ACCA F9 Financial Management - 2010 - Study text

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Paper F9

Financial management

CHAPTER

Business valuations

Contents

1 Natureandpurposeofbusinessvaluations

2 Incomebasedvaluationmodels

3 Dividendvaluationmodels

4 Cashflowvaluationmethod

5 Asset‐basedvaluationmodels

6Valuationofdebtandpreferenceshares

7 Efficientmarkethypothesis(EMH)

8 Behaviouralfinance

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Nature and purpose of business valuations

 Reasons for business valuation

 Valuation models

1 Nature and purpose of business valuations

1.1 Reasons for business valuation

This chapter describes various techniques for calculating a value for the shares of a

company, or the value of an entire company (equity plus debt). There are several

reasons why a valuation might be required.

Quoted companies. Quoted companies already have a share price valuation: this is

the current market price of the shares. The main reason for making a business

valuation for a quoted company is when there is a takeover bid. In a takeover bid,

the bidder always offers more for the shares in the target company than their

current market price. A valuation might be made by the bidder in order to establish

a fair price or a maximum price that he will bid for the shares in the target company.

The valuation placed on a target company by the bidder can vary substantially,

depending on the plans that the bidder has for the target company after the

takeover has been completed.

Unquoted companies. For unquoted companies, a business valuation may be

carried out for any of the following reasons:

 The company might be converted into a public limited company with the

intention of launching it on to the stock market. When a company comes to the

stock market for the first time, an issue price for the shares has to be decided.

 When shares in an unquoted company are sold privately, the buyer and seller

have to agree a price. The buyer has to decide the minimum price he is willing to

accept and the seller has to decide the maximum price he is willing to pay.

 When there is a merger involving unquoted companies, a valuation is needed as

a basis for deciding on the terms of the merger.

 When a shareholder in an unquoted company dies, a valuation is needed for the

purpose of establishing the tax liability on his estate.

1.2 Valuation models

There are two broad approaches to valuing companies.

 Income-based valuation models which focus on the future earnings or cash

flows of the company.

 Asset-based valuation models which focus on the value of the company’s assets.

There are many different techniques within these two broad approaches and they

lead to different valuations of the business.

Chapter 18: Business valuations

All the valuation methods described in this chapter have a rational basis. This

means that there is logic to the valuation, and the valuation is obtained through

objective analysis and assessment.

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Income based valuation models

 P/E ratio method

 Earnings yield method

2 Income based valuation methods

2.1 P/E ratio method

A price/earnings ratio or P/E ratio is the ratio of the market value of a share to the

annual earnings per share. For every company whose shares are traded on a stock

market, there is a P/E ratio. For private companies (companies whose shares are not

traded on a stock market) a suitable P/E ratio can be selected and used to derive a

valuation for the shares.

A simple method of estimating a value for a company in the absence of a stock

market value is:

Value = EPS × Estimated P/E ratio.

 The EPS might be the EPS in the previous year, an average EPS for a number of

recent years or a forecast of EPS in a future year

 The P/E ratio is selected as a ratio that seems appropriate or suitable. The

selected ratio might be based on the average P/E ratio of a number of similar

companies whose shares are traded on a stock market, for which a current P/E

ratio is therefore available.

Example

The EPS of a private company, ABC Company, was $1.50 last year and is expected

to rise to $1.80 next year. Similar companies whose shares are quoted on the stock

market have P/E ratios ranging from 10.0 to 15.6. The average P/E ratio of these

companies is 12.5.

A valuation of the company might be to take the prospective EPS and apply the

average P/E ratio for similar companies:

Valuation = $1.80 × 12.5 = $22.50 per share.

An alternative evaluation might be to take the actual EPS last year and apply the

lowest P/E ratio of any other similar stock market company, reduced by, say, 10%

to allow for the fact that ABC Company is a private company and does not have a

stock market quotation.

Valuation = $1.80 × (90% × 10) = $16.20.

Here, a P/E ratio of 9 (= 90% × 10) has been used in the valuation.

Chapter 18: Business valuations

Another valuation might be to use the EPS for last year and a P/E ratio of 9. This

would give a share value of $1.50 × 9 = $13.50.

From this example, it might be apparent that the P/E ratio valuation method has a

number of weaknesses:

 It is based on subjective opinions about what EPS figure and what P/E ratio

figure to use.

 It is not an objective or scientific valuation method.

 It is based on accounting measures (EPS) and not cash flows. However, the value

of an investment such as an investment in shares ought to be derived from the

cash that the investment is expected to provide to the investor (shareholder).

However, the P/E ratio valuation method is commonly used as one approach to

valuation for:

 the valuation of a private company seeking a stock market listing for the first

time

 the valuation of a company for the purpose of making a takeover bid.

The main advantage of a P/E ratio valuation is its simplicity. By taking the annual

earnings of the company (profits after tax) and multiplying this by a P/E ratio that

seems ‘appropriate’, an estimated valuation for the company’s shares is obtained.

This provides a useful benchmark valuation for negotiations in a takeover, or for

discussing the flotation price for shares with the company’s investment bank

advisers.

2.2 Earnings yield method

With the earnings yield method of valuation, a company’s shares are valued using

its annual earnings and a suitable earnings yield.

Earnings yield % = Annual earnings

Market value of shares

Using the earnings yield method of valuation, this formula is adapted as follows:

Market value of shares =

Annual earnings

Earnings yield %

A suitable earnings yield for a private company might be similar to the earnings

yield on shares in similar quoted companies.

It might be more appropriate to select an earnings yield that is higher than the

earnings yield for similar quoted companies, to allow for the higher risk of investing

in private companies.

The earnings yield method of valuation is essentially a variation of the P/E ratio

method of valuation and is subject to the same criticisms.

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Example

The earnings of Kickstart, a private company, were $450,000 last year.

Stock market companies in the same industry provide an earnings yield of about 9%

to their shareholders.

Using the earnings yield method of valuation, suggest a suitable valuation for the

equity shares in Kickstart.

Answer

If an appropriate earnings yield for Kickstart is 9%, the valuation of its equity would

be:

$450,000/9% = $5,000,000.

However since Kickstart is a private company, a higher earnings yield should

possibly be used for the valuation. If an appropriate earnings yield for Kickstart is

10%, say, the valuation of its equity would be:

$450,000/10% = $4,500,000.

The valuation depends on arbitrary assumptions about a suitable earnings yield to

apply, as well as assumptions about expected annual earnings.

Chapter 18: Business valuations

Dividend valuation models

 Dividend valuation model: constant annual dividends

 Dividend valuation method: constant rate of growth in annual dividends

 Retained earnings: the earnings retention valuation model

3 Dividend valuation models

3.1 Dividend valuation model: constant annual dividends

The dividend valuation model is a more objective and cash-based approach to the

valuation of shares. Like the P/E ratio method and earnings yield method, it is an

income-based valuation method. However the valuation is based on expected future

dividends rather than on total earnings.

The basic assumption with the dividend valuation models is that the value of shares

to shareholders is the value of all the future dividends that they expect to receive

from those shares in the future.

If the fair value of a share represents the value of all expected future dividends, this

value can be estimated by discounting expected future dividends to a present value

at the shareholders’ cost of capital. All expected future dividends ‘in perpetuity’

are therefore discounted to a present value at the cost of equity capital.

Without going into the mathematics to prove the valuation model, it can be shown

that if it is assumed that the company will pay a constant annual dividend every

year into the foreseeable future, the present value of those dividends, and so the

value of the shares, is:

P =

where:

= the current value of the share ex dividend. A share price ex dividend is a price

that excludes the value of the annual dividend in the current year.

D = the amount of the annual cash dividend.

= the shareholders’ cost of capital expressed as a proportion (so 9% = 0.09, etc).

This valuation model assumes that the dividend is paid annually, and that the

current year’s dividend has just been paid. This is the assumption that is commonly

used in examination questions. For an ‘exact’ valuation using this model, it should

be assumed the next dividend is payable in one year’s time.

If the annual dividend in the current year has not yet been paid, but will soon be

paid, the value of the share is its value ‘cum dividend’. You might be asked to

suggest a cum dividend valuation, where an annual dividend will be paid in the

near future. If so, you should estimate the ex dividend price using the dividend

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valuation model, and then add the current dividend to arrive at a cum dividend

valuation.

Example

A company is expected to pay an annual dividend of $0.48 per share into the

foreseeable future and the shareholders’ cost of capital is 12%. The most recent

annual dividend has just been paid.

Required:

(a) Using the dividend valuation model, suggest what the value of the shares

should be.

(b) Show how this valuation would change if the expected annual dividend in

future years is $0.54.

future years is $0.48 but the cost of equity capital is 12.5%

Answer

(a) Using the dividend valuation model, the value of the share (ex dividend)

ought to be $0.48/0.12 = $4.00.

(b) If expectations about future annual dividends change from $0.48 per share to

$0.54 per share, the valuation of the share will be $4.50 ($0.54/0.12). This is a

higher valuation than in (a) because the annual dividend is higher.

shareholders’ cost of capital changes to 12.5%, the valuation of the share will

fall to $3.84 ($0.48/0.125). This is a lower valuation than in (a) because the cost

of equity is higher.

The dividend valuation model therefore provides an explanation of how the value

of shares will rise or fall when there are changes in either:

 the expected annual dividend, or

 the shareholders’ required rate of return (the equity cost of capital).

3.2 Dividend valuation method: constant rate of growth in annual dividends

An alternative assumption in the dividend valuation model is that the annual

dividend will grow in the future. A simplifying assumption is that the dividends

will grow at a constant annual percentage rate.

Again, without going into the mathematics to prove the valuation model, it can be

shown that if it is assumed that the company will pay an annual dividend that

grows by a constant percentage amount every year into the foreseeable future, the

present value of those dividends, and so the value of the shares, is:

(1 + g)

– g)

Chapter 18: Business valuations

where:

is the current value of the share ex dividend

is the current annual dividend (that has recently been paid or will be paid in the

very near future)

g is the expected annual growth rate in dividends expressed as a proportion (3% =

0.03 etc)

(1 + g) is therefore the expected annual dividend next year, in Year 1. This is

sometimes written as D

is the shareholders’ cost of capital expressed as a proportion (so 9% = 0.09, etc)

This is the valuation of the share ex dividend. Note that this valuation formula is

based on the assumptions that:

 the dividend is paid annually, and

 the dividend for the current year has just been paid.

This formula is provided to you in your examination, in the formula sheet. However

it is a formula that you should try to learn.

Example

A company has just paid an annual dividend of $0.48. Dividends are expected to

grow by 4% each year into the foreseeable future. The shareholders’ cost of capital is

12%.

Using the dividend valuation model, the expected value of the share (ex dividend)

is:

0.48 1.04

()

0.12 − 0.04

= $6.24

If there is no expected growth in annual dividends, and the company is expected to

pay a constant annual dividend in the future, the share valuation would have been

$4.00 (see the earlier example). Because the annual dividend is expected to increase

every year, the valuation is much higher.

Using the dividend growth model, the valuation of shares changes with:

 changes in expected future dividends (for example, changes in the expected

annual growth rate in dividends), or

 changes in the shareholders’ required rate of return (the equity cost of capital).

Example

In the previous example, if the expected growth rate in annual dividends falls from

4% to 3%, the valuation of the shares will fall to:

Paper F9: Financial management

$0.48 1.03

()

(0.12−0.03)

= $5.49

This is a lower valuation, because future dividends are expected to be lower.

An examination question might test your understanding of the dividend growth

model by asking you to calculate the annual growth rate g, given an annual

dividend and the current market price of the shares.

Example

The share price of ABC Company is currently $4.00. The cost of equity capital is

12%. The annual dividend has just been paid. It is expected that the annual dividend

next year will be $0.20 per share and that annual dividends will then grow at a

constant annual rate into the foreseeable future.

Required:

(a) Calculate the expected annual growth rate in dividends from next year

onwards.

(b)

Suppose that the stock market now receives new and unexpected information

about the company that makes investors re-assess the future annual

dividends. Investors now expect that the annual dividend next year will be

10% lower than previously expected, and that annual growth in dividends in

subsequent years will be only 4%. Calculate the price that should now be

expected for shares in ABC Company.

Answer

(a) Let the annual growth rate in dividends be g.

g0.12

0.20

4.00

−

4.0 (0.12 – g) = 0.20

0.48 – 4g = 0.20

4g = 0.28

g = 0.07 or 7%.

(b) The annual dividend next year is now expected to be $0.18.

0.040.12

0.18

−

0.8 P = 0.18

P = 2.25.

The share price should fall to $2.25.

ACCA F9 Financial Management - 2010 - Study text - Emile Woolf Publishing

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