Earnings per Share Don't Count

CFA Institute

Earnings per Share Don't CountAuthor(s): Joel M. SternSource: Financial Analysts Journal, Vol. 30, No. 4 (Jul. - Aug., 1974), pp. 39-40+42-43+67-75Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4529716 .

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by Joel M. Stern

Earnings PerShr Don't Coun

Any evaluation of corporate policies in terms of their impact on earnings per share (EPS) is fraught with danger. EPS is too often a misleading indicator that can result in costly decisions that shortchange the common shareholders.

The EPS criterion confuses investment decisions with financing policies. Substandard projects can be made to appear desirable simply because of the way in which they are financed. Hence EPS is a misleading indicator particularly in making decisions on acquisition pricing and financing and capital structure planning. Furthermore, there is considerable evidence that the market is not in- terested in earnings or EPS per se. Both management and analysts need to focus more clearly on the key elements that determine a company's share price. Thus there are many reasons why management and the financial community should abandon EPS as an analytical tool.

Acquisition Analysis The rhetoric in many business publications

about acquisition analysis is outrageous. For instance, we are frequently told that companies should make acquisitions because of the "earnings leverage" that will result.

As an example, assume that company A sells at a price-earnings ratio (PE) of 20 and that company B sells at a PE of ten. Often, we are told that company A can offer B's shareholders a PE of, say, 15-a 50 per cent premium-and that A can still increase its EPS. For each dollar of earnings A is

buying, A has to give up shares earning only 75 cents. Thus if A uses its shares to buy B and form a new company AB, the new company's EPS will always exceed A's. Hence we. are told that the acquisition of B is good for A's shareholders. And, apparently, it is good for B's shareholders since they obtain a 50 per cent premium above the market price of their shares.

However, if the example is turned around, the danger of using EPS becomes obvious. If B buys A to form BA, B will pay at least A's PE of 20. But now BA's EPS will be less than B's because the company with the lower PE must offer more shares per dollar of acquired earnings. The same people who tell us that AB is good for both A's and B's shareholders tell us that BA is bad for B's shareholders, even though AB and BA are the same company, most often with the same assets and earnings expectations and, even, the same management. Should we therefore expect AB and BA to sell at different market prices when they are really the same company?

A's acquisition of B or B's acquisition of A is in fact good for the buyer's shareholders only if synergism is expected. And the synergism must be at least large enough to justify the premium paid above the seller's current share price.

Thus it is illogical to claim that IBM, for instance, can afford to pay more for B than could Chase Manhattan Bank simply because IBM sells at a much higher PE than The Chase. Furthermore, if IBM (or any company selling at a high PE) were to acquire firms for which it paid full value (i.e., for which there was no added benefit to the buyer's shareholders), all the evidence suggests that IBM's PE would fall to offset the gain in EPS.

"The AB-BA Fallacy" lies in the assumption

Joel M. Stern is Vice President of The Chase Manhattan Bank, N.A., columnist for the Financial Times in London and the Commercial and Financial Chronicle in New York, and adjunct professor at the University of Wisconsin.

FINANCIAL ANALYSTS JOURNAL I JULY-AUGUST 1974 O 39



Earnings Per Share Don't Count

that the pro forma EPS determines the pro forma share price. Because share prices are not in fact determined so simply, relying on EPS to evaluate alternative acquisition candidates often results in costly decisions.

Confusing Investment With Financing Another EPS pitfall in acquisition policy is confusing investment with financing. In a recent case, the president of a well-diversified manufacturer selling at 16 times earnings wanted to acquire a small, but exceptionally profitable, electronics manufacturer for a PE of 25. Since an equity swap would "dilute" the pro forma EPS, we suggested, somewhat facetiously, that it sell itself to the electronics firm, even though the latter was only a tenth the size of the manufacturer, so that the EPS would rise.

He suggested an alternative: use debt to finance the acquisition. The anticipated profits from the acquisition would more than cover the out-of- pocket cost of interest on debt and hence the company's income would rise, while the number of outstanding shares would remain unchanged. He was correct; the pro forma EPS would rise. However, there is a conceptual problem with his suggestion. Since EPS can be enhanced simply by employing debt, a bad investment often can be made to appear good merely by levering the firm sufficiently to increase the EPS at the time the investment is undertaken. Of course, if the leverage idea is sound, management can increase EPS without making any investment whatever, merely by borrowing to retire common shares.

Although there are many ways financing decisions can affect EPS, they cannot alter the intrinsic desirability of an acquisition, which is simply an unusually complicated decision. This means that investment decisions must be made in- dependently of financing decisions, or, in other words, on the basis of considerations other than the effect on EPS. Since EPS is calculated by dividing net profit after taxes and financing costs by the number of shares outstanding, basing investment decisions on EPS unfortunately implies that a specific source of funds finances a specific use of funds, which conceptually is wrong. If a company borrows to finance a plant, how can the lender be sure the borrower will not use a portion of the funds to pay dividends or build inventories? Clearly, specific sources of funds cannot be identified with specific uses of funds.

Thus there are two distinct shortcomings to em-

ploying EPS as an analytical tool in acquisition pricing. First, the existing PE's of the buyer and seller determine the decision, so that synergism may be excluded from consideration. Second, EPS can lead the decision-maker to believe that bad investments are good investments; if he levers the firm sufficiently at the time an investment is undertaken, EPS can be enhanced to any level he desires.

The Real Benefits of Debt Financing An emphasis on EPS not only misdirects

management in selecting and pricing acquisitions, it also leads to ridiculous conclusions about the proportions of debt and equity in a company's financial structure. Depending on the PE multiple, mechanical reliance on EPS can encourage expansion of debt to cover dubious projects, or the elimination of all debt by issuing common shares. Even though in most cases an increase in the amount of debt in relation to equity will enhance EPS, the benefits to a company's share price derived from its financing policies have nothing to do with EPS!

A company can use debt to increase its EPS as long as its after-tax return on fixed capital (i.e., all interest-bearing debt and equity) is larger than its after-tax interest costs. Today high-grade bonds cost the firm less than four per cent after taxes. Thus corporate investments in new plant and equipment and working capital that yield more than four per cent after taxes would appear desirable to analysts emphasizing EPS. It is cer- tainly not difficult to imagine the likely direction of IBM's share price if projects were undertaken earning a mere five per cent on fixed capital, even if EPS were rising.

The market will not ignore the fact that an increase in debt forces the common shareholder to assume greater financial risk, as a result of higher interest costs. Unless some other factor offsets part of this new risk, the PE will decline: The price of the common shares would remain unchanged despite the added EPS.

On the other hand, the EPS criterion would dic- tate that high PE firms should issue shares to retire debt. It works out mathematically that EPS can be increased by issuing shares to retire debt so long as the PE is larger than the reciprocal of the after-tax borrowing rate. If a company's after-tax cost of borrowed funds is four per cent, the reciprocal is one divided by four per cent, or 25. Whenever the PE exceeds 25, management can increase EPS sim-

40 O FINANCIAL ANALYSTS JOURNAL / JULY-AUGUST 1974




ply by issuing equity to retire debt. Hence supporters of EPS maximization would recommend that companies selling at very high PE's be debt- free, a policy hardly beneficial to the common shareholders.

Actually there is considerable evidence that debt financing does add to the market price of a firm's common shares. The reason is that part of the increase in relative risk due to the fixed interest expense is borne by the federal government-up to 48 per cent, the corporate income tax rate. The deductibility of interest expense in calculating taxable income means that a company's earnings are reduced by only 52 per cent of the cost of debt. *

A large body of empirical evidence confirms our intuition about borrowed capital-namely, that investors do not expect management to reduce debt. As it comes due, they expect management to refi- nance, hence to maintain a particular target debt ratio. A target debt ratio implies that sophisticated investors expect the annual tax saving to continue forever. The present value of this perpetual stream is simply the corporate income tax rate multiplied by the amount of interest-bearing debt that the market expects to be in the target capital structure. As long as the level of debt does not exceed prudent limits, the aggregate market price of a company's common shares will rise 48 cents for each dollar of interest-bearing debt in its target capital structure. The real benefit of debt financing to the common shareholders is not the added EPS; it is the government tax saving.

EPS Doesn't Count Clearly an EPS criterion frequently misallocates

valuable corporate resources and shortchanges the shareholders. Nor, to judge by market behavior, is EPS the criterion that impresses investors, especially the sophisticated investors who really determine share prices. What do these investors look for in evaluating a company's overall performance?

Investors do not discount earnings per se. Con- sider two companies, X and Y. Assume that, from all we know, they are the same in every way and that their profits are expected to increase at identical annual rates of 15 per cent. At this stage, a

foolish question would be: Which company should sell at a higher price, X or Y? Obviously, we would expect X and Y to sell at an identical price since, in the absence of additional information, X and Y are the same company!

However, with the addition of one other piece of information about the two companies, we must conclude that X would command the greater market price. Assume we learn that X requires almost no investment in new capital to increase its profits 15 per cent annually, whereas Y requires a dollar of additional capital for each incremental dollar of sales. X should sell at the higher price and PE because it requires less capital than Y to grow at a given rate despite the fact that X and Y are expected to have identical future profits. This is because X has a larger expected rate of return on incremental capital. The key determinant of market price in this case is the expected rate of return on incremental capital invested.

The implication of this example is that investors do not simply discount expected earnings; rather they discount anticipated earnings net of the amount of capital required to be invested in order to maintain an expected rate of growth in profits. We shall refer to the latter stream as the expected future "Free Cash Flow," the expected future stream of cash flows that remains after deducting the anticipated future capital requirements of the business. It is Free Cash Flow (FCF) that is important to the market. EPS is immaterial.

What Is "Sophistication"? One may argue intuitively or theoretically that sophisticated investors sort out the distortions created by EPS. Yet there is plenty of room to wonder whether the market really is as omniscient as this conception suggests. Observance of market behavior could convince some that share prices are affected by fads appearing to have little to do with market efficiency and FCF. Perhaps these are merely random errors of an ultimately efficient mechanism, but then again, perhaps not. An in- tuitive conception of market behavior could lead one to believe that the "sophisticated" investor recognizes that the market is merely a psychologi- cal game, and concentrates on spotting the next fad a week earlier than the rest. To accept the view that sophistication in the real world is an appreciation of underlying economic values based on FCF, one has to understand the "efficient markets" concept and the nature of the empirical evidence supporting it.

* Alternatively, the Internal Revenue Service of the Government can be viewed as a shareholder in the firm bearing the same risks that private shareholders take and sharing in the profits after interest costs. Thus the absolute risk borne by the IRS is virtually independent of the amount of debt financing.




Market Efficiency The essential role of a capital market is to allocate the ownership of an economy's capital efficiently. Ideally, a capital market should provide corporate management with a means for raising funds to undertake investment opportunities that add to investors' wealth, and investors with opportunities to purchase alternative securities at prices which "fully reflect" all available relevant information about the respective companies' activities and prospects. In an efficient market, security prices always fully reflect available relevant information.

The statistician would say that in efficient markets security prices are "unbiased estimates" of "intrinsic" or "fair" market values. That is, if current market prices are not fair market prices, there is as much likelihood that current prices are above, as they are below, fair prices.

The implication is that even if it is not certain that today's prices are fair, on average and over time, it will be impossible for investors to make profitable investments solely on the basis that current prices are overvalued or undervalued. Oc- casionally, investors employing such an investment strategy will be correct, but they will be incorrect often enough to eliminate any profits they have obtained.

In an efficient market, sophisticated investors perform an extremely useful function Their activities assure that fair prices and market prices are almost always the same. By attempting to estimate a firm's expected future FCF, they often pursue information in the hope that they will be the first to learn, and thus benefit from it. Transacting on the basis of their belief that they can identify overvalued or undervalued securities, they become the mechanism by which new information is translated into new market prices, causing market prices to make once-and-for-all adjustments to new information. Since in an efficient market a company's current share price is based on information available today about a firm's expected risk and future profitability (i.e., FCF), predicting future share prices consistently enough to outperform the market as a whole requires investors to forecast tomorrow's information.

Those who believe that there are enough imper- fections in the real world to impede the efficiency with which prices adjust to new information. may be skeptical because they have not had an op- portunity to review the huge body of empirical evidence published during the past decade. The work of Eugene Fama, Michael Jensen, Myron

Scholes, Irwin Friend, Marshall Blume, Jean Crockett, Richard Quandt, William Baumol, Bur- ton Malkiel, Richard Roll, Ray Ball, Phillip Brown, John Lintner, William Sharpe and many others provides considerable support for the view that the capital market in the United States more than satisfies the minimal conditions of efficiency in order for our FCF model to be a description of real world behavior.

Six Variables Our Free Cash Flow model is developed from ob- servations of market behavior. Sophisticated investors expect to obtain a return for bearing equity risk and their anticipated return takes the form of expected future cash dividends and/or capital appreciation. Because corporate management is likely to reinvest a portion of today's earnings in the business to generate tomorrow's earnings, sophisticated investors discount a firm's expected future earnings, less the amount of new capital needed to generate future earnings. The net stream is the firm's expected future Free Cash Flow (FCF).

The FCF model contains six key variables. Four describe the magnitude- and the rate of growth of FCF, and two determine the investors' discount rate.

The magnitude of current FCF is a function of (1) net operating profit after taxes and (2) the amount of new capital invested. The rate of growth in FCF is a function of the second variable, the amount of new capital, (3) the firm's expected rate of return on new capital invested and (4) the length of time (in years) for which the specified levels of variables two and three are expected to continue.

The discount rate is determined by (5) the degree of business risk sophisticated investors per- ceive in each of the firm's product lines and (6) the government tax saving provided from debt financing because interest expense reduces taxable income.

If security price movements are studied over a long period of time, one would observe that, although countless factors affect a company's share price, these six variables account for virtually all systematic price changes. (Although some investors may be misled by such factors as EPS, sophisticated investors who dominate securities markets are not fooled for very long, if they are fooled at all.) Thus factors affecting share prices unsystematically are absent in our FCF approach.

The six systematic determinants of a company's market value are described below in detail. (Sym-

continued on page 67

FINANCIAL ANALYSTS JOURNAL / JULY-AUGUST 1974 O 43



Earnings per share don't count continued from page 43

bols are employed for each variable in order to simplify the exposition.)

(1) NOPAT Expected net operating profit after taxes. This is

profits before financing costs, but after the provision for taxes to be paid on such profits, normalized to exclude temporary distortions, such as windfall gains or non- recurring losses. Thus NOPAT is equal to (1) the expected profit from operations multiplied by one minus the effective corporation income tax rate or equivalently, (2) bottom-line expected net profit after taxes, plus the after-tax interest expense, plus the current provision for deferred taxes. NOPAT is unaffected by financial leverage.

(2) I Expected new investment. This is the expected

amount of net fixed capital additions which will be required to produce the expected NOPAT. It may be defined as the amount by which the increase in total assets exceeds the increase in non-interest-bearing current liabilities-accruals and accounts payable.

(3) c The cost of capital for business risk. This is the

market's discount rate for NOPAT, if the company is unlevered (debt-free). It represents the rate of return investors could hope to earn through dividends and capital appreciation by investing elsewhere in the common shares of alternative, identically risky securities.

(4) tD The capitalized tax saving for interest-bearing debt,

the result of the tax deductibility of interest expense. It is equal to the marginal corporate income tax rate (t) multiplied by the amount of interest-bearing debt (D) in the market's estimate of management's target capital structure.

When a company employs interest-bearing debt as a source of financing, management's hurdle rate for new investments is the weighted average cost of debt and equity capital, which we denote by the symbol, c*.

(5) r The after-tax rate of return management is expected

to earn on new investment opportunities (Variable #2). For a single investment, the expected rate of return is the rate that discounts the expected future FCF back to the original cash outlay for the project. The firm's r is a weighted average of the expected rates of return for all expected projects.

(6) T The time horizon for which the market has confidence

that management can earn higher rates of return, r, on new investment, I, than the cost of capital c*.

If r is greater than c*, the firm is described as a "growth" company. Only growth companies can command high PE's, because only if r exceeds c* will management be capable of outperforming the expected returns investors could hope to earn elsewhere. It is for

management's unusual ability, which investors cannot duplicate, that the market is willing to pay a premium (i.e., a high PE). As we shall see, PE's can reach super- growth levels exceeding 30 only if I is large, the spread between r and c* is great and T is very long. Free Cash Flow (FCF)

Earlier, the market's attention was described as focusing on a firm's expected future FCF, not the expected future earnings (i.e., NOPAT) alone. As illustrated in an earlier example, two companies whose expected future NOPAT are identical will sell at different prices, if one of the companies requires less new capital (I) to achieve a given anticipated rate of growth in profits. This is because the market discounts expected NOPAT minus I, the FCF.t

FCF Growth Rate

Before illustrating the FCF model that describes market behavior, it may be helpful to describe the factors that account for the rate of growth in Free Cash Flow.

Since FCF is equal to NOPAT minus I, FCF's expected growth rate is a function of the rates of growth in NOPAT and I. NOPAT's expected growth rate is equal to the expected rate of return on incremental fixed capital (r) multiplied by the anticipated investment rate. The investment rate is the amount of incremental fixed capital (I) divided by NOPAT, I/NOPAT. It is the percentage of earnings invested in additional fixed capital.

Thus, if r is 15 per cent, NOPAT is $1 00,00 and I is $80,000, NOPAT would be expected to grow

Rate of Growth in NOPAT=(r)(N )'

-'015' ($ 80,000\ \$100,000!,

=(0.15) (0.80)

=0.12.

t The reason that NOPAT minus I is a cash flow item can be seen if we examine the components of I. Earlier, I was defined as net fixed capital additions, the increase in total assets minus the increase in non-interest-bearing current liabilities. An alternative, but equivalent, definition is capital expenditures on plant, equipment and other long-term investments minus depreciation (and other non-cash expenses, e.g., depletion expense) plus incremental working capital (i.e., the increase in current assets minus the increase in non-interest-bearing current liabilities). Hence, FCF is NOPAT plus depreciation-net operating cash flow-minus gross additions to fixed assets and incremental working capital. Thus, FCF is net operating cash flow that is free of capital requirements to sustain earnings growth.





12 per cent annually, if I/NOPAT of 80 per cent is expected to continue.

Most companies demonstrate a close relationship between the amount of fixed capital employed and the volume of sales. For example, paper manufacturers generally require a dollar of fixed capital to generate a dollar of sales. (However, the relationship between fixed capital and sales is usually closer for individual product lines than for the company as a whole.)

Thus there is likely to be a close relationship between incremental sales and incremental fixed capital (I). If this relationship is constant, and if the company's expected net operating profit margin (i.e., NOPAT divided by sales), is also constant, sales, NOPAT and I will grow at the same expected annual rate. And if NOPAT and I grow at the same rate, NOPAT minus I-FCF-will also grow at that rate. Consequently, for many companies, the market will expect sales, NOPAT, I and FCF to have identical expected growth rates.

FCF Model The FCF model synthesizes the six variables

into an analytical framework that describes the average behavior of intrinsic market values over time.

The model quantifies these market values by discounting the anticipated future FCF at the weighted average cost of capital (c*) in two steps. For a finite number of years (T), the expected rate of return (r) on new investment (I) may exceed the cost of capital (c*)-i.e., growth potential exists. Beyond T years, growth potential no longer exists, and r and c* are identical. Expansion (r = c*) replaces growth beginning in year T plus one, and this condition continues forever.

The existence of growth means that the discounted value of the expected future FCF is greater than the discounted value of a perpetual stream of profits (NOPAT) at the current level.

Diagram 1 illustrates the FCF model for our earlier example. For a finite time period (T years), r is expected to exceed c*. As indicated earlier, FCF is expected to grow at the same rate as NOPAT, I and sales. Beyond year T, say 15 years, the market expects growth to cease. Thenceforth r will equal c*, hence the company is only expanding.

FCF is positive beginning immediately, which means that the amount of incremental investment (I) is less than NOPAT. This pattern describes our earlier example, in which NOPAT was $100,000, I

was $80,000 and hence FCF was $20,000. Since r equals 15 per cent and the investment rate equals 80 per cent, NOPAT and FCF are expected to increase 12 per cent annually for T years. Beyond year T, growth ceases and r no longer exceeds c*. If c* is, say, ten per cent, the annual expected growth rates for NOPAT and FCF will decline at that point from twelve to eight per cent.

Rate of Growth=(r) ( IAT)

=(0.10) (0.80) =0.08.

Beyond year T, when r equals c*, the company is only expanding. Because the market can earn as much as the company simply by investing in alternative, identically-risky opportunities, expansion means that the market is indifferent between receiving cash dividends or having management invest in new projects. Thus the shape of the line beyond year T has no effect on a company's share price; r being equal to c*, the rate of expansion in FCF beyond year T is determined solely by the investment rate. Although a greater investment rate will result in a larger expected rate of expansion in FCF, it will add nothing to the share price.

Since the shape of the line beyond year T has no effect on the share price, we simplify the model considerably by assuming 100 per cent payout of earnings beyond year T. With the depreciation tax shield invested to maintain the plant, I is non- existent (i.e., the increase in total assets minus the increase in non-interest-bearing current liabilities is zero). Thus, beyond year T, NOPAT, FCF and sales are constant, and NOPAT and FCF are equal forever. This FCF model is shown in Diagram 2.

The pattern illustrated in Diagram 2 is only one of three possible variations-namely, the variation in which FCF is positive (NOPAT exceeds I). Oc- casionally the magnitudes of expected profits and new investment are equal, which means that FCF is equal to zero. Frequently the amount of new capital investment, I, is greater than the expected profits, NOPAT, and FCF is negative. In sum, FCF may be positive, zero or negative for a finite number of years (T) (i.e., NOPAT may be greater than, equal to or less than I, respectively).

Although zero and negative FCF present no additional difficulty in calculating a firm's intrinsic value, the distinction is important because the method for calculating the firm's value does differ slightly, but significantly, from the case of a positive FCF.

68 0 FINANCIAL ANALYSTS JOURNAL / JULY-AUGUST 1974



DIAGRAM #1. Positive FCF

(S thousands)

NOlp ?T0 gate)

100

lF Rsi00 Rate)

20

20

r exceedsc* T r equals c* 4 r= 15%, c*= .10 r= .10, c* =.10*

DIAGRAM #2. Positive FCF

($ thousands) Expected Free Cash Flow 0% Growth Rate (FCF) (FCF = NOPAT)

547.4

100

20

20

4-r exceeds c* l-4- -r equals c*--

If NOPAT today is $100,000 and T = 15 years, beginning in year 16 and continuing forever, FCF = NOPAT = $547,400, a result of today's NOPAT compounding 12 percent annually for 1 5 years.

Zero FCF When NOPAT and I are of the same magnitude,

the investment rate is 100 per cent and FCF is zero. Simultaneously, if r continues to be 15 per cent, sales, NOPAT and I will be expected to grow faster than in the case of the positive FCF, 15 per cent annually compared with the 12 per cent annual rate in our earlier example.

Rate of Growth =(r) (NOPAT)

=(0.15) (1.00)

=0.15.

Diagram 3 illustrates the model for zero FCF. FCF is zero until growth ceases. Thereafter NOPAT and FCF are equal in perpetuity. In the expansion period (beyond year T), FCF (or NOPAT) is much larger in this zero FCF case than in the first case when FCF was initially positive. This is because the initial NOPAT of $100,000 compounds at a faster rate (15 per cent versus 12 per cent) during the growth period. Furthermore, the resulting market value for our zero FCF example will be greater since relatively more investment opportunities are expected to earn 15 per cent.

Negative FCF When NOPAT is less than I, the investment rate

is greater than 100 per cent and FCF is negative. The negative magnitude of FCF becomes greater and greater until growth ceases. Concomitantly, if r remains at 15 per cent, sales, NOPAT and I will be expected to grow faster than the 12 per cent or 15 per cent rates cited in the two earlier cases when we had respectively a positive initial FCF and a zero initial FCF. If, for example, I is $120,000 when NOPAT is $100,000, the expected investment rate is 120 per cent and the annual expected growth rate of sales, NOPAT, and I is 18 per cent:

Rate of Growth=(r) (NOPAT)

=(0.15) (1.20)

=0.18. Diagram 4 shows the negative FCF. The initial

FCF is negative and becomes more negative still at the annual expected rate of 18 per cent until growth terminates in year T. Beginning in year T plus one, NOPAT and FCF are equal in perpetuity.

Because NOPAT compounds at the annual ex-




DIAGRAM #3. Zero FCF

(S thousands)

Expected 0% Growth Rate Free (FCF = NOPAT) Cash Flow 813.7 (FCF)

100-

FCF (0% Growth Rate)

4 - r exceeds c* - r equals c*-*

If NOPAT today is $100,000 and T = 15 years, beginning in year 1 6 and continuing forever, NOPAT = FCF = $813,700, a result of today's NOPAT compounding 1 5 percent annually for 1 5 years.

DIAGRAM #4. Negative FCF

($ thousands) 0% Growth Rate

Expected (FCF = NOPAT) Free 1,197.4 Cash Flow Ae>

(FCF)

100

r exceeds c* r equals c*_

-20

-239.5

If NOPAT today is $100,000 and T = 15 years, beginning in year 1 6 and continuing forever, NOPAT = FCF = S1,197,400, a result of today's NOPAT compounding 18 percent annually for 1 5 years. (Because of space limitations, Diagram #4 is half the scale size of Diagrams 1, 2 and 3.)

pected rate of 18 per cent, compared with the 12 per cent and the 15 per cent in the earlier cases, the perpetual stream of FCF (or NOPAT) is larger in this instance. Furthermore, the resulting market value in the case of the negative FCF exceeds the market value of the zero FCF case for the same reason that the market value of the zero FCF case exceeds the market value of the positive FCF case: There are more investment opportunities expected to earn 15 per cent.

Implementing The FCF Model

As noted in the foregoing examples, the FCF model consists of two distinct time frames: A finite period (T), during which "growth" may exist (i.e., during which the market expects management to undertake projects with expected rates of return (r) that exceed the cost of capital (c*) ); and a time frame that begins in year T plus one and continues in perpetuity (during which the market expects management to invest in projects earning only the cost of capital).

Hence it is convenient to obtain the discounted value of the expected future FCF in two steps: Discount anticipated FCF for the growth horizon, and then add the discounted value of the expected FCF for the period of expansion, after growth ceases. For this reason, we employ two tables to calculate a company's market value, a table for the growth horizon and a table for the period of expansion (Tables I and IL, respectively).

Although the length of the growth horizon (t) will vary for different companies, in the following example we assume that it is 15 years. Thus the title of Table I is the "Present Value of FCF For Years 1-15," and Table II covers the period of expansion, from year sixteen to eternity.

The value of T is a function of monetary policy, the degree of government regulation and cyclicality of a company's product line and the state of a firm's replaceable technology. The combined effect of an expansive monetary policy, a high degree of government regulation (e.g., banking, utilities), minimum cyclicality (e.g., food) and strong patent position (e.g., pharmaceuticals) will be T values of at least 15 years.

GS in Table I

The GS column running down the left-hand side of Table I presents a range of annual rates of growth (positive or negative) in FCF from zero to 25 per cent during the growth horizon. Since the FCF model assumes (for simplicity only) that the relationships between both NOPAT and sales and I and incremental sales are constant during the

70 D- FINANCIAL ANALYSTS JOURNAL / JULY-AUGUST 1974



TABLE 1. Present Value of FCF for Years 1-15

C*=.06 C*=.07 C*=.08 C*-.09 C*-.10 C*-.11 C*-.12 C*-.13 C*=.14 C*-.15 GS - .0 9.712 9.108 8.560 8.061 7.606 7.191 6.811 6.462 6.142 5.847 GS - .01 10.311 9.653 9.057 8.516 8.023 7.573 7.163 6.786 6.441 6.124 GS = .02 10.960 10.244 9.595 9.007 8.473 7.986 7.541 7.135 6.762 6.420 GS = .03 11.664 10.883 10.177 9.538 8.958 8.430 7.948. 7.509 7.107 6.738 GS = .04 12 426 11.575 10.807 10.111 9.481 8.909 8.387 7.912 7.477 7.079 GS = .05 13.254 12.325 11.488 10.731 10.046 9.425 8.860 8.345 7.875 7.445 GS - .06 14.151 13.138 12.225 11.402 10.657 9.982 9.369 8.812 8.303 7.839 GS = .07 15.125 14.019 13.024 12.127 11.317 10.584 9.919 9.314 8.764 8.262 GS =_.08 16.182 14.974 13.889 12.912 12.030 11.233 10.511 9.856 9.260 8.717 GS - .09 17.329 16.010 14.826 13.761 12.802 11.935 11.151 10.440 9.794 9.206 GS - .10 18.576 17.134 15.842 14.681 13.636 12.694 11.842 11.070 10.370 9.733 GS - .11 19.929 18.354 16.943 15.678 14.539 13.514 12.587 11.749 10.990 10.300 GS = .12 21.399 19.677 18.137 16.757 15.516 14.400 13.393 12.483 11.659 10.911 GS = .13 22.995 21.114 19.432 17.926 16.574 15.358 14.263 13.274 12.380 11.569 GS = .14 24.730 22.673 20.836 19.193 17.719 16.395 15.204 14.129 13.158 12.279 GS = .15 26.615 24.366 22.359 20.566 18.959 17.517 16.220 15.052 13.997 13.043 GS = .16 28.662 26.203 24.011 22.053 20.302 18.731 17.319 16.049 14.903 13.868 GS = .17 30.886 28.197 25.803 23.666 21.755 20.044 18.508 17.126 15.881 14.758 GS = .18 33.302 30.362 27.746 25.414 23.330 21.465 19.793 18.290 16.937 15.717 GS - .19 35.927 32.712 29.854 27.309 25.036 23.003 21.182 19.547 18.077 16.752 GS = .20 38.777 35.263 32.141 29.362 26.883 24.668 22.685 20.906 19.308 17.869 GS = .21 41.873 38.032 34.621 31.588 28.884 26.470 24.310 22.375 20.637 19.074 GS - .22 45.236 41.037 37.311 34.000 31.051 28.420 26.068 23.962 22.073 20.375 GS = .23 48.887 44.298 40.229 36.615 33.398 30.531 27.970 25.678 23.623 21.778 GS = .24 52.852 47.836 43.392 39.448 35.940 32.815 30.026 27.532 25.298 23.293 GS = .25 57.155 51.674 46.822 42.518 38.693 35.287 32.250 29.536 27.107 24.929

TABLE 11. Present Value of FCF = NOPAT for Years 16 - Forever

C*-.06 C*-.07 C*=.08 C*-.09 C*-.10 C*-.11 C*-.12 C*-.13 C*=.14 C*-.15 GS = .0 6.954 5.178 3.940 3.050 2.394 1.900 1.522 1.230 1.001 0.819 GS = .01 7.994 5.952 4.529 3.506 2.752 2.184 1.750 1.414 1.150 0.942 GS = .02 9.176 6.832 5.199 4.025 3.159 2.507 2.009 1.623 1.320 1.081 GS = .03 10.519 7.832 5.960 4.614 3.621 2.874 2.303 1.860 1.514 1.239 GS = .04 12.043 8.966 6.824 5.282 4.145 3.290 2.636 2.130 1.733 1.419 GS = .05 13.769 10.251 7.802 6.039 4.740 3.762 3.014 2.435 1.981 1.622 GS = .06 15.723 11.706 8.909 6.897 5.412 4.296 3.442 2.781 2.262 1.852 GS = .07 17.932 13.351 10.161 7.865 6.173 4.899 3.926 3.171 2.580 2.113 GS = .08 20.426 15.208 11.574 8.959 7.031 5.581 4.472 3.612 2.939 2.406 GS = .09 23.239 17.302 13.168 10.193 8.000 6.349 5.088 4.110 3.344 2.738 GS = .10 26.409 19.662 14.964 11.584 9.091 7.215 5.781 4.670 3.800 3.111 GS = .11 29.976 22.318 16.985 13.148 10.319 8.190 6.562 5.301 4.313 3.531 GS = .12 33.986 25.304 19.258 14.907 11.699 9.286 7.440 6.011 4.890 4.004 GS = .13 38.490 28.657 21.809 16.883 13.249 10.516 8.426 6.807 5.538 4.534 GS = .14 43.543 32.419 24.672 19.099 14.989 11.897 9.533 7.701 6.265 5.130 GS = .15 49.206 36.636 27.882 21.583 16.938 13.444 10.772 8.702 7.080 5.797 GS = .16 55.548 41.357 31.475 24.365 19.121 15.176 12.161 9.824 7.993 6.544 GS = .17 62.640 46.638 35.493 27.476 21.563 17.114 13.713 11.078 9.013 7.380 GS = .18 70.567 52.539 39.985 30.953 24.291 19.280 15.449 12.480 10.154 8.313 GS - .19 79.416 59.128 44.999 34.834 27.337 21.698 17.386 14.045 11.427 9.356 GS = .20 89.288 66.478 50.592 39.164 30.735 24.395 19.547 15.791 12.848 10.519 GS = .21 100.287 74.667 56.825 43.989 34.522 27.400 21.955 17.736 14.430 11.815 GS - .22 1 12.535 83.787 63.765 49.361 38.738 30.746 24.636 19.902 16.193 13.258 GS -.23 126.161 93.931 71 .486 55.338 43.428 34.469 27.619 22.312 18.153 14.863 GS - .24 141.305 105.206 80.067 61.980 48.641 38.606 30.935 24.990 20.332 16.647

GS -

.25 158.121 117.727 89.595 69.357 54.430 43.201 34.616 27.964 22.752 18.628




growth horizon, (when NOPAT exceeds I and FCF is thus positive) sales, NOPAT, I and hence FCF are all expected to grow at the same annual rate. Consequently, when FCF is positive, the GS column depicts the annual expected future rates of growth in sales, NOPAT and I, but, most important, it is also the annual expected rate of growth in FCF.

When NOPAT equals I during the growth horizon, Table I is not employed in the valuation calculation, because FCF (i.e., NOPAT minus I) is equal to zero in each year.

If NOPAT is less than I, FCF is negative. In this case, GS refers to the annual rate of growth in sales, NOPAT and I and the annual rate of decline in FCF.

GS in Table II While there is no growth beyond year 15 (i.e.,

beyond year T), it is necessary to refer to the same growth rate used in Table I to obtain the correct value of FCF (and NOPAT) in T plus one and subsequent years.

c* in Both Tables Across the top of both tables are various rates

for discounting the expected future FCF, ranging from six to fifteen per cent. The discount rate used is the weighted average cost of debt and equity capital (c*). c* may be calculated from the ex- pression

c *=c ( D1-t A ) where,

c=the cost of capital for business risk,

t=the marginal corporate income tax rate,

D AF=the target debt ratio expressed in terms of

interest-bearing debt as a percentage of total capital employed.

For example, if c=0.10, t=0.50 and D/AF=0.40, then c*=0.08. A Year Hence

Before the FCF model is applied to specific examples, it is important to note that the valuation tables are designed to utilize the expected amounts of FCF and NOPAT a year hence, not the current amounts. The fair market values obtained, however, are current values. The reason for this re- quirement is that FCF and NOPAT must be normalized for non-recurring windfall gains and ex- traordinary losses. Such normalized results are

more apt to be obtained if the current amounts of FCF and NOPAT are discarded and next year's magnitudes are estimated.

Valuation Process In summary, our FCF tables accomplish two

steps simultaneously. First, they calculate the future values of FCF by compounding next year's estimated normalized FCF at the expected annual rate of growth in sales (GS) imputed by the user. Second, they discount these future FCF amounts at the weighted average cost of capital (c*) to obtain the present value.

If the expected net operating profit margin and capital requirements do not conform to the assumptions upon which our tables have been con- structed, the amounts of expected FCF for each year of the growth horizon (i.e., years one through T) can be discounted separately at c* and the perpetual amount of expected FCF beginning in year T plus one can be discounted back to the present.

Since Tables I and II, like most annuity and mortgage tables, are scaled to one dollar of cash flow, the factors in the tables must be multiplied by the normalized amount of FCF in order to obtain the firm's market value. Thus the first step in using the tables is to multiply next year's FCF by the ap- propriate factor in Table I. The result is the discounted value of the expected future FCF for years one through fifteen (i.e., through year T). Second is to multiply next year's NOPAT by the proper factor in Table II. The result is the discounted value of the expected future FCF beginning in year 16 (year T plus one) and continuing forever. The figures thus obtained from the two tables are added to obtain the current fair market value of the firm. It is important to note that the market value obtained is that of the firm's debt and equity combined.

We have noted that c* is a function of the market's estimate of management's target ratio of interest-bearing debt to fixed capital. When this ratio is multiplied by the current level of fixed capital, the result is the normalized current level of interest-bearing debt. When this amount is subtracted from the fair market value of the debt and equity, the remainder is an estimate of what the current fair market value of the equity would be if the actual debt ratio were equal to the target ratio.

Hypothetical Examples It may be helpful to illustrate how the model is

used by working out valuations for each of the three cases that were used to show the positive,

72 0 FINANCIAL ANALYSTS JOURNAL / JULY-AUGUST 1974



TABLE Ill. Hypothetical Examples

Positive FCF Zero FCF Negative FCF

(1) Current Normalized NOPAT $100,000 $100,000 $100,000 (2) Current Expected I 80,000 100,000 120,000 (3) Current Normalized FCF: (1)-(2) 20,000 0 -20,000 (4) GS 12% 15% 18% (5) Next Year's Expected NOPAT 112,000 115,000 118,000 (6) Next Year's Expected I 89,600 115,000 141,600 (7) Next Year's Expected FCF: (5)-(6) 22,400 0 -23,600 (8) Factor From Table I 15.516 18.959 23.330 (9) Factor From Table II 11.699 16.938 24.291 (10) Expected FCF Times Factor

From Table l: (7)x(8) 347,500 0 -550,600 (11) Expected NOPAT Times Factor

From Table Il: (5)x(9) 1,310,300 1,947,900 2,866,300

(12) Total Fair Market Value (10)+(11) 1,657,800 1,947,900 2,315,700

zero and negative FCF situations (see Table III). For each case we assume that c* is ten per cent and T is 15 years. The valuations are performed in Table III with the results presented on line 12.

If no interest-bearing debt was assumed in the company's target capital structure, hence in the calculation of c*, the amounts on line 12 of Table III are the fair market values of the equity, NOPAT is equal to bottom-line profits, net profit after taxes, and the fair PE's are respectively 16.6, 19.5, and 23.2 (i.e, the total fair market values divided by current profits of $100,000).

When interest-bearing debt is assumed in arriving at c*, two extra steps are required in calculating the PE: First, the implied level of interest-bearing debt must be subtracted from the total fair market value to obtain the equity value. Second, the amount of after-tax interest expense must be subtracted from NOPAT to obtain the bottom-line figure. The PE is obtained by dividing the equity value by the net profit after taxes.

Real-World Applications Because the FCF model contains the six

variables that are the systematic determinants of a firm's intrinsic market value, the model's most important applications are in security analysis and corporate financial planning.

For top management, the model makes explicit the role that risk (c) plays in the determination of share prices, provides an understanding of the distinction between "growth" and "expansion," and assists management in setting goals that will benefit the common shareholders. Middle manage-

ment will understand why the goals are important and how to implement them. The model also has implications for financial reporting because it focuses on the elements of most concern to sophisticated investors.

In particular, the FCF model suggests that corporate management should report: - the extent of unusual profits or losses so that in-

vestors can normalize earnings (NOPAT); - capital spending forecasts including working capital

needs over the next three to five years (I); - the expected concentration of the firm's fixed capital

by product lines so that the market can better evaluate business risk (c);

- the target ratio of interest-bearing debt to fixed capital (tD) because debt is cheaper than equity;

- the rate of internal growth in NOPAT so that the ef- fects of arbitrary accounting of acquisitions, which do not alter FCF or market value, are not permitted to mislead the market.

Management should never forget that the market exacts a discount for uncertainty, not a premium.

Three Key Advantages The form of the FCF model provides three key

advantages to security analysts and top management that are absent in traditional investment analysis.

First, the model separates corporate investment decisions from financing policy. Consequently, poor quality projects do not appear to be desirable because of the way in which they are financed.

Second, the analyst or corporate planner can test the sensitivity of his assumptions about the firm's risk and expected profitability by varying the fac-





tors that affect the value of a decision. Third, and perhaps most important, because the

variables in the model are the primary determinants of share price, he can simulate the impact of decisions on the firm's share price before the decisions are implemented.

Investment vs. Financing Separating investment decisions from financing

policy is one of the most important principles in corporate finance. Too often, however, specific sources of funds are apparently identified with specific uses of funds. Thus projects with low expected rates of return are ofttimes undertaken when low cost debt is available, which if deferred until a year when high cost equity financing were required, would probably be rejected. The management committing this fallacy fails to recognize that debt financing requires underlying equity to maintain management's target capital structure, to maintain the expected ratio of interest-bearing debt to fixed capital. The vital question is whether the expected rate of return on the project will equal or exceed the company's weighted average cost of capital.

Ironically, many who claim that they avoid the specific source-specific use problem are the most ardent supporters of assessing the impact of investment decisions in terms of their firm's EPS, even though EPS requires specific sources and uses of funds to be pinpointed. EPS is equal to bottom- line profits divided by the average number of shares outstanding. And since bottom-line profits are obtained by subtracting the after-tax cost of debt financing from NOPAT, evaluating proposed prospects by examining their impact on EPS automatically necessitates identifying the sources of funds.

The FCF model completely separates investment decisions from financing policies. NOPAT and I, the determinants of FCF, are completely independent of financing policy. NOPAT is profit before financing costs but after the provision for taxes to be paid. I is the increase in total fixed capital employed, including all interest-bearing debt, reserves and shareholders' equity.

Long-run financing policy affects the discount rate for the expected future FCF. The discount rate is the weighted average cost of capital (c*) which is a function of the cost of capital for business risk (c) and the capitalized tax saving from debt financing (tD). The tax saving is based on the amount of interest-bearing debt in the firm's target capital structure.

The only aspect of financing policy that systematically affects a firm's share price is the target debt ratio. The target debt ratio is the frac- tion of total fixed capital that management expects to finance with interest-bearing debt on average and over time. Since this ratio expresses the long- run relationship, specific sources of funds are never identified with specific uses.

Sensitivity Because the determinants and interrelationships

of each of the six variables can be identified, analysts and management can test the sensitivity of their assumptions about proposed and announced corporate policies, respectively.

For example, since the cost of capital, c*, discounts the entire expected future stream of FCF, altering c* can have a pronounced impact on a firm's share price because each future year's FCF is affected. In our earlier calculations, we assumed that c* was ten per cent. If we assume that an an- nouncement by management of a 20 percentage point increase in the company's target debt ratio drops c* to nine per cent and that the magnitudes of the other variables remain the same, the resulting fair market values for our three hypothetical examples would increase 23, 27 and 32 per cent, respectively. The greater I, r and T are, the greater is the expected future FCF, hence the greater in turn the impact on a company's fair market value of a change in c*.

Simulation The merits of virtually all financing vehicles can

be evaluated in terms of their impact on the company's market value, including those involving leasing financing, share repurchase, call options, captive finance companies, convertible securities, warrants and many others.

Acquisitions can also be evaluated within the FCF. To price an acquisition, the prospective buyer must estimate each of the six variables giving effect to any anticipated operating and financial synergism. The resulting fair market value is the maximum price (MP) the buyer can afford to pay for the seller's total fixed capital: interest-bearing debt, plus preferred and common shareholders' equity.

If the buyer pays less than MP, the difference between MP and the price paid is the amount the market will be expected to add to the aggregate market value of the buyer's shares. Conversely, if the price paid by the buyer exceeds MP, the difference between the price paid and MP is the




amount the market will be expected to subtract from the aggregate market value of the buyer's common shares.

The FCF model can also be used in reverse. In acquisition pricing, for example, given the seller's desired price, the buyer's management can estimate the required rate of internal growth in profits necessary to justify the price without shortchanging the buyer's shareholders. Any of the six variables can be employed this way.

Conclusion That EPS is easy to understand and simple to

calculate is an insufficient excuse fo- employing it as an analytical device. An EPS criterion for corporate policy can result in costly decisions that severely misallocate a company's resources and shortchange the firm's common shareholders. Sophisticated investors, who dominate the market, focus their attention on FCF. EPS doesn't count! .

amount the market will be expected to subtract from the aggregate market value of the buyer's common shares.

The FCF model can also be used in reverse. In acquisition pricing, for example, given the seller's desired price, the buyer's management can estimate the required rate of internal growth in profits necessary to justify the price without shortchanging the buyer's shareholders. Any of the six variables can be employed this way.

Conclusion That EPS is easy to understand and simple to

calculate is an insufficient excuse fo- employing it as an analytical device. An EPS criterion for corporate policy can result in costly decisions that severely misallocate a company's resources and shortchange the firm's common shareholders. Sophisticated investors, who dominate the market, focus their attention on FCF. EPS doesn't count! .

The new performance concluded from page 60

return, such as 12 or 15 per cent, could impact on individuals' spending patterns, and many corporate treasurers began to believe that the return earned on their pension funds could be considered a profit center with a meaningful impact on the company's earnings per share.

During this period, the analysis of performance focused largely on possible rate of return with less emphasis on the concomitant factor of risk. Beta factors were used to.capitalize on volatility rather than to avoid it. However, since 1969, some investors have discovered that risk matters more to them than they believed previously. The stock market simply has not offered the returns that many had expected would be possible. Rate-of- return expectations and, therefore, rate-of-return goals are coming down and risk preference is changing toward lower risk exposure. Consistency of earnings performance appears to be more important than high levels of earnings per share

The new performance concluded from page 60

return, such as 12 or 15 per cent, could impact on individuals' spending patterns, and many corporate treasurers began to believe that the return earned on their pension funds could be considered a profit center with a meaningful impact on the company's earnings per share.

During this period, the analysis of performance focused largely on possible rate of return with less emphasis on the concomitant factor of risk. Beta factors were used to.capitalize on volatility rather than to avoid it. However, since 1969, some investors have discovered that risk matters more to them than they believed previously. The stock market simply has not offered the returns that many had expected would be possible. Rate-of- return expectations and, therefore, rate-of-return goals are coming down and risk preference is changing toward lower risk exposure. Consistency of earnings performance appears to be more important than high levels of earnings per share

growth. Second-tier stocks are approached cautiously. Third-tier stocks are ignored. Bonds seem to make some sense, but they too are subject to risk-interest rate risk.

An investor is now more cautious about setting a rate-of-return objective on a variable basis related to a market average. That is to say, he is now more conscious of absolute rates of return. A return ten per cent better than the market is not of much value in a period when the market is down sub- stantially and he still has fixed requirements to pay out of the total return earned in that year.

In fact, investor attitudes toward performance have changed. There is a preference for less risk of variance even if it means a lower return. The new attitude is forcing equity prices down to the point where they offer a premium adequate to attract investor interest. One might argue that the new attitude towards performance is merely the result of recent market conditions and that it will reverse itself if subsequent market experience is more en- couraging. In recent years, however, bond and money market yields have doubled, price-earnings ratios have fallen and the investor is as yet unable to foresee any meaningful increase in the earning power of the reinvested earnings.

At their current price-earnings ratios, some of the popular stocks may still seem to be discounting a far distant future. On the other hand, the earnings prospects of the unloved mass of other stocks in the coming period are still quite uncertain. Rather than waiting for a stock market fashion to develop, some investors are accepting a fixed return to maturity (or call date) in a debt security for a portion of their portfolios. The risk in so doing is that, if inflation expectations accelerate, interest rates may rise in the 1970's as they did in the 1960's. If this happens, it is not clear that common stocks will perform well, or, if so, which stocks will perform well in an economic scenario that the U.S. has never experienced before. The new concept of performance may involve an at- tempt at risk management rather than rate-of- return management and it leads to a balanced investment strategy conscious of a wide range of investment vehicles. a

growth. Second-tier stocks are approached cautiously. Third-tier stocks are ignored. Bonds seem to make some sense, but they too are subject to risk-interest rate risk.

An investor is now more cautious about setting a rate-of-return objective on a variable basis related to a market average. That is to say, he is now more conscious of absolute rates of return. A return ten per cent better than the market is not of much value in a period when the market is down sub- stantially and he still has fixed requirements to pay out of the total return earned in that year.

In fact, investor attitudes toward performance have changed. There is a preference for less risk of variance even if it means a lower return. The new attitude is forcing equity prices down to the point where they offer a premium adequate to attract investor interest. One might argue that the new attitude towards performance is merely the result of recent market conditions and that it will reverse itself if subsequent market experience is more en- couraging. In recent years, however, bond and money market yields have doubled, price-earnings ratios have fallen and the investor is as yet unable to foresee any meaningful increase in the earning power of the reinvested earnings.

At their current price-earnings ratios, some of the popular stocks may still seem to be discounting a far distant future. On the other hand, the earnings prospects of the unloved mass of other stocks in the coming period are still quite uncertain. Rather than waiting for a stock market fashion to develop, some investors are accepting a fixed return to maturity (or call date) in a debt security for a portion of their portfolios. The risk in so doing is that, if inflation expectations accelerate, interest rates may rise in the 1970's as they did in the 1960's. If this happens, it is not clear that common stocks will perform well, or, if so, which stocks will perform well in an economic scenario that the U.S. has never experienced before. The new concept of performance may involve an at- tempt at risk management rather than rate-of- return management and it leads to a balanced investment strategy conscious of a wide range of investment vehicles. a

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Reprints of articles published in the Journal are available at a nominal cost. Payment must accompany orders of $10 or less. Address your requests to Reprint Dept., Financial Analvsts Journal, 219 East 42nd Street, New York, N. Y. 10017 / (212) 687-3882.




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