Transcript Chapter 9

Chapter 9: Valuation of
Common Stocks
Objective
Explain equity evaluation
using discounting
1
Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley
Dividend policy
and wealth
Chapter 9 Contents
9.1 Reading stock listings
9.2 The discounted dividend model
9.3 Earning and investment opportunity
9.4 A reconsideration of the price multiple
approach
9.5 Does dividend policy affect shareholder
wealth?
2
9.1 Reading Stock Listings
• The following newspaper stock listing is
usually printed as a horizontal string of
information
• The listing is for IBM, which is traded on
the New York Stock Exchange
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Reading Stock Listings
Yr Hi
Yr Lo
123 1/8 93 1/8
Stock
IBM
Sym
IBM
Div
4.84
Yld %
4.2
PE
16
Vol 100
14591
Day Hi
Day Lo Close
115
113
Net Chg
114 3/4 +1 3/8
4
Reading Stock Listings
– Hi = 123 1/8: The highest price the stock
has traded at over the last 52 weeks
– Lo = 93 1/8: The lowest price the stock has
traded at over the last 52 weeks
– Stock = IBM: The stock’s name
– Sym = IBM: The stock’s symbol
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Reading Stock Listings
– Div = 4.84: The last quarterly dividend
multiplied by 4
– Yld % = 4.2: Dividend yield; (Annualized
dividend ÷ stock price)
– PE = 16: Price-to-earnings; (Latest price ÷
last 4 actual dividends)
– Vol 100s = 14591*100; Volume of
exchange traded shares
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Reading Stock Listings
– Hi = 115: Highest share price of the day
– Lo = 113: Lowest share price of the day
– Close = 114 3/4: Days closing share price
– Chg = 1 3/8: Change in closing price from
previous trading day
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Observation
• It is usual to trade shares in round lots of
100 shares
• If you decide to trade shares as odd lots
you will pay higher commissions
• Stock splits and stock dividends can
cause you to hold odd lots
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9.2 The Discounted Dividend
Model
• A discounted dividend model is any
model that computes the value of a
share of a stock as the present value of
the expected future cash dividends
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Equivalence of HPR and NPV
• The book starts from the holding period
return, and uses an inductive argument
to derive the NPV method for evaluating
stocks
• Equivalently, we start with the discounted
cash flow model, and obtain the holding
period return
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Notation
• Pj is the stock value in year j
• Dj is the cash dividend in year j
• K is the required rate of return on the
stock
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Present Value of Dividends
D3
D1
D2
D4
P0 



 ...
1
2
3
4
1  k  1  k  1  k  1  k 

D3
D1
1  D2
D4




 ...
1
1 
1
2
3
1  k  1  k   1  k  1  k  1  k  
D1
1
D1  P1
P1 


1
1
1 k
1  k  1  k 
D1  P1  P0
k
P0
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Expected Rate of Return
• The price and dividend next year are
expected prices, so
– The expected rate of return in any period
equals the market capitalization rate, k
D1  P1  P0
k
P0
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Rate Relationship
D1  P1  P0 D1 P1  P0
k


P0
P0
P0
• This relationship tells you that next year’s
expected dividend yield + the expected
capital gain yield is equal to the required
rate of return
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Price0 Is Discounted Expected
(Dividend1 + Price1)
• Price is the present value of the expected
dividend plus the end-of-year price
discounted at the required rate of return
D1  P1
P0 
1 k
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Ease of Use
• Estimating next year’s dividend is
straightforward, but estimating next
year’s price appears to be much more
difficult
• The problem is that next year’s price is
obtained (eventually) by estimating, and
discounting, every future dividend
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Ease of Use
• We have to introduce a simplifying
assumption that captures our
understanding of dividend behavior
• The second simplest assumption is that a
dividend in any future year is the
dividend in the prior year times a
constant growth factor (1+g)
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Ease of Use
• Think of this as some kind of dividend
inflation
• From chapter 5 we know that if k is the
nominal discount rate, then the real
discount rate, R, is given by R =
(1+k)/(1+g) - 1
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Ease of Use
• Recall from chapter 4 that, for a
perpetuity, the present value is the real
value of the first cash flow divided by the
real rate
Dnominal @ 1
Dreal
p0 

R
(1  g )
R
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Putting This Together
D1
p0 

(1  g ) R
D1
 1 k 
(1  g )
 1
1 g 
D1
D1


1  k   1  g  k  g
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Solving for K
D1
p0 

kg
D1
k
g
p0
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G = Capital Gains Yield
• Comparing prior results:
D1
D1 P1  P0
k
g & k 

p0
P0
P0
P1  P0
 g
P0
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Conclusion
• The capital gains yield is equal to the
dividend growth rate
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Generalization
• This model captures many of the
characteristics of dividend cash flows
• You could next assume that the rate of
growth, g1, is valid from a1 to b1,
followed by g2 from a2 (= b1+1) to b2, ...
– Just like the folk in chapter 5, businesses
grow, mature, and decay
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More General Models
• Chapter 5 contains an alternative
derivation of growing perpetuity formula
• It also contains the equations, Excel
workbooks, and worked examples for
growing annuity models of common stock
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9.3 Earning and Investment
Opportunity
• A second approach to DCF valuation
focuses on future earnings and
investment opportunities
• This focus, rather than the earlier
dividend focus, concentrates the analyst’s
attention on the core business
determinants of value
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Cash Flow Statements
• In chapter 3 we reviewed cash flow
statements. Algebraically,
Net income + depreciation - increased
working capital - increase P&E - dividends +
increase in debt - increase in investment in
marketable securities = 0
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Cash Flow Statements
• We simplify this
– By rolling changes in working capital, and
P&E, into change in investments
– By assuming pure equity funding (no debt)
– By assuming no marketable securities
• Net income + depreciation - dividends change in investments = 0
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Cash Flow Statements
– We want to retain net income as an
accounting entity in order to make the
analysis useful
– Depreciation is “accounting depreciation”
and not market value attrition. (Assume
these happen to be equal)
– Define net new investments as new
investments - depreciation
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Earning and Investment
Opportunity
• To simplify the analysis, suppose that no
new shares are issued, and no taxes
Dividends = earnings - net new investment
“D = E - I”. The formula for valuing stock is



Dt
Et
It
p0  


t
t
t
t 1 1  k 
t 1 1  k 
t 1 1  k 
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Interpretation
• The value of a company is not equal to
the present value of its expected
earnings
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Interpretation
– Net new investment may be positive or
negative
• The loss of existing asset value may not
always be compensated by new investment
– Earnings are what accountants understand
by the term, namely net income after
interest and tax
• We are finance folk, but the accountants
provide the information
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Nogrowth
– Nogrowth Co has a policy of no net new
investments
• This does not mean the firm does not invest
in new plant and equipment--only that
purchases match the loss of value of the
existing assets (as measured by depreciation)
• If we assume everything is in real terms, it is
reasonable to assume that Nogrowth will pay
a constant (say) $15/share each year
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Nogrowth
• If the real capitalization rate is 15%, then
the value of Nogrowth is 15/0.15 = $100
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Growth Stock
• Growthstock Co initially has the same
earnings as Nogrowth, but reinvests 60%
of its earnings each year into new
investments that yield a real rate of
return of 20% per year
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Growth Stock
• The management of Growthstock may be
thought of as taking 60% of the
shareholder’s value, and reinvesting it on
behalf of the shareholders
– That is the share holders have $100*0.4 =
$40 of the value of the old stream, and
management invests the remaining $100*0.6
= $60
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Growth Stock
– The first cash flow is the result of investing
$15*0.6 = $9 in year 1 to obtain
$15*0.6*0.20 = $1.8 forever
– In year 1 this has a value of $1.8/0.15 = $12
– There is a second, third, fourth, … flow
starting in year 3, 4, 5, … also $12
– The present value of these streams is
12/0.15 = $80
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Growth Stock Magic
– Management has taken shareholder value of
$60 and turned it into $80
– The magic does not stop here. Management
will take 60% of the new cash flows and
reinvest them to return a 80/60 reward to
the shareholders, and reinvest 60% of those
– The wealth of the shareholders will become
progressively multiplied
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Growth Stock
80
80
80
wealth  100 * (0.4  0.6 * * (0.4  0.6 * * (0.4  0.6 * * (...))))
60
60
60
wealth  100 * (0.4 
Kept
Original wealth
0.8 * (0.4 
0.8 * (0.4 
0.8 * (...))))
Wealth Multiplier
Reinvested
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Growth Stock
wealth  100 * (0.4  0.8 * (0.4  0.8 * (0.4  0.8 * (...))))
 100 * 0.4 * (1  0.8 * (1  0.8 * (1  0.8 * (...))))
wealth  100 * 0.4 * (1  0.8  0.82  0.83  ...)
 1 
 100 * 0.4 * 

 1 - 0.8 
 $200
1
1  a  a  a  ... 
1 a
2
3
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Generalize
• Let the
– V = value of the shares without reinvestment
– G = the growth from new investment
– R = retention ratio
– M = wealth multiplier = g/i
– Wealthg = wealth0*(1-r)/(1-w*r)
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Observation
• If management had selected a slightly
higher retention ratio r = i/g = 0.20/0.15
=0.75, then the value of the company
goes to infinity
• When this kind of thing happens in
finance, it is a sign that something has
been missed out of the analysis
– The required rate of return demanded by
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investors may need to be increased
Alternative Solution Method
• Recognizing that
G = change in earnings ÷ earnings
= (net investment ÷ earnings) *
(Change in earnings ÷ net investment)
Growth is then the product of the earningsretention rate and the rate of return on new
investment
Pricegrowth = 6 ÷(0.15 - (0.6*0.2)) = $200
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Alternative Solution Method
• The increase in the value of the stock is
the consequence of reinvestment at a
higher rate of return than the investor
required rate of return
• Normalgrowth has investment
opportunities of 15%, but still reinvests
60% of the earnings
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Reinvestment Under Normal
Growth
6
Price 
 $100
0.15  0.6 * 0.15
Cost of Capital
Retention Ratio
45
Growth Rate
Reinvestment Under Normal
Growth
• In this case there is no increased value to
the shareholders
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A Reconsideration of the Price
Multiple Approach
• Recall the
P0 = e1/k + NPV of future investments
In terms of P/E
P0/ E1 = 1/k + NPV/ E1 of future investments
– Firms with high PE ratios are then
interpreted as having low capitalization rates
or excellent future investment opportunities
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Does Dividend Policy Affect
Shareholder Wealth?
• Dividend policy of a corporation
– The policy regarding paying out cash to its
shareholders, holding constant its investment
and borrowing decisions
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9.4 Reconsideration of the
P/E Multiple Approach
• The formula for a growing perpetuity is:
E1
E1 g Po
E1
Po 
 Po 


 NPVfurure investment
kg
k
k
k
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9.5 Does Dividend Policy
Affect Shareholder Wealth?
• In a frictionless world where there are no
taxes nor transaction costs, the dividend
policy (as defined in the last slide) will
have no affect on the wealth of stock
holders
• We shall examine: tax, regulations, cost
of external financing, and information
content of dividends
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Cash Dividends and Share
Repurchases
• A corporation may distribute cash
– By paying dividends
• All shareholders are paid the same per share
– By repurchasing its own stock
• Shareholders choosing to liquidate some or all
of their holdings sell the shares at market
price (as they normally do), and the company
makes market purchases
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Illustration: Dividend Payment
• The following table shows a simplified
balance sheet of Cashrich Co
• Assume
– Number of shares outstanding = 500,000
– Share price = $20
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Illustration: Dividends
Assets
Cash
Liab\Equ
2
Debt
2
Other
10
Equity
10
Total
12
Total
12
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Illustration: Dividend Payment
• If Cashrich declares a dividend of $2 /
share it will pay 500,000 * $2 =
$1,000,000
– Given its level of risk, the payment will
reduce the market value of the shares by
$1,000,000 to $20 * 500,000 - $1,000,000 =
$9,000,000, so each share will be worth
$9,000,000 / 500,000 = $18 / share
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Illustration: Dividend Payment
Was 2
Assets
Cash
Was 10
Liab\Equ
1
Debt
2
9
Other
10
Equity
Total
11
Total
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11
Were 12
Illustration: Dividend Payment
• Before the dividend, every share was
worth $20
• After the $2 / share dividend, every
share was worth $18
• Conclusion
– Shareholders wealth is unchanged
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Illustration: Share Repurchase
• The original balance is shown below
– Share price is still $20
– Number of shares outstanding is 500,000
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Illustration: Share Repurchase
Assets
Cash
Liab\Equ
2
Debt
2
Other
10
Equity
10
Total
12
Total
12
58
Illustration: Share Repurchase
• The company repurchases 50,000 shares
at $20 per share = $1,000,000
– The market value of the firm is now
$10,000,000 less the loss of $1,000,000
cash, or $9,000,000
– The number of shares outstanding is now
500,000 - 50,000 = 450,000
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Illustration: Share Repurchase
– The share price is then $9,000,000/450,000
= $20
• The wealth of the shareholders who sold
out is unchanged
• The wealth of the shareholders who held
the stock is unchanged
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Illustration: Share Repurchase
Was 2
Assets
Cash
Was 10
Liab\Equ
1
Debt
2
9
Other
10
Equity
Total
11
Total
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11
Were 12
Stock Dividends
• Corporations sometimes declare a stock
split and distribute stock dividends
– These activities do not distribute cash to the
shareholders
– They increase the number of issued shares,
but do not change the % of the company
each shareholder owns
• They do not affect shareholder wealth
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Modigliani and Miller
• In a frictionless environment, where
there are no costs of issuing new shares
of stock, nor costs of repurchasing
existing shares, a firm’s dividend policy
can have no effect on the wealth of
current shareholders
63
The Real World: Share
Repurchase
• Smart Co has had a good year, and is
considering repurchasing some
outstanding stock in order to prevent
some of its shareholders paying personal
income tax on the dividend
• There are restrictions on this kind of
practice in many countries, including the
USA
64
The Real World: Retaining
Surplus Cash to Shelter It
• Smart Co has had a good year, but is
considering not declaring a dividend
• Smart doesn’t need the cash, but holding
cash tax shelters the shareholders
– IRS rules provide huge penalties for this kind
of activity
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The Real World: Asymmetric
Information
• The management of Cryptic Co is
concerned that the investment
community does not understand its
business
– It has decided to finance projects using
cheaper retained earnings rather than
issuing more stock at a discount from its
“true” market value
66
The Real World: Signaling
• The management of Trip Co has had a
single bad year, but has decided not to
reduce its dividend
– Reducing the dividend may send a signal to
the investment community saying
“The fundamentals of Trip have changed:
consider decreasing future dividend estimates
and/or consider increasing the cost of capital
to compensate for additional risk”
67
A Final Thought: Are
Frictionless Worlds Enough?
• Large firms usually have limited liability
• Earnings follow a stochastic trajectory
– Could repurchasing shares (or paying
dividends) change shareholder wealth
(despite our arguments)?
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