2 models for the valuation of shares

7/31/2019 2 Models for the Valuation of Shares

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2 MODELS FOR THE VALUATION OF SHARES.

2.1 The concept of a cost of equity

The cost of equity is the cost to the company of providing equity holders with the return they

require on their investment.

The primary financial objective is to maximize the return to equity shareholders. This return is as the

future dividend yield and capital growth.

Until new shareholders become members of the company, the objective above is concerned with

existing shareholders. Company management will need to offer new shareholders the minimum

acceptable future return on the funds they put into the company, thereby retaining as much benefit

as possible for existing shareholders.

In practice, this return will be such as to provide new shareholders with the same future returns as

existing shareholders expect to obtain on their investment at market values.

For example if the future return on ABC plc's shares is 15% and future return on new issue is 20% if

this is viewed quite simplistically, investors would sell their existing shares and take up the new

offer. The price of existing shares would fall, and as a result the percentage return would increase,

until it matched the 20% of new shares. This would mean existing shareholders would suffer a

capital loss as the price of their shares declined.

Thus, the object of management must be to offer the shares so as to provide a return identical tothat of existing shares (in this case 15%). They could not offer less than 15% as it might then be

difficult to find investors for the new issue.

Note: in all cases the relevant return is the future return anticipated by shareholders.

Thus, the problem of determining the cost of new equity becomes the problem of establishing the

anticipated market return on existing equity.


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The cost of equity ,equals the rate of return which investors expect to achieve on their equity

holdings.

2.2 Anticipated rate of return on existing equity

The anticipated rate of return on a share acquired in the market consists of two components:

Component I - Dividends paid until share sold

Component 2 - Price when sold

In this sense, the returns are directly analogous to those on a debenture, with dividends replacing

interest and sale price replacing redemption price.

Applying the concept of compound interest, in making a purchase decision it is assumed that the

investor discounts future receipts at a personal discount rate (or personal rate of time preference).

For the illustration below I will define this rate as 'i'.

In order to make a purchase decision, the shareholder must believe the price is below the value of

the receipts, i.e, -

Current price, Po < Dividends to sale + Sale price

Discounted at rate i

Algebraically, if the share is held for n years then sold at a price Pn and annual dividends to year n

are D1, D2, D3, ... Dn


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Then:

Po < D1/(1+i) + D2/(1+i) + D3/(1+i) + (Dn + Pn)/(1+i)

By similar logic, the seller of the share must believe that

Po > D1/(1+i) + D2/(1+i) + D3/(1+i) + (Dn + Pn)/(1+i)

These different views will occur for two reasons.

(a) Different forecasts for D1, D2 etc and for Pn by the different investors.

(b) Different discount rates being applied by different investors.

However, since the price of shares is normally in equilibrium, for the majority of investors who are

not actively trading in that security:

Po = D1/(1+i) + D2/(1+i) + D3/(1+i) + (Dn + Pn)/(1+i)

2.3 Limitations of the above valuation model

It is important to appreciate that there are a number of problems and specific assumptions in this

model.

(a) Anticipated values for dividends and prices - all of the dividends and prices used in the model are

the investor's estimates of the future.


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(b) Assumption of investor rationality - the model assumes investors act rationally and make their

decisions about share transactions on the basis of financial evaluation.

(c) Application of discounting - it assumes that the conventional compound interest approachequates cash flows at different points in time.

(d) Share prices are ex div

(e) Dividends are paid annually with the next dividend payable in one year.

2.4 The dividend valuation model

The dividend valuation model is a development of the share valuation model described above.

The important feature of the dividend valuation model is the recognition of the fact that shares are

in themselves perpetuities. Individual investors may buy or sell them, but only very exceptionally are

they actually redeemed.

2.5 One Period Valuation Model

To value a stock, you first find the present discounted value of the expected cash flows.

P0 = Div1/(1 + ke) + P1/(1 + ke) where

P0 = the current price of the stock

Div = the dividend paid at the end of year 1

ke = required return on equity investments


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P1 = the price at the end of period one

P0 = Div1/(1 + ke) + P1/(1 + ke)

Let ke = 0.12, Div = 0.16, and P1 = $60.

P0 = 0.16/1.12 + $60/1.12

P0 = $0.14285 + $53.57

P0 = $53.71

If the stock was selling for $53.71 or less, you would purchase it based on this analysis.

2.6 Generalized Dividend Valuation Model

The one period model can be extended to any number of periods.

P0 = D1/(1+ke)1 + D2/(1+ke)2 ++ Dn/(1+ke)n + Pn/(1+ke)n

If Pn is far in the future, it will not affect P0. Therefore, the model can be rewritten as:

P0 = S Dt/(1 + ke)t

The model says that the price of a stock is determined only by the present value of the dividends.


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If a stock does not currently pay dividends, it is assumed that it will someday after the rapid growth

phase of its life cycle is over.

Computing the present value of an infinite stream of dividends can be difficult. Simplified modelshave been developed to make the calculations easier.

2.7 The Gordon Growth Model

P0 = D0(1+g)1 + D0(1+g)2 +..+ D0(1+g)

(1+ke)1 (1+ke)2 (1+ke)

where

D0 = the most recent dividend paid

g = the expected growth rate in dividends

ke = the required return on equity investments

The model can be simplified algebraically to read:

P0 = D0(1 + g) D1

(ke - g) (ke g)

2.7.1 Assumptions:


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Dividends continue to grow at a constant rate for an extended period of time.

The growth rate is assumed to be less than the required return on equity, ke.

Gordon demonstrated that if this were not so, in the long run the firm would grow impossibly large.

2.7.2 Gordon Model: Example

Find the current price of Coca Cola stock assuming dividends grow at a constant rate of

10.95%, D0 = $1.00, and ke is 13%.

P0 = D0(1 + g)/ke g

P0 = $1.00(1.1095)/0.13 - 0.1095 =

P0 = $1.1095/0.0205 = $54.12

2.7.3 Gordon Model: Conclusions

Theoretically, the best method of stock valuation is the dividend valuation approach.

But, if a firm is not paying dividends or has an erratic growth rate, the approach will not work.

Consequently, other methods are required.

2.8 Price Earnings Valuation Method


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The price earning ratio (PE) is a widely watched measure of how much the market is willing to

pay for $1 of earnings from a firm.

A high PE has two interpretations:

A higher than average PE may mean that the market expects earnings to rise in the future.

A high PE may indicate that the market thinks the firm's earnings are very low risk and is

therefore willing to pay a premium for them.

2.9 Setting Security Prices

Stock prices are set by the buyer willing to pay the highest price.

The price is not necessarily the highest price that the stock could get, but it is incrementally greater

than what any other buyer is willing to pay.

The market price is set by the buyer who can take best advantage of the asset.

Superior information about an asset can increase its value by reducing its risk.The buyer who has the

best information about future cash flows will discount them at a lower interest rate than a buyer

who is uncertain

2.10 Cost of preference shares

By definition preference shares have a constant dividend

kp = D/MV(ex div)


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where D = constant annual dividend

If you have cumulative preference shares, the MV is increased by the outstanding amount to be

paid. Preference dividends are normally quoted as a percentage, eg 10% preference shares. Thismeans that the annual dividend will be 10% of the nominal value, not the market value..

Share prices change, often dramatically, on a daily basis. The dividend valuation model will not

predict this, but will give an estimate of the underlying value of the shares.

5 EFFICIENT MARKET HYPOTHESIS

Practical factors affecting share prices.

The dividend valuation model gives a theoretical value, given the assumptions inherent in the model,

for shares and debentures.

In practice there will be many factors other than the present value of cash flows from a security that

play a part in its valuation. These are likely to include:

interest rates

market sentiment

expectation of future events

inflation press comment

speculation and rumour

currency movements

takeover and merger activity

political issues.

The dividend valuation model helps us to understand how a change in these variables (or, to be

more accurate, an expected change) should effect the market value of the security.

5.1.1 Efficient markets


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The value of a share or of the equity shareholders funds is based upon expectations of future cash

flows either in the form of dividends or NPVs of investment projects. The strength of the link

between the performance of the company and the share price will depend upon the efficiency of the

capital markets. How much does the market know about a company? In other words, how good is it

at incorporating information into the share price?

5.2 The Efficient Market Hypothesis & The Random Walk Theory

An issue that is the subject of intense debate among academics and financial professionals is the

Efficient Market Hypothesis (EMH). The Efficient Market Hypothesis states that at any given time,

security prices fully reflect all available information. The implications of the efficient market

hypothesis are truly profound. Most individuals that buy and sell securities (stocks in particular), do

so under the assumption that the securities they are buying are worth more than the price that they

are paying, while securities that they are selling are worth less than the selling price. But if markets

are efficient and current prices fully reflect all information, then buying and selling securities in an

attempt to outperform the market will effectively be a game of chance rather than skill.

"An 'efficient' market is defined as a market where there are large numbers of rational, profit-

maximizers actively competing, with each trying to predict future market values of individual

securities, and where important current information is almost freely available to all participants. In

an efficient market, competition among the many intelligent participants leads to a situation where,at any point in time, actual prices of individual securities already reflect the effects of information

based both on events that have already occurred and on events which, as of now, the market

expects to take place in the future. In other words, in an efficient market at any point in time the

actual price of a security will be a good estimate of its intrinsic value."

The random walk theory asserts that price movements will not follow any patterns or trends and

that past price movements cannot be used to predict future price movements.

There are three forms of the efficient market hypothesis

The "Weak" form asserts that all past market prices and data are fully reflected in securities prices.

In other words, technical analysis is of no use.

The "Semistrong" form asserts that all publicly available information is fully reflected in securitiesprices. In other words, fundamental analysis is of no use.


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The "Strong" form asserts that all information is fully reflected in securities prices. In other words,

even insider information is of no use.

Securities markets are flooded with thousands of intelligent, well-paid, and well-educated investors

seeking under and over-valued securities to buy and sell. The more participants and the faster the

dissemination of information, the more efficient a market should be.

The debate about efficient markets has resulted in hundreds and thousands of empirical studies

attempting to determine whether specific markets are in fact "efficient" and if so to what degree.

Many novice investors are surprised to learn that a tremendous amount of evidence supports the

efficient market hypothesis. Early tests of the EMH focused on technical analysis and it is chartistswhose very existence seems most challenged by the EMH. And in fact, the vast majority of studies of

technical theories have found the strategies to be completely useless in predicting securities prices.

However, researchers have documented some technical anomalies that may offer some hope for

technicians, although transactions costs may reduce or eliminate any advantage.

Researchers have also uncovered numerous other stock market anomalies that seem to contradict

the efficient market hypothesis. The search for anomalies is effectively the search for systems or

patterns that can be used to outperform passive and/or buy-and-hold strategies. Theoreticallythough, once an anomaly is discovered, investors attempting to profit by exploiting the inefficiency

should result its disappearance. In fact, numerous anomalies that have been documented via back-

testing have subsequently disappeared or proven to be impossible to exploit because of transactions

costs.

The paradox of efficient markets is that if every investor believed a market was efficient, then the

market would not be efficient because no one would analyze securities. In effect, efficient markets

depend on market participants who believe the market is inefficient and trade securities in an

attempt to outperform the market.

In reality, markets are neither perfectly efficient nor completely inefficient. All markets are efficient

to a certain extent, some more so than others. Rather than being an issue of black or white, market

efficiency is more a matter of shades of gray. In markets with substantial impairments of efficiency,

more knowledgeable investors can strive to outperform less knowledgeable ones. Government bond

markets for instance, are considered to be extremely efficient. Most researchers consider large

capitalization stocks to also be very efficient, while small capitalization stocks and international

stocks are considered by some to be less efficient. Real estate and venture capital, which don't have


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fluid and continuous markets, are considered to be less efficient because different participants may

have varying amounts and quality of information.

2 models for the valuation of shares

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