Corporate finance chapter 09 valuation of commen stocks
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Chapter 9: Valuation of
Common Stocks
Objective
Explain equity evaluation
using discounting
1
Dividend policy
and wealth
Chapter 9 Contents
9.1 Reading stock listings
9.2 The discounted dividend model
9.3 Earning and investment opportunity
9.4 A reconsideration of the price multiple
approach
9.5 Does dividend policy affect shareholder
wealth?
2
Reading Stock Listings
Yr Hi
Yr Lo
123 1/8 93 1/8
Stock
IBM
Sym
IBM
Div
4.84
Yld %
4.2
PE
16
Vol 100
14591
Day Hi
Day Lo Close
115
113
Net Chg
114 3/4 +1 3/8
3
Present Value of Dividends
D1
D2
D3
D4
P0 =
+
+
+
+ ...
1
2
3
4
(1 + k ) (1 + k ) ( 1 + k ) (1 + k )
D3
D1
1 D2
D4
=
+
+
+
+ ...
1
1
1
2
3
(1 + k ) (1 + k ) ( 1 + k ) ( 1 + k ) ( 1 + k )
D1
1
D1 + P1
{ P1} =
=
+
1
1
1+ k
(1 + k ) (1 + k )
D1 + P1 − P0
k=
P0
4
Expected Rate of Return
• The price and dividend next year are
expected prices, so
– The expected rate of return in any period
equals the market capitalization rate, k
D1 + P1 − P0
k=
P0
5
Rate Relationship
D1 + P1 − P0 D1 P1 − P0
k=
=
+
P0
P0
P0
• This relationship tells you that next
year’s expected dividend yield + the
expected capital gain yield is equal to the
required rate of return
6
Price0 Is Discounted Expected
(Dividend1 + Price1)
• Price is the present value of the expected
dividend plus the end-of-year price
discounted at the required rate of return
D1 + P1
P0 =
1+ k
7
Ease of Use
• Recall from chapter 4 that, for a perpetuity,
the present value is the real value of the
first cash flow divided by the real rate
Dreal
p0 =
=
R
Dnominal @ 1
(1 + g )
R
8
Putting This Together
D1
p0 =
=
(1 + g ) R
D1
1+ k
(1 + g )
− 1
1+ g
D1
D1
=
=
(1 + k ) − (1 + g ) k − g
9
Solving for K
D1
p0 =
⇔
k−g
D1
k=
+g
p0
10
G = Capital Gains Yield
• Comparing prior results:
D1
k=
+g
p0
D1 P1 − P0
& k=
+
P0
P0
P1 − P0
⇒ g=
P0
11
Earning and Investment
Opportunity
• To simplify the analysis, suppose that no
new shares are issues, and no taxes
Dividends = earnings - net new investment
“D = E - I”. The formula for valuing stock is
∞
∞
∞
Dt
Et
It
p0 = ∑
=∑
−∑
t
t
t
t =1 (1 + k )
t =1 (1 + k )
t =1 (1 + k )
12
Growth Stock
80
80
80
wealth = 100 * (0.4 + 0.6 * * (0.4 + 0.6 * * (0.4 + 0.6 * * (...))))
60
60
60
wealth = 100 * (0.4 +
Kept
Original wealth
0.8 * (0.4 +
0.8 * (0.4 +
0.8 * (...))))
Wealth Multiplier
Reinvested
13
Growth Stock
wealth = 100 * (0.4 + 0.8 * (0.4 + 0.8 * (0.4 + 0.8 * (...))))
= 100 * 0.4 * (1 + 0.8 * (1 + 0.8 * (1 + 0.8 * (...))))
wealth = 100 * 0.4 * (1 + 0.8 + 0.82 + 0.83 + ...)
1
= 100 * 0.4 *
1 - 0.8
= $200
1
1 + a + a + a + ... =
1− a
2
3
14
Generalize
• Let the
– V = value of the shares without reinvestment
– G = the growth from new investment
– R = retention ratio
– M = wealth multiplier = g/i
– Wealthg = wealth0*(1-r)/(1-w*r)
15
Reinvestment Under Normal
Growth
6
Price =
= $100
0.15 − 0.6 * 0.15
Cost of Capital
Retention Ratio
16
Growth Rate
Illustration: Dividends
Assets
Cash
Liab\Equ
2
Debt
2
Other
10
Equity
10
Total
12
Total
12
17
Illustration: Dividend Payment
Was 2
Assets
Cash
Was 10
Liab\Equ
1
Debt
2
9
Other
10
Equity
Total
11
Total
18
11
Were 12
Illustration: Share Repurchase
Assets
Cash
Liab\Equ
2
Debt
2
Other
10
Equity
10
Total
12
Total
12
19
Illustration: Share Repurchase
Was 2
Assets
Cash
Was 10
Liab\Equ
1
Debt
2
9
Other
10
Equity
Total
11
Total
20
11
Were 12
