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Stock Valuation
Chapter 8
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin
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Chapter Outline
• Bond and Stock Differences• Common Stock Valuation• Features of Common Stock• Features of Preferred Stock• The Stock Markets
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Bonds and Stocks: Similarities• Both provide long-term
funding for the organization
• Both are future funds that an investor must consider
• Both have future periodic payments
• Both can be purchased in a marketplace at a price “today”
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Bonds and Stocks: Differences• From the firm’s perspective: a
bond is a long-term debt and stock is equity
• From the firm’s perspective: a bond gets paid off at the maturity date; stock continues indefinitely.
• We will discuss the mix of bonds (debt) and stock (equity) in a future chapter entitled capital structure
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Bonds and Stocks: Differences
• A bond has coupon payments and a lump-sum payment; stock has dividend payments forever
• Coupon payments are fixed; stock dividends change or “grow” over time
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A visual representation of a bond with a coupon payment (C) and a maturity value (M)
1 2 3 4 5
$C1 $C2 $C3 $C4 $C5
$M
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A visual representation of a share of common stock with dividends (D) forever1 2 3 4 5
$D1 $D2 $D3 $D4 $D5 $D∞
∞
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Comparison Valuations
1 2 3Bond
C CCM
P0
0
1 2 3Common Stock
D1 D2 D3 D∞P0
0
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Notice these differences:• The “C’s” are constant and equal• The bond ends (year 5 here)• There is a lump sum at the end
1 2 3 4 5
$C1 $C2 $C3 $C4 $C5
$M
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Notice these differences:• The dividends are different• The stock never ends• There is no lump sum
1 2 3 4 5
$D1 $D2 $D3 $D4 $D5 $D∞
∞
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Our Task:To value a share
of Common Stock
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BAEFEIPVT
BringAllExpectedFutureEarningsIntoPresentValueTerms
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BAEFEIPVTJust remember:
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Cash Flows for Stockholders
If you buy a share of stock, you can receive cash in two ways:
1. The company pays dividends
2. You sell your shares, either to another investor in the market or back to the company
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One-Period Example
Receiving one future dividend and one future selling price of a share of common stock
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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, and you believe that you can sell the stock for $14 at that time.
If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay?
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Visually this would look like:
1
D1 = $2
P1 = $14
R = 20%
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Compute the Present Value
1
D1 = $2
P1 = $14
R = 20%
$1.67
$11.67
PV =$13.34
1 year = N
20% = Discount rate
$2 = Payment (PMT)
$14 = FV
PV = ?
-13.34
1st
2nd
TI BA II Plus
8-198-19
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$14 = FV
1 year = N
$2 = Payment (PMT)20% = Discount rate
PV = ?
-13.34
HP 12-C
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Two Period Example
Now, 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. Now how much would you be willing to pay?
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Visually this would look like:
2
D1 = $2
P2 = $14.70
R = 20% 1
D2 = $ 2.10
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Compute the Present Value
2
D1 = $2
P2 = $14.70
R = 20% 1
D2 = $ 2.10$1.67$1.46
$ 10.21
$ 13.34 = P0
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What is the Observed Pattern?
We value a share of stock by bring back all expected future dividends into present value terms
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Future Dividends
So the key is to determine the future dividends when given the growth rate of those dividends, whether the growth is zero, constant, or unusual first and then levels off to a constant growth rate.
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So how do you compute the future
dividends?Three scenarios:
1.A constant dividend (zero growth)
2.The dividends change by a constant growth rate
3.We have some unusual growth periods and then level off to a constant growth rate
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1. Constant Dividend – Zero Growth• The firm will pay a
constant dividend forever
• This is like preferred stock
• The price is computed using the perpetuity formula:
P0 = D / R
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So how do you compute the future
dividends?Three scenarios:
1. A constant dividend (zero growth)
2. The dividends change by a constant growth rate
3. We have some unusual growth periods and then level off to a constant growth rate
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2. Constant Growth Rate of Dividends
Dividends are expected to grow at a constant percent per period.
P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + …
P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + …
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2. Constant Growth Rate of Dividends
With a little algebra this reduces to:
g-R
D
g-R
g)1(DP 10
0
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2. Constant Growth Rate of Dividends
Student caution:
g-R
D
g-R
g)1(DP 10
0
A. What happens if g > R?B. What happens if g = R?
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Dividend Growth Model (DGM) Assumptions
To use the Dividend Growth Model (aka the Gordon Model), you must meet all three requirements:
1.The growth of all future dividends must be constant,
2.The growth rate must be smaller than the discount rate ( g < R), and
3.The growth rate must not be equal to the discount rate (g ≠ R)
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DGM – Example 1
Suppose Big D, Inc., just paid a dividend (D0) of $0.50 per share. 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?
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DGM – Example 1 Solution
P0 = .50 ( 1 + .02) .15 - .02
g-R
D
g-R
g)1(DP 10
0
P0 = .51 .13
= $3.92
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DGM – Example 2
Suppose Moore Oil 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?
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DGM – Example 2 Solution
P0 = 2.00 .20 - .05
g-R
D
g-R
g)1(DP 10
0
P0 = 2.00 .15
= $13.34
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So how do you compute the future
dividends?Three scenarios:
1.A constant dividend (zero growth)
2.The dividends change by a constant growth rate
3.We have some unusual growth periods and then level off to a constant growth rate
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Using the DGM to Find R
gP
D g
P
g)1(D R
g-R
D
g - R
g)1(DP
0
1
0
0
100
Start with the DGM and then algebraically rearrange the equation to solve for R:
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Finding the Required Return - Example
Suppose a firm’s stock is selling for $10.50. It just paid a $1 dividend, and dividends are expected to grow at 5% per year. What is the required return? R = [1(1.05)/10.50] + .05 = 15%What is the dividend yield?
1(1.05) / 10.50 = 10%What is the capital gains
yield?
g =5%
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Stock Valuation Alternative
But my company doesn’t pay dividends!
How can I value the stock?
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Valuation Using Multiples
We can use the PE ratio and/or the price-sales ratio:
Pt = Benchmark PE ratio X EPSt
Pt = Benchmark price-sales ratio X Sales per sharet
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Stock Valuation Summary
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Features of Common Stock
• Voting Rights• Proxy voting• Classes of stock
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Dividend Characteristics
• Dividends are not a liability of the firm until a dividend has been declared by the Board
• Consequently, a firm cannot go bankrupt for not declaring dividends
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Dividend Characteristics
Dividends and Taxes
• Dividend payments are not considered a business expense; therefore, they are not tax deductible
• The taxation of dividends received by individuals depends on the holding period
• Dividends received by corporations have a minimum 70% exclusion from taxable income
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Stock Market, Dealers vs. Brokers
Dealer: trades with inventory for bid and ask pricesBroker: matches buyers and sellers for a fee
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Stock Market• New York Stock Exchange
(NYSE)
• Largest stock market in the world
• License holders (1,366)• Commission brokers• Specialists• Floor brokers• Floor traders
• Operations
• Floor activity
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NASDAQ• Not a physical exchange – it is a
computer-based quotation system
• Multiple market makers
• Electronic Communications Networks
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NASDAQ• Three levels of information:• Level 1 – median quotes,
registered representatives
• Level 2 – view quotes, brokers & dealers
• Level 3 – view and update quotes, dealers only
• A large portion of technology stocks are bought and sold each day on NASDAQ
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Reading Stock Quotes
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Comprehensive Problem
XYZ stock currently sells for $50 per share. The next expected annual dividend is $2, and the growth rate is 6%. What is the expected rate of return on this stock?
If the required rate of return on this stock were 12%, what would the stock price be, and what would the dividend yield be?
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Formulas
gP
D g
P
g)1(D R
g-R
D
g - R
g)1(DP
0
1
0
0
100
P0 = D R
Value of a Perpetuity:
Value of a Share of Common Stock using the DGM:
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Formulas
Value of a Share of Common Stock using Multiples
Pt = Benchmark PE ratio X EPSt
Pt = Benchmark price-sales ratio X Sales per sharet
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1. A stock’s value is the present value of all expected future earnings.
2. Computing the future dividends of a stock is the key to understanding its value
3. Issuing stock provides the firm long-term funding
What are the most important topics of this chapter?
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4. The Dividend Growth Model (DGM) provides us help with infinite dividend streams
5. Stocks are bought and sold each business day with reporting via stock quotes
What are the most important topics of this chapter?
