Chapter 2

Investor Valuation Frameworks

ACCOUN

CCOUNTING DATA, like other data in the world about us, are read and interpreted within the framework of particular theories. Without such a framework, the reader of a financial statement is likely to consider the data presented there to be a meaningless configuration, and the existence of important relationships will likely be missed.

The validity of these statements can be readily illustrated. Consider the assertion that data are read in terms of a theory. The ratio of debt to equity, or the difference between current assets and current liabilities have meaning to financial analysts because they are inputs to models that characterize corporate liquidity. Similarly, the product of the dividend payout ratio times earnings has meaning to investors because this product is part of a larger framework that helps an investor understand how a corporation operates and how the market price of a security is determined. Two other accounts that generally appear on corporate balance sheets are prepaid expenses and accrued taxes. As far as we know, neither the ratio nor the sum nor the difference nor the product of these two accounts has any particular meaning; i.e., transformations of these two balance sheet accounts neither enhance a shareholder's understanding of the corporation's operation nor contribute to management's ability to operate the firm in a manner that will enable it to achieve the goals it set for itself. These transforms are meaningless precisely because there is no theory to explain the role they play in corporate development or share price determination.

The second assertion that without a theory events may not be recognized and observations concerning them may not be recorded is more difficult to document. For once a need is recognized, data to fulfill the need can be collected. Some illustrations of the failure to

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recognize events, however, can be cited. Modern inventory theory requires the firm to balance the cost of carrying inventory against the cost of "outages." When firms began to implement this model, it became evident that few if any had systematically thought about or collected data that were relevant to the problem of measuring the cost of an outage. Once the need was recognized, however, data relevant to estimating the cost of outages were collected.

These remarks are pertinent to the problem of corporate disclosure for a number of reasons.

Accounting statements are designed to meet the requirements of such a varied group of users as managers, regulatory agencies, bankers, and investors. They do not exist as an end in themselves. If the analytical framework that investors use is not identical with the models used by managers or regulators or bankers, the data that investors require as inputs to their models will be different from that of other users.

If a corporation's statements do not specifically address themselves to the analytical frameworks that are used by investors, the financial data reported are likely to be deficient in two respects. First, the statements may include data that are useless if not misleading to investors. Second, the statements are likely to omit data that are required inputs to the models that are in fact used by investors in valuing corporate securities.

Before the problem of corporate disclosure to shareholders can be attacked directly, it is necessary to sketch the character of the analytical models that dominate the thinking of investors. This will be the task of the next section.

Investor Valuation Models

Perhaps the dominant analytical framework used by investors to value a corporation's shares is based upon the idea that the price of an. asset is the present value of its estimated future return. Thus:

n

(1)

Where P represents the price of the asset, R, is the return in the nth year and k1 is the discount rate that is used in each period.

This definition of the price of an asset is made operational by specifying the behavior of R and k through time.

1. First specification: R and k are constant.

Assume that R and k are constant through time. Equation 1 can

Consider the last term on the right hand side of equation 3. As n becomes large, that is, as the horizon of the investor extends further and further into the future, the value of this term becomes smaller and ultimately approaches zero. For a large n, equation 3 can be rewritten as:

Equation 3'' states that the price of an asset is the capitalized value of its annual return. Equation 3''' states that the price of an asset is some multiple of its annual return.

To illustrate this model, suppose that R, the expected annual return, is $2 and that k, the discount rate, is 10%. m is therefore 10. The price of the asset is:

2. Second specification: R increases at a constant rate and k is

constant.

Another specification of R and k that is frequently used by investors is that while k remains constant through time, R, the annual return increases each year by a constant percentage. Let g be the growth rate of the return. Then

and in general R1 = R1 (1+g)"-1

If k is constant through time, then equation 1 can be rewritten as:

The solution to this equation can be found by following a procedure similar to that used above. Multiplying both sides of equation 1'' by

Consider the last term on the right hand side of equation 5. If k> g, that is, the discount rate is greater than the growth rate, this term will approach zero as n increases. Thus, if the investor's horizon is long, i.e., n is large, we can ignore the term. Equation 5 therefore becomes:

year the

To illustrate this model, suppose that R1 is $2 and that cach return is expected to grow at a 5% rate. If the discount rate is 10%.

3. Third specification: two-period R, k = constant.

Both models described above required n, the time period under consideration, to be large. A third specification that is sometimes used by shareholders to value an asset makes use of a two-period model. In the first period, a return of R is received. In the second period, a second return of R is received and the asset is sold for a price of P2. To describe this model, equation (1) can be rewritten as:

where P. is the present price, R1 and R2 are the returns in the first and second periods, and P2 is the price in the second year.

Under certain assumptions, equation (1''') can be shown to be equivalent to (1') or (l''). For example, suppose that P2 the price that will prevail in two years is given by the future stream of revenues from that time forward discounted back to period 2. That is

yields equation l'. Thus, this two-period model is shown to be identical to the n period model.

Measures of Return

Equation 1 defined the price of an asset as the present value of its expected future return. If this is indeed the dominant model that investors use, it follows that the corporate disclosure problem is reduced to one of disclosing both the current return that an investor will receive and data that are pertinent to estimating the growth in future returns that are likely to result from the company's operations.

In subsequent chapters we will address ourselves to the problem of what data might be useful to the investor attempting to estimate the growth of returns. First, however, we must consider the question of what is meant by "returns." There are two dominant measures of the return from equity securities: earnings and dividends.

Earnings per share is a widely used measure of return by financial