Equity Valuation

1
Equity ValuationA Micro View

• Chapter 23

2
Introduction

• This chapter uses various versions of the
  dividend discount model (DDM) to value a single
  share of common and preferred stock

3
Dividend Discount Models

• Corporations may pay several different types of
  dividends
• Regular cash dividends
• Usually paid quarterly
• Most companies never decrease their cash
  dividends
• Usually increase or hold constant
• Extra dividends
• Cash dividends that may or may not be repeated in
  the future
• A few corporations pay an extra dividend if the
  firm had an unusually profitable year

4
Dividend Discount Models

• Special dividends
• Extraordinary cash dividends that may never be
  repeated
• Liquidating dividends
• Cash payment occurring when all or part of firm
  is liquidated

5
Payment Models for Cash Dividends

• Preferred stock generally pays a constant cash
  dividend
• Common stock dividends are more uncertain
• Each quarter the Board of Directors decides upon
  the common stocks cash dividend
• The dividend in the next period (t 1) will be
  equal to the previous periods dividend plus some
  level of growth
• Divt1 Divt (1 gt)
• This implies a single-period dividend growth rate
  of

6
Payment Models for Cash

• For preferred stocks the growth rate may be zero
• Most corporations experience a growth rate in
  common stock of ? 2
• However, some corporation consistently increase
  their dividends, such as Coca-Cola (g gt 0)
• Some corporations decrease their cash dividends
  (g lt 0) or never pay dividends
• Usually do so if
• Firm is unprofitable
• Firm is retaining all income to finance growth

7
Present Value of Constant Growth Stream

• Well-managed firms may stay in existence forever
• Old executives will retire and be replaced by new
  ones
• Mergers and Research Development will sustain
  the firm
• An equity share is worth the present value of the
  stream of cash dividends to infinity

• Assuming that dividends grow at a constant rate

8
Model-Building Assumptions

• K gt g (otherwise denominator would be negative,
  leading to a negative stock price)
• Both k and g represent long-run averages
• Ignores taxes, external financing and options
• Allowing for taxes and debt financing is
  relatively easy
• Allowing for executive stock options and warrants
  is more difficult

9
Example

• Battel Corporation has the following attributes
• Paid an annual dividend of 2 per share
• Cost of equity capital is 10
• Cash dividends are growing at 2 annually
• What is Battels stock worth?

10
Example

• Battel is now considering international expansion
  with the following adjustments
• Same dividend as above, but now the expected
  growth rate is 4, not 2, and the increased risk
  is expected to increase the cost of equity to 11
• Battels value should increase to

11
Guidelines for Determining Appropriate Discount
Rate

• The following table offers guidelines (under
  normal market conditions) for various stocks
• Note that the discount rate should be adjusted
  upward (downward) during bearish (bullish) markets

Stocks Quality Rating Description of Risk (Examples) Appropriate Discount Rate
AAA Maximum safety, bluest of the blue chips (Pfizer, Wal-Mart Stores) 8
AA High quality, established blue chip (Exxon, Wells Fargo) 10
A Medium grade investment bonds, established top 50 firms (Paine Webber, Sara Lee) 12
BBB Low-grade investment bonds, established top 100 firms (Weyerhaeuser Co, Dupont) 14
12
Guidelines for Determining Appropriate Discount
Rate
BB High-grade speculation, FORTUNE 500 firms (Delta Airlines, Texas Instrument) 16
B Speculative FORTUNE 1000 firms (Amerada Hess, Georgia-Pacific) 18
CCC Speculation, very risky (Classic Cable, PSINet, Revlon) 20
CC Very speculative, junk bond issuer (advanced Micro Devices, NEXTEL, Silicon Graphics) 22
C Gambling on bankruptcy (Allied Waste, RSL Communications, Universal Broadband Networks) 24
D Defaulted (Boston Chicken in 1999, Daewoo) 26
Not Rated Gamble, small firms, new firms (Joes Bar Grillif Joe never drinks) 40
Not Rated Bad gamble, small firms, new firms (Joes Bar Grillif Joe drinks) 60
13
Present Value of Stock with Finite Holding
Periods

• What if you hold a stock for a limited time
  period and then sell it?
• For example, in 3 years
• The DDM would be

• Where P3 represents the price of the stock when
  it is sold in three years

14
Present Value of Stock with Finite Holding
Periods

• P3 would represent the present value of all
  dividends from time 4 through infinity or

• Equation 2 is substituted into Equation 1 to
  obtain

• Thus, P0 includes P3 and P3 includes future
  capital gain

15
Two Stages of Growth DDM

• A firms common stock may have one of the
  following growth patters in dividends
• Two stages of positive growth (g1 and g2)
• One constant positive growth rate
• Zero growth
• One constant negative growth rate

16
Two Stages of Growth DDM
17
Two Stages of Growth DDM

• If a firm has two stages of growth (g1 and g2),
  the DDM can be re-formulated to

18
Example

• Continuing the Battel Example
• Initial stock price 25.50
• With international expansion 29.71
• What if the international expansion caused
  Battel's growth rate to rise to 4 for only four
  years and then the growth rate dropped to the
  original estimate of 2 forever?
• If the exposure to international risks increases
  Battels cost of equity to 11 permanently

19
Example

• Battels new value would be
• Present value of Stage 1 (g1 4)

Year Dividend Present Value (k11)
1 2.08 1.87387
2 2.1632 1.75570
3 2.2497 1.64496
4 2.3397 1.54123
The temporary increase in dividends from
expansion could not overcome the increase in
risk and the value dropped from its original
estimate.

• Present value of Stage 2 (g2 2)

20
DDM Criticism

• Critics argue that it is too difficult to
  accurately forecast future cash dividends
• This criticism is true for some firms but not
  others
• Example Coca-Colas dividend payment is
  relatively easy to forecast even though its
  operations cover over 200 different countries
• Critics then argue that, even if earlier
  dividends are relatively easy to forecast,
  longer-term dividends (say 50 to 100 years from
  now) are more difficult to determine
• These long-range forecasts are unimportant

21
DDM Criticism

• Because the present value of these amounts are
  very low

Time Present Value Of 1 (i10) Present Value Of 1 (i16)
10 39 23
25 9.2 2.5
50 lt 1 6/100 of 1
100 lt 1/100 of 1 3/100,000 of 1
Smaller firms are more risky and therefore have
a higher discount rate and lower present value.
22
Implications

• It is only essential to accurately forecast cash
  dividends for 10 years in order to use the DDM
• Cash dividends in years 11-30 only need to be
  forecasted within ? 40 of their actual values
• All cash dividends received from years 31 to
  infinity have a present value of only 1 or 2
• When a higher discount rate is used (as with
  smaller, riskier firms) it is only necessary to
  forecast dividends for a few years

23
Structural Changes in Cash Dividend Payments

• Corporate earnings will be used for
• Cash dividends paid to owners (shareholders)
• Retained earnings reinvested in firm
• Share buybacks to repurchase outstanding shares
• Recently firms have decreased cash dividend
  growth rates and begun buying back stock
• Examples IBM, American Express, Coca-Cola

24
Structural Changes in Cash Dividend Payments
Cash dividends on a per share basis have
increased smoothly for decades. However, the
cash dividends have not kept pace with the
increase in the SP500 Index in the 1980s and
1990s. Thus, the cash dividend yield has
decreased.
25
Restating Present Value Models in Terms of
Earnings

• The retention ratio (RR) represents the portion
  of earnings not paid as dividends
• Therefore, it is retained earnings
• The payout ratio is (1 RR)
• Thus, a firms dividend can be rewritten as
• Divt (1 RR)EPSt
• A firm can use retained earnings to either
  repurchase shares or to reinvest and earn the
  firms ROE
• Reinvested earnings can finance internal growth
  at a periodic rate of g RR x ROE
• Therefore, EPSt EPS0 x (1g)t EPS0 1
  (RR)(ROE)t

26
Restating Present Value Models in Terms of
Earnings

• Profitable firms can earn ROE gt 0 by reinvesting
  RE in profitable projects or repurchasing shares
• Share repurchases can increase EPS because the
  firms earnings are now spread out over fewer
  shares (called reverse dilution)
• If the RRgt0, then the following equations are
  equivalent
• Divt (1 RR) EPS1
• Divt (1 RR) (1 g)t EPS0
• Divt (1 RR) 1 (RR)(ROE)t EPS0

27
Reformulated Present Value Model

• Substituting the last equation from previous
  slide into the basic DDM

• Could have substituted any of the Divt equation
  from previous slide
• Thus, the DDM can be rewritten equivalently in
  many forms
• All the valuation models have presented the value
  on a per share basis
• Could value the entire firm by multiplying by the
  number of shares

28
Dividend Policy Irrelevance

• If Div1 is replaced with EPS1 (1 RR) in the
  constant DDM, we obtain

• This allows us the ability to examine how
  dividend policy impacts share value
• Dividend policy is reflected in the retention
  rate (RR)

29
Dividend Policy Irrelevance

• Since g (RR)(ROE)

• If a firm has an ROE on new investments equal to
  the risk-adjusted discount rate then

• Thus, regardless of a firms initial EPS or
  riskiness, the firms value is unaffected by
  dividend policy, as RR is no longer in the
  equation
• So, when ROE k dividend policy is irrelevant

30
Dividend Policy and Growth Firms

• The relationship between a firms ROE and its
  discount rate determine the impact of dividend
  policy on firm value
• A firm earning an ROE gt discount rate is
  considered a growth firm
• These firms earn an ROE gt k and should not pay
  dividends as doing so will reduce their true
  value
• Some firms that adhere to this policy include
  Microsoft, America Online, MCI WorldCom
• Other growth firms that do not follow this policy
  include Coca-Cola and Intel
• This can be due to market imperfections such as
  state laws required that certain institutions
  cannot invest in firms that do not pay consistent
  dividends (legal listing)

31
Dividend Policy and Declining Firms

• Declining firms are those that do not have
  profitable investment opportunities
• Declining firms have ROE below the discount rate,
  or ROE lt k
• These firms should pay all earnings out as
  dividends

32
Dividend Policy and Normal Firms

• Most firms have few growth opportunities
• Few internal investments offer ROE gt k
• In this case, ROE k and dividend policy is
  irrelevant

33
Example

• Assume a firm has
• An ROE of 15
• A discount rate, k, of 15
• A retention rate (RR) of 66.67
• Leads to a growth rate of 0.6667 x .15 10
• Cash dividends growth rate of 10
• If these assumptions hold, the firms value will
  remain a constant 50 (in present value terms)

34
Example
Future Value at g 10 Future Value at g 10 Present Value at k 15 Present Value at k 15 Present Value at k 15
Time Period Divt Stock Price PV of cumulative dividend PV of future price Total
T0 NA 50 NA 50 50
T1 2.50 55 2.18 47.82 50
T2 2.75 60.50 4.26 45.74 50
T3 3.03 66.55 6.25 43.76 50
T4 3.33 73.20 8.15 41.85 50
T5 3.66 80.53 9.97 40.03 50
T10 5.89 129.68 17.94 32.06 50
T20 15.29 336.37 29.44 20.56 50
T50 266.80 5869.55 44.58 5.42 50
T100 31,319.57 689,030.62 49.41 0.59 50
T? ? ? 50 0.0 50
The firms stock provides investors an annual
return of 15--10 in the form of capital gains
and 5 of dividend income.
35
The Price Earnings Ratio

• The Price-Earnings Ratio (PE) is often used to
  value stocks by
• Estimating EPS
• Estimating a PE ratio
• Multiplying the two to obtain an estimate of the
  share price

36
The Price Earnings Ratio
Stock prices and earnings tend to rise together.
SP500 P/E ratio exhibits mean-reversion.
While the SP500 trended upward, the P/E ratio
fluctuated without any trend.
37
Statistical Aggregation Problems

• When data is aggregated, tendencies are smoothed
  out, such as
• Business Cycle fluctuation
• As business activity increases, corporate
  earnings rise, P-E ratios rise and most stock
  prices increase (bull market)
• Later, anticipating a recession, stock prices
  begin decreasing (bear market)
• Business activity decreases, corporate sales
  decline as well as corporate earnings
• P-E ratios decrease

38
Statistical Aggregation Problems

• Reactions to earnings fluctuations
• Some stores have very predictable earnings
  fluctuations, such as high sales during December
• Thus, earnings are very seasonal
• Stock prices do not tend to fluctuate on a
  seasonal basis
• P-E ratios move inversely to offset the temporary
  (and predictable) seasonal earnings

39
Analyzing the P-E Ratio

• If the constant growth DDM is divided by EPS1

• Thus the P-E ratio has 3 primary determinants
• A risk-adjusted discount rate of k gt g
• As k increases the P-E ratio decreases
• A growth rate, g
• As g increases the P-E ratio increases
• A cash dividend payout ratio of Div1/EPS1 or (1
  RR)

40
Analyzing the P-E Ratio

• As the payout ratio increases, g decreases and
  the P-E ratio is unaffected
• This can also be demonstrated as

41
Analyzing the P-E Ratio
No relationship exists between the SP500 P-E
ratio, its cash dividend payout ratio, its cash
dividend per share or its cash dividend during
1935-2000, supporting the MM dividend
irrelevance theorem for a normal firm.
42
Battel Example

• Reconsider the Battel example
• Battels Div0 2, g 2, k 10 ? stock price
  of 25.50
• If we expect EPS1 to be 3, Battels P-E ratio is
  8.5

43
P-E Ratio

• Many fundamental analysts multiply a stocks EPS
  by the P-E ratio to estimate the stocks price
• Can even use this method if the firm does not pay
  a dividend by imputing a payout ratio
• Can also use this procedure for stocks that do
  pay dividends
• Can compare a stock price estimate obtained with
  the P-E ratio approach to the DDM approach
• The two methods will probably lead to similar
  values
• If the two values differ greatly, further
  analysis may enable the analyst to obtain a
  better estimate

44
P-E Ratios of Zero Dividend Stocks

• Companies that pay no dividends, such as
  Microsoft, are problematic for DDM
• cash dividends are the only cash flow in the
  model
• By reformulating the DDM in terms of earnings,
  this problem can be overcome
• Example Microsofts average cost of equity is
  40 (k) its growth rate is 36 and it has a P-E
  of 40. Based on this, we can impute a dividend
  payout ratio

As imputed payout ratio gt 100, it is difficult
to interpret. Most are in the range of 30-50.
45
Microsoft Example

• The imputed dividend payout ratio of 160
  suggests that market values 1 of Microsoft
  earnings at 1.60
• Perhaps the market places a high value on
  Microsofts policy of retaining all earnings to
  finance growth

46
Example of Two Approaches

• Given
• Coca-Cola paid a dividend in 1999 of 0.64 per
  share
• (1 RR) 65.3
• EPS 0.98
• k 20.7 per year for equity
• Growth of 19.7 in the annual dividend
• Using the DDM, Coca-Colas stock is valued at

47
Example of Two Approaches

• Using the P-E ratio approach, Coca-Cola is valued
  at

48
The k g Spread

• The denominator (k g) in both the DDM and the
  P-E ratio approach plays an important role in
  stock valuation
• For instance, in the Coca-Cola example on the
  previous slide, k g was 0.01 or 1
• Regardless of the actual values of k or g, if the
  difference had been 1, the value of Coca-Cola
  would have been the same
• Further examination of the constant growth DDM
  shows that

49
The k g Spread

• This analysis shows that
• The stocks k g spread should equal the stocks
  cash dividend yield (Div1 ? P0)
• Given that the SP500 cash dividend yield has
  steadily decreased since 1983, the k g spread
  should narrow, implying higher P-E ratios and a
  bullish stock market
• If SP500 cash dividend yields continue to fall,
  the rate of capital gains (or g) must rise in
  order for k to remain constant
• If g rises, the implication is a bullish market

50
Financial Analysis Through Time

• The perpetual constant DDM can be used to track
  an all-equity firm through time
• Adding time subscripts to the model links the
  investment in a share of common stock to the
  firms assets, earnings and cash dividends

51
Financial Analysis Through Time
52
Financial Analysis Through Time

• Assets are stock variables
• They can be bought and sold in an instant
• A balance sheet primarily lists stocks of assets
  and liabilities
• Other variables are flow variables
• Occur throughout a period of time and measured as
  rates of flow
• Sales revenue, purchases of raw material and
  income
• An income statement tabulates inflows and outflows

53
Analysis of Growth Investing

• The DDM can be used to analyze growth stocks
• Suppose a firm will earn EPS1 if it doesnt buy
  any new assets
• If it retains earnings (RR)(EPS1) and buys a new
  asset it will grow at ROE
• In year 2 the new asset will earn (ROE)(RR)EPS1
  per year
• After the first year the firm will again pay out
  all EPS as dividends
• This firm can be valued as

54
Analysis of Growth Investing

• The earnings in the numerator of that equation
  can be separated into
• Perpetual annual earnings from the old
  assetsEPS1
• Perpetual annual earnings from the new assetsROE
  x RR x EPS1that begin in year 2
• The previous equation can be rewritten as

55
Analysis of Growth Investing

• The Net Present Value (NPV) of an asset is
  defined as
• PVcash flows cost of asset
• The NPV (at t1) of the asset bought in year 1 is
  the PV of the perpetual cash flows less the new
  assets cost

• In time 0 terms the NPV0 is

56
Analysis of Growth Investing

• Substituting the NPV of the new asset into the
  previous equation

• If a firm buys new assets every year, the
  equation is reformulated as

The firms value will not increase unless the
firm invests in projects with NPV gt 0.
57
Growth Stock Investing

• Growth stocks have high growth rates in sales and
  earnings, and high P-E ratios
• Usually also have low cash dividend yields and
  high ROE
• Empirical evidence suggests that in the long-run
  value stocks (low P-E, below average growth rates
  and high dividends) tend to outperform growth
  stocks
• Perhaps because growth firms retain earnings and
  invest in zero or negative NPVs
• Results in a larger firm, but no growth in PV of
  stock price
• Above analysis suggests that security analysts
  should try to determine the profitability of
  firm's investment opportunities

58
The Bottom Line

• Valuing a common stock is more uncertain than
  valuing a bond
• Cash flows (dividends) are not guaranteed by
  contract
• Equities have all the risk bonds have plus more
• A firm may eliminate a dividend, although this is
  rarely done
• It is easier to forecast dividends in the near
  future vs the far future
• However far dividends have a very low PV

59
The Bottom Line

• Perpetual constant growth DDM is popular
• Sensitive to assumed growth rate
• Thus, two-stage growth model was developed
• Dividing perpetual constant growth DDM by EPS
  shows that P-E ratio
• Varies directly with dividend payout ratio and g
• Varies indirectly with k
• The stock and flow variables within a firm
  interact
• A firms stock price will not rise unless the
  firm invests in positive NPV projects
• Offers an explanation as to why growth firms may
  be increasing in size but not value (stock price)