Stock Valuation
Chapter 9.1,9.2
Outline
• Investing in stocks
– Capital gains, dividend yield, return
•
•
•
•
The Constant Dividend Growth Model
The Dividend and Growth Tradeoff
The DGM with Changing Growth rates
Further problems
Investing in Stocks
A One-Year Investor
There are two potential sources of cash flows form
owning a stock:
• The firm might pay out cash to shareholders in
the form of dividends
• The investor can generate cash flows by selling
shares at some future date
The investor pays the
current price P0 and at the
end of the year expects to
receive dividend Div1 and to
sell the stock at P1
Equity Cost of Capital
Both potential sources of cash flows form owning a stock
are risky
• Dividends change overtime
• Stock prices fluctuate considerably
Equity investors demand compensation for this higher
risk and require a risk-premium as reflected in the:
Equity cost of capital rE
Div1 + P1
P0 =
1+ rE
Capital Gains and Dividend Yield
The expected one-period total return on
investment in a stock is the sum of the expected
capital gain yield and dividend yield
Div1 P1 - P0
rE =
+
P0
P0
Total return
on the
stock
Dividend Yield
Capital Gain
Rate
5.31%
Dividend Yield for stocks
in the Dow Jones
Industrial Average
(2013)
3.9%
2.41%
3.04%
2.28%
1.10%
Dividend Yield for stocks
in the Dow Jones
Industrial Average (2014)
http://indexarb.com/dividendYieldSorteddj.html
Dividend Yield for stocks
in the Nasdaq 100 (2014)
Stock Prices and Returns
A Two Year Investment
Suppose that the investor wishes to hold the
stock for two years
Setting the stock price equal to the present
value of future cash flows implies
Div1 Div2 + P2
P0 =
+
2
1+ rE (1+ rE )
“N” Year Investment
Suppose that the investor wishes to hold the
stock for n years
Dividend Discount Model
Div1
Div2
DivN
PN
P0 =
+
+... +
+
2
N
N
1+ rE (1+ rE )
(1+ rE ) (1+ rE )
In Efficient Markets
¥
Div1
Div2
DivN
Divn
P0 =
+
+... +
+... = å
2
N
n
1+ rE (1+ rE )
(1+ rE )
n=1 (1+ rE )
The Constant Dividend Growth Model
Stock Valuation with Constant Growth
The simplest approach is to assume that Dividends grow
over time with a constant growth rate, g, forever
Constant Dividend Growth Model
Div1
P0 =
rE - g
Calculating Stock Price
Calculating the Required Return on
Equity for GE’s Stock
Applying the
Constant Dividend Growth Model
Historical Stock Price
Stock price appreciation (from $48.8 to $24.22): -50%
How can we use the constant dividend growth model to
estimate the return investors require on holding the stock
of GE?
Div1
P0 =
rE - g
We know the
current stock
price
We need to know the
Dividend Next Year
We can estimate the growth
rate
Constant Dividend Growth:
Application GE
Stock price
Historical Dividends
Dividends per-share (Dec 2000 – Sept 2013)
Average annual dividend growth (2000-2013):
g = 6.854%
Using growth rate 6.854%
implies the following
Dividend next year:
Div2014 =1.06854 ´$0.76 = $0.81
Using the CDGM and the
above information we
derive the implied return
on equity:
rE =
$0.81
+ 6.854% =10.2%
$24.23
P2013 =
Div2014
Div2014
Þ rE =
+g
rE - g
P2013
The Dividend and Growth Tradeoff
(within the Constant Dividend Growth model)
Dividends and Growth
The stock price increases with the level of
dividends and the growth rate
Div1
P0 =
rE - g
What determines the level of growth?
Can management increase the share price by
changing its dividend policy?
A Simple Model of Growth
Dividends are paid out of earnings according to
the dividend payout rate
Divn = EPSn ´ Dividend Payout Rate
Earningsn
EPSn =
Shares Outstandingn
Cash flows that are not paid out as dividends are retained
Retention Rate = 1- Dividend payout rate
Dividends and Investment
The firm can pay a higher current dividend by
increasing its payout rate
How would a higher payout rate affect future
dividends?
Earnings year n
Earnings year n+1
Div n
Div n+1
New
Investment n
New
Investment n+1
Calculating the Growth Rate of Earnins
Change in Earnings
g = Earnings growth rate =
Earnings
= Retention Rate ´ Return on Investment
Change in Earnings =
New Investment ´ Return on Investment
New Investment = Earnings ´ Retention rate
Cutting Dividends for Profitable Growth
Cutting Dividends for Profitable Growth
Cutting Dividends for Profitable Growth
Second Example
Comparing the two alternatives
Stocks in Nasdaq 100 that
have zero dividends
The DGM with changing Growth Rates
Changing Growth Rates
Often firms’ growth rates change overtime:
Young firms tend to retain a high fraction of earnings in
order to take advantage of investment opportunities and
as a result have high earnings growth rates
As firms mature, their growth slows to rates more typical
of established companies. At that point, their earnings
exceed their investment needs and they begin to pay
dividends
Discounted Dividend Model with
Constant Long-Term Growth
When growth rates only stabilize at a constant level
“g” after period “N+1” ends we value according to:
Div1
Div2
DivN
PN
P0 =
+
+... +
+
2
N
N
1+ rE (1+ rE )
(1+ rE ) (1+ rE )
Where the future price PN (or Terminal Value) is
DivN+1
PN =
rE - g
Varying Growth Rate
Varying Growth Rate
Varying Growth Rate
Further Problems
Acap Corporation
Question 3 (2nd Edition)
Suppose Acap Corporation will pay a dividend of $2.80 per share at the
end of this year and $3 per share next year. You expect Acap’s stock
price to be $52 in two years. If Acap’s equity cost of capital is 10%:
a.
b.
c.
What price would you be willing to pay for a share of Acap stock
today, if you planned to hold the stock for two years?
Suppose instead you plan to hold the stock for one year. What
price would you expect to be able to sell a share of Acap stock for
in one year?
Given your answer in part (b), what price would you be willing to
pay for a share of Acap stock today, if you planned to hold the
stock for one year? How does this compare to your answer in part
(a)?
Acap Corporation
Buy and hold for two years
Div1 Div2 + P2 $2.8 $55
P0 =
+
=
+ 2 = 48
2
1+ rE (1+ rE )
1.1 1.1
Price one year from now
P1 =
Div2 + P2 $55
=
= 50
(1+ rE ) 1.1
Price one year from now
P0 =
Div1 + P1
= 48
(1+ rE )
Colgate-Palmolive
Question 12 (2nd Edition):
Colgate-Palmolive Company has just paid an annual
dividend of $0.96. Analysts are predicting an 11% per
year growth rate in earnings over the next five years.
After then, Colgate’s earnings are expected to grow at the
current industry average of 5.2% per year.
If Colgate’s equity cost of capital is 8.5% per year and its
dividend payout ratio remains constant, what price does
the dividend-discount model predict Colgate Stock should
sell for?
Colgate-Palmolive
Expected price time 5
Div6
$1.7
P5 =
=
= $51.52
rE - gLongTerm 8.5%- 5.2%
Current Price
5ö
æ
æ
ö
Divt
P5
$1.07
1.11
$51.52
ç
÷
P0 = å
+
=
1+
= $39.43
ç
÷÷
t
5
5
ç
(1+ rE ) (-2.5%) è è 1.085 ø ø 1.085
t=1 (1+ rE )
5