Common Stock Valuation

Timothy R. Mayes, Ph.D.

FIN 3600: Chapter 14

What is Value?

In general, the value of an asset is the price that a willing and able buyer pays to a willing and able seller

Note that if either the buyer or seller is not both willing and able, then an offer does not establish the value of the asset

Several Kinds of “Value”

There are several types of value, of which we are concerned with four: Book Value – The carrying value on the balance sheet of the

firm’s equity (Total Assets less Total Liabilities) Tangible Book Value – Book value minus intangible assets

(goodwill, patents, etc) Market Value - The price of an asset as determined in a

competitive marketplace Intrinsic Value - The present value of the expected future cash

flows discounted at the decision maker’s required rate of return

Determinants of Intrinsic Value

There are two primary determinants of the intrinsic value of an asset to an individual: The size and timing of the expected future cash flows. The individual’s required rate of return (this is determined by a

number of other factors such as risk/return preferences, returns on competing investments, expected inflation, etc.).

Note that the intrinsic value of an asset can be, and often is, different for each individual (that’s what makes markets work).

Common Stock

A share of common stock represents an ownership position in the firm. Typically, the owners are entitled to vote on important matters regarding the firm, to vote on the membership of the board of directors, and (often) to receive dividends.

In the event of liquidation of the firm, the common shareholders will receive a pro-rata share of the assets remaining after the creditors (including employees) and preferred stockholders have been paid off. If the liquidation is bankruptcy related, the common shareholders typically receive nothing, though it is possible that they may receive some small amount.

Common Stock Valuation

As with any other security, the first step in valuing common stocks is to determine the expected future cash flows.

Finding the present values of these cash flows and adding them together will give us the value:

For a stock, there are two cash flows: Future dividend payments The future selling price

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Common Stock Valuation: An Example

Assume that you are considering the purchase of a stock which will pay dividends of $2 (D1) next year, and $2.16 (D2) the following year. After receiving the second dividend, you plan on selling the stock for $33.33. What is the intrinsic value of this stock if your required return is 15%?

2.00 2.1633.33

?

Some Notes About Common Stock

In valuing the common stock, we have made two assumptions: We know the dividends that will be paid in the future. We know how much you will be able to sell the stock

for in the future. Both of these assumptions are unrealistic,

especially knowledge of the future selling price. Furthermore, suppose that you intend on holding

on to the stock for twenty years, the calculations would be very tedious!

Common Stock: Some Assumptions

We cannot value common stock without making some simplifying assumptions. These assumptions will define the path of the future cash flows so that we can derive a present value formula to value the cash flows.

If we make the following assumptions, we can derive a simple model for common stock valuation: Your holding period is infinite (i.e., you will never sell the stock

so you don’t have to worry about forecasting a future selling price).

The dividends will grow at a constant rate forever. Note that the second assumption allows us to predict

every future dividend, as long as we know the most recent dividend and the growth rate.

The Dividend Discount Model (DDM)

With these assumptions, we can derive a model that is variously known as the Dividend Discount Model, the Constant Growth Model, or the Gordon Model:

This model gives us the present value of an infinite stream of dividends that are growing at a constant rate.

Estimating the DDM Inputs

The DDM requires us to estimate the dividend growth rate and the required rate of return.

The dividend growth rate can be estimated in three ways: Use the historical growth rate and assume it will continue Use the equation: g = br Generate your own forecast with whatever method seems

appropriate

The required return is often estimated by using the CAPM: ki = krf + i(km – krf) or some other asset pricing model.

The DDM: An Example

Recall our previous example in which the dividends were growing at 8% per year, and your required return was 15%.

The value of the stock must be (D0 = 1.85):

Note that this is exactly the same value that we got earlier, but we didn’t have to use an assumed future selling price.

The DDM Extended

There is no reason that we can’t use the DDM at any point in time.

For example, we might want to calculate the price that a stock should sell for in two years.

To do this, we can simply generalize the DDM:

For example, to value a stock at year 2, we simply use the dividend for year 3 (D3).

The DDM Example (cont.)

In the earlier example, how did we know that the stock would be selling for $33.33 in two years?

Note that the period 3 dividend must be 8% larger than the period 2 dividend, so:

Remember, the value at period 2 is simply the present value of D3, D4, D5, …, D∞

What if Growth Isn’t Constant?

The DDM assumes that dividends will grow at a constant rate forever, but what if they don’t?

If we assume that growth will eventually be constant, then we can modify the DDM.

Recall that the intrinsic value of the stock is the present value of its future cash flows. Further, we can use the DDM to determine the value of the stock at some future period when growth is constant. If we calculate the present value of that price and the present value of the dividends up to that point, we will have the present value of all of the future cash flows.

What if Growth Isn’t Constant? (cont.)

Let’s take our previous example, but assume that the dividend will grow at a rate of 15% per year for the next three years before settling down to a constant 8% per year. What’s the value of the stock now? (Recall that D0 = 1.85)

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2.1275 2.4466 2.8136 3.0387 …

g = 15% g = 8%

What if Growth Isn’t Constant? (cont.)

First, note that we can calculate the value of the stock at the end of period 3 (using D4):

Now, find the present values of the future selling price and D1, D2, and D3:

So, the value of the stock is $34.09 and we didn’t even have to assume a constant growth rate. Note also that the value is higher than the original value because the average growth rate is higher.

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Two-Stage DDM Valuation Model

The previous example showed one way to value a stock with two (or more) growth rates. Typically, such a company can be expected to have a period of supra-normal growth followed by a slower growth rate that we can expect to last for a long time.

In these cases we can use the two-stage DDM:

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Two-Stage DDM Valuation Model (cont.)

The two-stage growth model is not a complex as it seems: The first term is simply the present value of the first N dividends (those

before the constant growth period) The second term is the present value of the future stock price.

So, the model is just a mathematical formulation of the methodology that was presented earlier. It is nothing more than an equation to calculate the present value of a set of cash flows that are expected to follow a particular growth pattern in the future.

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PV of the first N dividends + PV of stock price at period N

Three-Stage DDM Valuation Model

One improvement that we can make to the two-stage DDM is to allow the growth rate to change slowly rather than instantaneously.

The three-stage DDM is given by:

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Other Valuation Methods

Some companies do not pay dividends, or the dividends are unpredictable.

In these cases we have several other possible valuation models: Earnings Model Free Cash Flow Model P/E approach Price to Sales (P/S)

The Earnings Model

The earnings model separates a company’s earnings (EPS) into two components: Current earnings, which are assumed to be repeated

forever with no growth and 100% payout. Growth of earnings which derives from future

investments. If the current earnings are a perpetuity with

100% payout, then they are worth:

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The Earnings Model (cont.)

VCE is the value of the stock if the company does not grow, but if it does grow in the future its value must be higher than VCE so this represents the minimum value (assuming profitable growth).

If the company grows beyond their current EPS by reinvesting a portion of their earnings, then the value of these growth opportunities is the present value of the additional earnings in future years.

The growth in earnings will be equal to the ROE times the retention ratio (1 – payout ratio):

Where b = retention ratio and r = ROE (return on equity).

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The Earnings Model (cont.)

If the company can maintain this growth rate forever, then the present value of their growth opportunities is:

Which, since NPV is growing at a constant rate can be rewritten as:

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The Earnings Model (cont.)

The value of the company today must be the sum of the value of the company if it doesn’t grow and the value of the future growth:

Where RE1 is the retained earnings in period 1, r is the return on equity, k is the required return, and g is the growth rate

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The Free Cash Flow Model

Free cash flow is the cash flow that’s left over after making all required investments in operating assets:

Where NOPAT is net operating profit after tax Note that the total value of the firm equals the

value of its debt plus preferred plus common:

CapOpNOPATFCF

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The Free Cash Flow Model (cont.)

We can find the total value of the firm’s operations (not including non-operating assets), by calculating the present value of its future free cash flows:

Now, add in the value of its non-operating assets to get the total value of the firm:

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The Free Cash Flow Model (cont.)

Now, to calculate the value of its equity, we subtract the value of the firm’s debt and the value of its preferred stock:

Since this is the total value of its equity, we divide by the number of shares outstanding to get the per share value of the stock.

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Relative Value Models

Professional analysts often value stocks relative to one another. For example, an analyst might say that XYZ is undervalued relative

to ABC (which is in the same industry) because it has a lower P/E ratio, but a higher earnings growth rate.

These models are popular, but they do have problems: Even within an industry, companies are rarely perfectly comparable. There is no way to know for sure what the “correct” price multiple is. There is no easy, linear relationship between earnings growth and price

multiples (i.e., we can’t say that because XYZ is growing 2% faster that it’s P/E should be 3 points higher than ABC’s – there are just too many additional factors).

A company’s (or industry’s) historical multiples may not be relevant today due to changes in earnings growth over time.

The P/E Approach

As a rule of thumb, or simplified model, analysts often assume that a stock is worth some “justified” P/E ratio times the firm’s expected earnings.

This justified P/E may be based on the industry average P/E, the company’s own historical P/E, or some other P/E that the analyst feels is justified.

To calculate the value of the stock, we merely multiply its next years’ earnings by this justified P/E:

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The P/S Approach

In some cases, companies aren’t currently earning any money and this makes the P/E approach impossible to use (because there are no earnings).

In these cases, analysts often estimate the value of the stock as some multiple of sales (Price/Sales ratio).

The justified P/S ratio may be based on historical P/S for the company, P/S for the industry, or some other estimate:

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