Stock
Market & Dividend Policy
Stock price
The cash payout to owners of common
stocks comes in 2 forms :
· cash dividend
· capital gains or losses
Example 1
Po : Current price : 100 €
P1 : expected price at the end of the year :
110 €
Div1 : Expected dividend on share : 5 €
The expected rate of return to
the shareholders is :
| r
= |
[5
+ 110] - 100 |
=
15 % |
100 |
This return that is expected
by shareholders is often called the "market
capitalization rate" that can be earned
in the capital market on securities of comparable
risk.
Correspondingly, if you are given
shareholders' forecasts of dividend and price
and the expected return offered by other equally
risky stocks, you can predict today's price
:
Example 2
P0 = ?
P1 = 110 €
Div1 = 5 €
r = 15 %
Po
= |
5
+ 110 |
=
100 |
(1,15) |
How do you know that
100 € is the right price ?
Because no other price could survive
on a competitive capital market.
What if Po where above
100 € ? Then the stock would
offer a "r" that was lower than other
securities of equivalent risk. Shareholders
would shift their capital to the other securities
and in the process would force down the price
of the stock.
If Po were less than 100
€, the process would reverse.
The stock would offer a higher "r"
than comparable securities. In that case, shareholders
would rush to buy, forcing the price up to 100
€.
The general conclusion is that at each point
in time all securities in an equivalent risk
class are priced to offer the same expected
"r". This is a condition for equilibrium
on well-functioning capital markets.
What determines next
year's price ?
If shareholders are interested
at stock's price at the end of year 1 (P1 )
it means they are interested at Div2 and P2
. We can forecast P1 by forecasting Div2 and
P2 .
We can also express Po
in terms of Div1, Div2 and P2 !
Example 3
Po = ? ; Div1 = 5 € ; P2
= 121 € ; Div2 = 5.50 € ; r = 15
%
P0
= |
Div1 |
+ |
Div2
+ P2 |
(1 +
r)1 |
(1
+ r)2 |
| P0
= |
5 |
+ |
5,5
+ 121 |
=
100 € |
(1,15)1 |
(1,15)2 |
General stock price formula :
| Po
=
|
Div1 |
+....+
|
DivH |
+ |
PH |
(1+r)1 |
(1+r)H |
(1+r)H |
Constant Infinite stream
of dividend
In principle the horizon period
"H" could be infinitely distant if
we exclude corporate hazards such as bankruptcy
or acquisition. As "H" approaches
infinity the present value of terminal price
ought to approach zero. We can therefore forget
about the terminal price entirely and express
today's price as the present value of a perpetual
stream of dividend.
Example 4
Div1 = 6 € ; r = 15 %
40 € is the present value
of a constant infinite stream of dividend of
6 € a year.
Constant Infinite stream
of dividend growing annually at the rate "g"
Example 5
Div1 : 6 € ; r = 15 % ; g = 10 %
| Po
= |
6
€ |
=
120€ |
(0,15
- 0,10) |
120 € is the present value
of an infinite stream of dividend growing annually
at a rate of 10%.
Estimate "g"
We can use the above formula to
estimate "r" where [DIV1 /
P0] is the expected dividend yield
and "g" the expected rate of growth
of dividends.
Estimating "g" is a
difficult task. One option is to consult the
views of security analysts who study the prospects
for each company (they often forecast growth
rate over the next 5 years).
Example 6
DIV1 = 1.87 € ; Po = 36
€ ; g = 4.1 %
Dividend yield : 1.87 € / 36 € =
5.2 %
Market Capitalization rate = 5.2 % + 4.1 % =
9.3 %
| Value of share |
36 |
37.48 |
39.01 |
| Dividend |
1.87 |
1.95 |
2.03 |
| Dividend growth rate |
|
4.1 % |
4.1 % |
| Dividend yield |
5.2 % |
5.2 % |
5.2 |
| Market Capitalization rate |
|
9.3 % |
9.3 % |
Alternative approach
An alternative approach is to
estimate long-run growth "g".
Example 7
Distribution rate of dividend:
70 %(that means a retention rate of 30 %: reinvestment
rate) : ROE
: 12,50 % (do not change in the future)
;
Dividend growth rate = g = 30
% x 12,50 % = 3,75 %
Market capitalization rate (r) = 12,50 % +
3,75 % = 16,25 %
In well-functioning capital market
shareholders - or investors - capitalize the
dividends of all securities belonging to the
same class of risk at exactly the same rate.
Good practice does not put too much weight on
single-company cost-of-equity estimates. It
is preferable to collect samples of similar
companies and estimate "r" for each,
and take an average. This average gives a more
reliable benchmark for decision taking.
Resist the temptation to take
firms having high current rates of growth. Such
growth can rarely be sustained indefinitely.
In practice, the return on investment will decline
gradually over time.
Example 8
Forecast of a company dividend
fot the next 4 years. For subsequent years the
dividend will increase at a rate of 1 %. Calculate
"r" if today's price is 80 €
| |
Year
1 |
Year
2 |
Year
3 |
Year
4 |
| Dividend
(€) |
11 |
11,6 |
12 |
13,1 |
| 80
€ = |
|
+ |
|
+ |
|
+ |
13,1 |
11 |
11,6 |
12,0 |
(r -
0,01) |
(1+r)1 |
(1+r)2 |
(1+r)3 |
(1+r)3 |
r = 16,31 %
Sources :
Principles of Corporate Finance, 8th edition, Richard A. Brealey & Stewart C. Myers, McGraw-Hill
Corporate
Finance Course, Bernard Jaquier, Professor
of Economics & Finance, Lausanne, Switzerland, , 2010
