Study Notes for Equity Valuation: Concepts and Basic Tools

Equity Valuation: Concepts and Basic Tools

We learned about how an analyst can value a stock using the dividend discount model, where the analyst considers the dividends investors expect to receive in the years to come. The idea behind this model is quite intuitive once you understand the concept of time value of money.

One problem with dividend discount models is that all companies do not pay dividends. In that case, how does one value a company? For example, Apple is a highly valuable company, however, at the time of this writing, it does not pay dividends to its shareholders. Instead of distributing dividends to its shareholders, Apple reinvests this money back in their business.

To value such companies, an alternative to dividends is to use the free cash flow model. The free cash flow model can also be useful for companies that do pay dividend but only a small portion of their earnings, and the dividends paid do not appropriately reflect the true capacity of the business.

What we are really concerned about here is the Free Cash Flow to Equity (FCFE). FCFE is defined as the amount of free cash flow the firm has after meeting all its obligations. This includes debt obligations, capital expenditure to maintain existing assets, and new asset purchases to maintain the growth rate assumed. This is the cash that can be paid to shareholders after paying for all expenses, debt repayments, and reinvestments.

FCFE is calculated using the following formula:

FCFE = Net Income – (Capital Expenditure – Depreciation) – Change in Non-cash Working Capital + (New Debt Issued – Debt Repayments)

The non-cash working capital is concerned with items such as inventory, and accounts receivables. We reduce the FCFE by any increase in non-cash working capital, for example, an increase in accounts receivables.

The value of the stock using FCFE can be calculated using the following formula:
<div class="formula1">
[latex size="3" background="#f0f0f0"]V_{0}=\sum_{i=1}^{\infty }\frac{FCFE_{t}}{\left ( 1+k_{e} \right )^{t}}[/latex]
</div>
Note that the required return on equity (k) is calculated using the CAPM model.

Equity Valuation - Free Cash Flow Model (FCFE)

Preferred stocks can be valued using the dividend discount model, as they usually pay a fixed dividend. Since preferred stocks have indefinite maturity, the DDM can be represented as:
<div class="formula1">[latex size="3" background="#F0f0f0"]V_{P}=\frac{D}{k_{p}}[/latex]</div>
Let’s say that a company has issued $100 par preferred stock, and pays an annual dividend of $6. The required return is 9%. The value of the preferred stock will be:
<div class="formula1">V = $6/0.09 =  $66.67</div>
The above calculation assumes that the preferred stock has indefinite maturity.

Let’s say that stock has a maturity of 2 years. The value will now be calculated as follows:
<div class="formula1">V = $6/(1.09) + $6/(1.09)^2 + $100/(1.09)^2 = $94.72</div>
The above calculations are for a plain vanilla preferred stock. Some preferred stocks have features such as convertible, callable, etc. With those features, the valuation will need to be adjusted according to the price of these features.

Valuation of Preferred Stocks

The Gordon Growth Model (GGM) is a variation of the standard discount model. The key difference is that the GGM model assumes the dividends will grow at a constant rate till perpetuity.

If the current year’s dividends are D0, and the dividend growth rate is g<sub>c</sub>, the next year’s dividend D<sub>1</sub> will be D<sub>0</sub> = (1+g<sub>c</sub>). D<sub>2</sub> will be D<sub>0</sub>(1+g<sub>c</sub>)^2 and so on.

With this assumption, the value of the stock can be calculated using the following simplified formula:
<div class="formula1">V<sub>0</sub> = D<sub>1</sub>/(k<sub>e</sub> - g<sub>c</sub>)</div>
<strong>Model Assumptions</strong>

The model has several assumptions:
<ul>
	<li>It assumes that the dividends are a suitable measure for valuation.</li>
	<li>It assumes that both the required return on equity and dividend growth rate will be constant forever.</li>
	<li>The required return on common equity must be greater than the expected growth rate of the dividend.</li>
</ul>
Let’s calculate the value of a stock that paid a dividend of $5 last year. The required return on equity is 10% and the dividend is expected to grow by 5%.

Using the GGM model, the value of the stock will be:

V = $5(1.05)/(10% - 5%) = $105

As you can notice, the value of the stock is sensitive to the denominator and therefore to the dividend growth rate. You can also determine how much of the stock value is attributed to the dividend growth rate. This can be done by recalculating the value with zero growth rate and then noting the difference.

With a zero growth rate, the stock value will be = $5/10% = $50. So, we can say that out of $105, $55 ($105 - $50) is attributed to the dividend growth rate.

<strong>Model Suitability</strong>

The GGM is suitable in the following cases:
<ul>
	<li>The analyst is looking at broad equity indexes.</li>
	<li>The analyst is valuing steadily growing companies that pay dividends.</li>
</ul>
<strong>Drawbacks</strong>
<ul>
	<li>Highly sensitive to small changes in required return on equity and dividend growth rate.</li>
	<li>The model cannot be used to value companies that do not pay dividends.</li>
	<li>The model cannot be used to value companies that don’t have a stable growth rate.</li>
</ul>

Gordon (Constant) Growth Dividend Discount Model

<p>This video demonstrates the valuation of stocks using GGM model with the help of an example in an excel sheet.</p>



<figure class="wp-block-embed aligncenter is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio"><div class="wp-block-embed__wrapper">
https://www.youtube.com/watch?v=cbRIhwkGAnQ
</div></figure>



<p>The spreadsheets used in the video can be downloaded from <a href="http://people.highline.edu/mgirvin/ExcelIsFun.htm" target="_blank" rel="noopener">this link</a>.</p>

Calculating Stock Value Using Dividend (Gordon) Growth Model in Excel

<p>We continue with our Dividend Growth Model and understand how the stock value changes with changes in the various inputs such as the required rate of return, and the dividend growth rate.</p>



<figure class="wp-block-embed aligncenter is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio"><div class="wp-block-embed__wrapper">
https://www.youtube.com/watch?v=poA5M5-y79w
</div></figure>



<p>The spreadsheets used in the video can be downloaded from <a href="http://people.highline.edu/mgirvin/ExcelIsFun.htm" target="_blank" rel="noopener">this link</a>.</p>

Dividend Growth Model: How inputs Impact Stock Value?

<p>In the previous videos we learned about how to calculate the current value of a stock using the dividend growth model. We can use the same model to calculate the stocks value at a future date. This video explains how to the stock price at a future date t.</p>



<figure class="wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio"><div class="wp-block-embed__wrapper">
https://www.youtube.com/watch?v=s49JvT8MWw0
</div></figure>



<p>The spreadsheets used in the video can be downloaded from <a href="http://people.highline.edu/mgirvin/ExcelIsFun.htm" target="_blank" rel="noopener">this link</a>.</p>

Calculate Stock Price at a Future Date using Dividend Growth Model

While calculating the value of a stock using the dividend discount model, an important input is the assumed growth rate. Analysts can estimate this growth rate using a variety of methods.
<ol>
	<li>Analysts can observe the historical growth in dividends of the company and assume a future growth rate based on this observation.</li>
	<li>Analysts can observe the dividend growth rate in the industry that the company operates in and use the median industry dividend growth rate.</li>
	<li>Analysts can use the sustainable growth rate calculated using return on equity (ROE), and dividend payout ratio.</li>
</ol>
<strong>Sustainable Growth Rate</strong>

Sustainable growth rate is the rate at which the company can continue to grow without securing any additional funding, i.e., without borrowing additional money or issuing new equity.

Sustainable growth rate can be calculated using the following formula:

<div class="formula1">Sustainable growth rate = ROE * (1 – Dividend payout ratio)</div>

Let’s say that a company has an ROE of 10%, and it pays out 40% in dividends. The company’s sustainable growth rate (g) will be:

G = 10%*(1-0.40) = 6%

This suggests that with an ROE of 10% and a payout ratio of 40%, the company can sustain a growth rate of 6% forever.

How to Estimate Dividend Growth Rate?

In the previous articles, we learned about how a <a href="https://financetrain.com/gordon-constant-growth-dividend-discount-model/" title="Gordon (Constant) Growth Dividend Discount Model">dividend discount model</a> can be use to value a stock using the future cash flows.  However, in the constant growth model, we made an assumption that the dividends will grow at a constant rate. However, in reality this may not be the case. A firm may experience a period of very high growth and then after a few years, the growth rate may fall to a lower sustainable growth rate. In such a case we cannot apply the simple formula that we saw in the Gordon Growth Model that assumed a constant growth rate.

A stock with such characteristics can be valued by adding the present value of cash flows in the initial period of high growth and the present value of the stock after this high growth period assuming a constant growth rate.
<div class="formula1">
[latex size=3 background="f0f0f0"]V_{0}=\frac{D1}{1+k}+\frac{D2}{\left ( 1+k \right )^{2}}+ \cdot \cdot \cdot  +\frac{Dn}{\left ( 1+k \right )^{n}}+\frac{Pn}{\left ( 1+k \right )^{n}}[/latex]

Here, P<sub>n</sub> is calculated using the Gordon Growth Model formula:

[latex size=3 background="f0f0f0"]P_{n}=\frac{D_{n+1}}{k-g}[/latex]
</div>
<h2>Example</h2>
Let’s take a simple example to understand this:

Assume that a stock that pays dividends is expected to grow at a high rate of 15% per year for the first 3 years, after which it will grow at 6% per year.

The last dividends pay were $1, and the required rate of return in 8%.

Let's see how multi-stage growth model can be used to value this stock.
<div class="formula1">
First we will calculate the dividends in the high growth period.

D1 = 1*1.15 = $1.15

D2 = 1.15*1.15 = 1.3225

D3 = 1.3225*1.15 = 1.521

Note that after D3, the dividends are expected to grow at a constant growth rate of 6%. So, D3 will grow at a constant rate of 6%. We can use D3 and the constant growth rate to calculate P2, that is, the value of the stock at t=2.

P2 = D3/(k-g) = 1.521/(8% - 6%) = 76.05

The present value of the stock will now be the sum of D1, D2, and P2.

V0 = 1.15/(1.08) + 1.3225/(1.08)^2 + 76.05/(1.08)^2

= 67.34
</div>
Note that you could also calculate D1, D2, D3, and P3 and then take the present value of all these to arrive at the value of the stock. The answer will be the same.

Multi-stage Dividend Discount Models

While valuing a stock, the analysts will need to make a choice about which valuation model should they use.

This is a difficult but important choice for arriving at the correct valuation. Some analysts will in fact value a stock using multiple models to arrive at a range of stock value.

Provided below are a few simple guidelines than an analyst can use while selecting a valuation model:
<ol>
	<li>As we know, the <a title="Gordon (Constant) Growth Dividend Discount Model" href="https://financetrain.com/gordon-constant-growth-dividend-discount-model/">Gordon Growth model</a> assumes a constant growth rate for dividends. This model is suitable for companies that are fairly stable and mature, and pay regular dividends. Also, these businesses should be non-cyclical in nature.</li>
	<li>For companies that are currently exhibiting a high growth rate for dividends, but expect to provide a more sustainable constant growth rate in the future should be valued using the <a title="Multi-stage Dividend Discount Models" href="https://financetrain.com/multi-stage-dividend-discount-models-2/">multi-stage dividend discount models</a>. In the multi-stage model, there can be many variations. For example, some companies may initially have high growth rate of dividends, followed by a low growth rate, followed by constant growth rate (three phases). The valuation model can be adjusted according to the requirements.</li>
	<li>For companies that do not pay dividends, the analysts will have to rely on <a title="Equity Valuation – Free Cash Flow Model (FCFE)" href="https://financetrain.com/equity-valuation-free-cash-flow-model-fcfe/">Free Cash flow to Equity (FCFE)</a> for valuation. In this case, analysts need to ascertain the growth rate for earnings instead of dividends.</li>
	<li>Analysts can also use valuation models based on price multiples in other cases.</li>
</ol>
&nbsp;

How Do Analysts Select an Equity Valuation Model?

Apart from the dividend discount models, many analysts use price multiples for valuing the stocks. There are many reasons for using the price multiples. One, the DDM models can be very sensitive to the inputs such as the growth rate. Two, price multiples are very easy to calculate and can be quickly used for comparing stocks within a sector. Usually an analyst will compare the price multiple for a stock with a benchmark value based on an index or industry group.

There are four commonly used price multiples:
<ol>
	<li><strong>Price to Earnings (P/E):</strong> Stock price divided by the earnings per share.</li>
	<li><strong>Price to Cash flow (P/CF): </strong>Stock price divided by the cash flow per share. The cash flow could be operating cash flow or free cash flow.</li>
	<li><strong>Price to Sales (P/S):</strong> Stock price divided by sales per share.</li>
	<li><strong>Price to Book Value (P/BV):</strong> Stock price divided by book value per share.</li>
</ol>
Price multiples can be used for equity valuation in two ways: <strong>price multiples based on comparables</strong> and <strong>price multiples based on fundamentals</strong>.

While using price multiples based on comparables, the price multiple is calculated based on the actual market price of the stock and is compared to a benchmark to evaluate whether the stock is undervalued, overvalued or fairly valued. This is the most commonly used form of price multiples. The idea behind this is that most stocks within the same industry or peer group should be trading at comparable prices.

When using price multiples based on fundamentals, the price multiple is calculated based on the forecasted value of the stock calculated using a valuation model such as DDM.

In this method, an analyst will first calculate the fair value of a stock using a <a title="Types of Equity Valuation Models" href="https://financetrain.com/types-of-equity-valuation-models/">valuation model,</a> for example, the Constant Dividend Discount Model. Then he will divide this fair value with one of the stock’s fundamental such as earnings, sales, book value, or cash flow to arrive at the price multiple.

A price multiple calculated using fundamentals is also called justified multiple. For example, if P/E ratio is calculated with price derived using dividend discount model, then it will be referred to as justified P/E.

Since such P/E is calculated using the expected value of the stock, it is also referred to as leading P/E, as compared to trailing P/E where past data is used.

The justified P/E is the P/E at which the stock should be trading based on its fundamentals. If the P/E based on the market price is different from justified P/E it signals that the stock is undervalued or overvalued. For example, if the justified P/E is 8, and the actual P/E based on market price is 12, then the stock is overvalued, and vice verse.

Stock Valuation Using Price Multiples

We have seen that the <a href="https://financetrain.com/price-to-earnings-pe-ratio-leading-pe-and-trailing-pe/" title="Price to Earnings (P/E) Ratio (Leading P/E and Trailing P/E)">P/E ratio</a> is a commonly used <a href="https://financetrain.com/stock-valuation-using-price-multiples/" title="Stock Valuation Using Price Multiples">price multiple</a> for valuing a company.

However, an analyst needs to analyze the P/E ratio in the larger context of the other financials of the company and need to be able to determine whether its P/E ratio is supported by the other factors.

In terms of fundamental valuation, the P/E ratio can be written as:
<div class="formula1">
[latex size=3 background="#f0f0f0"]P/E \text{ ratio}=\frac{\frac{D_{1}}{E}}{k-g}[/latex]

[latex size=3 background="#f0f0f0"]\text{Where } P_{0}=\frac{D_{1}}{{k-g}}[/latex]
</div>
Note here that D1/E is the dividend payout ratio, k is the required rate of return, and g is the growth rate.

Looking at this formula, we can say that:
<ol>
	<li><strong>Dividend payout ratio: </strong>If a company has a higher dividend payout ratio than the industry average, it supports a higher P/E ratio for the company.<strong></strong></li>
	<li><strong>Growth rate: </strong>If a company has a higher growth rate than the industry average, it supports a higher P/E ratio for the company.<strong></strong></li>
	<li><strong>Required rate of return:</strong> A lower required rate of return supports a higher P/E ratio for the company.<strong></strong></li>
</ol>
We can also infer that if a company has high debt, it indicates a higher required return on equity, which in turn means support for lower P/E ratio.

Using a simple analysis like this, an analyst can see what kind of support is there for P/E ratio.

Support for P/E Ratio of a Company

An analyst can also use a multiple based on enterprise value for valuing a firm.

The enterprise value here refers to the total market value of the whole business. You can also refer to it as the value at which the business can be sold.

<img class="aligncenter size-full wp-image-7630" title="Enterprise Value" src="https://financetrain.com/wp-content/uploads/ev.png" alt="" />

Apart from this, any minority interests will be added and any associate company will be deducted at market value.

In a value multiple, the numerator is the enterprise value of the firm, and the denominator is a measure of the revenue, earnings, or book value of the firm. The most commonly used measure if the EBITDA (Earnings Before, Interest, Tax, Depreciation, and Amortization). Since the enterprise value includes both the equity and the debt of the firm, EBITDA is a suitable measure because it includes earnings before debt payment.

While calculating the enterprise value multiple, most of the values are readily available, except the market value of debt. In such a case, the analyst can make an assumption about the market value of debt, by comparing it with the market values of similar bonds.

The following document from Aswath Damodar provides detailed examples of calculating the value multiples.

[gview file="http://pages.stern.nyu.edu/~adamodar/pdfiles/damodaran2ed/ch9.pdf" width="600" save="1"]

Enterprise Value Multiples in Equity Valuation

<p>The analyst can use a variety of models to estimate the intrinsic value of equities. One such model is the Dividend Discount Model. Under this model the value of a stock is calculated as the present value of all future dividends from the stock.</p>



<figure class="wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio"><div class="wp-block-embed__wrapper">
https://youtu.be/om5dAn4jTXQ
</div></figure>



<p>As you can see in the above video, the general form of the model shows that the stock value is equal to the present value of all cash flows, where D is the dividend for each period, k is the required rate of return on common equity, and V is the current stock value. Calculating the value of stock using this formula is impractical as we cannot determine the dividends for each period till infinity. A normal assumption is that an investor will hold the asset for a period and then sell it. With such an assumption, it becomes easy to calculate the stock value.</p>



<p>The one year holding period DDM assumes that the investor holds the stock only for one year and then sells it at the end of the year. In this scenario, the current stock value can be calculated using the dividend discount model if we know how much dividend will be paid at the end of the year and at what price the investor will be able to sell the asset.</p>



<p>Let’s take a simple example. Assume that a stock paid $10 dividend last year and the next year’s dividend is expected to be 10% higher. At the end of the year, the stock will sell for $110. The investor has a required rate of return of 15%. The value of the stock will be the present value of these cash flows as shown on screen. Note that the dividend paid was $10 last year, and the dividend will grow by 10% next year. Therefore, D1 is taken as $11. Using the formula, the current value of the stock is $105.22.</p>



<p>In a multi-year holding period scenario, we assume that the investor holds the asset for multiple years before selling it. We calculate the value of the asset by adding the present values of all dividends for the holding period and present value of the estimated sale value of the stock at the end of the holding period.</p>



<p>On screen, you can see the formula for a 2-year holding period. Let’s take the same example but this time assume that the investor holds it for two years. The dividend continues to grow by 10%, and the investor is expecting to sell the stock for $115 after two years. Assuming a required rate of return of 15%, the current value of the stock will be $105.67.</p>



<p>One problem with the dividend discount model is that it cannot be used to value stocks that don’t pay dividends. In such cases the analysts use free cash flow to equity instead of dividends to calculate the present value.</p>

Equity Valuation - Dividend Discount Model

Investors and stock analysts use a variety of valuation models to arrive at the fair value of stocks. In fact they will generally use more than one model with a variety of assumptions and arrive at a range of possible fair values.

In this article we will briefly discuss three types of models, namely, discounted cash flow models, multiplier models, and asset-based models.

<strong>Discount Models</strong>

The discounted cash flow models, determine the value of a stock by calculating the present value of expected cash flows. These cash flows are of two types: expected cash flow to shareholders (dividend discount models), and the free cash flow to equity.

<strong>Multiplier Models</strong>

The multiplier models determine the value of a company by analyzing and comparing the company's financial ratios. For example, a popular multiple is the price-earnings ratio. Other commonly used multiples are sales, book value, and cash flow per share.

There are other multiples, which are based on the enterprise value (EV), for example, EV/EBITDA, EV/EBIT, and EV/ Unlevered free cash flow (UFCF). These multiples are commonly used for valuing private firms.

Enterprise value, also called the firm value, is an economic measure that reflects the market value of the business. It includes claims to all security-holders, including equity, debt.

<strong>Asset-based Models</strong>

Asset-based models determine the fair value of a stock by calculating the value of the firm's assets and subtracting the value of its liabilities and preferred stock. Since the firm's assets and liabilities will be at book value, the analysts will adjust these values to their fair value.

Types of Equity Valuation Models

While investing in stocks, a very basic concept is to understand the value of a stock, and whether it is worth investing in the stock.

The stock prices observed in the market are called the market prices of the stocks.

Based on fundamental analysis and using equity valuation model, an investor will try to calculate the fair value of the stock, also called the intrinsic value. This is the value that the investor feels that the stock should actually be trading at.

Let’s say that an investor is analyzing ABC stock. The current market price of ABC stock is $90 per share. The investor does a lot of research and finally arrives at an intrinsic value of $100. According to the investor, the ABC stock should actually be selling at $100 based on its current fundamentals and under certain assumptions made by the investor.  Since the stock is currently selling at $90, the stock is undervalued according to the investor, and its value should rise up to its intrinsic value. In such a case, the investor will buy the stock at its current price of $90 expecting the price to rise.

In general:

If Intrinsic Value &gt; Market Price, the stock is undervalued. The investor will want to buy the stock.

If Intrinsic Value = Market Price, the stock is fairly valued. The investor is neutral about the stock price.

If Intrinsic Value &lt; Market Price, the stock is overvalued, and investor expects its price to fall.

One must note that the market itself is supposed to price the stocks quite fairly, however due to asymmetric flow of information, the market price may not reflect all the information available. An investor who is able to utilize the information available more efficiently than the market can take advantage of the mispricing and make abnormal profits.

The key here is how well the investor is able to calculate the value of the stock, and how true are the assumptions made by him while valuing the stock.

In the next article we will explore the valuation models that are commonly used to value stocks.

Determining the Value of a Stock

Asset-based Valuation Models

This quiz is a part of the CFA Level 1 reading 'Equity Valuation: Concepts and Basic Tools'. 

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