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
3
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
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
5
Present Value of Dividends
• P0 = D1/(1+k)+ D2/(1+k)2+ D3/(1+k)3
+...+
• With constant growth rate
• D2 = D1(1+g), D3 = D2(1+g), etc.
• Hence, P0 = D1/(k-g)
6
Present Value of Dividends
• P0 = D1/(1+k)+ D2/(1+k)2+ D3/(1+k)3
+...+
• P1 = D2/(1+k)+ D3/(1+k)2+ D4/(1+k)3
+...+
• Using the above equations P0 = (P1 + D1)/(1+k)
7
Capital gain yield = g =
dividend growth rate
• P0 = D1/(k-g)
• P1 = D2/(k-g)
• D2 = D1(1+g)
• Using the above equations (P1 - P0)/P0 = g
8
Discount rate k = rate of
return on the stock = market
capitalization rate on the
stock
• Recall that P0 = (P1 + D1)/(1+k)
• Subtracting P0/(1+k) from both sides of
the above equation and simplifying we
get:
k = (P1 + D1 - P0)/ P0 = rate of return on
the stock = market capitalization rate on
the stock
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Discount rate k = Dividend
yield plus capital gain yield
• k = (P1 + D1 - P0)/ P0 = annual rate of
return on the stock, or
• k = D1/ P0 + (P1 - 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
10
Solving for k
• k = D1/ P0 + (P1 - P0)/ P0
• g = (P1 - P0)/ P0
• Hence, k = D1/ P0 + g
11
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
12
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 
13
Interpretation
• The value of a company is not equal to
the present value of its expected
earnings
• The value of a company is equal to the
present value of its expected earnings
net of new investments
14
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
15
Nogrowth
• If the real capitalization rate is 15%, then
the value of Nogrowth is 15/0.15 = $100
16
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
17
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.
• The earnings retention rate is 60% and
the dividend payout ratio is 40%
18
Growth Stock
– The first year dividend is $15*0.4 = $6
– At the end of first period $9 is invested at
20% rate, which gives a perpetuity of $1.8
beginning second period.
– The total earnings at the end of the second
year are equal to $15 + $1.8 = $16.8
– Second year dividend is $16.8*0.4=$6.72
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Growth Stock
– At the end of second year $16.8*0.6 =
$10.08 is invested at 20% rate, which gives
a perpetuity of $2.016 beginning third
period.
– The total earnings at the end of the third
year are equal to $15 + $1.8 + $2.016 =
$18.816
– Third year dividend is $18.816*0.4=$7.5264
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Growth Stock
– First year dividend = $6
– Second year dividend = $6.72 = $6(1.12)
– Third year dividend = $7.5264 = $6.72(1.12)
– The dividend growth rate of 12% is not a
coincidence - it is equal to the earnings
retention rate of 60% times the 20% rate of
return of new investments.
– g = 20% * 60% = 0.20 * 0.60 = 0.12=12%
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Generalize
• Let the
– g = dividend growth rate
– b = earnings retention rate
– R = ROE on new investments
– Then g = b * R
22
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
25
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
26
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
31
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
34
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
36
Illustration: Share Repurchase
Was 2
Assets
Cash
Was 10
Liab\Equ
1
Debt
2
9
Other
10
Equity
Total
11
Total
37
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
39
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
40
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
41
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”
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