清华大学公司金融金融硕士课程CF5.pdf

Stock Valuation
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Stock price sensitivity to growth rate
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Stock Valuation
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Case 3: di¤erential growth
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Stock Valuation
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Dividend Growth Model (DGM)
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Stock Valuation
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Stock Valuation
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Example
A 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? The discount rate is 12%.
=
$2 0.12
1.08 0.08
1
#
(1.08)3 (1.12)3
+
$2 (1.08)3 (1.04) 0.12 0.04
(1.12)3
= $54
[1Βιβλιοθήκη 0.8966]+
$32.75 (1.12)3
= $5.58 + $23.31
= $28.89
Hao Wang (Tsinghua University)
Hao Wang (Tsinghua University)
Stock Valuation
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Case 2: constant growth
Assume that dividends will grow at a constant rate, g, forever, i.e.,
and future stock price at the appropriate discount rate.
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Stock Valuation
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Case 3: di¤erential growth
Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter.
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Stock Valuation
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With cash ‡ows
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Stock Valuation
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Solution
"
P0
0.50(1 + 0.02) P0 = 0.15 0.02 = $3.92
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Stock Valuation
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Stock price sensitivity to rate of return
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Div1 = Div0 (1 + g ) Div2 = Div1 (1 + g ) = Div0 (1 + g )2 Div3 = Div2 (1 + g ) = Div0 (1 + g )3
...
Since future cash ‡ows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity:
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Stock Valuation
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Case 1: zero growth
Assume that dividends will remain at the same level forever
Div1 = Div2 = Div3 = ...
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Stock Valuation
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Chapter outline
The Present Value of Common Stocks Estimates of Parameters in the Dividend Discount Model Growth Opportunities Price-Earnings Ratio The Stock Markets
Dividends Capital Gain: a pro…t made from buying an asset and reselling it at a higher price Valuation of Di¤erent Types of Stocks Zero Growth Constant Growth Di¤erential Growth
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Stock Valuation
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Case 3: di¤erential growth
We can value this as the sum of: P0 = PA + PB
a T -year annuity growing at rate g1
"
PA
=
Div1 R g1
1
# (1 + g1)T (1 + R)T
plus the discounted value of a perpetuity growing at rate g2 that starts
in year T + 1
DivT +1
PB
=
R g2
(1 + R)T
Hao Wang (Tsinghua University)
...
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Stock Valuation
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Illustration: di¤erential growth
Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter
Div1 = Div0 (1 + g1) Div2 = Div1 (1 + g1) = Div0 (1 + g1)2
... DivN = DivN 1 (1 + g1) = Div0 (1 + g1)N DivN +1 = DivN (1 + g2) = Div0 (1 + g1)N (1 + g2)
Stock Valuation
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The PV of common stock
The value of any asset is the present value of its expected future cash ‡ows. Stock ownership produces cash ‡ows from:
Assume that: A company pays dividends each period (usually quarterly) with certainty. the company will NEVER go bankrupt.
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P0
=
Div1 Rg
This is called “Gordon Growth Model”.
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Stock Valuation
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Example
Suppose Big D, Inc., just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk level, how much should the stock be selling for?
Since future cash ‡ows are constant, the value of a zero growth stock is the present value of a perpetuity:
P0
=
Div1 (1 + R)1
+
Div2 (1 + R)2
+
Div3 (1 + R)3
Corporate Finance
Hao Wang
Tsinghua University
Fall 2013