stock valuation understand how stock prices depend on future dividends and dividend growth estimates...
TRANSCRIPT
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Stock Valuation• Understand how stock prices depend on future
dividends and dividend growth• Estimates of Parameters in the Dividend-Discount
Model• Compute present value of stock prices using the
dividend growth model• Understand how growth opportunities affect stock
values• Understand the PE ratio• Understand how stock markets work
• Preferred stock• Efficient Market Hypothesis (EMH)
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Common Stock: Owners, Directors, and Managers
• Represents ownership.
• Ownership implies control.
• Stockholders elect directors.
• Directors hire management.
• Since managers are “agents” of shareholders, their goal should be: Maximize stock price.
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Different Approaches for Valuing Common Stock
• Dividend growth model
• Using the multiples of comparable firms
• Free cash flow method
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The Present Value of Common Stocks
• Dividends versus Capital Gains
• Valuation of Different Types of Stocks– Zero Growth– Constant Growth– Differential Growth
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Case 1: Zero Growth
• Assume that dividends will remain at the same level forever
rP
rrrP
Div
)1(
Div
)1(
Div
)1(
Div
0
33
22
11
0
321 DivDivDiv Since future cash flows are constant, the value of a zero
growth stock is the present value of a perpetuity:
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If g = 0, the dividend stream is a perpetuity.
2.00 2.002.00
0 1 2 3rs=13%
P0 = = = $15.38.PMT
r
$2.00
0.13^
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Stock Value = PV of Dividends
Case 2What is a constant growth stock?
One whose dividends are expected togrow forever at a constant rate, g.
P0 =^
(1+r)1 (1+r)2 (1+r)3 (1+r)∞
D1 D2 D3 D∞+ + +…+
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Case 2For a constant growth stock:
D1 = D0(1+g)1
D2 = D0(1+g)2
Dt = D0(1+g)t
If g is constant and less than rs, then:
P0 = ^ D0(1+g)
r - g=
D1
r - g
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Intrinsic Stock Value D0 = 2.00, rs = 13%, g = 6%.
Constant growth model:
= = $30.29.0.13 - 0.06
$2.12 $2.12
0.07
P0 = ^ D0(1+g)
r - g=
D1
r - g
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Case 3: Differential Growth• Assume that dividends will grow at different rates
in the foreseeable future and then will grow at a constant rate thereafter.
• To value a Differential Growth Stock, we need to:– Estimate future dividends in the foreseeable
future.– Estimate the future stock price when the stock
becomes a Constant Growth Stock (case 2).– Compute the total present value of the
estimated future dividends and future stock price at the appropriate discount rate.
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Case 3: Differential Growth
)(1DivDiv 101 g
Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter
210112 )(1Div)(1DivDiv gg
NNN gg )(1Div)(1DivDiv 1011
)(1)(1Div)(1DivDiv 21021 ggg NNN
...
...
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Case 3: Differential Growth
)(1Div 10 g
Dividends will grow at rate g1 for N years and grow at rate g2 thereafter
210 )(1Div g
Ng )(1Div 10 )(1)(1Div
)(1Div
210
2
gg
gN
N
…0 1 2
…N N+1
…
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Case 3: Differential GrowthWe can value this as the sum of:
an N-year annuity growing at rate g1
T
T
A r
g
gr
CP
)1(
)1(1 1
1
plus the discounted value of a perpetuity growing at rate g2 that starts in year N+1
NB r
grP
)1(
Div
2
1N
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Case 3: Differential GrowthTo value a Differential Growth Stock, we can use
NT
T
r
gr
r
g
gr
CP
)1(
Div
)1(
)1(1 2
1N
1
1
Or we can cash flow it out.
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A Differential Growth ExampleA common stock just paid a dividend of $2. The
dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity.
What is the stock worth if the rate of return is 12%?
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With the Formula
NT
T
r
gr
r
g
gr
CP
)1(
Div
)1(
)1(1 2
1N
1
1
3
3
3
3
)12.1(
04.12.)04.1()08.1(2$
)12.1(
)08.1(1
08.12.
)08.1(2$
P
3)12.1(
75.32$8966.154$ P
31.23$58.5$ P 89.28$P
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A Differential Growth Example (continued)
08).2(1$ 208).2(1$…
0 1 2 3 4
308).2(1$ )04.1(08).2(1$ 3
16.2$ 33.2$
0 1 2 3
08.
62.2$52.2$
89.28$)12.1(
75.32$52.2$
)12.1(
33.2$
12.1
16.2$320
P
75.32$08.
62.2$3 P
The constant growth phase
beginning in year 4 can be valued as a
growing perpetuity at time 3.
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Supernormal Growth Stock
• Supernormal growth of 30% for 3 years, and then long-run constant g = 6%.
• Can no longer use constant growth model.
• However, growth becomes constant after 3 years.
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Nonconstant growth followed by constant growth (D0 = $2):
0
2.3009
2.6470
3.0453
46.1135
1 2 3 4r=13%
54.1067 = P0
g = 30% g = 30% g = 30% g = 6%
2.60 3.38 4.394 4.6576
^P3 = ^ $4.6576
0.13 – 0.06= $66.5371
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Estimates of Parameters in the Dividend-Discount Model
• The value of a firm depends upon its growth rate, g, and its discount rate, r. – Where does g come from?– Where does r come from?
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Formula for Firm’s Growth Rate
g = Retention ratio × Return on retained earnings
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Where does r come from?
• The discount rate can be broken into two parts. – The dividend yield – The growth rate (in dividends)
• In practice, there is a great deal of estimation error involved in estimating r.
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Growth Opportunities
• Growth opportunities are opportunities to invest in positive NPV projects.
• The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100% of its earnings as dividends plus the net present value of the growth opportunities.
NPVGOR
EPSP
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NPVGO Model: Example
Consider a firm that has forecasted EPS of $5, a discount rate of 16%, and is currently priced at $75 per share.
• We can calculate the value of the firm as a cash cow.
• So, NPVGO must be: $75 - $31.25 = $43.75
25.31$16.
5$EPS0
RP
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Retention Rate and Firm Value
• An increase in the retention rate will:– Reduce the dividend paid to shareholders– Increase the firm’s growth rate
• These have offsetting influences on stock price
• Which one dominates?– If ROE>R, then increased retention increases
firm value since reinvested capital earns more than the cost of capital.
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Price Earnings Ratio• Many analysts frequently relate earnings per share to
price.• The price earnings ratio is a.k.a the multiple
– Calculated as current stock price divided by annual EPS
– The Wall Street Journal uses last 4 quarter’s earnings
• Firms whose shares are “in fashion” sell at high multiples. Growth stocks for example.
• Firms whose shares are out of favor sell at low multiples. Value stocks for example.
EPS
shareper Priceratio P/E
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PE and NPVGO
• Recall,
• Dividing every term by EPS provides the following description of the PE ratio:
• So, a firm’s PE ratio is positively related to growth opportunities and negatively related to risk (R)
NPVGOR
EPSP
EPS
NPVGO
RPE
1
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Other Price Ratio Analysis• Many analysts frequently relate earnings per share to
variables other than price, e.g.:– Price/Cash Flow Ratio
• cash flow = net income + depreciation = cash flow from operations or operating cash flow
– Price/Sales• current stock price divided by annual sales per
share– Price/Book (a.k.a Market to Book Ratio)
• price divided by book value of equity, which is measured as assets - liabilities
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Preferred Stock
• Hybrid security.
• Similar to bonds in that preferred stockholders receive a fixed dividend which must be paid before dividends can be paid on common stock.
• However, unlike bonds, preferred stock dividends can be omitted without fear of pushing the firm into bankruptcy.
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Expected return on preferred stock, given Vps = $50 and annual dividend =
$5
Vps = $50 =$5
rps
rps
$5
$50= = 0.10 = 10.0%
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Are volatile stock prices consistent with rational pricing?
• Small changes in expected g and rs cause large changes in stock prices.
• As new information arrives, investors continually update their estimates of g and r.
• If stock prices aren’t volatile, then this means there isn’t a good flow of information.
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What is market equilibrium?
• In equilibrium, stock prices are stable. There is no general tendency for people to buy versus to sell.
• The expected price, P, must equal the actual price, P. In other words, the fundamental value must be the same as the price.
(More…)
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What’s the Efficient MarketHypothesis (EMH)?
• Securities are normally in equilibrium and are “fairly priced.” One cannot “beat the market” except through good luck or inside information.
(More…)
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Weak-form EMH
• Can’t profit by looking at past trends. A recent decline is no reason to think stocks will go up (or down) in the future. Evidence supports weak-form EMH, but “technical analysis” is still used.
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Semistrong-form EMH
• All publicly available information is reflected in stock prices, so it doesn’t pay to pore over annual reports looking for undervalued stocks. Largely true.
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Strong-form EMH
• All information, even inside information, is embedded in stock prices. Not true--insiders can gain by trading on the basis of insider information, but that’s illegal.
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Markets are generally efficient because:
• 100,000 or so trained analysts--MBAs, CFAs, and PhDs--work for firms like Fidelity, Merrill, Morgan, and Prudential.
• These analysts have similar access to data and megabucks to invest.
• Thus, news is reflected in P0 almost instantaneously.
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Stock Market Reporting
52WEEKS YLD VOL NETHI LO STOCKSYMDIV % PE 100s HI LOCLOSE CHG
52.75 19.06 Gap Inc GPS 0.09 0.5 15 65172 20.50 19 19.25 -1.75
Gap has been as high as $52.75 in the last year.
Gap has been as low as $19.06 in the last year.
Gap pays a dividend of 9 cents/share
Given the current price, the dividend yield is ½ %
Given the current price, the PE ratio is 15 times earnings
6,517,200 shares traded hands in the last day’s trading
Gap ended trading at $19.25, down $1.75 from yesterday’s close
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Stock Market Reporting
52WEEKS YLD VOL NETHI LO STOCKSYMDIV % PE 100s HI LOCLOSE CHG
52.75 19.06 Gap Inc GPS 0.09 0.5 15 65172 20.50 19 19.25 -1.75
Gap Incorporated is having a tough year, trading near their 52-week low. Imagine how you would feel if within the past year you had paid $52.75 for a share of Gap and now had a share worth $19.25! That 9-cent dividend wouldn’t go very far in making amends.
Yesterday, Gap had another rough day in a rough year. Gap “opened the day down” beginning trading at $20.50, which was down from the previous close of $21.00 = $19.25 + $1.75
Looks like cargo pants aren’t the only things on sale at Gap.
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Summary and Conclusions
A stock can be valued by discounting its dividends. There are three cases:
1. Zero growth in dividends
2. Constant growth in dividends
3. Differential growth in dividends
rP
Div0
grP
1
0
Div
NT
T
r
gr
r
g
gr
CP
)1(
Div
)1(
)1(1 2
1N
1
1