This document provides an overview of equity valuation concepts covered in Chapter 6 of the fundamentals of corporate finance textbook. It discusses difficulties in valuing equity given uncertain cash flows and lifetime. It then covers models for valuing equity under scenarios of zero growth, constant growth, and non-constant growth. Key valuation models discussed include the dividend growth model and two-stage growth model. The lecture also examines components of the required return, the price earnings ratio, features of ordinary shares and preference shares, and stock market terms. Activities for this lecture include assigned reading and an assignment.
3. Corporate Finance in the News
Insert a current news story here to frame the material you will cover in the lecture.
4. Share Valuation
Difficulties
Cash flows are uncertain
Life of investment is uncertain
because an equity can theoretically
last forever
Difficult to measure the expected
return the market expects
5. Cash Flows
You are considering buying a share of
equity today. You plan to sell the equity
in one year. You somehow know that it
will be worth £70 at that time. You
predict that the equity will also pay a
£10 per share dividend at the end of
the year. If you require a 25 per cent
return on your investment, what is the
most you would pay for the equity?
7. The Present Value of Equity
1 1
0
Div
1 1
P
P
R R
2 2
1
Div
= +
1+ 1+
P
P
R R
2 2
0 1
1 2 2
2 2
1 Div
Div +
1 1
Div Div
+
1 (1 ) (1 )
P
P
R R
P
R R R
1 2 3 t
0 2 3
1
Div Div Div Div
...
1 (1 ) (1 ) (1 )
t
t
P
R R R R
9. Zero Growth
For a zero-growth share
of equity, this implies that:
D1 = D2 = D3 = D =
constant
10. Zero Growth
0 1 2 3 4 5
(1 ) (1 ) (1 ) (1 ) (1 )
D D D D D
R R R R R
D
R
P
11. Constant Growth
The dividend for some company always grows at a steady rate, g. If we let D0 be
the dividend just paid, then the next dividend, D1, is:
D1 = D0 (1 + g)
The dividend in two periods is:
D2 = D1 (1 + g) = [D0 (1 + g)] (1 + g) = D0 (1 + g)2
In general, we know that the dividend t periods into the future, Dt, is given by:
Dt = D0 (1 + g)t
An asset with cash flows that grow at a constant rate forever is called a growing
perpetuity.
12. Example 7.2
Dividend Growth
Oasis plc has just paid a
dividend of £3 per share. The
dividend of this company
grows at a steady rate of 8
per cent per year. Based on
this information, what will the
dividend be in five years?
13. Example 7.2
Dividend Growth
Here we have a £3 current amount
that grows at 8 per cent per year for
five years. The future amount is thus:
£3 1.085 = £3 1.4693 = £4.41
The dividend will therefore increase
by £1.41 over the coming five years.
14. Dividend Growth
3
1 2
0 1 2 3
1 2 3
0 0 0
1 2 3
(1 ) (1 ) (1 )
(1 ) (1 ) (1 )
(1 ) (1 ) (1 )
D
D D
R R R
D g D g D g
R R R
P
0 1
0
(1 )
D g D
P
R g R g
15. Dividend Growth Model
Suppose D0 is £2.30, R is 13 per cent,
and g is 5 per cent. The share price in
this case is:
P0 = D0 (1 + g)/(R g)
= £2.30 1.05/(.13 .05)
= £2.415/.08
= £30.19
16. Example 7.3
Gordon Growth Limited
The next dividend for Gordon Growth
Limited will be £4 per share.
Investors require a 16 per cent return
on companies such as Gordon.
Gordon’s dividend increases by 6 per
cent every year. Based on the
dividend growth model, what is the
value of Gordon’s equity today?
What is the value in four years?
17. Example 7.3
Gordon Growth Limited
The share price is given by:
P0 = D1/(R g)
= £4/(.16 .06) = £4/.10 = £40
Because we already have the dividend in one year, we know
that the dividend in four years is equal to D1 (1 + g)3 = £4
1.063 = £4.764. The price in four years is therefore:
P4 = D4 (1 + g)/(R g)
= £4.764 1.06/(.16 .06) = £5.05/.10
19. Example 7.4
Supernormal Growth
Kettenreaktion AG has been growing at a
phenomenal rate of 30 per cent per year
because of its rapid expansion and
explosive sales. You believe this growth rate
will last for three more years and will then
drop to 10 per cent per year. If the growth
rate then remains at 10 per cent indefinitely,
what is the total value of the equity? Total
dividends just paid were €5 million, and the
required return is 20 per cent.
20. Example 7.4
Supernormal Growth
The price at time 3 can be calculated as:
P3 = D3 (1 + g)/( R g )
where g is the long-run growth rate. So, we have:
P3 = €10.985 1.10/(.20 .10) = €120.835
21. Example 7.4
Supernormal Growth
3 3
1 2
0 1 2 3 3
2 3 3
8.45
(1 ) (1 ) (1 ) (1 )
€6.50 10.985 120.835
1.20 1.20 1.20 1.20
5.42 5.87 6.36 69.93
87.58
D P
D D
P
R R R R
22. Two Stage Growth
1 0 1 2
2 2
(1 ) (1 )
t
t
t
D D g g
P
R g R g
23. Example 7.6
Two Stage Growth
Alto Campo’s dividend is
expected to grow at 20 per cent
for the next five years. After
that, the growth is expected to
be 4 per cent forever. If the
required return is 10 per cent,
what’s the value of the equity?
The dividend just paid was €2.
24. Example 7.6
Two Stage Growth
5
6 0 1 2
5
2 2
5
(1 ) (1 )
€2 (1 .20) (1 .04) €5.18
.06
86.26
D D g g
P
R g R g
1 1
0
1
5
5
€2 (1 .20) €86.26
66.64
1
1
1 (1 )
1 .20
1
1 .10 (1 .10)
t
t
t
P
D g
P
R g R R
25. Components of the Required Return
Dividend
Yield
Capital
Gains
Yield
Total
Return
26. Components of the Required Return
Dividend Yield
• An equity’s
expected cash
dividend divided
by its current
price.
Capital Gains
Yield
• The dividend
growth rate, or
the rate at which
the value of an
investment
grows.
27. Components of the Required Return
R = Dividend yield +
Capital gains yield
R = D1/P0 + g
29. Features of Ordinary Equity and Preference
Shares
Ordinary Equity
Equity without priority for
dividends or in bankruptcy.
Preference Shares
Equity with dividend priority
over ordinary shares,
normally with a fixed
dividend rate, sometimes
without voting rights.
30. Stock Markets
Terms primary market
The market in which new
securities are originally sold to
investors.
secondary market
The market in which previously
issued securities are traded
among investors.
31. Stock Markets
Terms dealer
An agent who buys and sells
securities from inventory..
broker
An agent who arranges security
transactions among investors.
