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1FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Fin2808: Investments
Spring, 2010Dragon Tang
Fin2808: Investments
Spring, 2010Dragon TangLectures 13 & 14
Equity Valuation ModelsMarch 9&11 , 2010
Readings: Chapter 18Practice Problem Sets: 1,5,7,14, 16,17
2FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
How to make money in stocks?How to make money in stocks?
3FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
How to make money in stocks?How to make money in stocks?
• Capital gains: buy low/sell high
– Growth companies
• Dividend yields: income stream
– Matured (value) companies
4FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Equity ValuationEquity 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.
5FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Balance Sheet Valuation MethodsBalance Sheet Valuation Methods
• Book Value
• Liquidation Value
• Replacement Cost
costt replacemen
pricemarket Q sTobin'
6FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Expected Holding Period ReturnExpected Holding Period Return
yield
gain/losscapital
expected
yield
dividend
expected
P
PPE
P
DE
P
PPEDEE(HPR)
0
01
0
1
0
011
• If E(HPR) > Required Rate of Return(RRR), the stock is a good deal.• RRR is from a pricing model, e.g. CAPM:
•In market equilibrium, E(HPR) = RRR.
))(()( fmXYZfXYZ rrErrE
7FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Intrinsic Value versus Market PriceIntrinsic Value versus Market Price
•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
Intrinsic value --The present value of a firm’s expected future net cash flows discounted by the required rate of return.
k
PEDEV
1
)()( 110
8FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Dividend Discount ModelsDividend Discount Models
One Period Case:
k
PEDEV
1
)()( 110
Multi-period Case:
HHH
k
PD
k
D
k
DV
1
...11 2
210
Where D1,…, DH and PH are expected values
9FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Dividend Discount ModelsDividend Discount ModelsExample: 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?
10FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Dividend Discount ModelsDividend Discount Models
...
111 33
221
0
k
D
k
D
k
DV
Dividend discount model (infinite horizon):
11FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Constant Growth DDM (Gordon’s Model)
Constant Growth DDM (Gordon’s Model)
kg
gk
D
gk
gDV
, 1 10
0
...1
1
1
1
1
13
30
2
200
0
k
gD
k
gD
k
gDV
12FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Constant Growth DDMConstant Growth DDMExample: 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?
13FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Market Capitalization RateMarket Capitalization Rate
If V0 = P0 :
VD
k g01
kD
Pg 1
0Dividend
YieldCapital
Gains Yield
Gordon’s Model:
If g = 0: k
D
k
D
gk
gDV 100
0 0
011
Perpetuity
14FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Implications of this ModelImplications of this Model
• 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
VD
k g01
15FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Dividend Payout Ratioand
Plowback Ratio
Dividend Payout Ratioand
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
16FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Stock Prices and Investment Opportunities
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.
17FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Figure 12.1 Dividend Growth for Two Earnings Reinvestment
Policies
Figure 12.1 Dividend Growth for Two Earnings Reinvestment
Policies
18FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Plowback Ratio and GrowthPlowback Ratio and Growth
g b ROE
Where:
ROE = Return on Equityb = Plowback Ratio (or Earning Retention Ratio)
19FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Stock Prices and Investment Opportunities
Stock Prices and Investment Opportunities
Present valueno-growth
(b=0 or ROE=k)
Present value of growth OpportunitiesPVGO > 0 if ROE>kPVGO <0 if ROE<k
b)k-(ROE
-b)(E
gk
DP
111
0
PVGO 10
k
EP
20FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Estimating GrowthEstimating GrowthExample: 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?
21FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Life Cycles and the Constant Growth Model
Life Cycles and the Constant Growth Model
Changing growth rates:
temporary high(or low) growth
permanentconstant growth
V
D
k
D
k
D
k
D
k
H
H
H
H01 2
2
1
11 1 1 1
. . . . . .
22FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Changing Growth RateChanging Growth RateExample: 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?
23FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Price-Earning (P/E) RatiosPrice-Earning (P/E) Ratios
• Ratio of Stock price to its earnings per share• Useful for firm valuation:
• Problems:– Forecasts of E– Forecasts of P/E
E
PEP
24FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
P/E Ratios and GrowthP/E Ratios and Growth
PVGOk
EP 1 0
kEkE
P
11
0 PVGO1
1
If PVGO = 0: PEk0
1
25FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Numerical Example: No GrowthNumerical 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
26FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
P/E Ratios and ROEP/E Ratios and ROE
bk
b
E
P
ROE
1
1
0
P/E ratio rises with ROE but not necessarily with b
1/k
ROE<k
ROE>k
b
P/E
27FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Numerical Example with GrowthNumerical 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
28FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Figure 12-3 P/E Ratio of the S&P 500 Index and
Inflation
Figure 12-3 P/E Ratio of the S&P 500 Index and
Inflation
29FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Caveat with P/E RatiosCaveat with P/E Ratios
• High plowback ratio (b) High Growth Rate (g) (g = ROE*b)
BUT
• High g (if due to high b) High P/E ratio
• Practitioners: high P/E as proxy of high dividend growth (g)
30FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
P/E ratio and RiskP/E ratio and Risk
Holding everything equal:
High risk (k), Low P/E.
Why do small-risky firm have high P/E?
gk
b
E
P
1
31FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Pitfalls in P/E AnalysisPitfalls 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
32FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Figure 12-6 P/E RatiosFigure 12-6 P/E Ratios
33FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Combining P/E and DDMCombining P/E and DDM
VD
k
D
k
D
k
D P E EPS
k0
1 22
33
441 1 1 1
34FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
The Aggregate Stock Market:Earning Multiplier Approach
The Aggregate Stock Market:Earning Multiplier Approach
VPE
E
where
P EE P
and E P is the earnings yield
M
/1
35FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
Other Valuation Ratios & Approaches
Other Valuation Ratios & Approaches
• Price-to-book
• Price-to-cash flow
• Price-to-sales
• Present Value of Free Cash Flow
36FIN 2808, Spring 10 - TangChapter 18: Equity Valuation
SummarySummary• 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
• Constant growth model DDM:
• 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
gk
DV
1
0