Chapter 19: Business valuations and market efficiency

Chapter learning objectives

Upon completion of this chapter you will be able to:

• identify and discuss reasons for valuing businesses and financial assets
• identify information requirements for the purposes of carrying out a valuation in a scenario
• discuss the limitations of the different types of information available for valuing companies
• value a share using the dividend valuation model (DVM), including the dividend growth model
• define market capitalisation
• calculate the market capitalisation of a company using the DVM, including the dividend growth model
• explain the difference between asset- and income-based valuation models
• value a company using the balance sheet, net realisable value (NRV) and replacement cost asset-based valuation models
• discuss the advantages and disadvantages of the different asset-based valuation models
• value a company using the price/earnings (PE) ratio income-based valuation model
• value a company using the earnings yield income-based valuation model
• value a company using the discounted cash flow (DCF) income-based valuation model
• discuss the advantages and disadvantages of the different income-based valuation models
• value a company in a scenario question selecting appropriate valuation methods
• calculate the value of irredeemable debt, redeemable debt, convertible debt and preference shares.
• explain the concept of market efficiency
• distinguish between and discuss markets that are not efficient at all, weak form efficient, semi-strong form efficient and strong form efficient
• evaluate the efficiency of a market in a scenario
• describe the significance of investor speculation and the explanations of investor decisions offered by behavioural finance
• discuss the impact of the marketability and liquidity of shares in reaching a valuation
• discuss the impact of availability and sources of information in reaching a valuation
• discuss the impact of market imperfections and pricing anomalies in reaching a valuation.

1 Valuing business and financial assets

Valuations of shares in both public and private companies are needed for several purposes by investors including:

• to establish terms of takeovers and mergers, etc.
• to be able to make 'buy and hold' decisions in general
• to value companies entering the stock market
• to establish values of shares held by retiring directors, which the articles of a company specify must be sold
• for fiscal purposes (capital gains tax (CGT), inheritance tax)
• divorce settlements, etc.

Approaches to valuations

The three main approaches are:

• Asset based – based on the tangible assets owned by the company.
• Income/earnings based – based on the returns earned by the company.
• Cash flow based - based on the cash flows of the company

The real worth of a company

Valuation is described as 'an art not a science'. The real worth of a company depends on the viewpoints of the various parties:

• the various methods of valuation will often give widely differing results
• it may be in the interests of the investor to argue that either a 'high' or 'low' value is appropriate
• the final figure will be a matter for negotiation between the interested parties.

It is important to bring this out in the examination and show theexaminer you understand that the valuation is subjective and acompromise between two parties.

Valuation: An art and not a science

The acquisition of a major competitor may enable a company tosecure a dominant position in the market place. It is therefore likelyto place a higher value on the target company than a potential purchaserfrom outside the industry.

A realistic valuation will therefore require a full industryanalysis rather than an isolated assessment of the business to bevalued. In some cases, the circumstances giving rise to the valuationmay call for 'a value as would be agreed between a willing buyer and awilling seller' and may often be subject to independent arbitration.

Information requirements for valuation exercises

There is a wide variety of information that may be useful when trying to put a valuation on a business, including:

• Financial statements (including statements of financial position and comprehensive income, statements of changes in financial position and statements of shareholders equity for past years - may be as many as five).
• Supporting listings such as non-current assets with depreciation schedule, aged accounts receivable summary, aged accounts payable summary and inventory summary.
• Details of existing contracts (e.g. leases).
• Budgets or projections for the future (again, may be up to five years depending on the industry).
• Background information on the industry and key personnel.

This list is not exhaustive as much will depend on the situation.However, much of the above information does have limitations which mustbe accounted for. For example, budgets or projections may be veryoptimistic and perhaps unrealistic, statements of financial position maybe out of date and unrealistic.

Much of the information may be subjective and this can add to the overall subjectivity involved in valuing businesses.

2 Asset-based valuations

Types of asset-based measures

Problems with asset-based valuations

The fundamental weakness:

• investors do not normally buy a company for its balance sheet assets, but for the earnings/cash flows that all of its assets can produce in the future
• we should value what is being purchased, i.e. the future income/cash flows.

Subsidiary weakness:

The asset approach also ignores non-balance sheet intangible 'assets', e.g.:

• highly-skilled workforce
• strong management team
• competitive positioning of the company's products.

It is quite common that the non-balance sheet assets are more valuable than the balance sheet assets.

When asset-based valuations are useful

• For asset stripping.
• To identify a minimum price in a takeover.
• To value property investment companies.

When asset based methods are useful

Asset stripping

Asset valuation models are useful in the unusual situation that acompany is going to be purchased to be broken up and its assets soldoff. In a break-up situation we would value the assets at theirrealisable value.

To set a minimum price in a takeover bid

Shareholders will be reluctant to sell at a price less than the netasset valuation even if the prospect for income growth is poor. Astandard defensive tactic in a takeover battle is to revalue balancesheet assets to encourage a higher price. In a normal going-concernsituation we value the assets at their replacement cost.

To value property investment companies

The market value of investment property has a close link to futurecash flows and share values, i.e. discounted rental income determinesthe value of property assets and thus the company.

 Note:If we are valuing a profitable quoted company, in reality the minimumprice that shareholders will accept will probably be the marketcapitalisation plus an acquisition premium and not the net assetvaluation.

Types of asset based measures

Book value – this will normally be a meaningless figure asit will be based on historical costs. However with fair value accountingthe book value of many assets and liabilities will be the fair valueand therefore will be relevant for valuation purposes.

Break-up value – the break-up value of the assets in thebusiness will often be considerably lower than any other computed value.It normally represents the minimum price which should be accepted forthe sale of a business as a going concern, since if the income basedvaluations give figures lower than the break-up value it is apparentthat the owner would be better off by ceasing to trade and selling offall the assets piecemeal.

Replacement cost and deprival value – this should provide ameasure of the maximum amount that any purchaser should pay for thewhole business, since it represents the total cost of forming thebusiness from scratch. However, a major element of any business as agoing concern is likely to be the 'goodwill'. Since this can only bedefined by determining the 'income-based value of business less tangibleassets' it may be seen that there is no real way of applying a pure'asset-based value' to a business – it is always necessary to consideran 'income-based value' as well.

Test your understanding 1 – Asset based measures

The following is an abridged version of the statement of financialposition of Grasmere Contractors Co, an unquoted company, as at 30 AprilX6:

You ascertain that:

• loan notes are redeemable at a premium of 2%
• current market value of freehold property exceeds book value by $30,000
• all assets, other than property, are estimated to be realisable at their book value.

Calculate the value of an 80% holding of ordinary shares, on an assets basis.

3 Income/earnings-based methods

Income-based methods of valuation are of particular use when valuing a majority shareholding:

• ownership bestows additional benefits of control not reflected in the dividend valuation model (see later)
• majority shareholders can influence dividend policy and therefore are more interested in earnings.

PE ratio method

PE ratios are quoted for all listed companies and calculated as:

Price per share/Earnings per share (EPS)

This can then be used to value shares in unquoted companies as:

Value of company = Total earnings × PE ratio

Value per share = EPS × PE ratio

using an adjusted PE multiple from a similar quoted company (or industry average).

Problems with the PE ratio valuation

• It may be necessary to make an adjustment(s) to the PE ratio of the similar company to make it more suitable, e.g. if the company being valued:

Ensure that you explain the reasons why an adjustment is needed. Thisis essential as it shows you have an understanding of the biggerpicture.

Arbitrary rule: Adjusted by 10% per reason – but amounts are less important than the explanation.

• It can be difficult to estimate the maintainable or normal ongoing level of earnings of the company being valued. It may be necessary to adjust these earnings to obtain a maintainable figure, e.g. change a director's emoluments from an abnormal to normal level.

Remember to adjust for tax as the PE ratio is applied to profits after tax.

• PE ratios are in part based upon historical accounting information (the EPS) whereas the valuation should reflect future earnings prospects.

Finding a suitable PE ratio

The basic choice for a suitable PE ratio will be that of a quoted company of comparable size in the same industry.

However, since share prices are broadly based on expected futureearnings a PE ratio – based on a single year's reported earnings –may be very different for companies in the same sector, carrying thesame systematic risk.

For example a high PE ratio may indicate:

• growth stock – the share price is high because continuous high rates of growth of earnings are expected from the stock
• no growth stock – the PE ratio is based on the last reported earnings, which perhaps were exceptionally low yet the share price is based on future earnings which are expected to revert to a 'normal' relatively stable level
• takeover bid – the share price has risen pending a takeover bid
• high security share – shares in property companies typically have low income yields but the shares are still worth buying because of the prospects of capital growth and level of security.

Similarly a low PE ratio may indicate:

• losses expected – future profits are expected to fall from their most recent levels
• share price low – as noted previously, share prices may be extremely volatile – special factors, such as a strike at a manufacturing plant of a particular company, may depress the share price and hence the PE ratio.

Consequently the main difficulty in trying to apply the model is finding a similar company, with similar growth prospects.

A further difficulty is that the reported earnings are based onhistorical cost accounts, which in general makes a nonsense of trying tocompare two companies. Also it is important to ensure that the earningsin the victim company reflect future earnings prospects. It would beunwise to value a company on freakishly high earnings.

Test your understanding 2 – PE ratio method

You are given the following information regarding Accrington Co, an unquoted company:

(a)Issued ordinary share capital is 400,000 25c shares.

(b)Extract from the income statement for the year ended 31 July 20X4

(c)The PE ratio applicable to a similar type of business (suitable for an unquoted company) is 12.5.

You are required to value 200,000 shares in Accrington Co on a PE ratio basis.

Earnings yield

The earnings yield is simply the inverse of the PE ratio:

It can therefore be used to value the shares or market capitalisation of a company in exactly the same way as the PE ratio:

This is in effect an adaptation of the dividend growth model wheredividend per share has been replaced by earnings per share, the dividendgrowth rate by earning growth rate and the cost of equity with earningsyield.

Test your understanding 3 – Earnings yield

Company A has earnings of $300,000. A similar listed company has an earnings yield of 12.5%.

Company B has earnings of $420,500. A similar listed company has a PE ratio of 7.

Estimate the value of each company.

Market capitalisation

A firm's market capitalisation is found by multiplying its current share price by the number of shares in issue.

4 Cash flow based methods

Valuing shares using the dividend valuation model (DVM)

This method can be used for valuing minority shareholdings in acompany, since the calculation is based on dividends paid, somethingwhich minority shareholders are unable to influence. The DVM wasdiscussed in detail in the chapter on cost of capital. It is summarisedagain here.

The method

• The value of the company/share is the present value (PV) of the expected future dividends discounted at the shareholders' required rate of return.

Either:

Assuming: a constant dividend or constant growth in dividends

r_e = shareholders' required return, expressed as a decimal

g = annual growth rate

P_o =value of company, when D = Total dividend.

Strengths and weaknesses of the DVM

The model is theoretically sound and good for valuing a non-controlling interest but:

• there may be problems estimating a future growth rate
• it assumes that growth will be constant in the future, this is not true of most companies
• the model is highly sensitive to changes in its assumptions
• for controlling interests it offers few advantages over the earnings methods below.

To use this approach for valuation we need to be able to determinethe cost of equity. The examiner will either give the cost of equitydirectly or give sufficient information so that you can use CAPM todetermine the cost of equity.

Test your understanding 4 – Valuing shares: the DVM

A company has the following financial information available:

You also have the following market information:

Find the market capitalisation of the company.

Test your understanding 5 – Valuing shares: the DVM

A company has the following financial information available:

You also have the following market information:

Find the market capitalisation of the company.

Discounted cash flow basis

This alternative cash flow based method is used when acquiring amajority shareholding since any buyer of a business is obtaining astream of future operating cash flows.

The maximum value of the business is:

A discount rate reflecting the systematic risk of the flows should be used.

Method:

(1)Identify relevant ‘free’ cash flows (i.e. excluding financing flows)

• operating flows
• revenue from sale of assets
• tax
• synergies arising from any merger.

(2)Select a suitable time horizon.

(3)Calculate the PV over this horizon. This gives the value to all providers of finance, i.e. equity + debt.

(4)Deduct the value of debt to leave the value of equity.

Test your understanding 6 – Discounted cash flow basis

The following information has been taken from the income statement and balance sheet of B Co:

Corporation tax is 30%.

The WACC is 16.6%. Inflation is 6%.

These cash flows are expected to continue every year for the foreseeable future.

Required:

Calculate the value of equity.

Test your understanding 7 – Discounted cash flow basis

A company's current revenues and costs are as follows: sales $200million, cost of sales $110 million, distribution and administrativeexpenses are $20 million, tax allowable depreciation $40 million andannual capital spending is $50 million. Corporation tax is 30%. Thecurrent value of debt is $17 million.

The WACC is 14.4%. Inflation is 4%.

These cash flows are expected to continue every year for the foreseeable future.

Calculate the value of equity.

Advantages

• theoretically the best method.
• can be used to value part of a company.

Weaknesses

• it relies on estimates of both cash flows and discount rates – may be unavailable
• difficulty in choosing a time horizon
• difficulty in valuing a company's worth beyond this period
• assumes that the discount rate, tax and inflation rates are constant through the period.

5 Valuation post- takeover

It may be necessary to estimate the value of a company following atakeover of another company. In this situation, when estimating theeffect of the takeover on the total value of the company and on thevalue per share it is important to take into account:

(1)Synergy – any synergy arising from the takeover would be expected to increase the value of the company.

(2)The method of financing thetakeover. If cash is used to finance the takeover the value of thecompany will be expected to fall by the amount of cash needed. If sharesare used to finance the takeover then the extra shares issued need tobe taken into account when calculating the value per share.

Test your understanding 8 – Valuation in a takeover situation

Boston is an all equity financed company and has 10million sharesin issue. Its share price is 540c per share. It is considering a takoverof Red Socks, a company in the same industry. Red Socks is also allequity financed and has 5million shares in issue. The share price of RedSocks is 270c per share.

The takeover is likely to result in synergy gains estimated to be worth a total of $5million.

The financial advisers to Boston have indicated that if an offer ismade at a 20% premium to the current market price this is likely to beacceptable to the shareholders of Red Socks.

Required:

(a)If Boston has sufficient cashavailable to finance the takeover, estimate the total value of Bostonpost-takeover and the value of each share in Boston.

(b)If Boston offers a share forshare exchange for the shares in Red Socks, estimate the total value ofBoston post-takeover and the value of each share in Boston.

6 Valuation of debt and preference shares

In chapter 15 we looked at using the DVM to determine costs ofcapital and saw that many of the equations could be rearranged to givemarket value. These are summarised below:

where:

D = the constant annual preference dividend

P_o = ex-div market value of the share

K_p = cost of the preference share.

I = annual interest starting in one year's time

MV = market price of the debenture now (year 0)

PV = present value

r = debt holders' required return, expressed as a decimal

Test your understanding 9 – Valuation of preference shares

A firm has in issue 12% preference shares with a nominal value of$1 each. Currently the required return of preference shareholders is14%.

What is the value of a preference share?

Test your understanding 10 – Valuation of irredeemable debt

A company has issued irredeemable loan notes with a coupon rate of7%. If the required return of investors is 4%, what is the currentmarket value of the debt?

Test your understanding 11 – Valuation of redeemable debt

A company has in issue 9% redeemable debt with 10 years toredemption. Redemption will be at par. The investors require a return of16%.

What is the market value of the debt?

Convertible debt

The market value of a convertible is the higher of its value as debt and its converted value. This is known as its formula value.

Additional values you may be asked for regarding convertible debt are:

Test your understanding 12 – Valuation of convertible debt

Rexel Co has in issue convertible loan notes with a coupon rate of12%. Each $100 loan note may be converted into 20 ordinary shares at anytime until the date of expiry and any remaining loan notes will beredeemed at $100.

The loan notes have five years left to run. Investors wouldnormally require a rate of return of 8% pa on a five-year debt security.

Should investors convert if the current share price is:

(a)$4.00.

(b)$5.00.

(c)$6.00.

Test your understanding 13 – Convertible debt calculations

PO Co has in issue 8% bonds which are redeemable at their par valueof $100 in three years' time. Alternatively, each bond may be convertedon that date into 30 ordinary shares of the company.

The current ordinary share price of PO Co is $3.30 and this is expected to grow at 5% per year for the foreseeable future.

PO Co has a cost of debt of 6% per year.

Required

Calculate the following current values for each $100 convertible bond:

(i)market value

(ii) floor value

(iii)conversion premium

7 Market efficiency

The concept of market efficiency

Opening question:

• If N plc shares are valued at $1.30, is this value reliable (fair, true, accurate)?

Or put another way:

• How efficient is the stock market at valuing the shares of a company?

• An efficient market is one in which security prices fully reflect all available information.

• In an efficient market, new information is rapidly and rationally incorporated into share prices in an unbiased way.

Current position

In the sophisticated financial markets of today, there are

• cheap electronic communications
• large numbers of informed investors.

Conclusion

New information is rapidly (in minutes not days) incorporated into share prices.

Benefits of an efficient market

We need an efficient stock market to

• ensure investor confidence
• reflect directors' performance in the share price.

Benefits of an efficient market

Investor confidence

Investors need to know that they will pay and receive a fair pricewhen they buy and sell shares. If shares are incorrectly priced, manysavers would refuse to invest, thus seriously reducing the availabilityof funds and inhibiting growth. Investor confidence in the pricingefficiency is essential.

Motivation and control of directors

The primary objective of directors is the maximisation ofshareholder wealth, i.e. maximise the share price. In implementing apositive net present value (NPV) decision, directors can be assured thatthe decision once communicated to the market will result in anincreased share price. Conversely if directors make sub-optimaldecisions then the share price will fall. Like all feedback systems thestock market has a dual function. It motivates directors to maximiseshare price, whilst providing an early warning system of potentialproblems.

8 The efficient market hypothesis (EMH)

The EMH states that security prices fully and fairly reflect allrelevant information. This means that it is not possible to consistentlyoutperform the market by using any information that the market alreadyknows, except through luck.

The idea is that new information is quickly and efficientlyincorporated into asset prices at any point in time, so that oldinformation cannot be used to foretell future price movements.

Three levels of efficiency are distinguished, depending on the typeof information available to the majority of investors and hence alreadyreflected in the share price.

The forms of efficiency are cumulative, so that if the market is semi-strong it is also weak.

9 Types of efficiency

Market inefficiency

An inefficient market is one in which the value of securities is notalways an accurate reflection of the available information. Markets mayalso operate inefficiently, e.g. due to low volumes of trade.

In an inefficient market, some securities will be overpriced andothers will be underpriced, which means some investors can make excessreturns while others can lose more than warranted by their level of riskexposure.

Weak form efficiency

Information

In a weak form efficient market share price reflects information about all past price movements. Past movements do not help in identifying positive NPV trading strategies.

Evidence

Share prices follow a random walk:

• there are no patterns or trends
• prices rise or fall depending on whether the next piece of news is good or bad
• tests show that only 0.1% of a share price change on one day can be predicted from knowledge of the change on the previous day.

Conclusion

The stock market is weak form efficient and so:

• future price movements cannot be predicted from past price movements
• chartism/technical analysis cannot help make a consistent gain on the market.

Weak form efficiency

Random walks

In 1953 Kendall presented a paper which examined share pricemovements over time. He concluded that the prices of shares followed arandom walk, i.e. there are no patterns or trends. Any apparent patternor trend purely occurs by chance.

Why does the random walk occur?

Prices change because of new information. New information is bydefinition independent of the last piece of new information and thus theresulting share price movements are independent of each other, i.e. thenext piece of new information has equal chance of being good or bad,nobody knows.

If a pattern is identified from historical share price movementsand this information becomes known in the market, the patterndisappears, as the market buys and sells shares accordingly to takeadvantage of the pattern.

The market is weak form efficient, as the study of the history ofshare prices cannot be used to predict the future in any abnormallyprofitable way.

Semi-strong efficiency

Information

In a semi-strong efficient market the share price incorporates all past information and all publicly-available information(i.e. a semi-strong form efficient market is also weak form efficientand public information includes past information).

Evidence

Share prices react within 5–10 minutes of any new information being released and:

• rise in response to breaking good news
• fall in response to breaking bad news.

Conclusion

The stock market is (almost) semi-strong form efficient and so:

• fundamental analysis – examining publicly-available information will not provide opportunities to consistently beat the market
• only those trading in the first few minutes after the news breaks can beat the market
• since published information includes past share prices a semi-strong form efficient market is also weakly efficient.

Strong form efficiency

Information

In a strongly efficient market the share price incorporates all information, whether public or private, including information which is as yet unpublished.

Evidence

Insiders (directors for example) have access to unpublished information. If the market was strong form

• the share price wouldn't move when, e.g. news broke about a takeover, as it would have moved when the initial decision was made – in practice they do!
• there would be no need to ban 'insider dealing' as insiders couldn't make money by trading before news became public– it is banned because they do!

Conclusion

The stock market is not strong form efficient and so:

• insider dealers have been fined and imprisoned for making money trading in shares before the news affecting them went public
• the stock exchange encourages quick release of new information to prevent insider trading opportunities
• insiders are forbidden from trading in their shares at crucial times.

Insider dealing

It is well-known that shares can be traded on the basis ofinformation not in the public domain and thereby make abnormal profits.Stock markets are not strong form efficient. The engineer who discoversgold may buy shares before the discovery is made public. The merchantbanker who hear's a colleague is assisting in a surprise takeover bidhas been known to purchase shares in the target firm.

A breakdown in the fair game perception will damage investor confidence and reduce investment. To avoid a loss of confidence most stock markets have codes of conduct and most countries have introduced legislation to curb insider dealing.Insider dealing became a criminal offence in the UK in 1980. HoweverBritish regulators tend to be less effective than some of their foreigncounterparts. American and French regulators rely initially on civil lawwhere the burden of proof is lower than in a criminal case.

Another weapon against insiders is to make companies release price-sensitive information quickly.The London Stock Exchange has strict guidelines to encourage companiesto make announcements to the market as early as possible, on suchmatters as current trading conditions and profit warnings. Thereforethere is a mechanism to force private information into the public arenato attempt to ensure that share prices are reasonably accurate.

A third approach is to completely prohibit certain individuals fromdealing in a company shares at crucial time periods. The stock exchangeModel Code for Directors Dealings precludes directors of quotedcompanies (and indeed other employees in the possession ofprice-sensitive information) from trading shares for a period of twomonths before the announcement of the annual results. The Code alsoprecludes dealing before the announcement of matters of an exceptionalnature involving unpublished information, which is potentially pricesensitive.

Conclusions for the market

If the market is semi-strong then a number of key conclusions can be drawn:

• shares are fairly priced – the purchase is a zero NPV transaction (unless you are an insider dealer!)
• managers can improve shareholders' wealth by investing in positive NPV projects and communicating this to the market
• most investors (including professional fund managers) cannot consistently beat the market without inside information.

Conclusions for the market

In an efficient market, shares are priced to give investors theexact return to reward them for the level of (systematic) risk in theirshares. As a result the purchase of shares is a zero NPV transactionbecause the price paid for the share is an accurate reflection of itsworth i.e. shares are fairly priced and the concept of an over- orunder-valued security does not apply. Therefore the rationale behindmergers and takeovers must be questioned. Semi-strong efficiency impliesthat mergers could only be successful if synergies can be created, i.e.economies of scale or rationalisation.

Given the fact that well-developed stock markets are weak andsemi-strong market efficient most of the time, once new information iscommunicated to the market it is rapidly reflected in the share price.Thus managers can achieve the overall objective of maximisingshareholder wealth by making good decisions and communicating them tothe market.

Is it worth acquiring and analysing public information?

If semi-strong efficiency is true, it undermines the work ofmillions of fundamental (professional and amateur) analysts, whose workcannot be used to produce abnormal returns because all publicinformation is already reflected in the share price.

These analysts study the fundamental factors that underpin theshare price, i.e. revenues, costs and risk associated with the companyas well as many other sources of public information such asmacroeconomic and industry conditions, details of the company personnel,technological changes and so on.

They will then use this information, together with a sharevaluation model (e.g. like the dividend valuation model – DVM), toestimate the true or intrinsic value of the shares. This value is thencompared with the current market price of shares to see if the sharesare over- or under-valued (mispriced).

The fundamental analyst is attempting to beat the market to earn an abnormal return by:

• buying under-valued shares before the prices rise.
• selling over-valued shares before the prices fall.

But in an efficient market mis-priced shares do not exist.

Given that there are thousands of sophisticated investors examiningthe smallest piece of information about each company and itsenvironment, it would seem reasonable to postulate that the semi strongform of EMH is a reality in well-developed stock markets.

Conclusion:

The vast majority of investors (including professional fundmanagers) cannot consistently beat the market by analysing theinformation they have available to them, as this public information isalready reflected in the share price. So long as the market remainsefficient, fundamental analysis is a waste of money and the averageinvestor would be better off by simply selecting a diversifiedportfolio, thereby avoiding costs of analysis. This message has struck achord with millions of investors who have placed billions of pounds inlow cost Index Tracking Funds, which merely replicate a stock marketindex, rather than an actively managed fund which tries to pick winners.

The market paradox

In order for the market to remain efficient, investors must believe there is value in assessing information.

Because they assess it continuously the information is reflected inthe share price as soon as it is released and an investor cannot beatthe market.

The market paradox

The paradox of the EMH is that large numbers of investors have todisbelieve the hypothesis in order to maintain efficiency. Thecontinuous collective actions of fundamental analysts ensure that themarket reacts almost instantaneously to the disclosure of newinformation. Their actions safeguard market efficiency and are thusself-defeating, as they cannot then individually beat the market. Theircollective value to the market is that they guarantee its efficiency.

Investor behaviour

Despite the evidence in support of the theory, some events seem to contradict it:

• significant share price volatility
• boom/crash patterns.

e.g. the stock market crash of October 1987 where most stockexchanges crashed at the same time. It is virtually impossible toexplain the scale of those market falls by reference to any news eventat the time.

An explanation has been offered by the science of behavioural finance:

• naïve investors see high-performing shares (for example) and rush to buy
• this noise inflates the share price artificially
• informed investors then buy, planning to sell before the inevitable crash.

Investor behaviour

Events such as significant share price volatility and boom/crashpatterns seem at odds with the theory of efficient markets becauseprices are not supposed to deviate markedly from their fundamentalvalue.

One theory behind this seemingly irrational behaviour of themarkets is called noise trading by naïve investors. According to thistheory there are two types of investors, the informed and uninformed.The informed trade shares to bring them to their fundamental value. Theuninformed act irrationally. Perhaps they noticed that certain shareshave made investors high returns over the last number of years. So theyrush out and buy these shares to get their piece of the action i.e. theychase the trend.

The uninformed investors create lots of noise and push the marketup and up. The informed investor often tries to get in on the act.Despite knowing it will end in disaster, the informed investor buys inthe hope of selling before the crash. This is based on the idea that theprice an investor is willing to pay for a share today is dependent onthe price the investor can sell it for at some point in the future andnot necessarily at its fundamental value.

A summary

In summary:

Conclusion:

The stock exchanges of all developed nations are regarded as atleast semi-strong efficient for the shares traded actively on thosemarkets.

Test your understanding 14 – Market efficiency

What would you believe about the efficiency of the market if you thought you could make money by:

(1)insider dealing

(2)analysing past price movements

(3)only by pure luck

(4)analysing financial statements, directors’ statements, company activities, etc.?

Other factors to consider

Other factors to take into account when considering the value of shares

Marketability and liquidity of shares

As discussed in chapter 20, the shares in a private company areoften valued by using measures based on the 'fair' share prices ofsimilar listed companies.

However buying a share in an unlisted company is more of a gamble, as the share cannot be easily sold.

This is why the values given by methods such as price/earnings (PE) ratio and earnings yield, are often downgraded.

Available information

We discussed above the importance of information concerning a company being fully available if the share is to be fairly priced.

In unlisted companies, information may be less readily available for a number of reasons such as:

• a weaker control environment
• unaudited financial statements
• fewer compliance regulations apply
• no tradition of sharing information so channels of communication not set up
• less detailed record keeping.

The relative shortage of information in unlisted companies may also cause the initial valuation to be downgraded.

Equilibrium prices

In practice, as discussed above, the market does show sudden pricefluctuations that cannot be explained simply by the information beingnewly released. If a share price is highly volatile, then it isconsidered not in equilibrium.

Prices used to provide data for the valuation of unlisted sharesneed to be in equilibrium if meaningful values are to be obtained.

If only a few similar companies exist, and their shares are not in equilibrium, any share price calculated must be treated with caution.

Chapter summary

Test your understanding answers

Test your understanding 1 – Asset based measures

Calculation of value of 200,000 shares on an assets basis, as at 30 April year 20X6

Test your understanding 2 – PE ratio method

Valuation of 200,000 shares = 200,000 × [PE ratio × EPS]

Test your understanding 3 – Earnings yield

Test your understanding 4 – Valuing shares: the DVM

The formula

will provide the value of a single share. The market capitalisationcan then be found by multiplying by the number of shares in issue.

D_o = 24c

g can be found by extrapolating from past dividends:

R_e can be found using CAPM

R_f + ß (R_m – R_f) =

8 + 0.8 (15 – 8) = 13.6

Therefore

The market capitalisation is therefore:

4m × $16.80 = $67.2m

Test your understanding 5 – Valuing shares: the DVM

The formula

will provide the value of a single share. The market capitalisationcan then be found by multiplying by the number of shares in issue.

D_o = 18c

g using Gordon's Growth Model

g = r × b

r = 20%

If dividends per share of 18c are paid on EPS of 25c, then thepayout ratio is 18/25 = 72%. The retention ratio is therefore 28%.

So b = 0.28

Therefore g = 0.2 × 0.28 = 0.056.

r_e (using CAPM)

R_f + ß (R_m – R_f) =

5 + 1.1 (12 – 5) = 12.7

Therefore

The market capitalisation is therefore:

2m × $2.68 = $5.36m

Test your understanding 6 – Discounted cash flow basis

Operating profits = $350m – $210m – $24m = $116m

Tax on operating profits = $116m × 0.3 = $34.8m

Allowable depreciation = $31m (assumed not included in production or administration expenses)

Tax relief on depreciation = $31m × 0.3 = $9.3

Therefore free cash flow = $116 – $34.8 + $9.3 – $48 = $42.5

Equity = $425m – ($14m × 1.3) = $406.8m.

Note: because the cash flow is a perpetuity we have used thereal (uninflated) cash flow and the real discount rate (see chapter onfurther aspects of discounted cash flows).

Test your understanding 7 – Discounted cash flow basis

Operating profits = $200m – $110m – $20m = $70m

Tax on operating profits = $70m × 0.3 = $21m

Allowable depreciation = $40m

Tax relief on depreciation = $40m × 0.3 = $12

Therefore net cash flow = $70 – $21 + $12 – $50 = $11

Equity = $110m – $17m = $93m.

Test your understanding 8 – Valuation in a takeover situation

(a)The value of Boston after thetakeover can be estimated as the value of Boston before the takeover,plus the value of Red Socks before the takeover, plus the value of anysynergy arising from the takeover, less the cash paid by Boston tofinance the takeover.

Boston will need to pay $2.70 × 1.20 = $3.24 for each share in RedSocks. The total consideration needed to buy the whole of Red Socks willtherefore be

5million shares × $3.24 = $16,200,000.

The value of Boston post takeover will therefore be:

Boston will not have issued any new shares and therefore the posttakeover share price of Boston will be $56,300,000/10million = $5.63.This is an increase of 23 cents.

(b)In this case Boston will offershares worth $16,200,000 to finance the takeover. Based on thepre-takeover value of each Boston share this will mean offering$16,200,000/$5.40 = 3,000,000 shares.

The total value of the company will be higher in this case becauseBoston is not using up its cash reserves to finance the takeover.

Boston will now have (10,000,000 + 3,000,000) = 13,000,000 sharesin issue post-takeover and therefore the value per share will be$72,500,000/13,000,000 = $5.58.

Test your understanding 9 – Valuation of preference shares

Test your understanding 10 – Valuation of irredeemable debt

Test your understanding 11 – Valuation of redeemable debt

The market value is calculated by finding the PVs of the interest and the principal and totalling them as shown below.

Test your understanding 12 – Valuation of convertible debt

Value as debt

If the security is not converted it will have the following value to the investor:

Note the PV is calculated at 8% – the required rate of return on a straight debt security.

Value as equity

If the market price of equity rises to $6.00 the security should beconverted, otherwise it is worth more as debt. The 'breakeven'conversion price is $5.80 per share ($116/20 shares).

The value of the convertible will therefore be $116, unless theshare price rises above $5.80 at which point it will be the value of theequity received on conversion.

Test your understanding 13 – Convertible debt calculations

(i)Market value

(ii) Floor value

(iii) Conversion premium

Test your understanding 14 – Market efficiency

(1)It is at most semi-strong.

(2)It is not efficient at all.

(3)It is strong form.

(4)It is at most weak form.

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