# Chap018 - revised

```Equity Valuation
Models
CHAPTER 18
Valuation Methods
Valuation by comparables
 Price/Earning Ratios
 Balance Sheet Models
Book Value
http://finance.yahoo.com/q/ks?s=CSCO
http://biz.yahoo.com/ic/814.html
Expected Returns vs. Required Return
 CAPM
Intrinsic Value vs. Market price
 Dividend Discount Models
Table 18.1 Financial Highlights for Microsoft
Corporation, October 25, 2007
Limitations of Book Value
• Book value is an application of arbitrary
accounting rules
• Can book value represent a floor value?
• Better approaches
– Liquidation value
– Replacement cost
– Tobin’s q ratio
Expected Holding Period Return
• The return on a stock investment comprises cash
dividends and capital gains or losses
– Assuming a one-year holding period
Expected HPR= E (r ) 
E ( D1 )   E ( P1 )  P0
P0

Required Return
• CAPM gave us required return:
k  rf    E (rM )  rf 
• If the stock is priced correctly
– Required return should equal expected return
Intrinsic Value and Market Price
• Intrinsic Value
– Self assigned Value
– Variety of models are used for estimation
• Market Price
– Consensus value of all potential traders
– IV &lt; MP Sell or Short Sell
– IV = MP Hold or Fairly Priced
Specified Holding Period
D
D

V 
(1 k ) (1 k )
1
0
2
1
P
D
 ... 
(1 k )
H
2
H
H
PH = the expected sales price for the stock at time H
H = the specified number of years the stock is
expected to be held
Dividend Discount Models: General Model

Dt
Vo  
t
t  1 (1  k )
V0 = Value of Stock
Dt = Dividend
k = required return
No Growth Model
D
Vo 
k
• Stocks that have earnings and dividends that
are expected to remain constant
– Preferred Stock
No Growth Model: Example
D
Vo 
k
E1 = D1 = \$5.00
k = .15
V0 = \$5.00 /.15 = \$33.33
Constant Growth Model
Do(1  g )
Vo 
kg
g = constant perpetual growth rate
Constant Growth Model: Example
Do (1  g )
Vo 
kg
E1 = \$5.00
b = 40%
k = 15%
(1-b) = 60% D1 = \$3.00 g = 8%
V0 = 3.00 / (.15 - .08) = \$42.86
Estimating Dividend Growth Rates
g  ROE  b
g = growth rate in dividends
ROE = Return on Equity for the firm
b = plowback or retention percentage rate
(1- dividend payout percentage rate)
Figure 18.1 Dividend Growth for Two Earnings
Reinvestment Policies
Present Value of Growth Opportunities
• If the stock price equals its IV, growth rate is
sustained, the stock should sell at:
D1
P0 
kg
• If all earnings paid out as dividends, price should
be lower (assuming growth opportunities exist)
Present Value of Growth Opportunities Continued
• Price = No-growth value per share + PVGO (present
value of growth opportunities)
E1
P0 
 PVGO
k
Partitioning Value: Example
ROE = 20% d = 60% b = 40%
E1 = \$5.00 D1 = \$3.00 k = 15%
g = .20 x .40 = .08 or 8%
Partitioning Value: Example Continued
3
Vo 
 \$42.86
(.15.08)
5
NGVo 
 \$33.33
.15
PVGO  \$42.86  \$33.33  \$9.52
Vo = value with growth
NGVo = no growth component value
PVGO = Present Value of Growth Opportunities
Life Cycles and Multistage Growth Models
(1  g1 )
DT (1  g 2 )
P0  D0 

t
T
(1

k
)
(
k

g
)(1

k
)
t 1
2
T
t
• g1 = first growth rate
• g2 = second growth rate
• T = number of periods of growth at g1
Multistage Growth Rate Model: Example
D0 = \$2.00 g1 = 20% g2 = 5%
k = 15% T = 3 D1 = 2.40
D2 = 2.88 D3 = 3.46 D4 = 3.63
V0 = D1/(1.15) + D2/(1.15)2 + D3/(1.15)3 +
D4 / (.15 - .05) ( (1.15)3
V0 = 2.09 + 2.18 + 2.27 + 23.86 = \$30.40
Table 18.2 Financial Ratios in Two Industries
Figure 18.2 Value Line Investment Survey Report
on Honda Motor Co.
Price Earnings Ratios
• P/E Ratios are a function of two factors
– Required Rates of Return (k)
– Expected growth in Dividends
• Uses
– Relative valuation
– Extensive Use in industry
P/E Ratio: No Expected Growth
E1
P0 
k
P0
1

E1 k
• E1 - expected earnings for next year
– E1 is equal to D1 under no growth
• k - required rate of return
P/E Ratio: Constant Growth
D1
E1 (1  b)
P0 

k  g k  (b  ROE )
P0
1 b

E1 k  (b  ROE )
b = retention ratio
ROE = Return on Equity
Numerical Example: No Growth
E0 = \$2.50 g = 0 k = 12.5%
P0 = D/k = \$2.50/.125 = \$20.00
PE = 1/k = 1/.125 = 8
Numerical Example: Growth
b = 60% ROE = 15% (1-b) = 40%
E1 = \$2.50 (1 + (.6)(.15)) = \$2.73
D1 = \$2.73 (1-.6) = \$1.09
k = 12.5% g = 9%
P0 = 1.09/(.125-.09) = \$31.14
PE = 31.14/2.73 = 11.4
PE = (1 - .60) / (.125 - .09) = 11.4
Table 18.3 Effect of ROE and Plowback on Growth
and the P/E Ratio
P/E Ratios and Stock Risk
• Holding all else equal
– Riskier stocks will have lower P/E multiples
– Higher values of k; therefore, the P/E
multiple will be lower
P 1 b

E kg
Pitfalls in P/E Analysis
• Use of accounting earnings
– Earnings Management
– Choices on GAAP
• Inflation
• Reported earnings fluctuate around the business
cycle
Figure 18.3 P/E Ratios of the S&amp;P 500 Index and
Inflation
Figure 18.4 Earnings Growth for Two Companies
Figure 18.5 Price-Earnings Ratios
Figure 18.6 P/E Ratios for Different Industries,
2007
Other Comparative Value Approaches
• Price-to-book ratio
• Price-to-cash-flow ratio
• Price-to-sales ratio
Figure 18.7 Market Valuation Statistics
Free Cash Flow Approach
• Discount the free cash flow for the firm
• Discount rate is the firm’s cost of capital
• Components of free cash flow
– After tax EBIT
– Depreciation
– Capital expenditures
– Increase in net working capital
Comparing the Valuation Models
• In practice
– Values from these models may differ
– Analysts are always forced to make simplifying
assumptions
The Aggregate Stock Market
• Explaining Past Behavior
• Forecasting the Stock Market
Figure 18.8 Earnings Yield of S&amp;P 500
versus 10-Year Treasury-Bond Yield
Table 18.4 S&amp;P 500 Price Forecasts Under Various
Scenarios
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