs. Straight voting
– Boards are often staggered, or “classified”
– Proxy voting
• Classes of stock
– Founders’ shares
– Class A and Class B shares
Shareholders have the right to elect the board of directors and
vote on other important issues.
Cumulative voting—when the directors are all elected at once.
Total votes that each shareholder may cast
equals the number of shares times the number of directors to be
elected. In general, if N directors are to be
elected, it takes 1 / (N + 1) percent of the stock + 1 share to
assure a deciding vote for one directorship.

Increases the likelihood of minority shareholder representation
on the board.
Straight (majority) voting—the directors are elected one at a
time, and every share gets one vote. Can
freeze out minority shareholders.
Staggered elections—directors’ terms are rotated so they aren’t
elected at the same time. This makes it
harder for a minority to elect a director and complicates
takeovers.
A staggered board is a governance practice in which only a
fraction (typically a third) of the members of
the board of directors is elected each year, rather than all.
A staggered board consists of a board of director whose
members are grouped into classes; for example,
Class 1, Class 2, Class 3, etc.

Proxy voting—grant of authority by a shareholder to someone
else to vote his or her shares. A proxy fight
is a struggle between management and outsiders for control of
the board, waged by soliciting
shareholders’ proxies.
Shareholders can come to the annual meeting and vote in
person, or they can transfer their right to vote to
another party.
Different classes of stock can have different rights. Owners may
want to issue a nonvoting class of stock
if they want to make sure that they maintain control of the firm.
Ford Motor Company has always had two classes of stock: Class
B or “Founders’ Shares” are owned by

the Ford family and carry 40% of the voting rights though they
represent only 10% of the shares
outstanding.
Google has Class A shares that are publicly traded and carry
one vote per share. Class B shares are held
by insiders and carry 10 votes per share.
Slide 36
7-36
Features of Common Stock
• Other Rights
– Share proportionally in declared dividends
– Share proportionally in remaining assets
during liquidation

– Preemptive right
• Right of first refusal to buy new stock issue to
maintain proportional ownership if desired
Other rights usually include:
Sharing proportionately in dividends paid.
Sharing proportionately in any liquidation value.
Voting on matters of importance (e.g., mergers).
The right to purchase any new stock sold – the preemptive right.
In addition to the right to vote for directors, shareholders
usually have the following rights:
1. The right to share proportionally in dividends paid.

2. The right to share proportionally in assets remaining after
liabilities have been paid in a liquidation.
Essentially, a preemptive right means that a company that
wishes to sell stock must first offer it to the
existing stockholders before offering it to the general public
Slide 37
7-37
Dividend Characteristics
• Dividends are not a liability of the firm until
declared by the Board of Directors

dividends
• Dividends and Taxes
expense; therefore, they are not tax deductible.
idends received by individuals
depends on the holding period.
minimum 70% exclusion from taxable income.
Characteristics of dividends:
• Payment of dividends is at the discretion of the board. A firm
cannot default on an undeclared
dividend, nor can it be forced to file for bankruptcy because of
nonpayment of dividends.
• Dividends are not tax deductible for the paying firm.
• Dividends received by individuals are taxed based on the
holding period of the stock, while dividends

received by a corporation are at least 70% tax-exempt.
Dividend exclusion: If corporation A owns less than 20% of
corporation B stock, then 30% of the
dividends received from corporation B are taxable. If A owns
between 20% and 80% of B, then 20% of
the dividends received are taxable. If A owns more than 80%, a
consolidated statement can be filed and
dividends received from B are essentially untaxed.
Slide 38

7-38
Features of Preferred Stock
• Dividends
Stated dividend that must be paid before dividends can be
paid to common stockholders
dividends can be deferred indefinitely.
– any missed
preferred dividends have to be paid before common
dividends can be paid.
• Preferred stock generally does not carry
voting rights
Preferred stock is similar to bonds since interest payments on
bonds are quite similar to dividends on

preferred stock. The difference is that most of the bonds have a
finite maturity while preferred stock pays
a constant dividend in perpetuity. Its dividend is usually fixed,
and the stock is often without voting
rights. Preferred stock has a state liquidating value, usually,
$100 per share and it pays a cash dividend
expressed in terms of dollars per share. (e.g., Google' "$7
preferred," paying an annual cash dividend of
$7, translates to a dividend yield of 7% of stated liquidating
value). The stated value is the value paid to
preferred stockholders in the event of liquidation.
Cumulative dividends – current preferred dividend plus all
arrearages (unpaid dividends) to be paid
before common stock dividends can be paid. Non-cumulative
dividend preferred stock does not have this

feature.
Preferred stock represents equity in the firm, but has many
features of debt, including a stated yield,
preference in terms of cash flows and liquidation, and some
issues are callable and/or convertible into
common shares.
Corporations that own stock in other corporations are permitted
to exclude 50 percent of the dividend
amounts they receive and are taxed on only the remaining 50
percent (the 50 percent exclusion was
reduced from 70 percent by the Tax Cuts and Jobs Act of 2017).

7-39
The Stock Markets
• Primary vs. Secondary Markets
-issue market
investors
• Dealers vs. Brokers
Ready to buy or sell at any time
Think “Used car dealer”
Think “Real estate broker”

Primary market – the market in which new securities are
originally sold to investors
Secondary market – the market in which existing securities
trade among investors
A dealer is an agent who buys and sells securities from
inventory. In contrast, a broker is an agent who
brings buyers and sellers together but does not maintain an
inventory (An agent who arranges
security transactions among investors).
Bid price – the price at which a dealer is willing to buy a
security
Ask price – the price at which a dealer is willing to sell a
security
Spread – the difference between the bid and ask prices

7-40
• Dealers vs. Brokers
• New York Stock Exchange
(NYSE: https://www.nyse.com/index)
• Designated market makers (DMMs)
• Floor brokers
• Supplemental liquidity providers (SLPs)

Stock Market
Organization of the NYSE:
Prior to 2006, the exchange consisted of 1,366 members, said to
own seats. Since going public, there are
1,366 licensees who pay an annual fee to trade.
• DMMs, formerly known as “specialists,” act as dealers in
particular stocks. A DMM maintains an
inventory and stands ready to trade at quoted bid (DMM posts
the price at which they will buy) and
ask (DMM posts the price at which they will sell) prices. They
make their profit from the difference

between the bid and ask prices, called the bid-ask spread. The
smaller the spread, the more competition
and the more liquid the stock. The move to decimalization
allows for a smaller bid-ask spread. There
will be more discussion of this later.
• DMM’s post – fixed place on the exchange floor where the
specialist operates
• Trading in the crowd – trading that occurs directly between
floor brokers around the DMM’s post
• Floor broker: a broker matches buyers and sellers. They
perform the search function for a fee
(commission). They do not hold an inventory of securities.
• Floor traders: those who trade for their own accounts, trying
to anticipate and profit from temporary
price fluctuations

• SLPs: investment firms that agree to be active participants in
stocks assigned to them. They trade
purely for their own accounts. Unlike DMMs and floor brokers,
SLPs do not operate on the floor of
the stock exchange.
• Order flow – the flow of customer orders to buy and sell
securities
Slide 41
7-41
• Not a physical exchange – computer-based
quotation system

• Multiple market makers
• Electronic Communications Networks
• Three levels of information
– median quotes, registered representatives
– view quotes, brokers, and dealers
– view and update quotes, dealers only
• Large portion of technology stocks
NASDAQ
NYSE operations represent a premier example of the trading of
“listed” securities. Nasdaq operations, on
the other hand, represent the evolution of “over-the-counter”
trading of securities that do not rely on a
physical market place.

Nasdaq – National Association of Securities Dealers Automated
Quotation system – computer network of
securities dealers who disseminate timely security price quotes
to Nasdaq subscribers
The NASDAQ market site in Times Square is NOT an exchange.
It is just offices and basically a place for
reporters to report on what is happening with Nasdaq stocks.
Slide 1
6-1

Key Concepts and Skills
• Know the important bond features and
bond types
• Understand:
– Bond values and why they fluctuate
– Bond ratings and what they mean
– The impact of inflation on interest rates
– The term structure of interest rates and
the determinants of bond yields
When a corporation (or government) wishes to borrow money
from the public on a long-term basis, it
usually does so by issuing, or selling, debt securities that are
generically called bonds. In this Module, we

learn the various features of corporate bonds and some of the
terminology associated with bonds. We then
discuss the cash flows associated with a bond and how bonds
can be valued using our discounted cash flow
procedure.
Slide 2
6-2
Bond Definitions
• Bond
– Debt contract

– Interest-only loan
• Par value (face value) ~ $1,000
• Coupon rate
• Coupon payment
• Maturity date
• Yield to maturity
A bond is normally an interest-only loan, meaning that the
borrower will pay the interest every period, but
none of the principal will be repaid until the end of the loan.
The amount that will be repaid at the end of
the loan is called the bond's face value or par value. As in our
example, this par value is usually $1,000
for corporate bonds. The annual coupon divided by the face
value is called the coupon rate. The number

of years until the face value is paid is called the bond's time to
maturity. To determine the value of a bond
at a particular point in time, we need to know the number of
periods remaining until maturity, the face value,
the coupon, and the market interest rate for bonds with similar
features. This interest rate required in the
market on a bond is called the bond's yield to maturity (YTM).
Yield to maturity, required return, and
market rate are used interchangeably.
Coupon payment = Coupon rate X Par value
Note: Although the majority of corporate bonds have a $1,000
face value, there are an increasing number
of “baby bonds” outstanding, i.e., bonds with face values less
than $1,000. The use of the term “baby bond”

goes back at least as far as 1970, when it was used in
connection with AT&T’s announcement of the intent
to issue bonds with low face values. It was also used in
describing Merrill Lynch’s 1983 program to issue
bonds with $25 face values. More recently, the term has come to
mean bonds issued in lieu of interest
payments by firms unable to make the payments in cash. Baby
bonds issued under these circumstances are
also called “PIK” (payment-in-kind) bonds, or “bunny” bonds,
because they tend to proliferate in LBO
circumstances.
Slide 3
6-3

Bond Value
• Bond Value = PV of coupons + PV of par
• Bond Value = PV of annuity + PV of lump sum
• As interest rates increase, present values decrease.
• So, as interest rates increase, bond prices decrease
and vice versa.
The cash flows from a bond are the coupons and the face value.
The value of a bond (market price) is the
present value of the expected cash flows discounted at the
market rate of interest. Yield to maturity (YTM)
– the required market rate or return, or rate that makes the
discounted cash flows from a bond equal to the
bond’s market price

As time passes, interest rates change in the marketplace. The
cash flows from a bond, however, stay the
same. As a result, the value of the bond will fluctuate. When
interest rates rise, the present value of the
bond's remaining cash flows declines, and the bond is worth
less. When interest rates fall, the bond is
worth more.
Slide 4
6-4
The Bond-Pricing Equation
t

t
YTM)(1
F
YTM
YTM)(1
1
1-
C ValueBond
+
+

+
=
PV(Annuity) PV(lump sum)
C = Coupon payment; F = Face value

6-5
Valuing a Discount Bond with Annual
Coupons
• Consider a bond with a coupon rate of
10% and annual coupons. The par value
is $1,000, and the bond has 5 years to
maturity. The yield to maturity is 11%.
What is the value of the bond?
7-5
Slide 6

6-6
Valuing a Discount Bond with
Annual Coupons
• Coupon rate = 10%
• Annual coupons
• Par = $1,000
• Maturity = 5 years
• YTM = 11%
5
5
)11.1(
1000

−
=
Using the formula:
B = PV(annuity) + PV(lump sum)
B = 369.59 + 593.45 = 963.04
Using the calculator:
5 N
11 I/Y
100 PMT
1000 FV
CPT PV = -963.04
Bond”

Remember the sign convention on the calculator. The easy way
to remember it with bonds is we pay the
PV (-) so that we can receive the PMT (+) and the FV(+).
Discount bond – a bond that sells for less than its par value.
This is the case when the YTM is greater than
the coupon rate.
The coupon rate and the face value are fixed by the bond
indenture when the bond is issued (except for
floating-rate bonds). Therefore, the expected cash flows don’t
change during the life of the bond. However,
the bond price will change as interest rates change and as the
bond approaches maturity.

6-7
Valuing a Premium Bond with Annual
Coupons
• Suppose you are reviewing a bond that
has a 10% annual coupon and a face
value of $1000. There are 20 years to
maturity, and the yield to maturity is 8%.
What is the price of this bond?
7-7

6-8
Valuing a Premium Bond with
Annual Coupons
• Coupon rate = 10%
• Annual coupons
• Par = $1,000
• YTM = 8%
20
20

)08.1(
1000
08.0
)08.1(
1
1
100 +

−
=B
Using the formula:
B = PV(annuity) + PV(lump sum)
B = 981.81 + 214.55 = 1196.36
Bond”
20 N
8 I/Y

100 PMT
1000 FV
CPT PV = -1196.36
Premium bond – a bond that sells for more than its par value.
This is the case when the YTM is less than
the coupon rate.
Slide 9
6-9
Graphical Relationship Between
Price and Yield-to-maturity

600
700
800
900
1000
1100
1200
1300
1400
1500
0% 2% 4% 6% 8% 10% 12% 14%
B
o

n
d
P
ri
c
e
Yield-to-maturity
Negative relation between Bond Price (PV) and YTM (I/Y).
Slide 10
6-10

Bond Prices:
Relationship Between Coupon and Yield
• If YTM = coupon rate, then par value = bond price
• If YTM > coupon rate, then par value > bond price
▪ Why? The discount provides yield above coupon rate.
▪ Price below par value, called a discount bond
• If YTM < coupon rate, then par value < bond price
▪ Why? Higher coupon rate causes value above par.
▪ Price above par value, called a premium bond
There are the purely mechanical reasons for these results. We
know that present values decrease as rates
increase. Therefore, if we increase our yield above the coupon,
the present value (price) must decrease

below par. On the other hand, if we decrease our yield below
the coupon, the present value (price) must
increase above par.
Slide 11
6-11
The Bond-Pricing Equation
Adjusted for Semi-annual Coupons
2t
2t
YTM/2)(1

F
YTM/2
YTM/2)(1
1
-1
2
C
ValueBond
+
+

+
=
-annual coupon
-annual
YTM
-month
periods to maturity
In practice, bonds issued in the United States usually make

coupon payments twice a year
Slide 12
6-12
Example
• If an ordinary bond has a coupon rate of
14 percent, then the owner will get a total
of $140 per year, but this $140 will come in
two payments of $70 each. The yield to
maturity is quoted at 16 percent. The bond

matures in seven years.
• How many coupon payments are there?
• What is the semiannual coupon payment?
• What is the semiannual yield?
• What is the bond price?
Slide 13
6-13
Semiannual Bonds
• Coupon rate = 14% - Semiannual

• YTM = 16% (APR)
– Number of coupon payments? (2t or N)
• 14 = 2 x 7 years
– Semiannual coupon payment? (C/2 or PMT)
• $70 = (14% x 1000)/2
– Semiannual yield? (YTM/2 or I/Y)
• 8% = 16%/2
Note: Bond yields are quoted like APRs; the quoted rate is
equal to the actual rate per period multiplied by
the number of periods.
Coupon rate = 14%, semiannual coupons

YTM = 16%
Maturity = 7 years
Par value = $1,000
Slide 14
6-14
Example 7.1
• Semiannual coupon = $70
• Semiannual yield = 8%
• Periods to maturity = 14

• Bond value =
• 70[1 – 1/(1.08)14] / .08 + 1000
/ (1.08)14 = 917.56
( )
( )2t
2t
2
YTM1
F
2
YTM
2
YTM1
1
-1

+
=
14
14
)08.1(
1000
08.0
)08.1(
1
1
70B +

−
=
14 N
8 I/Y
70 PMT

1000 FV
CPT PV = -917.56
Slide 15
6-15
Interest Rate Risk
• Price Risk
▪ Change in price due to changes in interest rates
▪ Long-term bonds have more price risk than short-term bonds.
▪ Low coupon rate bonds have more price risk than high coupon
rate

bonds.
• Reinvestment Rate Risk
▪ Uncertainty concerning rates at which cash flows can be
reinvested
▪ Short-term bonds have more reinvestment rate risk than long-
term
bonds.
▪ High coupon rate bonds have more reinvestment rate risk than
low
coupon rate bonds.
The risk that arises for bond owners from fluctuating interest
rates is called interest rate risk. How much
interest rate risk a bond has depends on how sensitive its price
is to interest rate changes. This sensitivity
directly depends on two things: the time to maturity and the
coupon rate. As we will see momentarily, you
should keep the following in mind when looking at a bond:

All other things being equal, the longer the time to maturity, the
greater the interest rate risk.
All other things being equal, the lower the coupon rate, the
greater the interest rate risk.
If we compared a 10-year bond to a 1-year bond, we would see
that the 10-year bond has much greater
interest rate risk. However, if you were to compare a 20-year
bond to a 30-year bond, you would find that
the 30-year bond has somewhat greater interest rate risk because
it has a longer maturity, but the difference
in the risk would be fairly small.
The value of a bond depends on the present value of its
coupons. As a result, all other things being equal,
its value will fluctuate more as interest rates change. Put

another way, the bond with the higher coupon has
a larger cash flow early in its life, so its value is less sensitive
to changes in the discount rate.
Bonds are usually not issued with maturities longer than 30
years. However, low interest rates have led to
the issuance of bonds with much longer maturities. In the
1990s, Walt Disney issued “Sleeping Beauty”
bonds with a 100-year maturity. This company wanted to lock in
the historically low interest rates for a
long time.
One potentially undesirable feature of high-coupon bonds is the
required reinvestment of coupons at the
computed yield-to-maturity if one is to actually earn that yield.
Those who purchased bonds in the early
1980s (when even high-grade corporate bonds had coupons over

11%) found, to their dismay, that interest
payments could not be reinvested at similar rates a few years
later without taking greater risk. A good
example of the trade-off between interest rate risk and
reinvestment risk is the purchase of a zero-coupon
bond – one eliminates reinvestment risk but maximizes interest-
rate risk.
Slide 16
6-16
Figure 7.2

6-17
• Yield to Maturity (YTM) is the rate implied by the
current bond price.
• Finding the YTM requires trial and error if you do
not have a financial calculator and is similar to
the process for finding r with an annuity.
• If you have a financial calculator, enter N, PV,
PMT, and FV, remembering the sign convention
(PMT and FV need to have the same sign, PV the
opposite sign.)
Computing Yield to Maturity

6-18
YTM with Annual Coupons
Consider a bond with a 10% annual coupon
rate, 15 years to maturity and a par value of
$1000. The current price is $928.09.
– Will the yield be more or less than 10%?
15 N
928.09 PV (enter as a negative)
1000 FV
100 PMT

The YTM is more than the coupon since the price is less than
par.
Slide 19
6-19
YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rate and
semiannual coupons, has a face value of
$1000, 20 years to maturity and is selling for

$1197.93.
– Is the YTM more or less than 10%?
– What is the semiannual coupon payment?
– How many periods are there?
Slide 20
6-20
YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rate and
semiannual coupons, has a face value of $1,000, 20
years to maturity and is selling for $1,197.93.

40 N
1197.93 PV (negative)
1000 FV
50 PMT
CPT PV 4% (= ½ YTM)
YTM = 4%*2 = 8%
NOTE: Solving a semi-
annual payer for YTM
results in a 6-month yield.
The calculator & Excel
solve what you enter.

The 4% value is the 6-month interest rate. YTM is an annual
rate.
Slide 21
6-21
The Bond Indenture
“Deed of Trust”
Contract between issuing company and
bondholders includes:
– Basic terms of the bonds
– Total amount of bonds issued
– Secured versus Unsecured

– Sinking fund provisions
– Call provisions
• Deferred call
• Call premium
– Details of protective covenants
The bond indenture is the written legal agreement between the
corporation (the borrower) and its creditors.
It can run several hundred pages.
• Sinking fund—an account managed by the bond trustee for
early redemption. Reduces risk of
default, but bondholders may not receive all of expected
coupons.
• Call provision—allows company to “call” or repurchase part

or all of issue.
• Call premium—amount by which the call price exceeds the par
value.
• Deferred call—firm cannot call bonds for a designated period.
• Protective covenants – indenture conditions that limit the
actions of firms.
Slide 22
6-22
The Bond Indenture

Many of these features will be detailed in the bond indenture.
Slide 23
6-23
Bond Classifications
• Registered vs. Bearer Bonds
• Security
▪ Collateral – secured by financial securities
▪ Mortgage – secured by real property, normally
land or buildings
▪ Debentures – unsecured
▪ Notes – unsecured debt with original maturity

less than 10 years
• Seniority
– Senior versus Junior, Subordinated
Corporate bonds are usually in registered form: company has a
registrar who will record the ownership of
each bond and record any changes in ownership. The company
will pay the interest and principal directly
to the owner of record. The bond could be in bearer form.: A
bond issued without record of the owner's
name; payment is made to whomever holds the bond. This
means that the certificate is the basic evidence
of ownership, and the corporation will “pay the bearer.”
Ownership is not otherwise recorded, and, as with
a registered bond with attached coupons, the holder of the bond
certificate detaches the coupons and sends
them to the company to receive payment. There are two

drawbacks to bearer bonds. First, they are difficult
to recover if they are lost or stolen. But they are now much less
common (in the United States) than
registered bonds.
Debt securities are classified according to the collateral and
mortgages used to protect the bondholder.
Collateral is a general term that frequently means securities (for
example, bonds and stocks). A debenture
is an unsecured bond, for which no specific pledge of property
is made. This is standard terminology in the
US – but it may not transfer to other countries. For example,
debentures are secured debt in the United
Kingdom.
Note: Since bearer bonds are not registered with the
corporation, it is easier for bondholders to receive

interest payments without reporting them on their income tax
returns. In an attempt to eliminate this
potential for tax evasion, all bonds issued in the US after July
1983 must be in registered form. It is still
legal to offer bearer bonds in some other nations, however.
Some foreign bonds are popular among
international investors particularly due to their bearer status.
Seniority In general terms, seniority indicates preference in
position over other lenders, and debts are
sometimes labeled as senior or junior to indicate seniority.
Seniority—order of precedence of claims in the event of
bankruptcy. Senior debt is paid first. Junior or
subordinated debt is lower in priority.
In the event of default, holders of subordinated debt must give

preference to other specified creditors.
Slide 24
6-24
Bond Characteristics and
Required Returns
• Coupon rate
–
– Usually ≈ yield at issue
• Which bonds will have the higher coupon, all
else equal?
– Secured debt versus a debenture
– Subordinated debenture versus senior debt

– A bond with a sinking fund versus one without
– A callable bond versus a non-callable bond
Higher coupons:
Debenture—secured debt is less risky because the income from
the security is used to pay it off first.
Subordinated debenture—will be paid after the senior debt.
Bond without sinking fund—company has to come up with
substantial cash at maturity to retire debt, and
this is riskier than systematic retirement of debt through time.
Callable bond—call potential is unattractive to investors. Debt
is usually purchased with the expectation of
receiving periodic coupon payments for many years. If a bond
is called before maturity, the coupon stream
stops. Bondholders bear the risk of the bond being called early,

usually when rates are lower. They don’t
receive all of the expected coupons and they have to reinvest at
lower rates.
Slide 25
6-25
Bond Ratings – Investment
Quality
Investment grade
• High Grade
– Moody’s Aaa and S&P AAA – capacity to pay is extremely

strong
– Moody’s Aa and S&P AA – capacity to pay is very strong
• Medium Grade
– Moody’s A and S&P A – capacity to pay is strong, but
more susceptible to changes in circumstances
– Moody’s Baa and S&P BBB – capacity to pay is adequate,
adverse conditions will have more impact on the firm’s
ability to pay
Debt ratings are an assessment of the credit worthiness of the
corporate issuer. Bond ratings are important
to a firm because a higher rating indicates lower default risk
and translates into a lower coupon rate
Firms typically pay rating agencies to have a bond issue rated.
The major rating agencies are Moody’s,

Standard & Poor’s, and Fitch. The rating categories of the three
agencies are similar, dividing bonds into
two main groups: investment grade and speculative grade.
Investment-grade bonds have the lowest degree of default risk
(rated at least BBB by S&P or Baa by
Moody's).
The question sometimes arises as to why a potential issuer
would be willing to pay rating agencies tens of
thousands of dollars in order to receive a rating, especially
given the possibility that the resulting rating
could be less favorable than expected.

6-26
Bond Ratings - Speculative
speculative grade
• Low Grade
– Moody’s Ba, B, Caa and Ca
– S&P BB, B, CCC, CC
– Considered speculative with respect to capacity
to pay. The “B” ratings are the lowest degree
of speculation.
• Very Low Grade
– Moody’s C and S&P C – income bonds with no
interest being paid

– Moody’s D and S&P D – in default with principal
and interest in arrears
Speculative grade bonds are also called “junk” bonds.
A bond's credit rating can change as the issuer's financial
strength. Bonds that drop into junk territory from
above are called “fallen angels.”
Slide 27
6-27
• Treasury Securities
▪ Federal government debt

▪ T-bills – pure discount bonds with original maturity of one
year or
less
▪ T-notes – coupon debt with original maturity between one and
ten years
▪ T-bonds – coupon debt with original maturity greater than ten
years
• Municipal Securities
▪ Debt of state and local governments
▪ Varying degrees of default risk, rated similar to corporate debt
▪ Interest received is tax-exempt at the federal level.
Government Bonds
Long-term debt instruments issued by a governmental entity.
Treasury bonds are bonds issued by a federal

government; a state or local government issues municipal bonds
(munis).
Municipal securities (munis) - varying degrees of default risk,
and, in fact, they are rated much like
corporate issues. Also, they are almost always callable. The
most intriguing thing about munis is that their
coupons are exempt from federal income taxes (though not
necessarily state income taxes), which makes
them very attractive to high-income, high–tax bracket investors.
Slide 28
6-28

Example
A taxable bond has a yield of 8% and a
municipal bond has a yield of 6%
• If you are in a 40% tax bracket, which bond do
you prefer?
▪ 8%(1 - .4) = 4.8%
▪ The after-tax return on the corporate bond is 4.8%,
compared to a 6% return on the municipal
• At what tax rate would you be indifferent
between the two bonds?
▪ 8%(1 – T) = 6%
▪ T = 25%
You should be willing to accept a lower stated yield on
municipals because you do not have to pay taxes

on the interest received. Why are you willing to accept a lower
rate of interest? It may be helpful to take
the example and illustrate the indifference point using dollars
instead of just percentages. The discount you
are willing to accept depends on your tax bracket.
Consider a taxable bond with a yield of 8% and a tax-exempt
municipal bond with a yield of 6%.
Suppose you own one $1,000 bond in each and both bonds are
selling at par. You receive $80 per year
from the corporate and $60 per year from the municipal. How
much do you have after taxes if you are in
the 40% tax bracket? Corporate: 80 – 80(.4) = 48; Municipal =
60
Why should the federal government exempt munis from

taxation? It provides an incentive for local
governments to raise capital on their own.
Slide 29
6-29
Treasury Quotations
Figure 6.3 shows a portion of the daily Treasury note and bond
listings from The Wall Street Journal online.
The only difference between a Treasury note and a Treasury
bond is that notes have 10 years or less to

maturity at the time of issuance. The entry that begins
“05/15/2030” is highlighted. Reading from left to
right, the “05/15/2030” tells us that the bond's maturity is May
15, 2030. The 6.250 is the bond's coupon
rate. Treasury bonds all make semiannual payments and have a
face value of $1,000, so this bond will pay
$31.25 per six months until it matures.
The difference between the two prices is called the bid-ask
spread (or just “spread”), and it represents the
dealer's profit. The bid price, or what a dealer is willing to pay
for the bond, on the 05/15/2030 bond is
150.7188. With a $1,000 face value, this quote represents
$1,507.188. The asked price, or the price at which
the dealer is willing to sell the bond, is 150.7500, or
$1,507.500. The next number quoted is the change in
the asked price from the previous day, measured as a percentage

of face value, so this issue's asked price
rose by .8906 percent, or $8.906, in value from the previous
day. Finally, the last number reported is the
yield to maturity, based on the asked price. Notice that this is a
premium bond because it sells for more than
its face value.
Slide 30
6-30
Zero Coupon Bonds
• Make no periodic interest payments (coupon
rate = 0%)

• Entire yield-to-maturity comes from the
difference between the purchase price and
the par value (capital gains)
• Cannot sell for more than par value
• Sometimes called zeroes, or deep discount
bonds
• Treasury Bills and U.S. Savings bonds are good
examples of zeroes
A bond that pays no coupons at all must be offered at a price
that is much lower than its stated value. Such
bonds are called zero coupon bonds, or just zeroes. Zero-coupon
bonds are bonds that are offered at deep
discounts because there are no periodic coupon payments.

6-31
Floating Rate Bonds
• Coupon rate floats depending on some index
value
• Examples – adjustable rate mortgages and
inflation-linked Treasuries
• Less price risk with floating rate bonds
– Coupon floats, so is less likely to differ
substantially from the yield-to-maturity
• Coupons may have a “collar” – the rate cannot go
above a specified “ceiling” or below a specified
“floor”

The conventional bonds we have talked about in this module
have fixed-dollar obligations because the
coupon rate is set as a fixed percentage of the par value.
Similarly, the principal is set equal to the par value.
With floating-rate bonds (floaters), the coupon payments are
adjustable. Adjustments are tied to an interest
rate index such as the Treasury bill interest rate or the 30-year
Treasury bond rate.
The coupon rate has a floor and a ceiling, meaning that the
coupon is subject to a minimum and a maximum.
The coupon rate is said to be “capped,” and the upper and lower
rates are sometimes called the collar.
Whereas there is less price risk, there is greater reinvestment
(or refinancing) risk.

6-32
Other Bond Types
• Structured notes
based on stocks, bonds, commodities, or currencies
• Convertible bonds
can be swapped for a fixed number of shares of stock
anytime before maturity at the holder's option
• Put bonds
force the issuer to buy the bond back at a stated price
• Catastrophe bonds

• Income bonds
Structured notes are bonds that are based on stocks, bonds,
commodities, or currencies. One particular type
of structured note has a return based on a stock market index.
At expiration, if the stock index has declined,
the bond returns the principal. However, if the stock index has
increased, the bond will return a portion of
the stock index return, say 80 percent. Another type of
structured note will return twice the stock index
return, but with the potential for loss of principal.
Convertible bonds – bonds can be converted into shares of
common stock at the bondholders discretion
Lower required return.

Put bond – bondholder can force the company to buy the bond
back prior to maturity Lower required return.
Catastrophe bonds – issued by property and casualty companies.
Pay interest and principal as usual unless
claims reach a certain threshold for a single disaster. At that
point, bondholders may lose all remaining
payments. Higher required return
Income bonds – coupon payments depend on level of corporate
income. If earnings are not enough to cover
the interest payment, it is not owed. Higher required return
There are many other types of provisions that can be added to a
bond and many bonds have several
provisions – it is important to recognize how these provisions
affect required returns

6-33
Bond Markets
• Primarily over-the-counter transactions
with dealers connected electronically
• Extremely large number of bond issues,
but generally low daily volume in single
issues
• Getting up-to-date prices difficult,
particularly on small company or municipal
issues

• Treasury securities are an exception
There is no particular place where buying and selling occur.
Instead, dealers around the country (and around
the world) stand ready to buy and sell. The various dealers are
connected electronically.
Because the bond market is almost entirely OTC, it has
historically had little or no transparency. A financial
market is transparent if it is possible to easily observe its prices
and trading volume. On the New York
Stock Exchange, for example, it is possible to see the price and
quantity for every single transaction. In
contrast, in the bond market, it is often not possible to observe
either. Transactions are privately negotiated
between parties, and there is little or no centralized reporting of
transactions.

Bonds are bought and sold in enormous quantities every day.
You may be surprised to learn that the trading
volume in bonds on a typical day is many, many times larger
than the trading volume in stocks
What is the largest securities market in the world? Most people
would guess the New York Stock Exchange.
In fact, the largest securities market in the world in terms of
trading volume is the U.S. Treasury market.
One reason the bond markets are so big is that the number of
bond issues far exceeds the number of stock
issues. There are two reasons for this. First, a corporation
would typically have only one common stock
issue outstanding. However, a single large corporation could
easily have a dozen or more note and bond
issues outstanding. Beyond this, federal, state, and local

borrowing is simply enormous. For example, even
a small city would usually have a wide variety of notes and
bonds outstanding,
Although the total volume of trading in bonds far exceeds that
in stocks, only a very small fraction of the
total bond issues that exist actually trade on a given day. This
fact, combined with the lack of transparency
in the bond market, means that getting up-to-date prices on
individual bonds is often difficult or impossible,
particularly for smaller corporate or municipal issues. Instead, a
variety of sources of estimated prices exist
and are very commonly used.
Slide 34

6-34
• Sukuk are bonds that have been created to
meet a demand for assets that comply with
Shariah, or Islamic law.
• Shariah does not permit the charging or
paying of interest.
• Sukuk are typically bought and held to
maturity, and they are extremely illiquid.
Sukuk
Bonds issued to comply with Sharia, or Islamic law, which does
not permit charging or paying interest.
The bonds typically confer partial ownership of some aspect of
the firm to the bondholder.

6-35
• Bond quotes are available online.
• One good site is FINRA’s Market Data Center
(http://finra-markets.morningstar.com/BondCenter/Default.jsp).
• Go to the site, choose a company, enter it in
the Issuer Name bar, choose Corporate,
and see what you can find!
Work the Web Example

6-36
Quoted Price vs. Invoice Price
• Quoted bond prices = “clean” price
– Net of accrued interest
• Invoice Price = “dirty” or “full” price
– Price actually paid
– Includes accrued interest
• Accrued Interest
– Interest earned since last coupon payment is
owed to bond seller at time of sale

If you buy a bond between coupon payment dates, the price you
pay is usually more than the price you are
quoted. The reason is that standard convention in the bond
market is to quote prices net of “accrued interest,”
meaning that accrued interest is deducted to arrive at the quoted
price. This quoted price is called the clean
price.
The price you actually pay, however, includes the accrued
interest. This price is the dirty price, also known
as the “full” or “invoice” price.
Example: Suppose the last coupon was paid 50 days ago and
there are 182 days in the current coupon period.
If the semiannual coupon payment is $40, then the accrued
interest would be (50 ⁄ 182) × 40 = $10.99. This

amount would be added to the quoted price to determine the
“dirty price.”
Suppose you buy a bond with a 12 percent annual coupon,
payable semiannually. You actually pay $1,080
for this bond, so $1,080 is the dirty, or invoice, price. Further,
on the day you buy it, the next coupon is due
in four months, so you are between coupon dates. Notice that
the next coupon will be $60. The accrued
interest on a bond is calculated by taking the fraction of the
coupon period that has passed, in this case two
months out of six, and multiplying this fraction by the next
coupon, $60. So, the accrued interest in this
example is 2/6 × $60 = $20. The bond's quoted price (i.e., its
clean price) would be $1,080 − 20 = $1,060.
Bond prices are traditionally quoted “clean” or without accrued
interest. If a bond is purchased (or sold)

between coupon payment dates, then any interest earned since
the last coupon payment is due to the holder
(seller) of the bond.
At the time of the exchange, accrued interest is computed and
added to the quoted price to arrive at the
“invoice price,” also called the “full” or “dirty” price.
Slide 37
6-37
Clean vs. Dirty Prices
• Clean price: quoted price
• Dirty price: price actually paid = quoted price plus accrued

interest
• Example: Consider a T-bond with a 4% semiannual yield
and a clean price of $1,282.50:
▪ Number of days since last coupon = 61
▪ Number of days in the coupon period = 184
▪ Accrued interest = (61/184)(.04*1000) = $13.26
▪ Dirty price = $1,282.50 + $13.26 = $1,295.76
• So, you would actually pay $ 1,295.76 for the bond
7-37
Assuming that the November maturity is November 15, then the
coupon dates would be November 15
and May 15. Therefore, July 15 would be 16 + 30 + 15 = 61
days since the last coupon

The number of days in the coupon period would be 16 + 30 + 31
+ 31 + 30 + 31 + 15 = 184
Slide 38
6-38
Inflation and Interest Rates
• Real rate of interest
=Change in purchasing power
• Nominal rate of interest
= Quoted rate of interest,
= Change in purchasing power and inflation

• The ex ante nominal rate of interest includes
our desired real rate of return plus an
adjustment for expected inflation
So far, we haven't considered the role of inflation in our various
discussions of interest rates, yields, and
returns. Because this is an important consideration, we consider
the impact of inflation next.
In examining interest rates, or any other financial market rates
such as discount rates, bond yields, rates of
return, and required returns, it is often necessary to distinguish
between real rates and nominal rates.
Nominal rates are called “nominal” because they have not been
adjusted for inflation. Real rates are rates
that have been adjusted for inflation.

6-39
The Fisher Effect
The Fisher Effect defines the relationship
between real rates, nominal rates and
inflation
(1 + R) = (1 + r)(1 + h)
R = nominal rate (Quoted rate)
r = real rate
h = expected inflation rate

Approximation: R ≈ r + h
The Fisher Effect is a theoretical relationship between nominal
returns, real returns, and the expected
inflation rate. Let R be the nominal rate, r the real rate, and h
the expected inflation rate.
The approximation works pretty well with “normal” real rates of
interest and expected inflation. If the
expected inflation rate is high, then there can be a substantial
difference.
It is important to note that financial rates, such as interest rates,
discount rates, and rates of return, are almost
always quoted in nominal terms.

6-40
Example
If we require a 10% real return and we
expect inflation to be 8%, what is the
nominal rate?
▪ R = (1.1)(1.08) – 1 = .188 = 18.8%
▪ Approximation: R = 10% + 8% = 18%
▪ Because the real return and expected inflation
are relatively high, there is significant

difference between the actual Fisher Effect
and the approximation.
Slide 41
6-41
• Term structure is the relationship between time to
maturity and yields, all else equal.
• It is important to recognize that we pull out the effect of
default risk, different coupons, etc.
• Yield curve – graphical representation of the term
structure

▪ Normal – upward-sloping; long-term yields are higher than
short-
term yields
▪ Inverted – downward-sloping; long-term yields are lower than
short-term yields
Term Structure of Interest Rates
Slide 42
6-42
Figure 7.6 – Upward-Sloping Yield
Curve

Term structure of interest rates – relationship between nominal
interest rates on default-free, pure discount
bonds and maturity
Inflation premium – portion of the nominal rate that is
compensation for expected inflation
Interest rate risk premium – reward for bearing interest rate risk
Slide 43
6-43
Figure 7.6 – Downward-Sloping Yield
Curve

Term structure of interest rates – relationship between nominal
interest rates on default-free, pure discount
bonds and maturity
Inflation premium – portion of the nominal rate that is
compensation for expected inflation
Interest rate risk premium – reward for bearing interest rate risk
Slide 44
6-44
Figure 7.7
Current yield curve

https://www.bloomberg.com/markets/rates-bonds/government-
bonds/us
Bloomberg to get the current Treasury yield curve
Slide 45
6-45
Factors Affecting Bond Yields
• Real rate of interest
• Expected future inflation premium
• Interest rate risk premium

• Default risk premium – bond ratings
• Taxability premium – municipal versus taxable
• Liquidity premium – bonds that have more frequent
trading will generally have lower required returns
• Maturity premium – longer term bonds will tend to have
higher required returns.
Anything else that affects the risk of the cash flows to the
bondholders will affect the required returns
If we combine all of the things we have discussed regarding
bond yields, we find that bond yields represent
the combined effect of no fewer than six things. The first is the
real rate of interest. On top of the real rate
are five premiums representing compensation for (1) expected
future inflation, (2) interest rate risk, (3)
default risk, (4) taxability, and (5) lack of liquidity. As a result,
determining the appropriate yield on a bond

requires careful analysis of each of these effects.
• Treasury yield curve – plot of yields on Treasury notes and
bonds relative to maturity
• Default risk premium – the portion of a nominal rate that
represents compensation for the possibility of
default
• Taxability premium – the portion of a nominal rate that
represents compensation for unfavorable tax
status
• Liquidity premium – the portion of a nominal rate that
represents compensation for lack of liquidity
Slide 46

6-46
• What is the price of a $1,000 par value bond with
a 6% coupon rate paid semiannually, if the bond
is priced to yield 5% and it has 9 years to
maturity?
• What would be the price of the bond if the yield
rose to 7%.
• What is the current yield on the bond if the YTM
is 7%?
Comprehensive Problem
5% YTM: 18 N; 2.5 I/Y; 30 PMT; 1,000 FV; CPT PV =
1,071.77
7% YTM: 18 N; 3.5 I/Y; 30 PMT; 1,000 FV; CPT PV = 934.05
Current yield = 60/934.05 = 6.42%

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