Fin2808: Investments
Spring, 2010
Dragon Tang
Lectures 13 & 14
Equity Valuation Models
March 9&11， 2010
Readings: Chapter 18
Practice Problem Sets: 1,5,7,14, 16,17
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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How to make money in stocks?
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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How to make money in stocks?
• Capital gains: buy low/sell high
– Growth companies
• Dividend yields: income stream
– Matured (value) companies
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Equity Valuation
Objectives:
•
Calculate the intrinsic value of a firm using either a
constant growth or multistage dividend discount model.
•
Calculate the intrinsic value of a stock using a dividend
discount model in conjunction with a price/earnings
ratio.
•
Assess the growth prospects of a firm from it P/E ratio.
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Balance Sheet Valuation Methods
• Book Value
• Liquidation Value
• Replacement Cost
market price
Tobin' s Q 
replacemen t cost
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Expected Holding Period Return
E(HPR) 
E D1   E P1   P0 
P0

E D1   E P1   P0 

P0
P0
expected
expected
 dividend  capital gain/loss
yield
yield
• If E(HPR) > Required Rate of Return(RRR), the stock
is a good deal.
• RRR is from a pricing model, e.g. CAPM:
E (rXYZ )  rf   XYZ ( E (rm )  rf )
•In market equilibrium, E(HPR) = RRR.
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Intrinsic Value versus Market Price
Intrinsic value --The present value of a firm’s expected future
net cash flows discounted by the required rate of return.
E ( D1 )  E ( P1 )
V0 
1 k
•V0 (intrinsic value) > P0 (market price)  buy
•V0 (intrinsic value) < P0 (market price)  sell or sell short
•In market equilibrium, V0 = P0
•k is the market capitalization rate which equates V0 and P0
•If V0 P0, then EMH implies the estimate of k is wrong
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Dividend Discount Models
One Period Case:
E ( D1 )  E ( P1 )
V0 
1 k
Multi-period Case:
D1
D2
DH  PH
V0 

...
2
H
1  k 1  k 
1  k 
Where D1,…, DH and PH are expected values
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Dividend Discount Models
Example: Whitewater Rapids Company is expected to have
dividends grow at a rate of 12% for the next three years. In
three years, the price of the stock is expected to be $ 74.46. If
Whitewater just paid a dividend of $2.00 and its level of risk
requires a discount rate of 10%, what is the intrinsic value of
Whitewater stock?
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Dividend Discount Models
Dividend discount model (infinite horizon):
D3
D1
D2
V0 



...
2
3
1  k 1  k 
1  k 
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Constant Growth DDM
(Gordon’s Model)
D0 1  g  D0 1  g 
D0 1  g 
V0 


...
2
3
1 k
1  k 
1  k 
2
D0 1  g 
D1
V0 

,
kg
kg
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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gk
11
Constant Growth DDM
Example: Whitewater Rapids Company is expected to have
dividends grow at a constant rate of 6% for the foreseeable
future. If Whitewater just paid a dividend of $2.81 and its level
of risk requires a discount rate of 10%, what is the intrinsic value
of Whitewater stock?
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Market Capitalization Rate
D1
Gordon’s Model: V0 
k g
If V0 = P0 :
D1
k 
g
P0
Dividend
Capital
Yield
Gains Yield
If g = 0:
D0 1  g  D0 1  0 D1
V0 


kg
k 0
k
Perpetuity
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Implications of this Model
D1
V0 
k g
• If D1 increases, then V0 increases.
• If k decreases, then V0 increases.
• If g increases, then V0 increases.
• If D1 increases X%, then V0 will
increase X%.
• g = the capital gains yield
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Dividend Payout Ratio
and
Plowback Ratio
• Dividend Payout Ratio: Percentage of earnings paid
out as dividends
• Plowback (or Earning Retention) Ratio:
Fraction of earnings retained and reinvested in the firm
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Stock Prices and
Investment Opportunities
• If a firm retains earnings and reinvest
them in a profitable investment
opportunity, dividend may grow “faster”.
• If a firm pays out all dividends nothing
gets re-invested, nothing growths.
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Figure 12.1 Dividend Growth for
Two Earnings Reinvestment Policies
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Plowback Ratio and Growth
g  ROE  b
Where:
ROE = Return on Equity
b
= Plowback Ratio
(or Earning Retention Ratio)
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Stock Prices and
Investment Opportunities
D1
E1  ( 1-b)
P0 

k  g k-(ROE  b)
E1
P0 
 PVGO
k
Present value
no-growth
(b=0 or ROE=k)
FIN 2808, Spring 10 - Tang
Present value of growth
Opportunities
PVGO > 0 if ROE>k
PVGO <0 if ROE<k
Chapter 18: Equity Valuation
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Estimating Growth
Example: Takeover Target has a plowback ratio of 60% and an
ROE of 10%. If it expects earnings to be $ 5 per share, what is
the present value of Takeover’s growth opportunities if the
appropriate capitalization rate is 15%? What is the PVGO?
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Life Cycles and the
Constant Growth Model
Changing growth rates:
D1
D2
DH
DH  1
V0 

 ... 

 . ..
2
H
H 1
1  k 1  k 
1  k  1  k 
temporary high
(or low) growth
FIN 2808, Spring 10 - Tang
permanent
constant growth
Chapter 18: Equity Valuation
21
Changing Growth Rate
Example: Whitewater Rapids Company is expected to have
dividends grow at a rate of 12% for the next three years. In three
years, the dividends will settle down to a more sustainable growth
rate of 6% which is expected to last “forever.” If Whitewater just
paid a dividend of $2.00 and its level of risk requires a discount
rate of 10%, what is the intrinsic value of Whitewater stock?
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Price-Earning (P/E) Ratios
• Ratio of Stock price to its earnings per share
• Useful for firm valuation:
P
P  E
E
• Problems:
– Forecasts of E
– Forecasts of P/E
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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P/E Ratios and Growth
E1
P0 
 PVGO
k


P0
1 
PVGO 

1 

E
E1
k 
1

k


E1
If PVGO = 0: P 0 
k
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Numerical Example: No Growth
E0 = $2.50
g=0
k = 12.5%
P0 = D/k = $2.50/.125 = $20.00
P/E = 1/k = 1/.125 = 8
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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P/E Ratios and ROE
P0
1 b

E1 k  ROE  b 
P/E ratio rises with ROE but not necessarily with b
P/E
ROE>k
1/k
b
ROE<k
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Numerical Example with 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
P/E = 31.14/2.73 = 11.4
P/E = (1 - .60) / (.125 - .09) = 11.4
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Figure 12-3 P/E Ratio of the
S&P 500 Index and Inflation
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Caveat with P/E Ratios
• High plowback ratio (b)
(g = ROE*b)
High Growth Rate (g)
BUT
• High g (if due to high b)
High P/E ratio
• Practitioners: high P/E as proxy of high dividend
growth (g)
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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P/E ratio and Risk
P 1 b

E kg
Holding everything equal:
High risk (k), Low P/E.
Why do small-risky firm have high P/E?
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Pitfalls in P/E Analysis
• Earnings are based on accounting data
Current price and current earnings
Future expected earnings is more appropriate
• In P/E formula, E is an expected trend
• In financial pages, E is the actual past
period's earnings
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Figure 12-6 P/E Ratios
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Combining P/E and DDM
D4   P E  EPS 
D1
D2
D3
V0 



2
3
4
1  k 1  k 
1  k 
1  k 
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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The Aggregate Stock Market:
Earning Multiplier Approach
VM
P

E
E
where
P/ E 
1
E P
and E P is the earnings yield
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Other Valuation Ratios & Approaches
•
•
•
•
Price-to-book
Price-to-cash flow
Price-to-sales
Present Value of Free Cash Flow
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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Summary
• Valuation approaches:
-Balance sheet values
-Present value of expected future dividends
• DDM states that the price of a share of stock is equal to the
present value of all future dividends discounted at the appropriate
required rate of return
D1
V

• Constant growth model DDM: 0
kg
• P/E ratio is an indication of the firm's future
growth opportunities
• Models used for the firm can be used to forecast the
behavior of the aggregate stock market
FIN 2808, Spring 10 - Tang
Chapter 18: Equity Valuation
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