Stock Valuation

STOCK VALUATION

A beginning point on stock valuation is to calculate the required rate of return of the stock that we are valuing. Since every company functions differently, even those in the same industry, their risk/return combinations will be unique. As an investor, one of our first tasks will be to choose firms that have risk/return elements that will fit our own investment objective.

The Required Rate of Return of a Risky Asset

Before the 1950's, investment professionals and investors had a loose definition of risk and how it related to the expected return of an investment. The Capital Asset Pricing Model is a mathematical formula to assist investors in understanding where an investment may be on the risk-return graph. We know that risk and return are direct variables. When one increases, the other variable is expected to increase.

Risk in this model is measured by the volatility of a stock compared to market volatility. The Beta (ß). The Beta of the market is always equal to one. If a stock has a beta of one, it is expected to be as volatile as the market. A beta of 1.5 is indicative of a security that is 50% more volatile than the market. The more volatility in an investment, the more risk.

The Capital Asset Pricing Model is used to calculate the required rate of return on a risky asset - a share of stock.

The Model: K_e = R_F + ß (R_F + Premium - R_F )

K_e is the required rate of return of a risky asset.

We also need to mention here that the expected return of the market is equal to: R_F + Premium. and is usually denoted as K_m.The above model can be re-written as: K_e = R_F + ß (K_m - R_F )

R_F is the risk free rate of money. This can be measured as the rate of return on a bank savings account or usually the rate on a treasury bill.

Premium is the equity risk premium. This is the rate of return required to entice an investor out of risk free investments into risky ones. The risk premium, measured over time has been about 7%.

Beta was described above.

THE DIVIDEND DISCOUNT MODEL (DDM)

Before the 1980's, dividends on stocks comprised an average of 46% of the total return on a stock investment, the remaining 54% came from capital gains.
The 1980's brought the technology boom and numerous rapidly growing companies that served investors healthy returns and no mention of dividends.
The "tech-wreck" of 1999-2001, renewed many investor's interest in stable firms that provided both ingredients of total return: capital gains and dividends.

Check out this article from Money Magazine on the subject, it will supplement the lecture on the idea of dividends on stocks. "Dividends Are Back in Style"

Another article that I found on "The Motley Fool" (August, 2006) reiterated how important stock dividends are to investor's total return: The Secret of Dividends.

A traditional stock valuation model that will appear in almost every finance text on investments is the Dividend Discount Model or the Dividend Valuation Model. [If you typed that title in your favorite internet search engine, you will get some 30,000 hits on the subject.] The idea is similar to bond valuation. Finance professionals get excited over any idea that has a known cash flow; first because it is known (as opposed to being unknown), secondly because it is cash. A present value calculation can be made on these cash flows to form a value. With dividends comprising such a large part of total return, this model was and still is a popular valuation method.

The Value of a Stock is the present value of its expected dividends plus the present value of the expected share price at some point in the future. One model that I found on the internet is:

The dividend discount model:

where

	t, n -- the year
	V -- the value of the stock.
	D -- the dividend.
	R -- the discount rate (the required rate of return for a risky asset, as required by the investor)

We can see in this "compact" version of the model that the dividends are represented by "D" and that part of the equation is added to the "V" (stock value component). The large [greek] Sigma letter in front of the formula is simply saying that we are summing or adding several components.

The models that we use in this class are: The General Dividend Model and the Constant Growth model.

The General Model: This model has only a dividend (D) in the numerator; the dividend is divided by the investors required rate of return for this stock (ke). The present value of the dividend is being taken using the required rate of return as the "i" in a present value formula. The (1+k_e)¹ looks like (1+i)ⁿ in a present value model. The negative sign on the exponent is not present because (1+k_e)¹ is in the denominator, this is mathematically equivalent to a negative exponent in the numerator. I know that you are confused.

V_o = D₁/(1+k_e)¹ + D₂/(1+k_e)² + D₃/(1+k_e)³ + D₄/(1+k_e)⁴ + V₄/(1+k_e)⁴

The Constant Growth Model:

V_o = D₁(1+g)¹ / (1+k_e)¹ + D₂(1+g)² / (1+k_e)² + D₃(1+g)³ / (1+k_e)³ +D₄(1+g)⁴ / (1+k_e)⁴ + V₄(1+g)⁴ / (1+k_e)⁴

This model has a growth rate in the numerator (1+g)¹

If dividends of the firm are being increased over time, a growth rate must be added to the model. In the general model, there was no dividend growth, the firm is paying the same dividend quarter after quarter. This model is more cumbersome to calculate due to the added component, but it is more realistic. Firms that pay dividends want to increase dividends over time. We are increasing dividends by applying the future value of a single sum formula then, dividing it by the present value of a single sum formula! The dividends are being appropriately increased by the growth rate, the present value must be taken to value those amounts today.

What Investopedia says about dividend signaling:

Dividend Signaling
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A theory that suggests company announcements of an increase in dividend payouts acts as an indicator of the firm possessing strong future prospects. The rationale behind dividend signaling models stems from game theory. A manager that has good investment opportunities is more likely to "signal", than one who doesn't, because it is in their best interest to do so.

Investopedia Says:
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Over the years the concept that dividend signaling can predict positive future performance has been a hotly contested subject. Many studies have been done to see if the markets reaction to a "signal" is significant enough to support this theory. For the most part the tests have shown that dividend signaling
does occur when companies either increase or decrease the amount of dividends they will be paying out.

The theory of dividend signaling is also a key concept used by proponents of inefficient markets.

Smart Money Article on the Dividend Discount Model

Motley Fool Article about Stock Dividends and how important they are