equity valuation - weeblykarlvincentroberts.weebly.com/.../equity_valuation.pdf · 2019-09-08 · 4...
TRANSCRIPT
2
OVERVIEW
I INTRODUCTION
II HOW EQUITY IS VALUED
III ESTIMATING THE COST OF EQUITY
IV EQUITY PRICE AND EARNINGS PER SHARE
V EXAMPLES
VI CONCLUSION
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I. INTRODUCTION
Equity is Issued at a stated par or nominal value and is
limited by Authorised Capital, specified in firm’s Articles of Association;
Each share represents a share in ownership of company and carries voting rights;
Dividends only paid after meeting all “prior claims”;
The liability for the firm’s debts are limited to the amount invested and shareholders rank last in queue for distribution of proceeds in a liquidation.
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INTRODUCTION
It is important to appreciate the significance of corporate valuation
of equity.
Valuation is at the heart of the corporate finance concept.
However, there are a number of the problems surrounding the
equity valuation of both public and private companies.
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INTRODUCTION
We need to value equity for many reasons:
to assess the impact of financial decisions;
to value IPO floatations;
to value privatisations;
to value acquisition candidates;
to value break-up situations and divestments;
to value MBOs and MBIs.
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II. HOW EQUITY IS VALUED
The value of any equity is the present value of its future cash flows and is reflected in the DCF formula.
Dividends represent the future cash flows of the firm.
PV(Equity) = PV (expected future dividends)
The Expected Return is the percentage yield that an investor forecasts from a specific investment over a set period of time (sometimes called the market capitalisation rate).
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HOW EQUITY IS VALUED
Expected Return = r = D1 + P1 – P0
P0
D1 – expected dividend per share;
P0 – current share price;
P1 – expected share price at the end of year;
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HOW EQUITY IS VALUED
Example
If Fledgling Electronics Plc is selling for £100 per share today and is expected to sell for £110 one year from now, what is the expected return if the dividend one year from now is forecasted to be £5.00?
Expected return = 5 +110 – 100
100
= 0.15 = 15%
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HOW EQUITY IS VALUED
The price of any share can be thought of as the present value of the future cash flows.
For equity, the future cash flows are dividends and the ultimate equity sales price.
Price = P0 = D1 +P1
1 + r
For Fledgling Electronics Plc, D = 5 and P1 = 110. If the expected return for Fledgling is 15%, then today’s price will be:
P0 = 5 +110
1.15
= £100
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HOW EQUITY IS VALUED
Many shares will be safer than Fledgling and many will be riskier.
Those with the same level of risk will have the same risk class where
they will be priced to offer the same expected rate of return.
If Fledgling’s price were above £100 then investors would shift
their investment to other securities and thereby force the price of
Fledgling downwards.
If Fledgling’s price were less than £100 then investors would shift
their investment Fledgling and thereby force the price of Fledgling
upwards.
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HOW EQUITY IS VALUED
Where we assess the value of equity beyond a single time horizon, it
is referred to as the Dividend Discount Model.
This states that the share value equals the present value of all
expected future dividends and the ultimate equity sales price.
H – Time Horizon
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H
HH
2
2
1
10
)r1(
PD...
)r1(
D
)r1(
DP
H
HH
1tt
t
)r1(
P
)r1(
D
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HOW EQUITY IS VALUED
Example 1
Fledgling Electronics Plc is forecasted to pay a £5.00 dividend at
the end of year one and a £5.50 dividend at the end of year two. At
the end of the second year the equity will be sold for £121. If the
discount rate is 15%, what is the current price of the equity?
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21 )15.1(
12150.5
)15.1(
00.5PV
100£
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HOW EQUITY IS VALUED
Example 2
Current forecasts are for BTG Plc to pay dividends of £3, £3.24,
and £3.50 over the next three years, respectively. At the end of
three years you anticipate selling the equity at a market price of
£94.48. What is the current price of the equity given a 12%
expected return?
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321 (1.12)
94.483.50
(1.12)
3.24
(1.12)
3.00PV
£75.00
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III. ESTIMATING THE COST OF EQUITY
Estimating the cost of equity depends upon whether there is
constant or non-constant dividend growth.
Valuing Constant Dividend Growth
P0 = D
r – g
Where:
P0 – current share price;
D – expected dividend per share;
r – equity cost of capital;
g – dividend growth.
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ESTIMATING THE COST OF EQUITY
Dividend Growth
g = b x R
Where:
g – dividend growth;
b – the retention ratio;
R – the Internal Rate of Return.
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ESTIMATING THE COST OF EQUITY
Therefore:
r = D + g
P0
Where:
r – equity cost of capital;
D – expected dividend per share;
g – dividend growth;
P0 – current share price.
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ESTIMATING THE COST OF EQUITY
Example
Northwest Natural Gas has equity selling at £41.67 at the beginning
of 2012 with dividend payments being £1.49 per share with annual
growth of 5.1%.
r = D + g
P0
= 1.49 + 0.051
41.67
= 0.036 + 0.051
= 0.087 = 8.7%
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ESTIMATING THE COST OF EQUITY
Valuing Non-Constant Dividend Growth
Growth rates can vary for many reasons. Sometimes growth is high
in the short-run not because the firm is unusually profitable, but
because it is recovering from an episode of low profitability.
Any difference between the estimated and the actual share price
may be due to inaccurate dividend forecasts.
When there is a non-constant growth of dividends, it is important
to treat each year’s level of dividends separately.
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ESTIMATING THE COST OF EQUITY
Example – Phoenix Plc produces dividends in three consecutive
years of £0, £0.31, and £0.65, respectively.
The dividend in year four is estimated to be £0.67 and should grow
in perpetuity at 4%.
Given a discount rate of 10%, what is the price of the equity?
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)04.010.0(
67.0
)1.1(
1
)1.1(
65.0
)1.1(
31.0
)1.1(
0P
33210
£9.13 =
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IV. EQUITY PRICE AND EARNINGS PER SHARE
Investors separate growth shares from income shares.
They buy growth shares primarily for the expectation of capital
gains rather than next year’s dividends.
They buy income shares primarily for the cash dividends.
If a company does not grow at all and does not retain any earnings,
it will produce a constant stream of dividends. This equity would
resemble a perpetual bond.
Since all earnings are paid as dividends, the expected return is equal
to the EPS. 20
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EQUITY PRICE AND EARNINGS PER SHARE
Example
If the dividend is £10 per share and the share price is £100.
The expected return = dividend yield = EPS
= D = EPS
P
= £10 = 0.10
£100
The expected return for growing firms can also equal the EPS ratio.
The key is whether earnings are reinvested.
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EQUITY PRICE AND EARNINGS PER SHARE
Example
Kenmare Resources Plc forecasts to pay a £8.33 dividend next
year, which represents 100% of its earnings. This will provide an
Equity Cost of Capital of 15%.
An alternative is to retain 40% of the earnings at the firm’s current
IRR of 25%.
What is the value of Kenmare Resources equity before and after
the retention decision?
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EQUITY PRICE AND EARNINGS PER SHARE
Without Dividend Retention (No Growth)
P0 = D
r – g
= 8.33
0.15
= £55.53
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EQUITY PRICE AND EARNINGS PER SHARE
With Dividend Retention (Growth)
g = b x R
= 0.25 x 0.40
= 0.10
P0 = 8.33
0.15 – 0.10
= £166.60
The equity value will always be much higher when there is dividend
growth. 24
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V. EXAMPLES
Example 1
Consider the following three forms of equity:
(a) Equity A is expected to provide a dividend of £0.10 a share in perpetuity.
(b) Equity B is expected to provide a dividend of £5 next year. Thereafter, dividend growth is expected to be 4% a year perpetuity.
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EXAMPLES
(c) Equity C is expected to provide a dividend of £5 next year.
Thereafter, dividend growth is expected to be 20% a year
for 5 years and zero thereafter.
If the cost of capital for each equity is 10%, which equity is the
most valuable?
What if the equity cost of capital is 7%?
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EXAMPLES
Pc =
Equity C is the most valuable.
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6654321 1.10
1
0.10
12.44
1.10
12.44
1.10
10.37
1.10
8.64
1.10
7.20
1.10
6.00
1.10
5.00
104.50£
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EXAMPLES
Pc =
Equity B is the most valuable.
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6
6
6
6
5
5
4
4
3
3
2
2
1
1
71.0
1
70.0
DIV
71.0
DIV
71.0
DIV
71.0
DIV
71.0
DIV
71.0
DIV
71.0
DIV
6654321 71.0
1
70.0
12.44
71.0
12.44
71.0
10.37
71.0
8.64
71.0
7.20
71.0
6.00
71.0
5.00
48.561£
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EXAMPLES
Example 2
Carillion Plc is about to pay a dividend of £1.35 per share.
Future EPS and dividends are expected to grow with inflation at
the rate of 2.75% per year.
(a) What is Carillion Plc’s current share price if the
nominal cost of capital is 9.5%?
(b) Redo (a) using forecasted real dividends and a real
discount rate.
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EXAMPLES (a) P0 = DIV0 + DIV1
r – g
=£1.35 + £1.35 x 1.0275
0.095 – 0.0275
= £21.90
(b) First, compute the real discount rate as follows:
(1 + rnominal) = (1 + rreal) (1 + inflation rate)
1.095 = (1 + rreal) 1.0275
(1 + rreal) = (1.095/1.0275) – 1 = .0657 = 6.57%
In real terms, g = 0. Therefore:
= £21.90 34
0.0657
1.35 £ 1.35 £
g r
DIV DIV P 1
0 0
=
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EXAMPLES
Example 3
Lamprell Plc has an equity cost of capital is 14% and it has a 50%
payout ratio with a current book value per share of £50.
The equity cost of capital and payout ratio stay constant for the
next four years after which the competition forces the equity cost
of capital down to 11.5% and the payout ratio increases to 0.8.
(a) What are Lamprell Plc ’s EPS and dividends next year?
How will EPS and dividends grow in each of the years after year
one?
(b) What is Lamprell Plc ’s equity worth per share? How does
that value depend on the payout ratio and growth rate after
year 4?
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EXAMPLES
(a)
Retention Ratio = 1 – Payout Ratio = 1.0 – 0.5 = 0.5
Dividend Growth Rate (g)
= Retention Ratio (b) × Equity Cost of Capital (r)
= 0.5 × 0.14
= 0.07
Equity Cost of Capital = EPS0/P0
0.14 = EPS0/£50
EPS0 = £7.00
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EXAMPLES
Therefore: DIV0 = payout ratio × EPS0 = 0.5 × £7.00 = £3.50
Year EPS DIV
0 £7.00 £7.00 × 0.5 = £3.50
1 £7.00 × 1.07 = £7.4900 £7.4900 × 0.5 = £3.7450
2 £7.00 × 1.072 = £8.0143 £8.0143 × 0.5 = £4.0072
3 £7.00 × 1.073 = £8.5753 £8.5753 × 0.5 = £4.2877
4 £7.00 × 1.074 = £9.1756 £9.1756 × 0.5 = £4.5878
5 £7.00 × 1.074 × 1.023 = £9.3866 £9.3866 × 0.8 = £7.5093
Year 5 Retention Ratio = 1 – Payout Ratio = 1.0 – 0.8 = 0.2
Year 5 Dividend Growth Rate (g) = b × r
= 0.2 × 0.115
= 0.023
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EXAMPLES
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4
5
4
4
3
3
2
2
1
10
1.115
1
0.115
DIV
1.115
DIV
1.115
DIV
1.115
DIV
1.115
DIVP
The last term in the above calculation is dependent on the payout ratio
and the growth rate after year 4.
545.£6
(b)
44321 151.1
1
0.023-0.115
9350.7
1.115
874.58
1.115
774.28
1.115
24.007
1.115
3.745
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VI. CONCLUSION
We looked at the reasons why equity valuation is important.
Equity value calculations found by discounting dividends were
undertaken.
The differences between the case of zero, constant and
differential growth was looked at.
The link between equity Price and Earnings per Share were
viewed.
We looked at the price-earnings ratio form being a function of
the firm’s valuable growth opportunities, the risk of the equity
and the accounting methods used by the firm.
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