Valuation models, methods and issues: an overview

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Valuation models, methods and

issues: an overview

Robert Herman Jan Lange 0207780

Third draft: 06-09-2007

Supervisor: Dr G. Georgakopoulos, FEE, University of Amsterdam

Abstract

Valuation models and methods used to value a firm’s assets or equity are as numerous as grains of sand on a beach. The premise of each of these models or methods, is that they capture the intrinsic, “real” value of either the firm’s assets or equity. Rarely however will they produce the same results given the same input (Francis et al. 2000 p. 46). Several different methods are discussed in this paper.

This paper focuses on 3 groups of methods specifically, namely: First up are the Discounting-based models, including the Discounted free cash flows- and Abnormal Earnings models. Second are the Relative Valuation methods, including P/E-ratio analysis. Third and last is the Linear Information Dynamic model (also called the “Feltham/Ohlson-“ or “Ohlson model”).

This discussion shows that in practice, given a certain input of accounting numbers, every model or method will produce different results. In fact, the discounted dividend derivatives should, in theory at least, yield the exact same answer, even though they usually don’t in practice (Francis et al. 2000 p. 46). This explains why investment banks for instance use up to ten different models to estimate the fairness of a takeover bid (Palepu et al. 2004 chpt. 7 pg. 1).

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Tables and illustrations

Figure 1 Financial statement analysis 8

Table 1 Forecasting assumptions for TJX Company 10

Table 2 Beginning balance sheet and income statement forecasts 2002 - 2012 10

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1. Introduction

In March of this year, the ABN Amro Corporation entered into takeover negotiations with the British bank Barclays, in order to avoid being split up by activist shareholders led by The Children's Investment Fund (TCI). In April, Barclays makes an offer of 36.80 euro per share. An international banking consortium however, makes an offer of 39.00 euro per share a few days later. In July, the consortium finalizes its bid at 39.05 while Barclays said it was still considering its final bid. But these companies aren’t the only ones that are interested in the value of ABN Amro shares. Investment banks for instance would also be interested in the share’s true value in order to advise their clients to either buy, hold or sell the stock. Clearly, considering the amounts of money

involved, the figures mentioned above are more than just educated guesses. But how do they arrive at these numbers? What method or methods did they use?

There are many different methods and models that are used to establish a share’s true value. In fact, most firms that analysts work for produce their own, specialized model. The fact that there are so many different models and methods used to determine a firm’s true, intrinsic value, seems to indicate that there is no one perfect model or method, and that each method has it’s own advantages and disadvantages.

The purpose of this paper is twofold: first, to provide an overview of the different methods and models used to value the assets and/or equity of a firm; and second, to describe the advantages and disadvantages of the different methods and models and then to compare them to see if there is a “best” model or method. The question that will be answered is: What is the best model or method to determine the value of a firm’s equity or assets?

To this end, the elements, advantages and disadvantages, and underlying

assumptions will be discussed for each of the models and methods highlighted in this paper. For example, the papers by Penman and Sougiannis (1998), Francis et al. (2000) and Kenton (2005) will be used to discuss and evaluate the discounting-based models. Also, the papers by Lundholm (1995), Feltham and Ohlson (1995), DeChow et al. (1999), Clubb (1996), Bernard (1995) and Ahmed et al. (2000) will be used to discuss the model proposed by Ohlson (1995 pg. 668).

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Furthermore, numerical examples will be provided for several of the models. For instance it will be shown that, in theory at least, the three discounting-based models should yield the same value of the firm’s equity or assets, given the same accounting data (Francis et al. 2000 p. 46).

It will be shown that, the Abnormal Earnings model has a practical advantage over other models (Francis et al. 2000 pg. 69; Penman and Sougiannis 1998 pg. 376 - 377). The source of this advantage seems to be that earnings are a better predictor of value than are cash flows (Francis et al. 2000 pg. 69).

It will be argued that the main appeal of relative valuation methods, such as P/E-ratio analysis, is their ease of use. They however do have their problems as well, such as problems with selecting “comparable” firms.

It will also be shown that the model presented by Ohlson (1995 pg. 668) does show promise, however the evidence on the validity of the model is not very good.

The paper’s findings are that there is not one perfect model or method to value equity or assets, but that each have their merits and that each are best suited to be used in specific situations.

The paper’s limitation however is that it does not include any empirical data. For instance, the models described in the paper could be subjected to empirical testing in order to determine which is better at predicting share prices than others. Another suggestion for future research might be an adaptation of one of the models to see if that may increase the performance of that model. Finally, the models presented here might be used to determine the value of companies in extreme situations, in order to see if certain models produce better results than others in certain situations. For example, companies with very high or very low profitability, dot-com startups, or companies with extreme capital structures (near-all equity or near-all debt).

The paper is structured as follows: Section 2 provides an in-depth overview of the abnormal earnings model (see for example Penman and Sougiannis 1998 pg. 350). Section 3 describes the other main discounting-based model, namely the discounted free-cash-flow model (see for example Penman and Sougiannis 1998 pg. 349). Section 4 then proceeds to discuss relative valuation methods like P/E-ratio analysis (see for example McGirt 2004 pg. 73). Section 5 considers a possible alternative to the other

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models and methods (see for example Ohlson 1995 pg. 668). Lastly, section 6 provides some concluding thoughts.

2. Abnormal Earnings Model

As stated above, the discounted abnormal earnings model (from this point on also referred to as the “AE-model”) (see for example Penman and Sougiannis 1998 pg. 350; Francis et al. 2000 pg. 50) is one method commonly used to value either a firm’s equity or its assets. The other main discounting-based model considered in this paper, the discounted free-cash-flow model (see for example Penman and Sougiannis 1998 pg. 349; Francis et al. 2000 pg. 49), will be discussed in the next section. This section of the paper will discuss the fundamental elements of the AE-model. Then the discussion will shift to the underlying assumptions of the model, including how it is derived from the dividend discount model (Penman and Sougiannis 1998 pg. 348; Francis et al. 2000 pg. 48), followed by a numerical example of the AE-model.

2.1 Elements of the model:

The discounted abnormal earningsmodel relates a firm’s abnormal earnings to the value of its equity or assets (Francis et al. 2000 pg. 50). The model is based on

valuation techniques developed by Preinreich (1938) and Edwards and Bell (1961), and then further developed by Ohlson (1995) (as cited by Francis et al. 2000 pg. 49 - 50). The formula used to determine value is defined as (Penman and Sougiannis 1998 pg. 350; Francis et al. 2000 pg. 50):

(1) Where:

AE t

V = The value of the firm’s equity at time t

0

BVE = The beginning book value of equity at time t = 0

(

)

∑

=

+

=

T t t e t AE t

r

AE

BVE

V

1 0

1

(6)

t

AE = Abnormal earnings in year t e

r = The cost of equity capital1

Abnormal earnings reflect the difference between book- and market value of the equity of a firm. A stocks market value (V_tAE) can thus be seen as the cost of the firms existing assets (its book equity) plus the net present value of the firms future growth opportunities (the stream of discounted future abnormal earnings) (Palepu et al. 2004 ch. 7 pg. 3). Abnormal earnings are defined as follows (Francis et al. 2000 pg. 50):

(1a) Where:

t

AE = Abnormal earnings in year t t

NI = Net Income in year t e

r = The cost of equity capital

0

BVE = The beginning book value of equity at time t = 0 The AE-model, along with the other two models described in the next section, builds on the notion that today’s share price is determined by the expected future payoffs generated by the share (Francis et al. 2000 pg. 48).

2.2 Assumptions underlying the model:

The main underlying assumption that must be made in order to use the AE-model, is the assumption of clean surplus accounting. Under this assumption, all non-capital gains and losses are assumed to flow through the income statement. Also, accounting is assumed to be unbiased, and there is dividend irrelevancy (Kenton 2005 pg. 466).

Changes in equity book value also include capital contributions and withdrawals. However, capital transactions do not affect firm value, because an assumption of the model is that new capital is issued at fair value, so that any incremental book value increases are exactly offset by the discounted value of future dividends to the new shareholders.

1

e

r is generally computed using the CAPM model: r_e = r_f + β

(

r_m −r_f

)

, where r_m −r_f is the risk premium usually set at 5 – 10% (Palepu et al. 2004 ch. 8 pg. 3 )

1 −

×

−

=

_t _e _t t

NI

r

BVE

AE

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The clean surplus assumption can also be viewed as the following relation, called the clean surplus relation (Francis et al. 2000 pg. 50; Penman and Sougiannis 1998 pg. 348; Kenton 2005 pg. 465):

(1b) Where:

t

BVE = The book value of equity at time t t

NI = Net Income in year t t

DIV = Dividends in year t

The assumption is important because it is needed to arrive at formula (1) (Kenton 2005 pg. 465). This can be proven with some simple rearranging of terms (DeChow et al. 1999 pg. 3; Palepu et al. 2004 ch. 7 pg. 2). The dividend discount model (upon which the AE-model is based), states that:

Equity value

=

PV of expected future dividends

Which is analogous with:

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Rearranging formula (1b) yields (Palepu et al. 2004 ch. 7 pg. 20):

(2a) Substituting expression (2a) into formula (2) yields:

t t t t

BVE

NI

DIV

BVE

=

₋₁

+

−

(

+

)

+

(

+

)

+

L

=

1 2₂

1

_e

r

_e

DIV

r

DIV

value

Equity

t t t t

NI

BVE

DIV

=

+

₋₁

−

(

)

(

+

)

+

L

−

+

−

+

=

1 0 1 2 1 ₂ 2

1

_e

r

_e

BVE

NI

r

BVE

NI

value

Equity

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This can be simplified as (DeChow et al. 1999 pg. 3 - 4):

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2.3 Equity valuation using the AE-model, a numerical example:

Now that the model has been described and its underlying assumptions examined, the question can be asked, how the model is used in practice. Valuation, or prospective analysis as it is also called (Palepu et al. 2004 ch. 1 pg. 7), is only a small part of financial statement analysis as a whole. Financial statement analysis is important because it attempts to derive management’s inside knowledge of the firm through public financial statements (Palepu et al. 2004 ch. 1 pg. 2).

Financial statement analysis can be broken down into four steps (Palepu et al. 2004 ch. 1 pg. 7): (1) Business strategy analysis, (2) accounting analysis, (3) financial analysis and (4) prospective analysis (the focus of this paper).

Figure 1: Financial statement analysis

Source: Palepu et al. 2004 ch. 1 pg. 7

( )

∑

(

)

=

+

=

T t t e t AE t

r

AE

BVE

V

value

Equity

1 0

1

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Analysis of the firm’s business strategy is the obvious starting point, since it affects all aspects of the firm. This mainly qualitative analysis includes the identification of key profit drivers and its ability to create and maintain a competitive advantage.

Accounting analysis entails the identification and undoing of accounting distortion. In essence, the purpose here is to assess the degree to which the accounting captures the underlying business reality.

Financial analysis focuses on the current and past performance of the firm, and the sustainability of that performance. Cash flow- and ratio analysis are important and often used tools.

Finally, prospective analysis uses the insights provided by the previous three steps to synthesize a prediction about the firm’s future. This part of the analysis includes the forecasting of a firm’s balance sheet and income statement using estimates of certain key variables such as sales growth, net working capital as a proportion of total assets and others. These estimates are then cast in a table such as table 1 presented below. The goal of this phase of the analysis is to get multi-year estimates of a certain financial measure, such as free-cash flows, or in this case, abnormal earnings (Palepu et al. 2004 ch. 1 pg. 7 - 8).

A numerical example of how the AE-model would be used in prospective analysis is given below (see table 1 below). As stated above, the valuation process starts by

making several assumptions about certain key variables that make up the firm’s balance sheet and income statement. These estimates are usually made for 5 to 10 years into the future, starting from the current year. This is called the forecasting horizon. All the years after the forecasting horizon are summarized by the terminal value(Palepu et al. 2004 ch. 8 pg. 5).

The starting point for the analysis is the projection of sales growth rates. Then, estimates of NOPAT margin and several balance sheet ratios are made, as well as estimates of the cost of debt and equity capital.

This is all the information needed to construct the forecasts of the two financial statements which are presented in 2. Table 2 shows a 10 year forecast of the balance sheet and income statement for TJX Company. This table is then used to compute the variables that are needed in each of the different discounting-based valuation methods, such as abnormal earnings and free-cash flows (Palepu et al. 2004 ch. 8 pg. 6).

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Table 1: Forecasting assumptions for TJX Company

Table 2: Beginning balance sheet and income statement forecasts 2002 - 2012

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Table 3: Valuation summary for TJX Company under different scenarios

Table 3 summarizes the outcome of the analysis under different scenarios. Also the terminal value is listed here. The final part of the valuation is to enter each element into the relevant valuation formula (free-cash flow or AE formula) and then divide the

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outcome (total asset or equity value) by the number of shares to arrive at the share price (Palepu et al. 2004 ch. 8 pg. 7).

One particular detail that stands out is that each of the methods used produces the same outcome. Though theoretically this should occur, in practice however this will almost never happen. This has to do with the properties of the abnormal earnings to better capture the value of a company. However, this will be discussed further in the next section of the paper, which will wrap up the discussion of the discounting-based models.

3. Free-Cash Flow model

Section 2 above described the features and underlying assumptions of the abnormal earnings model. This section will consider the other main discounting-based model, namely the discounted free-cash flow model (Francis et al. 2000 pg. 49; Penman and Sougiannis 1998 pg. 349). This model, along with the abnormal earnings model, is derived from the same model, namely the dividend discount model, as described in section 2.2.

This section will first discuss the elements of the free-cash flow model. Included in this discussion will be how the formula is derived from the discounted dividend model. Also provided is a numerical example based on the data provided in section 2.3. Lastly, the different discounting-based models will be compared to each other, and the

advantages and disadvantages will be discussed.

3.1 Elements of the free-cash flow model:

Like the abnormal earnings model, the free-cash flow model is derived from the

dividend discount model. It follows the same pattern as the AE-model in that it forecasts a financial measure over a finite horizon (usually 5 – 10 years), in this case free-cash flows, and then discounts these forecasts using a relevant discount rate. A terminal value is also determined, discounted and then added to the discounted stream of

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free-cash flows from the forecasting horizon to arrive at an estimate of firm value (Palepu et al. 2004 ch. 8 pg. 7).

The formula for the free-cash flow model used to value equity is as follows:

Equity value

=

PV of free-cash flows to equity claim holders

Which equals:

(

)

t e equity t T t FCF t

r

FCF

V

+

=

∑

=1

1

(3) Where: FCF t

V = The value of the firm’s equity at time t equity

t

FCF = The free-cash flows to equity holders in year t e

r = The cost of equity capital

equity t

FCF is defined as (Francis et al. 2000 pg. 49; Penman and Sougiannis 1998 pg. 349):

Dividends

=

Free-cash flows to equity holders

Which equals: t t t equity t

NI

BVA

BVND

FCF

=

−

Δ

+

Δ

_(3a) Where: t

NI = Net Income in year t t

BVA

Δ = The change in the book value of assets in year t t

BVND

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The model can also be used to value a firm’s assets. The formula that needs to be used in this case is (Francis et al. 2000 pg. 49; Penman and Sougiannis 1998 pg. 349):

(

)

t wacc assets t T t FCF t

r

FCF

V

+

=

∑

=1

1

(4)

Where FCF_tassets is the free-cash flows to debt- and equity holders and equals:

t t

assets

t

NOPAT

BVA

FCF

=

−

Δ

_(4a)

And r_wacc is the weighted average cost of capital, which is defined as (Francis et al. 2000 pg. 49):

(

)

e d wacc

r

V

E

T

r

V

D

r

=

×

1

−

+

×

_(4b) Where:

D = Total market value of debt E = Total market value of equity

V = Total market value of the firm (i.e. D + E)

T = The tax rate

d

r = The cost of debt capital

Valuing a firm’s equity using this model is now pretty straight forward. The first step, making assumptions of key variables from the balance sheet and income statement, is the same as with the AE-model described above in table 1. These

assumptions are then used to create forecast balance sheets and income statements for about 5 – 10 years, depending on the length of the forecasting horizon (see table 2). Table 2 produces forecasts of the variable we are interested in, which in this case is the free-cash flows to equity, for each of the years in the forecasting horizon. A terminal

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value also needs to be determined in order to complete the analysis (Palepu et al. 2004 ch. 8 pg. 7).

Table 3 again summarizes the analysis. One thing to note is how the terminal value component is much larger than with the abnormal earnings model. Also, both models yield the same result, a share price of $ 11.91. Subsection 3.2 will discuss why.

3.2 Comparison of the DCF-based models:

Up until now, 3 different valuation models have been discussed: the abnormal earnings model, the dividend discount model and the free-cash flows model. This subsection will compare the three models and describe their advantages and disadvantages. Since all three models are based on the same foundation, no one model can be viewed as being superior to the other two. As long as the analyst makes the same assumptions about firm fundamentals, value estimates will be the same with all three models (Francis et al. 2000 pg. 48).

But each model does estimate a different attribute, so there must be some advantages of using one model instead of another. These differences fall in three categories (Palepu et al. 2004 ch. 7 pg. 14), namely:

• Focusing on different issues

• Different levels of structure needed for the analysis

• Implications for terminal value estimates

The dividend discount model only needs forecasts of future dividends in order to determine value. This shouldn’t be too difficult, since dividend policy doesn’t tend to change too radically in the short run.

The other two models require extensive, multi-year forecasts of key variables from the firm’s balance sheet and income statement. Then they require the construction of tables such as those presented above in section 2 (Palepu et al. 2004 ch. 8 pg. 6), in order to determine the forecasts of the variables they actually need to create an estimate of value. Simply put, they require a lot more work than the relatively simple dividend discount model.

Another difference between the approaches is the way in which the terminal value is determined. With the AE-model, the terminal value represents a much smaller

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proportion of the total value estimate than with the other two models (see table 3). Since the terminal value is always the hardest part to estimate, it logically follows that the AE-model has an accuracy advantage over the others. This is only true however, if the beginning book value of equity is accurate (Palepu et al. 2004 ch. 7 pg. 15).

This is due to how the AE-model is structured. The terminal value of the cash flow and dividend models includes the present value of all cash flows beyond the forecast horizon. In the AE-model, terminal value only includes the present value of all abnormal earnings, but not the present value of all normal earnings as well2. The present value of normal earnings is already represented by the beginning book value of equity and the growth (if any) of the book value of equity over the forecast horizon (Palepu et al. 2004 ch. 7 pg. 15).

This is a clear advantage since the AE-model assumes that the accrual process has already done a lot of the valuation. The free-cash flow model on the other hand “unravels” the accruals into cash flows and then “recreates” its own accruals in the form of discounted estimates of future cash flows (Palepu et al. 2004 ch. 7 pg. 15; Penman and Sougiannis 1998 pg. 377). Therefore, with the AE-model, the book values of equity at different points in time need to accurately represent value. Accounting needs to be unbiased.

No one model can be viewed as being superior to the other two, since all are based on the same theoretical foundation. However, recent research has indicated some advantage to using the AE-model. Francis et al. (2000 pg. 69) find that, over shorter time horizons such as 5 – 10 years, the AE-model produces more accurate forecasts and explain more of the variation in security prices than the other two models do. They believe it is likely due to the accuracy of book value of equity as a predictor of value and the greater precision and predictability of abnormal earnings (Francis et al. 2000 pg. 69). However, they do conclude that there is little to gain from choosing abnormal earnings over free-cash flows or dividends as the fundamental element to be valued (Francis et al. 2000 pg. 69).

2

Which are defined as: r_e ×BVE_t₋₁. Since abnormal earnings are defined as the difference between book- and market value of the equity of a firm, which is represented by: NI_t −r_e ×BVE_t₋₁ (Francis et al. 2000 pg. 50)

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Penman and Sougiannis (1998 pg. 376 - 377) also find that the abnormal earnings model has a practical advantage over the other two.

With regards to the dividend discount model this advantage is due to the fact that dividends need to be forecasted into infinity. But, according to Miller and Modigliani (1961) (as cited by Penman and Sougiannis 1998 pg. 348), the dividend irrelevancy proposition states that price is unrelated to the timing of expected payout prior to or after any finite horizon. This means that price cannot be (fully) explained by forecasted dividends over a finite horizon (Penman and Sougiannis 1998 pg. 348).

And with regards to the discounted cash flow model, the advantage the AE-model has is due to the fact that cash flows seem to leave out a portion of the value. That value does seem to be captured when using the AE-model. It should be noted however that the cash flow model used in their analysis is usually modified in practice so it may resolve the above discussed issue to a certain extent (Penman and Sougiannis 1998 pg. 377).

It has been the author’s experience that the AE-model is the easiest to use and that it gives the most precise estimate of the value of a firm’s equity or assets. The author has found the free-cash flow model in particular difficult to use because of the problems with determining the free-cash flows themselves. The author always had difficulties with determining which entries on a firm’s balance sheet should be deducted or added to the free-cash flow. Abnormal earnings are much easier to calculate, since normal earnings are much easier to forecast than other variables. Based on this, it is the author’s opinion that the AE-model has a definite advantage over the other models.

This wraps up the discussion of the discounting based models. The next two sections describe two different approaches to the valuation issue, namely: relative valuation methods including P/E-ratio analysis and the Feltham-Ohlson model.

4. Relative Valuation Methods

The models discussed up until now, the abnormal earnings model and the free-cash flow model, both have the same common ancestor, namely the dividend discount model. They all use the same method for valuing a firm’s assets or equity. They all use

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forecasts of a particular financial measure, like abnormal earnings or free-cash flows, then discount that financial measure to arrive at an estimate of firm value.

Relative valuation methods use a completely different method to gain insight into asset or equity value. They are very widely used by analysts and investors alike do to the fact that they are very simple to use (McGirt 2004 pg. 73).

This section will begin by discussing how this method of valuation works. Also, several issues with the method are discussed. Then, several widely used methods are described.

4.1 How the method works:

Valuation using multiples is very popular because of the simple fact that it is relatively easy. The method doesn’t require detailed, multi-year forecasts of a host of different variables. All that is needed are the following steps (Palepu et al. 2004 ch. 7 pg. 6):

1. Select the measure of performance or value as the basis for the analysis 2. Find a group of comparable firms and determine their price multiples. 3. Compare these multiples to the one from the firm that’s being analyzed, or average these multiples out and then compare them to the firm’s multiple.

Basically, this approach entails the making of short- and long term growth and profitability estimates, based on the values for comparable firms. This seems pretty straight forward. All that is needed are two sets of numbers for several firms, namely share price and another variable such as earnings per share, or total assets minus intangibles. However, there are several practical issues that need to be taken into account when undertaking this type of analysis.

4.2 Practical issues with using price multiples:

These issues fall into three categories: Problems with selecting comparable firms, calculating multiples for firms with poor performance and adjustments needed when dealing with leverage.

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Using multiples requires that the performance of one firm be compared to the performance of other, comparable firms. But therein lays a problem. Most firms operate in multiple industries, and even if they don’t, they still differ on things like growth opportunities and profitability. The solution to dealing with this problem is to average the ratios of all firms in an industry. It is implicitly assumed that this way, the factors that cause the non-comparability are filtered out. The firm is compared to an “average” industry member (Palepu et al. 2004 ch. 7 pg. 6; McGirt 2004 pg. 73).

Another issue arises when using multiples for firms that are performing poorly, especially when it affects the denominator. If earnings are lagging for instance, then the price-earnings ratio will be very high. And if a firm has a net loss, then the P/E-ratio will be negative. One way to overcome this problem, when the loss is caused by a one-time write-off or a special item, is to exclude this effect from net earnings and then calculate the ratio. Another way to deal with this is to simply exclude these firms from the analysis altogether (Palepu et al. 2004 ch. 7 pg. 7).

It is important to preserve consistency between the numerator and the denominator. Sometimes this is an issue when the denominator for example does not take into account the effect of debt on income. This happens when measures like EBITDA and such are used as the measure of performance instead of net earnings. The effect of debt on income should always be included in the measure of performance (Palepu et al. 2004 ch. 7 pg. 7).

4.3 Widely used multiples:

This subsection will describe some of the most widely used multiples. The price earnings ratio relates a company’s current share price with its earnings-per-share:

EPS

price

Market

E

P

/

=

If the ratio is high, then that means that investors expect that the earnings growth of that firm will be higher relative to those of other firms with lower P/E-ratios. The ratio is usually calculated using earnings over the last four quarters, this is called the trailing

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P/E-ratio. However it is possible to use forecast of EPS in order to calculate the ratio, it is then called a leading multiple (Palepu et al. 2004 ch. 7 pg. 7).

Another widely used multiple is the price-to-book ratio, or P/B-ratio. It is defined as:

share

per

BVE

price

Market

B

P

/

=

This ratio relates current share price to the book value of equity per share. In other words, it relates market to book values. A lower P/B-ratio could indicate that the stock is undervalued. However, the low ratio could also mean that there is a fundamental flaw in the company. It also indicates whether an investor is paying too much for the equity if the firm goes bankrupt at this moment (Pratt 2001 pg. 44).

4.4 Relative methods versus discounting-based methods:

So far, two broad categories of valuation methods have been discussed: the

discounting-based models and the relative valuation measures. The main difference between the two is how they work. Discounting-based models use forecast and then discount those to arrive at an estimated share price. Relative measures just give indications that shares are either over- or undervalued. They don’t give a precise estimate of share price. What relative measures do have working for them, is their simplicity. The discounting-based models all require about two to three full pages of spreadsheets. In order to use relative measures, you just need two variables for a number of companies.

The last section will discuss the Ohlson (1995) model. This model was presented as a possible alternative to the other models and methods described in this paper.

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5. Linear Information Dynamic

The last section of the paper will discuss the model that Ohlson proposed (Ohlson 1995 pg. 668) and was presented as a possible alternative to other methods of valuation. As will be shown below, the premise of this model was that valuation could be based on current numbers, thus eliminating the need for multi-year forecasts of financial measures, and especially eliminating the need for a terminal value estimate, which is always the most uncertain part of the analysis (Palepu et al. 2004 ch. 8 pg. 7).

The appeal of this model is obvious: it has the simplicity of ratio analysis and the accuracy of fundamental analysis, since, as will be shown, one using the model only needs a forecast of earnings to make it work (DeChow et al. 1999 pg. 6 – 7). However as the discussion will show, the evidence unfortunately isn’t very positive about the model.

The discussion will proceed as follows. Section 5.1 will describe how the model is derived. The discussion then proceeds to highlight the main features of the model and its advantages over other models. Lastly, section 5.3 will present the evidence on the validity of the model.

5.1 Deriving the model:

Basically the model that Ohlson describes in his article is a “logically consistent frameworks for thinking about the valuation of accounting numbers” (as cited by Lundholm 1995 pg. 749). Deriving the model starts with the following equations:

)

(

1 τ τ τ + ∞ = −

∑

=

_f _t _t t

R

E

d

P

₍₅₎ And: t t t t

y

x

d

y

=

₋₁

+

−

_(5a)

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Formula (5) is the dividend discount model where: t

P = Ex-dividend equity price at date t t

d = Dividends in year t

f

R = Risk free return (is the discount rate)

And formula (5a) is the clean surplus relation where: t

y = Equity book value at time t t

x = Net Income in year t

t

d = Dividends in year t

He then arrives at the abnormal earnings model by combining the two formulas above:

[

1

]

1

)

1

(

₊ ₋ + ∞ = −

−

=

∑

_τ _τ τ τ t f t t f t t

y

R

E

x

R

y

P

(5b) Since abnormal earnings are equal to the last part of equation (5b):

1

)

1

(

₊ ₋ + +τ

=

t τ

−

f

−

t τ a t

x

R

y

x

_(5c) So rewriting (5b) yields:

[ ]

a t t f t t

y

R

E

x

P

_τ τ τ + ∞ = −

∑

=

1 (5d)

Which is the abnormal earnings model presented above in section 2. The discussion then proceeds to introduce a feature of the new model that Ohlson (1995) proposes, called the linear information dynamic:

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1

+

=

+

t

+

t

a

t

a

t

x

v

x

τ

ω

ε

₍₆₎ And: 1 2 1 + +

=

t

+

t t

v

γ

ε

_(6a) Where:

ω and γ = Known parameters between 0 and 1

γ = Net Income in year t

t

v = Other, non-accounting information

Linear information dynamics links abnormal earnings to non accounting information. It states that both abnormal earnings and other information are

autoregressive, which is illustrated by the fact that ω and γ both have values between 0 and 1. ω and γ represent the persistence of respectively earnings and other

information (DeChow et al. 1999 pg. 6).

If the LID-assumption is combined with equation (5d) then the valuation model as proposed by Ohlson (1995) becomes:

t a t t t

y

x

v

P

=

+

α

₁

+

α

₂ With:

(

ω

)

ω

α

−

+

=

f

R

1

1 And:

(

)

(

)(

)

[

ω

γ

]

α

−

+

−

+

=

f f f

R

1

2

So all that is needed in order to use this model is: current abnormal earnings, which can easily be calculated; a measure of “other information”; and figures for ω andγ.

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The “other information” can be estimated from analysts’ forecasts as DeChow et al. show in their paper (DeChow et al. 1999 pg. 6 – 7). All that is needed now are figures for ω andγ. This is what DeChow et al. (1999) do in their paper.

They find that ω has an approximate value of 0.62 (DeChow et al. 1999 pg. 16). andγ has an approximate value of 0.32 (DeChow et al. 1999 pg. 20). With these estimates, it is now possible to use the model.

5.2 Features and advantages of the model:

Now that the model has been derived, its features and advantages can be discussed. The most striking feature is that the analysis does not require an estimate of the terminal value, which is usually the most uncertain part of the analysis (Palepu et al. 2004 ch. 8 pg. 7). This means that, in theory, the model should be better at estimating securities prices than analysts would be. Section 5.3 however will show that this is probably not the case.

Another feature is the fact that all the forecasts that are needed are those of future normal earnings, which is amongst the most widely forecast variables and should be readily available. With these estimates, “other information” v_t can be estimated. All that is needed now is current abnormal earnings, which can be easily calculated and then the model is ready to be used (DeChow et al. 1999 pg. 6 – 7).

The main advantage of the Ohlson (1995) model is that extensive forecasts of several variables are no longer needed. Forecasts are always accompanied by

uncertainty, so this model should produce more accurate estimates of value than other models (Palepu et al. 2004 ch. 8 pg. 7). However, as section 5.3 will show, this is, in practice, not exactly the case.

5.3 Evidence on the validity of the model:

DeChow et al. for instance find in their study that analysts’ forecasts are actually more accurate than the models predictions about securities prices (DeChow et al. 1999 pg. 22). Their study indicates that the model ranks behind analysts forecasts.

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Ahmed et al. find some support for the model in their paper (Ahmed et al. 1996 pg. 291), but only under certain circumstances. They only find support for the model for firms with high profitability. They also suggest that future research should focus on identifying other factors where the Ohlson (1995) model best describes market value. They suggest firm life cycle, growth and productivity of assets as possible other factors.

Bernard suggests that while the model may seem primitive, it does show promise (Bernard 1995 pg. 745). He describes the study by Ohlson as “offering a theoretical grounding moving research away from price explanation as the dominant paradigm and toward research designs built around the prediction of fundamentals such as earnings”.

Clubb (1996) finds that, “The usefulness of the Feltham-Ohlson (1995) model in relation to capital market research lies in its contribution to a clearer understanding of the factors affecting the form of the relationship between share prices and accounting data” (Clubb 1996 pg. 335).

To summarize, the model is viewed as showing promise, meaning that with more research it could be a useful contribution to the valuation issue.

6. Conclusion

In this paper, several different models and methods used for the valuation of stock or assets have been discussed. The abnormal earnings model (see for example Penman and Sougiannis 1998 pg. 350) was discussed in section 2 and it was shown how that model can be derived from the dividend discount model (Penman and Sougiannis 1998 pg. 348; Francis et al. 2000 pg. 48) given a certain assumption, the clean surplus relation.

The free-cash flow model (see for example Penman and Sougiannis 1998 pg. 349) was also discussed. The paper showed that it, although it along with the abnormal earnings model are both derived from the dividend discount model, was less accurate than its earnings-based counterpart. Reasons given for this were that book value of equity was a better predictor of value and the greater precision and predictability of abnormal earnings over cash flows.

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Then the discussion turned to relative valuation methods. Several different multiples were discussed, namely the P/E-ratio and the value-to-book ratio, and also how to use them. Also discussed where the differences between the discounting models and the multiples method.

The Ohlson (1995) model was discussed last. The paper showed how the model was derived, and what its underlying assumptions were. Then the discussion turned to its features and its advantages over the discounting models. Finally, the evidence on the validity of the model was discussed, and although viewed as promising, the model still needs to be further researched.

It is clear from the discussion above, that there is no perfect model or method that best describes the value of a firm’s equity or assets. It is the author’s view that each model or method has its merits, and some work better in certain situations than others. That is not to say that some models don’t have practical advantages over the others. The AE-model for instance has a practical advantage over the other discounting models due to the fact that it is based on accrual accounting.

Areas for future research include finding more evidence on the validity of the Ohlson (1995) model. Also, field work comparing the discounting models and the Ohlson (1995) model could be done.

Finally, it should be noted that, since most of the models and methods illustrated in this paper use forecasts of certain variables, the outcome of each model is only as good as the forecasts and assumptions underlying them.

References

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Bernard V. L. 1995. The Feltham-Ohlson framework: Implications for empiricists. Contemporary accounting research 11: 733-748

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Clubb C. D. B. 1996. Valuation and clean surplus accounting: some implications of the Feltham and Ohlson model for the relative information content of earnings and cashflows. Contemporary accounting research 13: 329-338

Dechow, P. M., A. P. Hutton, and R. G. Sloan. 1999. An Empirical Assessment of the Residual Income Valuation Model. Journal of Accounting and Economics 26: 1-34

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Accounting Research 22: 453-480

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Penman, S. H. and Sougiannis, T. 1998. A comparison of dividend, cash flow and earnings approaches to equity valuation. Contemporary Accounting Research 15: 343-383

Valuation models, methods and issues: an overview