1

EQUITY VALUATION

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

2

3

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.

3

4

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.

4

5

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.

5

6

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).

6

7

7

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;

8

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%

8

9

9

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

10

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.

10

11

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

11

H

HH

2

2

1

10

)r1(

PD...

)r1(

D

)r1(

DP

H

HH

1tt

t

)r1(

P

)r1(

D

12

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?

12

21 )15.1(

12150.5

)15.1(

00.5PV

100£

13

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?

13

321 (1.12)

94.483.50

(1.12)

3.24

(1.12)

3.00PV

£75.00

14

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.

14

15

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.

15

16

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.

16

17

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%

17

18

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.

18

19

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?

19

)04.010.0(

67.0

)1.1(

1

)1.1(

65.0

)1.1(

31.0

)1.1(

0P

33210

£9.13 =

20

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

21

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.

21

22

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?

22

23

EQUITY PRICE AND EARNINGS PER SHARE

Without Dividend Retention (No Growth)

P0 = D

r – g

= 8.33

0.15

= £55.53

23

24

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

25

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.

25

26

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%?

26

27

27

EXAMPLES

10% Equity Cost of Capital

PA = D

r

= £0.10

0.10

= £1

28

EXAMPLES

PB = D

r- g

= £5

0.10 – 0.04

= £83.33

28

29

EXAMPLES

Pc =

Equity C is the most valuable.

29

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£

30

30

EXAMPLES

7% Equity Cost of Capital

PA = D

r

= £0.10

0.07

= £1.43

31

EXAMPLES

PB = D

r- g

= £5

0.07 – 0.04

= £166.67

31

32

EXAMPLES

Pc =

Equity B is the most valuable.

32

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£

33

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.

33

34

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

=

35

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?

35

36

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

36

37

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

37

38

EXAMPLES

38

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

39

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.

39