## Introduction

This paper researches and analyzes the concept of equity valuation and the different techniques used for equity valuation. The characteristics and scope of equity valuation models are described with benefits and shortcomings of the models. The different models applied to valuate equity are described with practical application and the uses of these models are discussed in detail. The concept of equity is discussed and how the price, dividends, risks, and growth rates affect the valuation of equity. The different variables applied by the valuation models are discussed in detail to help in the overall understanding of the concept. The equity of a corporation is valued for many reasons by different groups. The investors need to know what prices to pay for a particular share and the level of risk attached with that share. Financial managers need to value equity to help them in increasing the overall value of the firm. Research analysts use equity valuation methods to predict the prices of different shares in the future.

**Equity Defined**

Equity or common stock represents the interest of ownership in companies and corporations. The common stock could be privately owned or publicly traded. The equity models are discussed here concerning publicly traded corporations. Equity ownership gives the privilege of dividends to owners if the company has earned profits which can be distributed as dividends. The common stock is different from bonds or debt in that the bonds have a promise of interest payments without the consideration of profits whereas the common stock owner can only receive dividends if the company manages to earn profits and even then the payment relies on the discretion of management. Another advantage for equity holders other than this dividend income is the gain from the purchase and sale of shares which is called capital gain. Suppose a person buys 50 shares of a company for $10 he would have to invest $500. If he sells the shares at $11 each he would have a capital gain of $50. This does not necessarily mean that a shareholder would receive again every time and there might also be a capital loss if the share prices go down.

**Equity Valuation**

When one needs to buy shares of stock of a particular corporation, equity valuation plays a critical role. If the expected or estimated share price is determined one can easily make decisions on buying or selling shares. This valuation is performed through various techniques and methods. Equity Valuation is completed by management, investors, and research analysts to meet their respective requirements and help in decision making.

**Uses and Scope of Equity Valuation**

Equity valuation is performed by investors, research analysts, and other users of financial data to interpret the value of equity for different corporations to make various decisions. Usually, equity valuation is performed for choosing stocks, assessing events, evaluating strategies, appraisal of private businesses, and facilitating communication with shareholders. The first and foremost use of equity valuations is selecting from a wide range of stocks. Different stocks are valued and compared to analyze and choose the best among these stocks. The value calculated is compared with the market value of stocks to find out if they are overpriced, underpriced, or fairly priced. The second application of equity valuation is to determine the effect of corporate events such as mergers and acquisitions on the cash flows and eventually the value of equity. The third purpose of equity valuation is evaluating the strategies of a business. The impact of different strategies and decisions on the value of the firm is calculated time and again to assess what options are viable and more helpful in maximizing the value for shareholders. The shares of a private firm are not listed and traded on stock exchanges so there is no comparative measure for the stocks of these companies. When these companies want to go public analysts value the stock to help the business and the investors analyze the fair value of the stock. Equity valuation also helps the communication process between management, shareholders, and analysts as the value of the stock provide a focal point to all three parties. The value of the stock is equally important to the management, shareholders, and analysts (Stowe, Robinson, and Pinto).

**Importance of Equity Valuation**

Equity valuations are performed to estimate the values of stocks for various decisions. The valuation of equity is equally important to managers, shareholders, and research analysts. The objective of the management of a company is wealth maximization and this maximization is achieved not only through an increase in the overall earnings and value of a company but also an increase in returns to the shareholders. The management values stock regularly to compare with other stocks of a company in the same industry, measure the growth in terms of stock value with past performance, and comparison of this value with the overall market and economy. Equity valuation becomes even more important to the management of companies before mergers and acquisitions as the value of the stock of the target company would be valued very carefully before the actual transaction takes place. The investors or shareholders need to make decisions about investing in different shares and before doing so they must know the estimated fair price of a share. They perform equity valuation to judge whether a stock is fairly priced, overpriced, or underpriced. Based on these decisions of valuation they can buy specific shares of a particular company. Research analysts give equity valuation methods high importance as they use these models to value stocks of different companies and prepare reports for investors and decision-makers. These evaluations are used to forecast the movements in different stock prices and formulate recommendations on different stocks concerning buying and selling strategies.

**Methods of Equity Valuation**

The approaches of valuation as suggested by Professor Aswath Damodaran are Discounted Cash flow valuation, relative valuation, and contingent claim valuation (Damodaran). These evaluations are suggested for assets and in the case of equity valuation, the suggestion is the discounted cash flow valuation and relative or alternate valuation techniques which are used most widely by investors, managers, and research analysts. The value of common stocks can be estimated through the earnings of the company and the relative dividends of the company. In some cases the expected earnings of a company are discounted through a discount rate which is usually the cost of common stock and the net present value is calculated by adding up all the present values to achieve the intrinsic value of the firm which is divided by the number of shares outstanding to estimate the intrinsic value per share of the firm. Another and more popular method is to discount the expected dividends by a rate which is usually the cost of common stock to calculate present values and sum up all the present values to estimate the current price of the stock. The valuation of equity helps investors, managers, and analysts to compare this value with the current market value to analyze if the stock is overpriced, underpriced, or fairly priced in the market.

### Discounted Cash Flow Approach

The discounted cash flow approach of equity valuation is most widely used by investors and management to estimate the value of a stock. It involves the expected dividends over some time and their present values. The cash flows from dividends to a stockholder are discounted to arrive at the present value of the stock. This is true in cases where the stocks are held for an indefinite period or perpetuity and we could mathematically express it as:

P_{0} = D_{1} / (1 + K_{s})^{1} + D_{2} / (1+K_{s})^{2} + D_{3} / (1+K_{s})^{3} + …… + D_{t} / (1+K_{s})^{t}

Here P_{0} is the current price of a stock, D is the expected dividends corresponding to each future year as D_{1} represents an expected dividend of the first year D_{2} represents the expected dividend of year 2, and so on whereas K_{s} is the cost of common stock. The cost of common stock is significant while valuing stocks in the discounted cash flow model as it is the rate of the discount applied. This entails that the value of the stock is highly dependent on the cost of common stock, so the cost of common stock has to be valued with great caution as well. The Applied Finance Group – AFG is one of the financial firms that use discounted cash flow equity valuation to calculate the intrinsic value and provide research on different companies and describe the stock as overpriced, underpriced, or fairly priced. They also base decisions on the performance of management using this valuation. A website describes the performance of management in one of AFG reports, “GM’s management team has had a consistent track record of destroying shareholder value, while Porsche has done a great job of creating wealth for its shareholders.” (Value Expectations)

## Advantages and Disadvantages of Discounted Cash Flow

Equity valuation has a wide scope and is done in various ways out of which discounted cash flow is the most widely used valuation method. Analysts and investors usually prefer this method over others and there are some benefits and shortfalls of the method. Discounted cash flow method is the most widely used method of the equity valuation for valuing stocks and deciding on investment options. The DCF technique in theory presents the value closest to the exact value of a stock. As this approach is based on original discounted cash flows it does not fluctuate with the trends of the market like other approaches. In this approach, an analyst can trace the performance and growth of a company when making assumptions about the future (Pratt). The discounted cash flow approach though most widely used also falls short in various areas. It is controversial as it requires an estimation of future cash flows. It relies on more variables than other methods and these variables affect the intrinsic value of the stock. It relies on the proper estimation of growth rates and cost of common stock and if these variables are not estimated properly they affect the actual value of the stock. As it is derived from the future cash flows of a company, the market changes are not reflected in the value of the stock. It is difficult to explain the concept of discounted cash flow approach to people with a low or minimum finance background. The comparison of estimated prices to market prices would reveal most shares as being overvalued.

## Estimating Cost of Common Stock

The first important variable used in the discounted cash flow technique is the cost of common stock. The cost of common stock is usually estimated through three models which are Capital Asset Pricing Model – CAPM, Discounted Cash Flow Model – DCF, and bond-yield-plus-risk premium model. Among the three models, CAPM is the most widely used model as it reflects the risk-free rate, market risk premium and a stock’s beta. The Capital Asset Pricing Model is expressed mathematically as:

K_{s} = K_{RF} + (RP_{M}) b_{i}

Here K_{RF} is the risk free rate, RP_{M} is the market risk premium and b_{i }is the beta of a stock.

The discounted cash flow approach was discussed earlier for the valuation of stock and uses the same mathematical model:

P_{0} = D_{1} / K_{s} – g

K_{s} = (D_{1} / P_{0}) + g

The third and last approach to estimate the cost of capital is bond-yield-plus-risk premium model. This model incorporates the yield on the long term debt of a corporation with a risk premium and is mathematically expressed as:

K_{s} = Bond yield + Risk Premium

## Estimating Growth Rate

The second important variable while estimating the value of equity through the discounted cash flow model is the growth rate. The growth rates are usually estimated using three approaches; using past growth rates, retention growth model, and the forecasts of growth rates by analysts (Brigham and Ehrhardt).

The historical growth rates are applied when the earnings and dividend yield of a corporation has been steady in the past and the investors expect the pattern to continue in future periods. The retention growth model depends on the expected return on equity and the portion of earnings the corporation intends to keep. Mathematically the retention growth model can be expressed as

g = b(r)

Where b is the portion of earnings retained by the firm and r is the expected rate of return on equity. The portion of retained earnings the firm will retain can be calculated by deducting the payout ratio from 1. The third and most widely used method for estimating growth rate is the analysts’ forecasts. The research analysts publish research reports on various stocks from time to time. The growth rates contained in these reports are not constant, but a constant growth rate can be derived from these rates by taking an average and arriving at a constant growth rate.

## Constant Growth Rate

As mentioned earlier that only discounting dividends with the cost of common stock is true in cases where the stock is held for an indefinite period but considering this concept from a more practical perspective it would render useless as the stockholder would want to sell the stock at some future point of time. For this model to apply to the practical approach the growth rate of the dividends is embedded into the mathematical expression. The investor sometimes expects a constant growth rate throughout the life of the stock. The expression with the growth rate inserted now becomes:

P_{0} = D_{0} (1+g) / (1 + K_{s}) ^{1} + D_{1} (1+g) / (1+K_{s}) ^{2} + D_{2} (1+g) / (1+K_{s}) ^{3} + …… + D_{t} (1+g) / (1+K_{s}) ^{t}

P_{0} = D_{0} (1+g) / K_{s} – g

P_{0} = D_{1} / K_{s} – g

Notice that the price of the stock is now dependent on three variables; the expected dividend, the cost of common stock and the growth rate. This model is referred to as the constant growth rate model (Brigham and Ehrhardt). The constant growth model can be explained through the following example. Suppose Alpha Company has expected dividends of $5, the growth rate of the stock is 5% and the cost of common stock is 9%. The value of its stock price would be $125.

P_{0} = D_{1} / K_{s} – g

P_{0} = 5 / 9% – 5%

P_{0} = 5 / 4%

P_{0} = $125

## Zero Growth Rate

There are also some common stocks which may have a zero growth rate or pay dividends at the same rate similar to preferred stock. These stocks are said to have a zero growth rate. The price of the stock is calculated similarly but ignores the growth rate as it is zero. The mathematical expression for zero growth rates can be expressed as follows:

P_{0} = D / K_{s}

## Inconsistent Growth Rate

The growth rates are normally inconsistent for various companies and this is specifically more applicable to companies with uneven earnings and which are in their initial phases. Companies tend to have rapid growth rates in the initial stages of operations and the later years, these growth rates are tied with the industry and economic growth rates. Some other factors may cause the growth rates to change significantly which include extraordinary earnings or losses during a year. An example is that of the Information Technology boom and the recent financial crisis. The IT boom saw earnings of various IT-related companies jump to significant levels and the growth rate also increased with these rapid changes. In the recent financial crisis earnings of companies and specifically the financial companies were evaporated and they were left with huge losses which caused the growth rates to decrease considerably. The constant growth approach of the discounted cash flow model can be adjusted to reflect changing growth rates. In the non-constant growth model, the terminal or horizon value of the stock is also discounted with the expected dividends in the different growth periods. Mathematically we can express the inconsistent growth model as follows:

P_{0} = D_{1} / (1 + K_{s})^{1} + D_{2} / (1+K_{s})^{2} + D_{3} / (1+K_{s})^{3} + …… + D_{t} + P_{t} / (1+K_{s})^{t}

## Illustration of DCF Approach

To further explain the concept of discounted cash flow approach for equity valuations consider the following example.

Alpha Company has a required rate of return – K_{s} of 12% and dividends – D of $3. The price of the share would be calculated as follows:

P_{0} = D / K_{s}

P_{0} = 3 / 12%

P_{0} = $25

Now consider the same company with a constant growth rate in dividends – g of 7%. The price of the share now would be:

P_{0} = D_{1} / K_{s} – g

P_{0} = D_{0 }(1+g) / K_{s} – g

P_{0} = 3(1+7%) / 12% – 7%

P_{0} = 3.21 / 5%

P_{0} = $64.2

The price of the share has increased due to the constant growth rates and if we apply inconsistent growth rates to the same scenario we will achieve a different price of a stock. If we also change the cost of common stock it would also alter the price of the stock.

### Alternate Valuation Techniques

Apart from the traditional discounted cash flow technique analysts also use some alternative valuation techniques. These techniques use comparisons to estimate the value of equity. The techniques use estimates such as the P/E ratio and compare some other benchmarks for the valuation of the stock. By using these techniques the hectic estimation of the cost of common stock in the discounted cash flow approach can be avoided. Some of the alternate valuation techniques available are the P/E ratio or earning multiplier approach, the price to book value approach, the price/sales ratio approach and Economic Value Added – EVA.

## P/E Ratio Approach

The P/E ratio or earnings multiplier approach is the most widely used alternative technique after discounted cash flow technique. P/E ratio is the price-to-earnings ratio of a stock and is usually calculated by dividing the market price of the stock by the earnings of the corporation. This price is used as a close estimate of the value of a stock. To make the P/E ratio more applicable in equity valuation a forward-looking approach is used by adjusting the current earnings to expected future earnings by applying a suitable growth rate. As an example consider the analysis of Affiliated Computer Services by Standard & Poors. In the January 2004 issue of The Outlook, S&P suggests that the stock was selling at a “discount to the S&P MidCap 400 on a P/E-to-growth basis” and estimating a target price of $67 per share (Standard & Poor’s). We can well see the practical application of the P/E ratio for the valuation and estimation of equity.

## Price / Book Value Approach

The price to book value ratio is similar to the P/E ratio but substitutes the earnings of the company with the book value of the shares on the financial statements of the company. The analysts recommend the use of this approach with comparisons to the company’s ratio and the average ratio of the industry. The Price to book value approach is also supported in empirical testing. It is important to note that during the estimation of the value in the price to book value approach the investors or analysts need to be very careful as the book values of different corporations in the same industry might have a significant difference (Jones).

## Price / Sales Approach

As the name suggests this approach uses the price of the share divided by the revenue per share of a corporation. This can also be calculated by dividing the market capitalization of the corporation by the total revenues. The investors or analysts use this approach to gauge the value of equity based on revenues rather than earnings on the belief that sales are not likely to be controlled by management as opposed to earnings. As with the price to book value approach, this approach should also be compared with the company’s past ratios and the average ratios of the industry to reflect more realistic values.

## Economic Value Added

This is one of the recent techniques to evaluate the value of equity or stock. Economic Value Added or more commonly known as EVA is the difference between the operating profits and weighted average cost of capital including common stock and debt. EVA measures the return on equity of a company and is also used for the valuation of equity and it is mathematically expressed as:

EVA = (Operating Capital) (ROIC – WACC)

Here, ROIC is the return on invested capital and WACC is the weighted average cost of capital.

## Advantages and Disadvantages of Alternate Valuation Techniques

The alternate valuation approaches provide an alternative to equity valuation, though these approaches are not used as commonly as the discounted cash flow approach they are used to value stocks relative to the market prices of these stocks. The alternate valuation approaches reflect the more precise perception of the market than the discounted cash flow approach as these techniques are relative to the market price of stocks. These approaches take into account the present price of a stock rather than the estimation of future cash flow streams. The alternate valuation models present the investor with an actual trend-based strategy to invest in a stock. The prices of stock can be compared to the market prices to determine overvalued and undervalued stocks easily. Portfolio managers are more concerned with the performance of their portfolios relative to the market so these valuation approaches prove to be a good benchmark for them. The alternate valuation models are not based on too many variables and are quite easy to understand. The alternate valuation approaches rely on the assumption that the markets are accurate as a whole and the individual stocks may be over or undervalued. This is not true in the sense that markets are also over or undervalued. Another drawback to the alternate valuation approach is the fact that it is not necessary that if a portfolio contains stocks that are overvalued then the portfolio will also be overvalued. The assumptions for these models are based on the market perceptions rather than the actual cash flows of the firm so they do not reflect the actual position of a stock’s value.

### Comparison of Techniques

The valuation of equity is not an easy job and requires much time and effort as it involves the estimates of future values which are approximations and guesses only and not exact. All of the methods and techniques including the Discounted Cash Flow technique and the alternative approaches to valuation of equity are used by different analysts in different scenarios at different times. Although the Discounted Cash Flow technique reveals the price of stock closest to the actual price some people argue that it is an unrealistic approach as the dividends of future periods cannot be estimated accurately. The alternative techniques use actual figures but cannot reflect the value of equity for future periods. Whatever approach is used it has to be considered that all approaches result in an estimate and not an actual value or amount so there is a reasonable chance of error.

## Summary

The valuation of equity is a complex but important technique that helps investors and management of companies in making critical decisions. The equity of a company is the amount invested by the shareholders in a company. The valuation of equity is performed to estimate the share prices of a company reflective of the market conditions or the actual earnings of a company. The management of a company uses the valuation tool to gauge the performance, growth, and earnings of the company, and estimates are made to increase this value of equity by making adjustments in the overall operations of the company and evaluating equity. The higher value of equity achieved by management means a higher return for the shareholders. The shareholders use this tool to make investment decisions and select stocks with higher prospects. The investors can perform equity valuation on different stocks and estimate if the price of that stock is underpriced, overpriced, or fairly priced in the market, or the valuation and research provided by research analysts can be used. Equity valuations are most commonly practiced by research analysts who help management, shareholders, and the general public in making investment and operational decisions. The most widely used valuation technique is the discounted cash flow technique which is based on the future cash flows from dividends of a particular stock of a company. These expected dividends are discounted with the firm’s cost of capital to arrive at the value of the stock. The discounted cash flow model is based on the variables of growth rate and cost of common stock. These variables need to be estimated carefully to calculate the accurate value of equity. The cost of common stock is usually estimated through the Capital Asset Pricing Model as it incorporates the relevant risks into the cost of capital. There are three different growth rate approaches to the discounted cash flow approach. The first scenario holds that growth rates are zero and dividends are paid at a constant rate each year. The second scenario implies a constant growth rate which means the dividends or earnings will rise at a constant rate each year. The inconsistent growth rate model implies that the growth rates are different in some periods but remain constant after a certain period of time. The prices in the different growth rate models change with the change in growth rates. Growth rate estimation is done through three methods. The first is to take the historical growth rates of the company but this is applicable where the past earnings and dividends of the company are stable. The second estimate of growth rate can be taken through the retention growth model and the third and best estimate of growth rate is the one estimated by research analysts. The other methods available for equity valuation which are termed here as alternate methods are the P/E, Price / Book Value, Price / Sales and Economic Value Added models. The P/E ratio takes into account the price and earnings of the share to derive the value of equity. The Price / Book Value model implements the price and book value of equity to calculate the estimated price of shares. The Price / Sales model is the same as P / E and Price / Book value but instead of earnings or book value it applies the sales amount to arrive at the value of a company’s shares. The Economic Value Added approach uses the operating profit and Weighted Average Cost of Capital to calculate the value of equity. The discounted free cash flow model presents a realistic value of the firm’s equity but it does not consider the market fluctuations whereas the alternate methods do not implement the actual cash flows of the firm but rely more on the market fluctuations. The approach most commonly used by research analysts is the discounted free cash flow technique to value a firm’s equity as it is more close to the realistic price. The importance of equity valuation cannot be ignored as it provides a benchmark for management and investors alike to make crucial decisions. The equity valuation model though very important can present estimates which may be incorrect interpretations of value.

## Works Cited

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