### FI 3300 * Chapter 9 Valuation of Stocks and Bonds

```Instructor: Ryan Williams
Learning Objectives
 Value a bond given its coupon rate, par value, yield-to-
maturity, time to maturity and payment frequency.
 Given all but one of the factors of a bond’s value, find
the remaining factor.
 Value a stock using the dividend discount model under
assumptions of constant growth and non-constant
growth.
 Given all but one of the factors of a stock’s value, find
the remaining factor.
Remember – different words for
the same thing
 Cost of capital (from firm’s point of view) = required
rate of return (from investor’s point of view) = interest
rate in problems.
 Cost of debt = investor’s required rate of return on
debt
 Cost of equity = investor’s required rate of return on
equity.
What is a financial security?
 It’s a contract between the provider of funds and
the user of funds.
 The contract specifies the:
 amount of money that has been provided
 terms & conditions of how the user is going to repay the
provider
 Provider: you (ordinary investor), the bank, venture
capitalist, etc.
 User: entrepreneur or firm with good business
idea/product but no (or not enough) money to execute the
idea.
TVM and valuing
financial securities
 To an investor who owns a financial security (a stock or a
bond), the security is a stream of future expected cash
flows.
 The value of any security is the Present Value of all the
future expected cash flows from owning the security,
discounted at the appropriate discount rate (required rate
of return).
 When we learn to value stocks and bonds later, we are just
applying TVM concepts we already know.
Common financial securities
Debt security
Equity security
1) Holder is a creditor of the firm.
No say in running of the firm.
1) Holder is an owner of the firm.
Have a say in running of the firm
(by voting).
2) Fixed payment.
2) Payment is not fixed. No
guaranteed cash flow from firm.
anything is paid to equity holders.
3) Receives what’s left over after
all debt holders/creditors are paid.
4) If firm cannot pay, debt holders
will take over ownership of firm
assets.
4) If firm cannot pay debt holders,
loses control of firm to debt
holders.
5) Limited liability.
5) Limited liability.
Types of debt securities
 Fixed-coupon bonds
 Zero-coupon bonds
 Consols (Perpetual bonds)
 Variable-rate bonds
 Income bonds
 Convertible bonds
 Callable bonds
Fixed coupon bonds
 Firm pays a fixed amount (‘coupon’) to the investor
every period until bond matures.
 At maturity, firm pays face value of the bond to
investor.
 Face value also called par value. Most common face
value is \$1000.
 Period: can be year, half-year (6 months), quarter (3
months).
General Motors 30 year bond
Par Value = \$1000
Interest paid Semi-annual
Interest Rate = 8%.
Zero coupon and consul bonds
Zero-coupon bond
 Zero coupon rate, no coupon paid during bond’s life.
 Bond holder receives one payment at maturity, the face
value.
Consol bond
 Pays a fixed coupon every period forever.
 Has no maturity.
Other types of bonds
 Variable-rate bond: Coupon rate is not fixed, but is tied to a
specific interest rate.
 Income bond: pays the coupon only when borrower’s
earnings are high enough.
 Convertible bond: allows holder to convert it to another
security, usually issuer’s common stock.
 Callable bond: issuer has the right to buy back the bond
(before maturity) at a predetermined price.
Equity securities
 Equity security means common stock.
 Common stock holders have control privileges, i.e., have a
say in firm’s operating decisions.
• Exercise control privileges by voting on matters of importance
facing the firm. Voting takes place during shareholder meetings.
 Board of directors: Elected by shareholders to make sure
management acts in the best interests of shareholders.
 Common stock holders can expect two types of cash flows:
 Dividends
 Money received from selling shares
Preferred Stock
 Owners of preferred stock are paid after payment to
debt holders, but before payment to equity holders.
 No maturity.
 Has stated par value and stated dividend.
• Firm can omit paying preferred stock dividend without
going into default.
 Usually non-voting.
Stock/Bond payoffs
 Pretend a firm only exists for one year, and debt has
face value of \$600,000. The distribution of funds is as
follows:
Total Profit
\$1,000,000
\$800,000
\$600,000
\$400,000
Profit to debt
holders
\$600,000
\$600,000
\$600,000
\$400,000
Profit to equity
holders
\$400,000
\$200,000
\$0
\$0
Securities Markets
 Securities markets: markets for the trading of financial
securities.
 Primary market:
 Markets in which companies raise money by selling securities to
investors.
 Every security sells only once in the primary market.
 Initial public offering market: firms become publicly owned by
issuing (selling) shares to investors for the first time.
 Secondary market:
 Trading is primarily among investors. Issuers are usually not
involved.
Securities Markets
 Money market: markets for trading of debt securities with
less than one-year maturity.
 Capital markets: market for trading of intermediate-term
and long-term debt and common stock.
 Spot markets: securities are bought and sold for ‘on-thespot’ delivery.
 Futures markets: trading takes place now, but full payment
and delivery of the asset takes place in the future, e.g., 6
months or 1-year.
Console is just a perpetuity!
Price of consol
=
fixed coupon in dollar ter ms
investor'
s required
rate of return on consol
All debt securities have similar
form
 Will list a “par value” and a coupon rate.
 Par value is NOT Present Value, and
 Coupon rate is NOT the cost of debt/required rate of
return
Consol problem
 Problem 9.2
ABC Corp. wants to issue
perpetual debt in order to raise capital. It plans to
pay a coupon of \$90 per year on each bond with
face value \$1,000. Consols of a comparable firm
with a coupon of \$100 per year are selling at \$1,050.
What is the cost of debt capital for ABC? What will
be the price at which it will issue its consols?
Consol problem
 Problem 9.3
If ABC (from the problem above)
wanted to raise \$100 million dollars in debt, how
many such consols would it have to issue (to
nearest whole number)?
Consol problem
 Problem 9.4
If ABC wanted to issue it’s consols
at par, that is, at a price of \$1,000, what coupon
must it pay?
Zero coupon bond
 Zero coupon rate, no coupon paid during bond’s
life.
 Bond holder receives one payment at maturity, the
face value (usually \$1000).
 Most common example are government bonds
 How does investor get a return?
Zero coupon bond - 2
 This is just a lump sum problem!
 You have a Future Value (par value)
 Present Value (today’s price or market price)
 Rate
Example problems – zero coupon
bonds
 Find the price of a zero coupon bond with 20 years to
maturity, par value of \$1000 and a required rate of return of
15% p.a.
 XYZ Corp.’s zero coupon bond has a market price of \$ 354.
The bond has 16 years to maturity and its face value is
\$1000. What is the cost of debt for the ZCB (i.e., the
required rate of return).
Fixed-coupon bonds
 Firm pays a fixed amount (‘coupon’) to the investor every
period until bond matures.
 At maturity, firm pays face value of the bond to investor.
 Face value also called par value. Unless otherwise stated,
always assume face value to be \$1000.
 Period: can be year, semi-annual (6 months), quarter (3
months). Most common are semi-annual.
This is just a lump-sum + annuity!
 PV is today’s price or market price
 FV is the par value lump sum
 PMT is the period coupon payments.
Example problem - FCB
 A \$1,000 par value bond has coupon rate of 5% and the
coupon is paid semi-annually. The bond matures in 20
years and has a required rate of return of 10%.
Compute the current price of this bond.
Useful relationships
Coupon rate < discount rate Price < face value Bond is
selling at a
discount
Coupon rate = discount rate Price = face value Bond is
selling at
par
Coupon rate > discount rate Price > face value Bond is
selling at a
Useful relationship example
A 10-year annual coupon bond was issued four
years ago at par. Since then the bond’s yield to
maturity (YTM) has decreased from 9% to 7%.
Which of the following statements is true about
the current market price of the bond?
 The bond is selling at a discount
 The bond is selling at par
 The bond is selling at a premium
 The bond is selling at book value
 Insufficient information
Example - 2
One year ago Pell Inc. sold 20-year, \$1,000 par value,





annual coupon bonds at a price of \$931.54 per bond. At
that time the market rate (i.e., yield to maturity) was 9
percent. Today the market rate is 9.5 percent; therefore
the bonds are currently selling:
at a discount.
at par.
above the market price.
not enough information.
Other types of FCB problems
 Finding yield-to-maturity. THIS IS IDENTICAL TO
SOLVING FOR R.
 Finding coupon rate
Other FCB problems
 1)A \$1,000 par value bond sells for \$863.05. It matures
in 20 years, has a 10 percent coupon rate, and pays
interest semi-annually. What is the bond’s yield to
maturity on a per annum basis (to 2 decimal places)?
 2) ABC Inc. just issued a twenty-year semi-annual
coupon bond at a price of \$787.39. The face value of
the bond is \$1,000, and the market interest rate is 9%.
What is the annual coupon rate (in percent, to 2
decimal places)?
Two part FCB problem
 HMV Inc. needs to raise funds for an expansion
project. The company can choose to issue either zerocoupon bonds or semi-annual coupon bonds. In either
case the bonds would have the SAME required rate of
return, a 20-year maturity and a par value of \$1,000. If
the company issues the zero-coupon bonds, they
would sell for \$153.81. If it issues the semi-annual
coupon bonds, they would sell for \$756.32. What
annual coupon rate is Camden Inc. planning to offer
terms, rounded to 2 decimal places.
Stocks/equity
 All of these are related to perpetuities
Preferred stock
 You have a constant dividend (or cash flow) and
assume it will go forever.
P ps 
D
rp
Common stock
 With debt, cash flows can come from coupon payments +
repayment of par.
 With common stock, cash flows come from dividends or
selling your stock. However, expected future dividends are
the only thing that matters. Why?
 Three different ways to make assumptions when we value:
 Common dividend stream
 Constant growth in dividends
 Uneven growth (non-constant) in dividends
How do we price a stock? Constant
Dividend
stock price=> Pe 
D
re
<= dividend
<= required
return on equity
Comment – where does required return on equity come
from?
How do we price a stock? Constant
dividend growth
 Assume that dividends grow at constant growth rate, g,
to infinity:
D0 = Dividend
that the firm
just paid
Don’t panic.
Pe 
Required rate
of return on
equity
D 0 1  g 
re  g

D1
D1 = D0(1 + g)
re  g
Dividend
growth rate
How do changes in these affect
Stock Price?
Pe 
D 0 1  g 
re  g

D1
re  g
Algebra – rearrange to solve for
growth
Required rate
of return on
equity
re 
D1
Pe
 g
Capital gains
yield
Dividend
yield
 Note that we can find rate by using this formula (if we
have dividend, price, and growth).
 If we don’t have this info – what do we use?
Example problem – constant
growth
 Jarrow Company will pay an annual dividend of \$3 per
share one year from today. The dividend is expected to
grow at a constant rate of 7% permanently. The market
requires 15% What is the current price of the stock (to 2
decimal places)?
Example problem 2 – constant
growth
 Johnson Foods Inc. just paid a dividend of \$10 (i.e., D0 =
10.00). Its dividends are expected to grow at a 4% annual
rate forever. If you require a 15% rate of return on
investments of this risk level, what is Johnson Foods’s
current stock price? (to 2 decimal places)
Example problem 3 – constant
growth
 The price of a stock in the market is \$62. You know that the
firm has just paid a dividend of \$5 per share (i.e., D0 = 5).
The dividend growth rate is expected to be 6 percent
forever. What is the investors’ required rate of return for
this stock (to 2 decimal places)?
Example problem 4 – constant
growth
 A firm is expected to pay a dividend of \$5.00 on its
stock next year. The price of this stock is \$40 and the
investor’s required rate of return is 20%. The firm’s
dividends grow at a constant rate. What is this
constant dividend growth rate (g)?
Example problem 5
 A stock’s expected growth rate is 4% and they just paid
a dividend yesterday of \$10 per share. This stock has a
beta of 1.5, the risk free rate is 2% and the market
premium is 7%. What is the price of this stock?
Non-constant growth
 With this assumption, dividends grow at different
rates for different periods of time. Eventually,
dividends will grow at a constant rate forever.
 Time line is very useful for valuing this type of stocks.
 To value such stocks, also need the constant growth
formula.
 Best way to learn is through an example.
From book
 in valuing the stock of ABC Corp. suppose that you
forecast that dividends will be \$2, \$3, and \$3.50 in the
next three years, respectively. After that you expect
dividends to grow at a rate of five percent per year
forever. Let us suppose that the appropriate discount
rate for ABC's stock is 15 percent. The projected future
dividends are: D1 = \$2.00, D2 = \$3.00, D3 = \$3.50, D4 =
\$3.50 x (1.05) = \$3.675, and so on.
Non-constant dividend growth 2
 Consider ABC Co.’s dividend stream:
T=0
\$2.00
\$3.00
\$3.50
T =1
T=2
T=3
 Discount rate is 15%.
 WORK BACKWARDS!!!!!
Dividends grow at
5% forever
T=4
Another example
Malcolm Manufacturing, Inc. just paid a \$2.00 annual
dividend (that is, D0 = 2.00). Investors believe that the firm
will grow at 10% annually for the next 2 years and 6%
annually forever thereafter. Assuming a required return of
15%, what is the current price of the stock (to 2 decimal
places)?
Use timeline to ‘see’ the problem better.
Verify that stock price = \$25.29
Summary
 Consol bonds
 Zero coupon bonds
 Fixed coupon bonds
 Preferred Stock
 Common stock – constant dividend
 Common stock – constant growth
 Common stock – non-constant growth
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