Do Accounting Earnings or Free Cash Flows Provide a Better Estimate of Capital Gain Rates of Return on Stocks? James A. Gentry

David T. Whitford

University of Illinois at Urbana−Champaign

University of Illinois at Urbana−Champaign

Theodore Sougiannis

Shigeo Aoki

University of Illinois at Urbana−Champaign

Toyko International University

Abstract There are two widely accepted approaches used to estimate the market value of a firm’s equity (Vs). The accounting approach assumes the estimated Vs is based on the discounted value of a firm’s future net income stream (NI). A finance model assumes that the value of a firm’s stock (Vs) is related to the performance of its discounted future free cash flows to equity (FCFE). The motivation of this paper is to discover whether the accounting earnings approach or the finance FCFE approach provides a better explanation for estimating the capital gain rates of return on American and Japanese equities. Three sets of hypotheses were developed and regression analysis was used to test the hypothesized relationships. Financial data from a large sample of American and Japanese companies provided the information for testing the hypotheses. The regression results found a strong statistical relationship existed between net earrnings and capital gain rates of return for both American and Japanese companies. However, the Fama−MacBeth t value was only significant for the Japanese data, which cast doubt on the predictability of the net earnings approach based on American data. The study found the free cash flow to equity measure was not closely related to the capital gain rates of return for either the American or Japanese companies. However, a strong relationship was discovered to exits between the capital gain rates of return and the cash flow associated with operations, interest and financing for the American companies. Cash flows related to net investment and working captial were not consistently related to the capital gain returns for American and Japanese companies.

The authors are very grateful to CIBER for the support provided that made the completion of this research project possible. Published: 2002 URL: http://www.business.uiuc.edu/Working_Papers/papers/02−0111.pdf

DO ACCOUNTING EARNINGS OR FREE CASH FLOWS PROVIDE A BETTER ESTIMATE OF CAPITAL GAIN RATES OF RETURN ON STOCKS?

James A. Gentry IBE Distinguished Professor of Finance University of Illinois, Urbana-Champaign [email protected] David T. Whitford Associate Professor of Finance University of Illinois, Urbana-Champaign [email protected] Theodore Sougiannis Associate Professor of Accountancy University of Illinois, Urbana-Champaign [email protected] Shigeo Aoki Professor of Accounting Tokyo International University [email protected]

2002 FMA European Conference Copenhagen June 6, 2002

The authors are very grateful to CIBER for the support provided that made the completition of this reseach project possible.

ABSTRACT There are two widely accepted approaches used to estimate the market value of a firm’s equity (Vs). The accounting approach assumes the estimated Vs is based on the discounted value of a firm’s future net income stream (NI). A finance model assumes that the value of a firm’s stock (Vs) is related to the performance of its discounted future free cash flows to equity (FCFE). The motivation of this paper is to discover whether the accounting earnings approach or the finance FCFE approach provides a better explanation for estimating the capital gain rates of return on American and Japanese equities. Three sets of hypotheses were developed and regression analysis was used to test the hypothesized relationships. Financial data from a large sample of American and Japanese companies provided the information for testing the hypotheses. The regression results found a strong statistical relationship existed between net earrnings and capital gain rates of return for both American and Japanese companies. However, the Fama-MacBeth t value was only significant for the Japanese data, which cast doubt on the predictability of the net earnings approach based on American data. The study found the free cash flow to equity measure was not closely related to the capital gain rates of return for either the American or Japanese companies. However, a strong relationship was discovered to exits between the capital gain rates of return and the cash flow associated with operations, interest and financing for the American companies. Cash flows related to net investment and working captial were not consistently related to the capital gain returns for American and Japanese companies.

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DO ACCOUNTING EARNINGS OR FREE CASH FLOWS PROVIDE A BETTER ESTIMATE OF THE CAPITAL GAIN RATES OF RETURN ON STOCKS?* There are two widely accepted approaches used to estimate the market value of a firm’s equity (Vs). The accounting approach assumes the estimated Vs is based on the discounted value of a firm’s future net income stream (NI), where the difference between earnings and free cash flow is the sum of its accrual accounts. Penman and Sougiannis (1998) found that forecasted GAAP accrual earnings of American companies generate lower valuation errors than those based on forecasted cash flows. A finance model assumes that the value of a firm’s stock (Vs) is related to the performance of its discounted future free cash flows to equity (FCFE), Rappaport (1998), Heckel and Livnat (1992), Brealey and Myers (1999) and Damodaran (2001). The motivation of the study is to discover whether the accounting earnings approach or the finance FCFE approach provides a better explanation for estimating the capital gain rates of return on American and Japanese equities. There may be differences in earnings and cash flows because of alternative accounting systems within the two countries. Also there are numerous other reasons that could affect the outcomes in the study, such as differences in corporate cultures, structure, strategies, objectives, size and managerial styles. There are multiple objectives for the study. The relevant literature for this academic debate is developed in Section I. The hypotheses and the regression models used to test the hypothesized relationships are presented in Section II. Section III provides an interpretation of the underlying financial information used to test the hypotheses. Section IV provides an analysis of the regression coefficients that measure the relationships between the market rates of return (r) on American and Japanese common stocks and their FCFE, NI, SIZE and Book / Market ratios, respectively. An analysis of the regression coefficients that measure the relationships between the same market rates of return (r) and the FCFE components, NI components, SIZE and Book / Market ratios is found in Section V. The conclusions are found in Section VI. I. LITERATURE REVIEW In recent years research has attempted to provide empirical evidence on the relative performance of free cash flow and earnings based valuation techniques. Kaplan and Ruback (1995) examine the performance of discounted free cash flow techniques in the valuation of management buyouts and leveraged recapitalizations. They report results indicating that free cash flow techniques perform at least as well as valuation techniques using comparable firms and transactions. However, they do not compare free cash flow techniques to earnings techniques. Penman and Sougiannis (P&S) (1998) are the first to make this comparison. Their valuations are based on average ex post free cash flows and earnings. They find that earnings techniques consistently outperform cash flow techniques over alternative forecast horizons. Their analysis concludes that the primary superiority of earnings techniques occurs for two reasons. First, the free cash flow technique expenses the anticipated investment, while the earnings approach *

We are grateful to the Center for International Business Education and Research (CIBER) for their financial support of this project. We are also very appreciative for the research assistance provided by Taie Wang, a doctoral student in the Department of Finance.

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capitalizes it. Second, the earnings technique recognizes non-cash (accrual) value changes. These two features of the earnings technique “bring the future forward in time”. Thus in estimating the value of a firm the earnings forecasts requires a shorter horizon vis-a-vis free cash flows. The ex post based results of Penman and Sougiannis (P&S) appear to be robust. Francis et al. (2000) confirm the P&S results by using ex ante Value Line forecasts for earnings and cash flows. Given the results of these two studies, research attention has recently concentrated on the specification of terminal value calculations for each technique. Thus Penman (1997) derives theoretically “ideal” terminal value expressions that make the earnings and free cash flow techniques equivalent over a given forecast horizon. Using Value Line forecasts Claude et al. (2000) present additional empirical support on the ability of these terminal values to make the two techniques equivalent. Hackel and Livnat (HL)(1992, p. 6) believe that free cash flows are superior to the earning approach for several reasons. For example, they indicate that earnings are subject to managerial discretion, such as having some latitude in applying accounting standards to their specific situation. That is, firms may have different approaches to revenue recognition, expense recognition and the allocation of costs across periods. Additionally, HL state that free cash flows are not affected by choice of accounting methods and are unaffected by managerial discretion with respect to real cash expenditures. Also Hackel and Livnat (1992, pp. 138-149) discuss the limitations in earnings reports in general and develop specific shortcomings of the earning approach for investment purposes. For example, accrual accounting requires estimation of depreciation expense for a period. Firms estimate the depreciation expense by predicting the useful lives of depreciable assets and their salvage values. These estimates can contain errors and furthermore, when firms update their estimates of useful lives of fixed assets the result can be an increase or decrease in earnings. Throughout the book, HL make the case that for the purposes of investment analysis and management, free cash flows are preferable to earnings. II.

HYPOTHESES AND REGRESSIONS

Hypothesis 1 The first set of hypotheses is that free cash flows to equity (FCFE) provide a more accurate estimate of equity market rates of return (r) than accounting earnings (NI). Because the study uses financial data for American and Japanese companies, the first hypothesis uses four regression equations to test the relationships empirically. Equations 1 and 2 test the relationship that the cumulative free cash flow to equity (FCFE) per share / initial stock price of American and Japanese companies is significantly related to the stock’s market rates of return (rij). The equations used throughout this paper reflect the methodology presented in Penman and Sougiannis (1998). Equations 1 and 2, plus an explanation of the variables are below: 5

rij = a1 + b1 ∑ FCFEij/Pi0 + e

(1)

j=0

3

[American Company data]

5

rij = a2 + b2 ∑ FCFEij/Pi0 + e

(2)

[Japanese Company data]

j=0

Where: rij = [Pij – Pi0]/Pi0, where j represents a five year window. and Pij = Ending Market Price of ith stock for the jth period, and Pi0 = Beginning Market Price of the ith stock in period zero of the jth period. FCFEij/P0 = [(NOFij + NIFij + NWCij + INTij + PFDDIVij + NFFij)/P0]/SHARES. FCFEij/P0 equals the sum of the preceding six components for the ith stock in the jth time period divided by P0, that are, in turn, divided by the weighted number of shares outstanding for the ith stock in the jth period, (SHARESij), Penman and Sougiannis (1998), Appendix I, pp. 378-379. Hereafter, the FCFEij/P0 will be referred to as free cash flow per share. NOFij = Sales ij – [CGSij – Depreciationij] – SGAij – Taxesij for the ith company in jth time period, where CGSij, SGAij and Taxesij are outflows. NOF is normally a major cash inflow, that is reflected as a positive sign. NIFij = δ NFA + Depreciation Expense. Where δ reflect a change in net fixed assets between two time periods. NIF is usually an outflow component, which means it carries a minus sign. NWCij = δ ARij + δ INVij + δ OCAij + δ APij and δ OCLij, where an outflow is reflected as a minus sign (-) and an inflow is reflected with a (+) sign. The working capital components can be either an inflow or an outflow. Cash and Notes Payable are not included in the definition of NWCij. INTij = net interest: INTij is usually an outflow, but it can represent a cash inflow. PFDDIVij = preferred dividends for the ith company and in the jth time period and is always an outflow. NFFij = a new issue of short and/or long-term interest bearing debt, δNFFij, is added to the FCFEij or a reduction in short and/or long-term debt, δNFFij, is subtracted from the FCFEij. NFFij represents net changes in debt financing in the jth year. Regressions 3 and 4 test the relationships between the cumulative net income (NI) per share / initial stock price and market rates of return (rij) on American and Japanese companies, respectively. The equations for regressions 3 and 4 are: 5

rij = a3 + b1 ∑ [NIij - PFDDIVij]/Pi0 + e 0

4

(3)

[American Company data]

5

rij = a4 + b2 ∑ [NIij – PFDDIVij]/Pi0 + e

(4)

[Japanese Company data]

0

Where: (NIij – PFDDIVij)/Pi0 = [(Net Income – Preferred Dividends)/Pi0]/SHARES, hereafter referred to as net income per share. See explanation of FCFEij/P0 in equations 1&2. Pi0 = Closing Market Price of ith company in period zero. Hypothesis 2 The second hypothesis is an extension of the first. Prior research has shown that there is a negative relationship between the rate of return (rij) and the size of a firm’s stock value (ln SIZE), referred to as the small firm effect. Also previous studies indicate there is a positive relationship between rij and a firm’s book/market (B/M) ratio. The B/M ratio is a proxy for a firm’s cost of equity capital. Because size (ln SIZE) and book/market (B/M) measures, can be significantly related to the rate of return on a company’s stock (rij), they are included in the analysis and are presented in equations 5-8. The second hypothesis is that the addition of a SIZE and a B/M measures will increase the number of significant FCFE and NI coefficients found in Table 11. The dependent variable in regressions 5 and 6 is the capital gain rates of return (rij) on American and Japanese companies, respectively, and the independent variables are free cash flow per share (FCFE), plus ln SIZE and B/M at the beginning of the five-year period. Equations 5 and 6 are presented below along with a definition of the components. 5

rij = a5 + b5 ∑ FCFE ij/Pi0 + b6 ln SIZEi0 + b7 Bi0/Mi0

(5) [American Company data]

j=0 5

rij = a6 + b8 ∑ FCFEij/Pi0 + b9 ln SIZEi0 + b10 Bi0/Mi0

(6) [Japanese Company data]

j=0

Where: FCFEij / Pi0 = definition, presented in equations (1) and (2) ln SIZEij = natural log of the price of the ith stock at the beginning of the jth period times the number of shares outstanding in time period zero, Bi0 / Mi0 =

Book Value Per Share of the ith stock in time period zero / Market Value Per Share (M) of the ith stock in time period zero. M = Pij times number of shares outstanding.

Regression 7 utilizes rij and net income per share (NI) for American companies, plus the natural log (ln) of SIZE and B/M ratios for American companies and regression 8 uses comparable data for Japanese companies. The equations for regressions 7 and 8 are:

5

5

Rij = a7 + b11 ∑ [NIij – PFDDIVij]/Pi0 + b12 ln SIZEi0 + b13 Bi0Mi0 + e

(7)

j=0 5

Rij = a8 + b10 ∑ [NIij – PFDDIVij]/Pi0 + b15 ln SIZEi0 + b16 Bi0/Mi0

(8)

j=0

Where:

[NIij - PFDDIVij] is defined in equations 3 and 4 Pi0 is defined in regression 3 and 4.

Hypothesis 3 The third hypothesis incorporates the specific components associated with FCFE and NI. Thus, it is hypothesized that the six components of FCFE, plus ln SIZE and B/M ratios, provide a more accurate estimate of capital gain rates of return (rij) than the two components of NI, plus ln SIZE and B/M ratios for American and Japanese companies. Regression 9 uses rij as the dependent variable and the six components of FCFE, ln SIZE and B/M as independent measures. The six measures of FCFE are net operating flows (NOF), net investment flows (NIF), net working capital flows (NWC), interest (INT), preferred dividends (PFDDIV) and net financing flows (NFF). Equation 9a uses data from American companies and equation 9b utilizes data from Japanese companies. The equation for regression 9a and 9b is: Rij = a9 + b17 NOFij/Pi0 + b18 NIF/Pi0 + b19 δ NWCij/Pi0 – b20 INTij/Pi0 + b21 PFDDIVij/Pi0 + b22 NFFij + b23 ln SIZEi0 + b24 Bi0/Mi0 + e

(9a and 9b)

The components of FCFE were defined in equation 1 and the size and B/M ratio are defined in equations 5 and 6. Equation 10a and 10b use rij as the dependent variable and the two components of NI as independent variables for American and Japanese companies, respectively. The two components of NI are net operating cash flow (NOCF) and accruals (ACC). They are defined in equation 10. The equation for regression 10a and 10b is: 5

Rij = a10 + b25 ∑ NOCFij / Pi0 + b26 j=0

5

∑

ACCFij/Pi0 + b27 ln SIZEi0 + b28 Bio/Mi0 + e

j=0

(10a and 10 b) Where: NOCFij/P0 = [(SALESij – ((CGS–Depreciation)) – SGAij + δ NWCij + INTij + PFDDIVij )/Pi0 + NFFij/P0]/ SHARESij. ACCFij/P0 = [(NIij – PFDDIVij)/P0] / SHARESij – [(NOCFij)/P0] / SHARESij. The objectives of the analysis are to test each hypothesis and interpret the regressions

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results, namely the coefficients, R-squares, and F-M t-values. The analysis compares the regression results of the American and Japanese data. III. ANALYSIS An Overview of Financial Data The objective of Section III is to interpret the regression results associated with each hypothesis. The American data were acquired from the Compustat data base, and the Japanese data were obtained from the Nikkei data base. The American data in Table 1 covers 14 five-year periods from 1981-85 to 1994-98 and one four year period--1995-99. For simplicity it is assumed the 1995-99 represents a non-overlapping period. In total the data represent 19 years of non-overlapping data. The Japanese data found in Table 2 represent 9 five-year windows from 1985-90 to 1994-98 and one four year period—1995-99. Each five-year window presents the mean, median and standard deviation for the each independent variable. The sample size of the American companies ranged from 881 to 1034, while the Japanese sample ranged from 166 to 365. The sample companies included primarily industrial companies, and did not include companies in the financial services, transportation or public utilities industries. The analysis is based on the performance of key independent variables in the non-overlapping five-year periods for the American and Japanese companies. To set the stage for the analysis a brief overview of the important characteristics and performance patterns of the free cash flow (FCFE) and the net income (NI) measures were presented. Table 1 shows the free cash flow per share (FCFE) data for the American companies were positively skewed (right) frequency distributions. However, Table 2 shows the three nonoverlapping FCFE data for the Japanese companies were skewed to the right in 1986-90, but shifted to a slight positive (left) skewness during the 1991-99 period. The mean and median FCFE were positive for the American data, but the mean FCFE for the Japanese sample were positive in 1986-90 and negative in 1991-95 and 1995-99 windows. Relatively speaking, the coefficients of variation (standard deviation/Mean), were markedly larger for the Japanese companies than the American companies. Thus the relative volatility of the Japanese free cash flow per share (FCFE) was much larger than the American free cash flow per share (FCFE). The frequency distribution patterns of the Japanese net income per share (NI) data in Table 2 were substantially different from the distribution patterns associated with the FCFE. The NI patterns for the Japanese companies were more stable and markedly smaller than its FCFE patterns. For the American companies, the distributions of the net income per share data were similar to its free cash flow per share. These differences in the frequency distributions between the Japanese and American NI and FCFE data have a direct effect on the regression results and, in turn, the interpretation of the performance results.

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Analysis of Hypotheses 1 and 2 A primary motivation of this study is to discover whether the capital gain rates of return were better explained by accounting earnings (NI) or the free cash flow to equity (FCFE) for American and Japanese equities. The first hypothesis was the most simplistic of the three hypotheses. It asserts that free cash flow per share (FCFE) provides a more accurate explanation of capital gain rates of return (r) than net income per share (NI). The analysis focuses on Table 11 where a summary of the statistical results were presented in boxes that represent the nonoverlapping five-year windows. The summarized results in Table 11 indicate that for the FCFE coefficients were not a reliable predictor of capital gain rates of return for either the American or the Japanese companies in the sample. That is the FCFE coefficients were only significant at the .05 level for the American companies during the period 1981-85, one of four periods. Likewise, the Japanese FCFE coefficients were significant at the .05 level in 1995-99 or one-third (1/3) of the time. However, all of the NI coefficients were positively related the capital gain rates of return, as hypothesized, for the American and Japanese companies in the sample. Also, Table 4 shows the R2 relationship between Japanese NI coefficients and capital gain rates of return were greater than .20 during the 1986-99 non-overlapping periods. The R2 relationship for the American companies was greater than .20 during the period 1981-1995. Thus the accounting earnings provided a more accurate explanation of the capital gain rates of return than the free cash flow to equity measures. Fama – MacBeth (F-M) t-values are given at the bottom of Table 3 and 4. These t-values measure the stability of the regression coefficients across time. The F-M t-values for the American and Japanese NI coefficients were 1.17 and 1.92, respectively. These F-M t-values indicate that statistically it is impossible to predict how long-run changes in NI will affect longrun changes in the capital gain rates of return of the American and Japanese equities (r) in the sample. Finding the F-M t-values were not statistically significant casts a shadow over the credibility of the previously significant NI coefficients. Prior studies have found that rates of return are closely related to size and book/market (B/M) metrics. Regressions 5-8 incorporate the size and the B/M measures. The statistical results of regressions 5-8 for American and Japanese companies are presented in Tables 5 and 6. The patterns of the intercept, FCFE, SIZE and B/M coefficients are presented in Table 5 and the intercept, NI, SIZE and B/M coefficients are shown in Table 6. An analysis of the statistical results associated with the second hypothesis is based on a summary of Tables 5 and 6 and is located in Table 12. A review of Table 12 shows that the addition of ln SIZE and B/M ratio resulted in no change in the number of significant FCFE and NI for American or Japanese companies. The number of companies reported in Table 12 with R2 greater than .20 and .30 were modestly greater. Only the F-M t-value for the Japanese NI coefficient in Table 6 was significant at the .05 levels with a value of 3.19. None of the remaining F-M t-values in Tables 5 and 6 were statistically significant. Table 12 shows that approximately 50 percent of the ln SIZE coefficients for the American and Japanese companies were significant at the .05 levels for both

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the FCFE and NI measures. Less than one-half of the B/M coefficients for American companies were significant at the .05 level of significance, while 67 percent (2/3) of the Japanese FCFE and NI coefficients associated with the B/M ratio were significant. On balance, incorporating size the and B/M measures made only modest improvements in the statistical results reported in regressions 1-4. Thus, the second hypothesis did not receive strong support. IV.

ANALYSIS OF FCFE AND NI COMPONENTS

An important contribution of this study depends on whether the components of the FCFE or the components of NI provide a better explanation for estimating the capital gain rates of return of American and Japanese equities. The preceding analysis of hypothesis 1 and 2 focused on the regression coefficients of free cash flow per share (FCFE) and net income per share (NI). Thus far the NI measure has provided substantially greater explanation of the capital gain rates of return (r) than the FCFE for both American and Japanese companies. The approach in Section IV is to disaggregate FCFE and NI into their basic components. The disaggregated FCFE produces five critical cash flow components—net operating cash flows (NOF), net investment flows (NIF), working capital flows (WCF), interest expense flows (INT) and net financing flows (NFF). Preferred dividends (PFDDIV) were included in the regression, but they have a relatively small effect because only a small percentage of the American companies in the sample pay preferred dividends. Size and B/M ratios were included in the analysis. Likewise, when NI is disaggregated, the outcome is two important segments—net operating cash flow per share (NOCF) and accrual flows per share (ACCF). Interpreting the Performance of FCFE Components Do free cash flow components provide valuable insights into understanding the creation of capital gain/loss returns by the American and Japanese companies in this study? To answer this question we turn to a summary of the free cash flow information in Tables 7 and 13. The coefficients of the six FCFE components for American companies along with ln SIZE and B/M ratios in Table 7. The coefficients for the two NI components for American companies, plus ln SIZE and B/M ratios, were depicted in Table 9. A summary of statistical results for Table 7 and 9 were presented in Table 13. The summary in Table 13 shows two FCFE components of American companies were positively related with the capital gain rates of return (r) at the .05 level of significance during the 1981-99 period. The two coefficients were net operating flows (NOF) and interest flows (INT). The net financing flows (NFF) represent the inflows and outflows of cash associated with annual changes in short and long term debt within a non-overlapping window. During the period 1981-95 Table 7 shows that the American NFF coefficients were significant at a .05 level of significance with the hypothesized negative relationship with r. These three cash flow components highlight the importance of operating and financing flows in explaining capital gain/loss performance of American companies during the period 1981 to 1999. The coefficients for American net investment (NIF) and working capital flows (WCF) were significantly related to r at the .05 level of significance with the hypothesized negative

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relationship during the period 1991-99, as shown in Table 13. That is, it was hypothesized that as NIF and WCF increased the capital gain returns would also increase or vice versa, but the data show this only occurred during the 1991-1999 period or one-half of the total period. The preferred dividends were not closely related to the rates of return on the equity. Finally, the coefficients for firm size (ln SIZE) were significant at the .05 level in two or the four (2/4) fiveyear windows with the hypothesized negative significant. However, only one of the four B/M coefficients was positively significant for the American companies. Thus, size and B/M made only a modest contributions in explaining the capital gain returns of American companies. The coefficients for the Japanese FCFE components, plus ln SIZE and B/M ratios, are located in Table 8. Between 1991-99, or two-thirds of the time, Table 8 shows Japanese net operating flow (NOF) coefficients were significant during the period 1991-99. That is as NOF increased the capital gain returns also increased, or vice versa. To further explain the relationship between NOF and r we turn to Tables 1 and 2. These data show that the level of the Japanese NOFs were markedly lower than the American NOFs. Furthermore, the mean NOFs were always greater than the median NOFs for both samples indicating a positively skewed distribution. On average net operating flows for Japanese companies were less volatile than the NOFs of American companies, as measured by the standard deviation and coefficients of variation (CV) of the NOF. In summary, Table 13 indicates during the period 1981-99 the NOF of American companies were positively related to capital gain returns at the .05 level, while the NOFs of Japanese companies were significantly related to r at the .05 level of significance during the period 1991-99. During the period 1986-99 Japanese interest expense flows (INT) were significantly related to return at the .05 level of significance, as shown in Table 13. Likewise the American INT coefficients were also significantly related to return during 1981-99 at the .05 level. The INT data in Tables 1 and 2 support the significance of the relationship between INT and the capital gain/loss rates of return. That is, capital gain returns increased as interest cost decreased or vice versa. Tables 1 and 2 show all INT measures were left skewed for all time windows and the CV were similar, which indicates the relative volatility of the interest flows were reasonably close. The Japanese data in Table 13 shows during the 1986-99 period none of the coefficients for NIF nor WCF were statistically significant related to return at the .05 level. That is, a significant relationship does not exist between capital gain returns and the investment in fixed and working capital. The pattern of the NIF in Tables 1 and 2 indicates the relative size of the American net investment flows is two to three times larger than the NIF of the Japanese companies. Likewise, the standard deviation of NIF for the American companies was 2 to 8 times larger than the standard deviation of the Japanese companies. Table 13 shows the American NIF coefficients were more significant than the Japanese NIF coefficients by a margin of 2/4 vs. 0/3, respectively. The distribution patterns of the working capital flows were markedly different between the American and the Japanese companies, as shown in Tables 1 and 2. The WCF of the American companies were left skewed during 1981-99. However, in 1986-90 Japanese WCF were left skewed but not significant at the .05 level; but during the 1991-99 period the WCF were right skewed, and Table 8 shows they were positively related to return. In other words during 1991-99 Japanese working capital flows were increasing as the capital

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losses on stock returns were increasing. In summary, the relationship between American free cash flow components and capital gain/loss returns during 1981-99 period is mixed. The relationship between capital gain returns and operating and financing flow falls between within the strong and relatively strong classification, but the relationship between r and NIF or WCF is rated moderate, at best. The Japanese data show no significant relationship between net investment, net working capital and net financing flows and r during the period 1986-1999. There is a moderately strong relationship between operating flows and return during the period 1991-99, and a strong relationship between return and interest costs for the 1986-99 non-overlapping periods. Unfortunately, none of the Fama-MacBeth t-values were significant for the decomposed components of FCFE. Interpreting the Performance of NI Components The accounting approach is based on the discounted value of a firm’s future net income stream (NI). The net income stream is divided into two parts—net operating cash flow per share (NOCF) and accrual flow per share (ACCF). Equation 10 defines net operating cash flow per share (NOCFij /P0) as having the same components that are found in free cash flow to equity per share (FCFEij/P0). That is, on a per share basis NOCFij/P0 = FCFEij/P0. The accrual flow per share (ACCFij/P0) equals net income per share [NIij – PFDDIVij]/P0 minus net operating cash flow per share (NOCFij/P0). That is, ACCFij/P0= [NIij – PFDDIVij]/P0 - NOCFij/P0. The accrual flow per share were negative values in Tables 1 and 2, where ACCF is a raw number. However, in Tables 9 and 10 the coefficient for ACCF is a positive value, that means capital gain returns were positively related to accrual flows. There are two important findings in the study related to the performance NOCFij/P0 and ACCFij/P0 of the American and Japanese companies. One finding is that a significant relationship at the .05 level exists between net operating cash flow per share and capital gain returns for both American and Japanese companies during the total period of 1981-99 and 198699, respectively. Table 13 shows the higher the NOCF per share the higher the capital gain returns. Another equally important relationship in Table 13 was that the higher the ACCF per share the higher the capital gain returns for both the American and Japanese companies throughout the total period of 1981-99 and 1986-99, respectively. These two highly significant relationships between capital gain returns and NOCF as well as between capital gain returns and ACCF were highly supportive of the net income approach as a strong predictor returns, that were developed under the discussion associated with hypothesis 3.

CONCLUSIONS The objective of the paper was to discover whether an earnings approach (NI) or a free cash flow (FCFE) approach would provide a better explanation for estimating the capital gain returns and likewise the valuation of American and Japanese companies. A few important conclusions emerge from the study. Hypothesis 1 asserted that free cash flows to equity (FCFE) would provide a more

11

accurate estimate of capital gain rates of return (r) than accounting earnings. The regression results in the study showed the opposite. For the period 1981-1999 and 1986-99, the accounting earnings for American and Japanese companies, respectively, were significantly related to capital gain rates of return at the .05 level of significance. In contrast, the FCFE were significantly related to the capital gain rates of return at the .05 level of significance during the period 1981-85 for the American companies and during the period 1995-1999 for the Japanese companies. In hypothesis 2 incorporated two additional independent measures, size measure and a book/market. The significance of the relationships between FCFE and r were unaffected by the addition of size and book/market variables. Turning to the analysis of hypothesis 3, the free cash flow to equity and net earnings were decomposed into their component parts. This decomposition provides a richer and more insightful explanation of the relationship between individual FCFE components and capital gain rates of return. Most importantly, the two components of the accounting earnings approach--net operating cash flow and accrual flows--were found to be significantly related to the capital gain rates of return of the American and Japanese companies during the entire period of the study, 1981-99 and 1986-99, respectively. Additionally, the Fama-MacBeth t–values were significant at the .05 level for both of the Japanese accounting earnings measures. Returning to the FCFE decomposition, it was discovered that net Cash flows from operations, interest and debt financing were closely related to the capital gain rates of return for the American companies in nearly all non-overlapping periods. For the Japanese companies only the net operating cash flows were significantly related to r during the period 1986-99. The significance of the relationship between American fixed and working capital flows and capital gain returns were mixed for the period studied. However, for the Japanese companies, there were no significant relationships between r and cash flows associated with capital investment, working capital and net financing. Finally, the Fama-MacBeth t-values were not significant for any of the American free cash flow components, and were only significant at the .05 level for the Japanese net operating cash flows. In summary, the study found strong support for using the net earnings approach to explain the capital gain rates of return for both American and Japanese companies during the period 1981-99 and 1986-99, respectively. Additionally the study found strong support for the relationship between capital gain returns and net cash flows associated with operations, interest and debt financing. Why is it that the accrual accounting information is more useful in explaining capital gain rates of return than free cash flow components? Accrual information tends to be more stable than cash flow data. Thus further research is needed to explore the volatility effect between accrual accounting information and cash flow data. Another effect that needs exploration is the stability of the cash flow rates of return and the association with the net earnings and free cash flow measures.

12

References Brealey, Richard A. and Myers, Stewart C. (1996), Principles of Corporate Finance, 5th Edition, New York, The McGraw-Hill Companies, Inc., pp. 71-78. Claude, S., Kao, J. and Richardson, G. (2000) "The Equivalence of Dividend, Cash Flows and Residual Earnings Approaches to Equity Valuation Employing Ideal Terminal Value Expressions." Working Paper, University of Waterloo. Damodaran, Aswath (2001), Corporate Finance: Theory and Practice, 2nd Edition, New York, John Wiley & Sons, Inc., pp. 774-775. Fama, Eugene F. and MacBeth, James D. (1973), “Risk, Return, and Equilibrium: Empirical Tests,” Journal of Political Economy, May-June, 607-636. Francis, J., Olsson, P. and Oswald, D. R. (2000) “Comparing the Accuracy and Explainability of Dividend, Free Cash Flow, and Abnormal Earnings Equity Value Estimates.” Journal of Accounting Research, 38, 45-70. Gentry, James A., Whitford, David T., Aoki, Shigeo and Chan, Konan (2000), “The Relationship Between Long-Run Excess Growth in Firm Value and Cash Flow Components: A Traditional and Behavioral Interpretation,” CIBER Working Paper, 44 pages. Heckel, K. S. and Livnat, J. (1992), Cash Flow and Security Analysis, Homewood, IL, Business One Irwin Kaplan, Stephen and Ruback, Richard (September 1995) “The Valuation of Cash Flow Forecasts: An Empirical Analysis.” Journal of Finance, 1059-93. Penman, Stephen (1997) "A Synthesis of Equity Valuation Techniques and the Terminal Value Calculation for the Dividend Discount Model.” Review of Accounting Studies, 2, 303-23. Penman, Stephen H. and Sougiannis, Theodore (1998), “A Comparison of Dividend, Cash Flow and Earnings Approaches to Equity Valuation,” Contemporary Accounting Research, 15, Fall, 343-383. Rappaport, Alfred (1998), Creating Shareholder Value: The New Standard for Business Performance, New York, The Free Press.

S:/word-processing/gentry/do accounting earnings or free cash flows1

13

Table 1 U.S. Data Summary Statistics Years

Parameters Mean 1981-1985 Median Standard Deviation Mean 1982-1986 Median Standard Deviation Mean 1983-1987 Median Standard Deviation Mean 1984-1988 Median Standard Deviation Mean 1985-1989 Median Standard Deviation Mean 1986-1990 Median Standard Deviation Mean 1987-1991 Median Standard Deviation Mean 1988-1992 Median Standard Deviation Mean 1989-1993 Median Standard Deviation Mean 1990-1994 Median Standard Deviation Mean 1991-1995 Median Standard Deviation Mean 1992-1996 Median Standard Deviation Mean 1993-1997 Median Standard Deviation Mean 1994-1998 Median Standard Deviation Mean 1995-1999 Median Standard Deviation

NI 0.61 0.52 0.85 0.65 0.52 2.65 0.48 0.48 0.74 0.39 0.40 0.47 0.46 0.46 0.57 0.40 0.40 0.47 0.35 0.35 0.45 0.34 0.35 0.44 0.29 0.32 0.44 0.28 0.30 0.49 0.38 0.35 1.12 0.40 0.33 1.33 0.35 0.34 0.49 0.32 0.33 0.59 0.34 0.36 0.67

FCFE 1.23 0.83 1.57 1.34 0.83 2.71 1.23 0.74 1.74 0.96 0.61 1.20 1.17 0.74 1.76 1.05 0.67 1.58 1.06 0.64 1.77 1.18 0.70 2.00 1.11 0.68 2.20 1.15 0.60 6.08 1.24 0.66 3.91 1.00 0.59 3.16 0.92 0.55 1.95 0.76 0.51 1.38 0.85 0.56 1.76

NOF 1.57 1.21 1.55 1.70 1.24 4.27 1.39 1.13 1.29 1.08 0.89 0.89 1.28 1.04 1.04 1.15 0.90 0.99 1.08 0.86 1.12 1.09 0.89 1.16 0.98 0.80 0.91 1.00 0.74 2.74 1.47 0.85 6.94 1.36 0.79 7.36 1.08 0.80 2.06 0.95 0.77 0.97 1.04 0.88 1.41

NIF -0.94 -0.62 1.17 -1.08 -0.64 3.48 -0.86 -0.59 1.05 -0.69 -0.47 0.99 -0.81 -0.55 1.03 -0.73 -0.49 1.05 -0.67 -0.44 1.10 -0.67 -0.46 1.13 -0.60 -0.43 0.67 -0.58 -0.41 0.66 -0.82 -0.47 1.64 -0.77 -0.44 1.85 -0.67 -0.42 1.37 -0.69 -0.42 1.30 -0.73 -0.47 1.04

WCF -0.20 -0.06 0.70 -0.25 -0.08 1.17 -0.25 -0.11 0.89 -0.23 -0.12 0.77 -0.23 -0.12 0.64 -0.20 -0.09 0.72 -0.11 -0.06 0.42 -0.08 -0.04 0.45 -0.04 -0.02 0.41 -0.05 -0.03 0.65 -0.06 -0.04 1.07 -0.14 -0.05 0.54 -0.14 -0.05 0.59 -0.13 -0.05 0.49 -0.12 -0.05 0.43

INT -0.39 -0.23 0.53 -0.41 -0.23 0.72 -0.35 -0.20 0.53 -0.26 -0.16 0.38 -0.31 -0.18 0.45 -0.29 -0.17 0.46 -0.28 -0.16 0.55 -0.30 -0.16 0.64 -0.26 -0.14 0.43 -0.26 -0.13 0.91 -0.36 -0.14 1.38 -0.30 -0.12 1.15 -0.25 -0.12 0.80 -0.22 -0.11 0.53 -0.23 -0.12 0.46

PFDDIV -0.01 0.00 0.04 -0.01 0.00 0.04 -0.01 0.00 0.04 -0.01 0.00 0.03 -0.01 0.00 0.04 -0.01 0.00 0.03 -0.01 0.00 0.03 -0.01 0.00 0.04 -0.01 0.00 0.05 -0.01 0.00 0.17 -0.01 0.00 0.06 -0.01 0.00 0.05 -0.01 0.00 0.05 -0.01 0.00 0.05 -0.01 0.00 0.05

NFF 1.00 0.56 1.55 1.27 0.64 3.37 1.19 0.61 2.27 0.94 0.52 1.98 1.15 0.64 2.20 1.00 0.55 2.03 0.90 0.50 1.96 0.91 0.52 1.99 0.84 0.46 1.72 0.89 0.43 4.61 1.22 0.52 4.68 1.12 0.47 5.23 0.90 0.48 1.99 0.88 0.48 2.01 0.98 0.57 1.63

NOCF 0.88 0.74 1.16 0.88 0.72 3.82 0.68 0.62 1.38 0.56 0.54 0.86 0.69 0.66 0.84 0.63 0.58 0.81 0.69 0.59 0.65 0.74 0.61 0.62 0.68 0.62 0.62 0.64 0.56 0.81 0.90 0.62 2.37 0.79 0.56 2.68 0.63 0.55 0.73 0.56 0.52 0.67 0.64 0.59 0.76

ACCF -0.27 -0.22 0.90 -0.23 -0.25 2.09 -0.21 -0.19 1.31 -0.17 -0.17 0.88 -0.23 -0.22 0.83 -0.23 -0.20 0.83 -0.34 -0.24 0.61 -0.39 -0.29 0.60 -0.39 -0.32 0.60 -0.37 -0.26 0.94 -0.51 -0.30 1.75 -0.39 -0.22 1.57 -0.29 -0.21 0.68 -0.24 -0.18 0.60 -0.30 -0.23 0.64

SIZE 4.85 4.75 1.91 4.85 4.76 1.89 5.04 4.95 1.87 5.31 5.22 1.80 5.22 5.15 1.84 5.42 5.37 1.85 5.50 5.44 1.91 5.46 5.36 1.97 5.53 5.49 1.97 5.63 5.63 2.00 5.51 5.41 2.09 5.75 5.75 2.08 5.89 5.88 2.02 6.02 6.03 1.98 6.02 6.04 1.93

BM 0.96 0.82 0.67 1.00 0.85 0.81 0.88 0.74 0.60 0.66 0.60 0.37 0.73 0.66 0.43 0.65 0.58 0.39 0.60 0.54 0.39 0.66 0.57 0.44 0.63 0.56 0.48 0.58 0.56 1.71 0.65 0.67 5.14 0.50 0.58 5.72 0.58 0.52 0.72 0.51 0.45 0.66 0.52 0.48 0.70

Global 5-Year Mean Avg. Median Std. Dev. Glob. Mean

0.40 0.35 0.11

1.08 0.66 0.16

1.21 0.88 0.23

-0.75 -0.47 0.13

-0.15 -0.05 0.07

-0.30 -0.16 0.06

-0.01 0.00 0.00

1.01 0.52 0.14

0.71 0.59 0.11

-0.30 -0.22 0.09

5.47 5.41 0.37

0.67 0.58 0.16

N 1034

985

943

903

887

881

918

969

986

1005

990

1003

997

1010

926

Table 2 Japanese Data Summary Statistics Years

Parameters Mean 1986-1990 Median Standard Deviation Mean 1987-1991 Median Standard Deviation Mean 1988-1992 Median Standard Deviation Mean 1989-1993 Median Standard Deviation Mean 1990-1994 Median Standard Deviation Mean 1991-1995 Median Standard Deviation Mean 1992-1996 Median Standard Deviation Mean 1993-1997 Median Standard Deviation Mean 1994-1998 Median Standard Deviation Mean 1995-1999 Median Standard Deviation

NI 0.22 0.18 0.15 0.19 0.17 0.18 0.19 0.17 0.14 0.13 0.12 0.10 0.10 0.08 0.09 0.09 0.08 0.08 0.09 0.09 0.09 0.13 0.12 0.13 0.14 0.14 0.14 0.13 0.12 0.10

FCFE 0.37 0.14 1.04 0.29 0.13 0.74 0.18 0.08 0.50 0.08 0.04 0.28 0.03 0.03 0.16 0.01 0.02 0.15 0.00 0.01 0.18 -0.01 0.01 0.27 -0.02 0.00 0.22 -0.02 0.01 0.19

NOF 0.59 0.47 0.43 0.51 0.41 0.36 0.52 0.42 0.40 0.38 0.32 0.26 0.32 0.26 0.25 0.31 0.26 0.22 0.35 0.29 0.25 0.47 0.40 0.35 0.48 0.41 0.38 0.43 0.38 0.30

NIF -0.60 -0.45 0.51 -0.56 -0.45 0.43 -0.56 -0.45 0.45 -0.41 -0.34 0.30 -0.33 -0.27 0.26 -0.30 -0.25 0.21 -0.32 -0.27 0.24 -0.42 -0.35 0.31 -0.45 -0.37 0.34 -0.41 -0.35 0.30

WCF -0.04 -0.06 0.41 -0.09 -0.06 0.39 -0.16 -0.09 0.51 -0.12 -0.07 0.43 -0.09 -0.05 0.28 -0.06 -0.03 0.17 -0.06 -0.03 0.16 -0.07 -0.04 0.19 -0.06 -0.05 0.17 -0.04 -0.04 0.13

INT -0.05 -0.02 0.16 -0.05 -0.01 0.17 -0.06 -0.02 0.16 -0.05 -0.03 0.11 -0.04 -0.02 0.09 -0.05 -0.03 0.09 -0.06 -0.03 0.09 -0.07 -0.04 0.11 -0.07 -0.04 0.11 -0.05 -0.03 0.09

PFDDIV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

NFF 0.49 0.22 1.07 0.48 0.27 0.88 0.44 0.25 0.76 0.29 0.16 0.55 0.17 0.11 0.35 0.11 0.06 0.21 0.09 0.05 0.21 0.08 0.04 0.31 0.07 0.03 0.34 0.06 0.03 0.24

NOCF 0.12 0.17 0.76 0.10 0.16 0.62 0.13 0.18 0.64 0.15 0.18 0.53 0.18 0.18 0.37 0.23 0.23 0.23 0.27 0.24 0.26 0.38 0.34 0.38 0.43 0.37 0.39 0.43 0.37 0.32

ACCF 0.10 0.00 0.78 0.09 -0.02 0.57 0.06 -0.03 0.65 -0.02 -0.07 0.54 -0.08 -0.09 0.37 -0.14 -0.15 0.23 -0.17 -0.16 0.25 -0.26 -0.21 0.36 -0.29 -0.24 0.35 -0.30 -0.25 0.30

SIZE 24.91 24.88 1.28 25.14 25.19 1.24 25.25 25.17 1.31 25.48 25.34 1.25 25.67 25.63 1.35 25.71 25.68 1.20 25.52 25.54 1.22 25.11 25.06 1.29 25.07 25.00 1.29 25.20 25.18 1.29

BM 2.41 1.62 3.11 1.86 1.39 2.01 1.71 1.33 1.83 1.30 0.99 1.43 1.08 0.87 0.95 1.18 0.92 1.05 1.44 1.20 1.15 2.01 1.63 1.64 2.12 1.70 1.58 1.80 1.49 1.32

Global 5-Year Mean Avg. Median Std. Dev. Global Mean

0.14 0.13 0.04

0.09 0.05 0.14

0.44 0.36 0.09

-0.44 -0.35 0.11

-0.08 -0.05 0.04

-0.06 -0.03 0.01

0.00 0.00 0.00

0.23 0.12 0.18

0.24 0.24 0.13

-0.10 -0.12 0.15

25.31 25.27 0.27

1.69 1.31 0.44

N 166

197

207

231

269

306

341

361

365

316

Table 3 Capital Gain Return as a Function of the Five-Year Cumulative Free Cash Flow Per Share Divided by Initial Stock Price YEARS 1981-1985 1982-1986 1983-1987 1984-1988 1985-1989 1986-1990 1987-1991 1988-1992 1989-1993 1990-1994 1991-1995 1992-1996 1993-1997 1994-1998 1995-1999

Avg. Coefficent Fama-MacBeth t-Value

Panel A -- US Data INTERCEPT FCFE -0.18 1.41 -1.11 17.42 -4.47 5.05 -12.44 42.41 0.97 0.13 12.96 3.62 0.57 0.10 10.99 2.96 0.95 0.08 12.88 2.36 0.53 0.01 9.04 0.29 0.72 -0.02 8.37 -0.58 0.83 -0.03 11.45 -1.07 0.88 -0.02 12.13 -0.62 0.67 0.07 10.04 6.08 1.74 -0.17 16.36 -6.73 1.71 -0.36 13.22 -9.18 1.15 0.24 14.35 6.39 0.56 0.42 8.45 9.95 0.97 0.00 10.73 -0.06 0.51 0.35

0.46 0.35

N Adj R-Sqd. 1038 0.23 987

0.65

945

0.01

905

0.01

889

0.01

883

0.00

920

0.00

971

0.00

988

0.00

1007

0.03

992

0.04

1005

0.08

997

0.04

1010

0.09

926

0.00

Panal B -- Japanese Data FCFE YEARS INTERCEPT 1986-1990 1.63 0.20 10.73 1.42 1987-1991 0.89 0.00 8.35 -0.03 1988-1992 0.23 0.05 4.08 0.43 1989-1993 -0.20 0.21 -6.48 2.02 1990-1994 -0.26 0.03 -11.32 0.19 1991-1995 -0.41 0.05 -31.10 0.57 1992-1996 -0.19 0.18 -12.52 2.10 1993-1997 -0.10 0.23 -3.98 2.51 1994-1998 -0.23 0.30 -9.31 2.72 1995-1999 -0.33 0.54 -11.50 3.72 0.10

0.18

0.16

1.08

* t-Values appear below the regression coefficients; t-Values that are not significant at the 5 percent level of significance (or higher) are bold and italizied.

N 166

Adj R-Sqd. 0.01

197

-0.01

207

0.00

231

0.01

269

0.00

306

0.00

341

0.01

361

0.01

365

0.02

316

0.04

Table 4 Capital Gain Return as a Function of the Five-Year Cumulative Net Income Available to Common Per Share Divided by Initial Stock Price YEARS 1981-1985 1982-1986 1983-1987 1984-1988 1985-1989 1986-1990 1987-1991 1988-1992 1989-1993 1990-1994 1991-1995 1992-1996 1993-1997 1994-1998 1995-1999

Avg. Coefficent Fama-MacBeth t-Value

Panel A -- US Data INTERCEPT NI -1.06 4.28 -9.21 38.69 -1.58 5.92 -13.79 149.36 0.49 1.31 8.23 20.56 0.02 1.61 0.53 26.79 0.17 1.86 2.65 22.35 -0.05 1.45 -0.94 16.41 0.00 1.95 -0.06 13.15 0.06 2.20 0.84 18.72 0.29 2.03 4.32 16.76 0.59 0.51 9.22 11.98 1.35 0.34 15.13 19.23 1.10 0.47 11.16 26.64 1.06 0.84 13.81 10.17 0.58 0.93 8.67 9.24 0.66 0.86 7.80 8.96 0.24 0.32

1.77 1.17

N Adj R-Sqd. 1034 0.59 985

0.96

943

0.31

903

0.44

887

0.36

881

0.23

918

0.16

969

0.27

986

0.22

1005

0.12

990

0.27

1003

0.41

997

0.09

1010

0.08

926

0.08

Panal B -- Japanese Data YEARS INTERCEPT NI 1986-1990 0.35 6.34 1.46 6.61 1987-1991 0.47 2.36 3.80 5.28 1988-1992 -0.37 3.39 -5.10 10.46 1989-1993 -0.51 2.71 -12.89 10.55 1990-1994 -0.50 2.51 -17.75 11.30 1991-1995 -0.57 1.94 -34.43 12.57 1992-1996 -0.31 1.55 -17.24 10.09 1993-1997 -0.33 2.15 -11.59 12.08 1994-1998 -0.41 1.71 -15.82 11.69 1995-1999 -0.51 2.09 -16.69 9.92 -0.27 -0.73

* t-Values appear below the regression coefficients; t-Values that are not significant at the 5 percent level of significance (or higher) are bold and italizied.

2.67 1.92

N 166

Adj R-Sqd. 0.21

197

0.12

207

0.34

231

0.32

269

0.32

306

0.34

341

0.23

361

0.29

365

0.27

316

0.24

Table 5 Capital Gain Return as a Function of the Five-Year Cumulative Free Cash Flow Per Share Divided by Initial Stock Price, Initial Firm Size and Initial Book to Market YEARS 1981-1985 1982-1986 1983-1987 1984-1988 1985-1989 1986-1990 1987-1991 1988-1992 1989-1993 1990-1994 1991-1995 1992-1996 1993-1997 1994-1998 1995-1999

Avg. Coefficent Fama-MacBeth t-Value

INTERCEPT 3.58 7.85 7.92 9.57 1.36 6.08 0.37 2.34 1.12 4.79 0.53 2.69 1.27 4.39 1.65 6.66 2.06 8.06 1.92 7.63 4.21 16.05 3.23 10.57 2.23 8.63 0.65 2.99 1.36 4.22 2.23 1.16

Panel A -- US Data FCFE SIZE 1.80 -0.43 19.30 -6.29 4.78 -0.63 54.21 -4.90 0.08 -0.09 1.97 -2.71 0.08 0.02 2.06 0.74 0.08 -0.03 2.11 -0.84 0.00 -0.01 0.09 -0.21 -0.03 -0.08 -0.69 -2.09 -0.05 -0.14 -1.61 -4.16 -0.05 -0.18 -1.69 -5.24 0.04 -0.21 1.36 -6.03 0.03 -0.46 1.03 -10.64 0.33 -0.34 7.17 -6.96 0.20 -0.20 5.35 -5.32 0.41 0.01 9.57 0.19 -0.08 -0.02 -1.53 -0.41

BM -2.24 -9.93 -9.00 -30.61 0.15 1.20 0.20 1.59 -0.02 -0.14 0.06 0.46 -0.13 -0.64 -0.05 -0.31 -0.22 -1.54 -0.08 -0.76 -0.28 -11.74 -0.55 -21.76 0.20 1.96 -0.24 -2.65 -0.41 -3.05

0.51 0.40

-0.84 -0.36

-0.19 -0.95

N Adj R-Sqd. 1038 0.30 987

0.82

945

0.02

905

0.01

889

0.00

883

0.00

920

0.00

971

0.02

988

0.02

1007

0.07

992

0.26

1005

0.42

997

0.07

1010

0.09

926

0.01

YEARS INTERCEPT 1986-1990 16.55 6.69 1987-1991 8.65 4.51 1988-1992 6.15 6.19 1989-1993 1.91 3.10 1990-1994 1.93 4.49 1991-1995 -1.05 -3.79 1992-1996 -0.81 -2.60 1993-1997 -1.28 -2.58 1994-1998 -1.57 -3.23 1995-1999 -2.48 -4.46 2.80 0.46

Panal B -- Japanese Data FCFE SIZE -0.15 -0.61 -0.87 -6.20 -0.41 -0.32 -2.26 -4.24 -0.02 -0.24 -0.14 -6.12 0.26 -0.08 1.95 -3.47 0.21 -0.09 1.46 -5.23 0.26 0.02 2.45 2.07 0.29 0.02 3.01 1.83 0.29 0.05 2.78 2.32 0.27 0.05 2.31 2.86 0.43 0.09 2.64 4.03

BM 0.18 3.25 0.23 3.36 0.06 1.56 0.01 0.20 0.03 1.29 0.05 3.54 0.04 2.39 0.02 1.11 -0.02 -1.11 -0.03 -1.44

0.14 0.56

0.06 0.66

-0.11 -0.50

* t-Values appear below the regression coefficients; t-Values that are not significant at the 5 percent level of significance (or higher) are bold and italizied.

N 166

Adj R-Sqd. 0.25

197

0.14

207

0.18

231

0.06

269

0.09

306

0.05

341

0.03

361

0.03

365

0.04

316

0.09

Table 6 Capital Gain Return as a Function of the Five-Year Cumulative Net Income Available to Common Per Share Divided by Initial Stock Price, Initial Firm Size and Initial Book to Market YEARS 1981-1985 1982-1986 1983-1987 1984-1988 1985-1989 1986-1990 1987-1991 1988-1992 1989-1993 1990-1994 1991-1995 1992-1996 1993-1997 1994-1998 1995-1999

Avg. Coefficent Fama-MacBeth t-Value

INTERCEPT 0.56 1.55 -0.14 -0.34 0.49 2.59 -0.14 -1.14 0.28 1.45 0.08 0.47 0.69 2.60 0.79 3.65 0.52 2.32 -0.29 -1.37 2.11 8.16 1.88 5.80 1.16 4.51 1.06 5.10 0.32 1.12 0.62 0.90

Panel A -- US Data NI SIZE 4.22 -0.23 37.68 -4.44 5.84 -0.19 126.37 -3.01 1.31 -0.06 20.88 -2.27 1.61 0.00 26.87 -0.19 1.86 -0.04 22.43 -1.53 1.45 -0.02 16.41 -0.82 1.97 -0.09 13.29 -2.52 2.19 -0.12 18.73 -4.17 2.13 -0.10 17.13 -3.34 1.94 -0.06 19.19 -2.04 1.02 -0.28 16.73 -7.17 1.08 -0.25 12.19 -5.20 1.25 -0.14 12.99 -3.91 0.90 -0.06 9.01 -1.84 0.93 0.04 8.69 0.87 1.98 1.47

-0.11 -1.14

BM -0.47 -3.16 -0.47 -2.89 0.36 4.13 0.26 3.16 0.15 1.25 -0.04 -0.38 -0.32 -1.77 -0.11 -0.83 0.47 3.66 1.33 15.42 0.69 11.71 0.62 7.17 0.96 8.40 -0.27 -3.03 0.19 1.52 0.22 0.42

N Adj R-Sqd. 1034 0.60 985

0.96

943

0.33

903

0.45

887

0.36

881

0.23

918

0.16

969

0.28

986

0.25

1005

0.32

990

0.42

1003

0.47

997

0.18

1010

0.09

926

0.08

YEARS INTERCEPT 1986-1990 12.87 5.17 1987-1991 8.41 4.66 1988-1992 3.58 4.12 1989-1993 0.61 1.20 1990-1994 0.92 2.49 1991-1995 -1.13 -5.00 1992-1996 -1.10 -3.97 1993-1997 -1.92 -4.60 1994-1998 -2.20 -5.27 1995-1999 -2.91 -5.89 1.71 0.33

Panal B -- Japanese Data NI SIZE 4.22 -0.49 4.38 -5.09 2.17 -0.32 5.14 -4.53 2.88 -0.15 8.72 -4.60 2.61 -0.04 9.94 -2.22 2.33 -0.05 10.51 -3.90 1.93 0.02 12.79 2.31 1.60 0.03 10.53 2.71 2.28 0.06 12.77 3.68 1.76 0.07 12.01 4.31 2.08 0.10 9.78 4.97

BM 0.10 2.60 0.11 2.40 0.02 0.67 0.00 0.21 0.01 0.55 0.03 3.22 0.02 2.16 0.03 2.31 0.01 0.58 -0.01 -0.26

2.39 3.19

0.03 0.84

-0.08 -0.41

* t-Values appear below the regression coefficients; t-Values that are not significant at the 5 percent level of significance (or higher) are bold and italizied.

N 166

Adj R-Sqd. 0.33

197

0.22

207

0.40

231

0.33

269

0.36

306

0.37

341

0.25

361

0.32

365

0.30

316

0.29

Table 7 US Data for Capital Gain Return as a Function of Five-Year Individual Cash Flow Components Plus Size and Book to Market * YEAR 1981-1985 1982-1986 1983-1987 1984-1988 1985-1989 1986-1990 1987-1991 1988-1992 1989-1993 1990-1994 1991-1995 1992-1996 1993-1997 1994-1998 1995-1999

Avg. Coefficent Fama-MacBeth t-Value

INTERCEPT 1.14 3.39 1.60 4.17 0.17 0.90 -0.05 -0.38 0.42 2.09 0.11 0.63 0.65 2.36 0.85 3.76 0.83 3.45 0.06 0.25 1.69 6.57 0.01 0.02 1.04 4.06 -0.24 -1.15 -0.17 -0.49

NOF 3.41 26.26 3.69 29.06 0.98 15.10 1.33 19.88 1.56 16.78 1.08 11.02 1.52 9.57 1.71 13.48 1.38 10.96 1.60 14.24 0.65 10.64 0.01 0.10 0.54 6.80 0.87 9.74 0.77 7.65

NIF 0.38 2.68 -0.53 -3.32 -0.12 -1.60 0.16 2.79 0.16 1.94 -0.01 -0.06 0.21 1.55 0.19 1.79 -0.27 -2.37 0.16 1.29 -0.30 -3.39 -0.61 -8.99 -0.41 -6.56 0.07 1.06 -0.32 -3.45

WCF 1.20 8.12 1.14 8.10 -0.60 -8.05 -0.18 -2.82 -0.13 -1.27 -0.14 -1.59 -0.59 -3.15 -0.36 -2.53 -0.56 -3.67 -0.62 -5.02 -0.96 -8.30 -2.22 -13.97 -0.50 -3.25 -0.38 -2.51 -0.50 -2.39

INT 4.05 12.68 5.58 17.69 1.10 6.16 1.88 9.92 2.75 10.20 2.30 8.64 2.72 6.41 2.46 8.79 2.50 10.08 3.26 12.29 1.85 9.50 0.93 5.42 1.84 9.57 1.05 4.30 1.85 5.63

PFDDIV 5.82 2.33 2.11 0.76 0.17 0.14 2.34 2.06 0.47 0.36 1.56 1.17 3.58 1.56 0.88 0.56 2.98 1.70 7.46 4.58 -1.82 -1.38 1.09 0.65 4.19 2.93 0.65 0.61 -0.62 -0.34

NFF 0.94 9.79 0.54 6.97 -0.05 -1.33 0.05 1.45 0.17 3.15 0.17 2.94 0.14 1.42 0.03 0.37 0.06 1.09 0.29 4.36 0.27 6.18 0.66 15.39 0.38 7.87 0.36 4.88 -0.03 -0.35

SIZE -0.29 -5.69 -0.41 -7.12 -0.03 -0.90 -0.01 -0.56 -0.06 -1.90 -0.02 -0.77 -0.08 -2.21 -0.14 -4.49 -0.13 -4.04 -0.08 -2.52 -0.23 -6.08 0.00 0.08 -0.10 -2.81 0.07 2.54 0.07 1.67

BM -2.35 -14.61 -2.21 -13.51 -0.10 -1.02 -0.23 -2.35 -0.44 -3.15 -0.35 -2.75 -0.64 -3.25 -0.54 -3.76 -0.28 -1.97 0.45 3.71 0.27 5.22 0.19 3.26 0.22 1.92 -0.43 -4.36 0.11 0.79

0.54 0.86

1.41 1.42

-0.08 -0.27

-0.36 -0.45

2.41 1.98

2.06 0.84

0.26 0.96

-0.09 -0.71

-0.42 -0.51

N 1034

Adj R-Sqd. 0.65

985

0.97

943

0.40

903

0.42

887

0.33

881

0.22

918

0.14

969

0.23

986

0.24

1005

0.33

990

0.49

1003

0.70

997

0.27

1010

0.27

926

0.11

* t-Values appear below the regression coefficients; t-Values that are not significant at the 5 percent level of significance (or higher) are bold and italizied.

Table 8 Japanese Data for Capital Gain Return as a Function of Five-Year Individual Cash Flow Components Plus Size and Book to Market * YEAR 1986-1990 1987-1991 1988-1992 1989-1993 1990-1994 1991-1995 1992-1996 1993-1997 1994-1998 1995-1999

Avg. Coefficent Fama-MacBeth t-Value

INTERCEPT 13.68 5.19 8.25 4.24 4.09 4.26 0.74 1.31 1.12 2.69 -1.42 -5.94 -1.47 -5.19 -2.55 -5.64 -2.80 -6.23 -3.07 -5.72

NOF 1.20 1.67 2.05 2.78 2.03 5.60 1.75 6.44 0.91 4.07 1.01 7.96 0.79 6.20 1.03 7.58 0.96 7.13 1.03 5.72

NIF 0.00 0.00 0.84 1.57 0.96 3.51 0.81 3.82 0.08 0.42 0.30 2.38 0.07 0.55 0.25 1.71 0.32 2.22 0.52 2.83

WCF -0.57 -1.70 0.04 0.15 0.08 0.56 0.32 2.51 0.32 2.09 0.28 2.28 0.17 1.38 0.02 0.13 0.03 0.19 0.03 0.13

INT 2.18 1.99 1.41 1.79 2.51 5.66 2.76 8.01 2.57 7.72 1.36 6.59 1.22 5.82 1.47 5.15 1.21 4.16 1.24 2.90

PFDDIV 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

NFF -0.03 -0.16 0.13 0.52 0.01 0.07 0.20 1.63 0.22 1.68 0.06 0.70 0.03 0.33 0.07 0.75 0.15 1.42 0.08 0.46

SIZE -0.52 -5.07 -0.32 -4.20 -0.17 -4.65 -0.05 -2.19 -0.06 -4.04 0.03 3.27 0.04 3.81 0.09 4.86 0.09 5.40 0.10 5.04

BM 0.16 2.26 0.05 0.58 0.07 1.61 0.06 1.99 0.09 3.38 0.07 3.64 0.03 1.48 0.00 0.24 -0.03 -1.65 -0.04 -1.68

1.66 0.30

1.28 2.67

0.41 1.19

0.07 0.28

1.79 2.83

0.00 n/a

0.09 1.12

-0.08 -0.37

0.04 0.74

N 166.00

Adj R-Sqd. 0.28

197.00

0.18

207.00

0.33

231.00

0.29

269.00

0.28

306.00

0.36

341.00

0.29

361.00

0.25

365.00

0.24

316.00

0.19

* t-Values appear below the regression coefficients; t-Values that are not significant at the 5 percent level of significance (or higher) are bold and italizied.

Table 9 US Data for Capital Gain Return as a Function of Statement of Cash Flow Variables Plus Size and Book to Market * YEAR 1981-1985 1982-1986 1983-1987 1984-1988 1985-1989 1986-1990 1987-1991 1988-1992 1989-1993 1990-1994 1991-1995 1992-1996 1993-1997 1994-1998 1995-1999

Avg. Coefficent Fama-MacBeth t-Value

INTERCEPT 1.15 3.52 0.26 0.63 0.25 1.31 -0.14 -1.21 0.24 1.22 0.02 0.13 0.67 2.52 0.84 3.93 1.33 6.07 1.37 7.30 2.92 11.55 2.36 7.61 2.03 9.29 1.28 6.21 0.43 1.49

NOCF 4.46 44.66 6.09 120.02 1.37 20.44 1.74 26.42 1.96 21.34 1.48 15.13 1.93 12.11 2.26 17.83 2.08 15.09 2.49 19.18 1.53 15.96 2.12 14.48 2.41 17.76 0.74 6.86 1.15 9.09

ACCF 3.44 26.49 5.78 67.35 1.63 22.78 1.76 27.41 2.00 21.31 1.55 16.64 2.16 12.90 2.31 17.48 2.17 15.42 2.27 18.18 1.34 12.97 2.45 14.23 2.43 16.72 1.02 8.56 0.93 6.38

SIZE -0.35 -7.15 -0.27 -4.37 -0.03 -1.15 -0.01 -0.45 -0.04 -1.58 -0.01 -0.45 -0.09 -2.35 -0.13 -4.64 -0.17 -5.59 -0.21 -7.51 -0.38 -9.67 -0.29 -6.54 -0.23 -7.23 -0.06 -2.03 0.02 0.44

BM -0.95 -6.63 -0.66 -4.10 0.50 5.54 0.26 3.07 0.21 1.73 0.01 0.12 -0.16 -0.81 -0.12 -0.88 -0.19 -1.47 -0.39 -8.90 0.00 0.08 -0.06 -1.40 -0.25 -2.82 -0.39 -4.24 -0.08 -0.64

1.00 1.11

2.25 1.67

2.22 1.89

-0.15 -1.15

-0.15 -0.42

* t-Values appear below the regression coefficients; t-Values that are not significant at the 5 percent level of significance (or higher) are bold and italizied.

N 1034

Adj. R-Sqd. 0.68

985

0.96

943

0.37

903

0.47

887

0.37

881

0.24

918

0.17

969

0.29

986

0.23

1005

0.33

990

0.41

1003

0.51

997

0.29

1010

0.08

926

0.09

Table 10 Japanese Data for Capital Gain Return as a Function of Statement of Cash Flow Variables Plus Size and Book to Market * YEAR 1986-1990 1987-1991 1988-1992 1989-1993 1990-1994 1991-1995 1992-1996 1993-1997 1994-1998 1995-1999

Avg. Coefficent Fama-MacBeth t-Value

INTERCEPT 15.53 6.46 8.72 4.92 4.29 4.93 0.71 1.41 0.98 2.70 -1.06 -4.76 -1.08 -3.83 -1.64 -3.80 -1.87 -4.34 -2.52 -5.31

NOCF 3.21 3.10 2.97 5.70 2.85 8.08 2.56 9.97 2.35 10.98 1.74 12.58 1.45 9.46 1.91 10.99 1.67 10.72 2.68 11.31

ACCF 3.52 3.39 3.35 5.77 2.81 7.84 2.49 9.59 2.33 10.82 1.47 10.39 1.20 7.68 1.71 9.30 1.60 9.15 2.72 10.50

SIZE -0.59 -6.19 -0.34 -4.80 -0.18 -5.35 -0.05 -2.43 -0.06 -4.13 0.02 1.91 0.03 2.48 0.05 2.98 0.06 3.46 0.08 4.24

BM 0.04 0.78 0.02 0.43 -0.02 -0.82 -0.01 -0.64 -0.01 -0.51 0.03 2.87 0.01 1.14 -0.01 -0.96 -0.05 -3.07 -0.08 -3.48

2.21 0.38

2.34 3.83

2.32 2.89

-0.10 -0.46

-0.01 -0.23

N 166

Adj R-Sqd. 0.30

197

0.24

207

0.38

231

0.33

269

0.37

306

0.39

341

0.24

361

0.27

365

0.26

316

0.34

* t-Values appear below the regression coefficients; t-Values that are not significant at the 5 percent level of significance (or higher) are bold and italizied.

Table 11 Number of FCFE and NI Coefficients That were Significant at the .05 Level American

Japanese

FCFE

NI

FCFE

NI

Statistics are in Table Number

3

4

3

4

Number of Five Year Non-Overlapping Windows Number of Five Year Overlapping Windows

4 15

4 15

3 10

3 10

Number of Significant Intercepts • Non-Overlapping Five Year Windows • Overlapping Five Year Windows

4 15

2 11

3 5

3 10

Number of Significant Intercepts-Positive • Non-overlapping Five Year Windows • Overlapping Five Year Windows

3 13

1 5

1 5

1 2

1

4

1

3

8

15

5

10

Number of R2 >.20 • Non-overlapping Five Year Windows • Overlapping Five Year Windows

1 2

3 11

0 0

3 7

Number of R2 >.30 • Non-overlapping Five Year Windows • Overlapping Five Year Windows

1 1

2 7

0 0

1 3

Sample Size

(881 to 1034)

Number of Significant Coefficients with the hypothesized positive relationship to the rate of return FCFE or NI • Non-overlapping Five Year Windows • Overlapping Five Year Windows

(166 to 365)

Table 12 Number of Free Cash Flow to Equity (FCFE), Net Income (NI), Size, and Book/Market Coefficients That were Significant at the .05 Level American

Japanese

FCFE

NI

FCFE

NI

Statistics are in Table Number

5

6

5

6

Number of Five Year Non-overlapping Windows Number of Five Year Overlapping Windows

4 15

4 15

3 10

3 10

Number of Significant Intercepts • Non-overlapping Five Year Windows • Overlapping Five Year Windows

4 15

4 15

3 10

2 5

Number of Significant Intercepts – Positive • Non-overlapping Five Year Windows • Overlapping Five Year Windows

4 15

4 15

1 5

2 5

1+a 8+

4 15

1 6

4 15

210-b

2 9

2 5

1 5

0 1

1 7

2 4

2 5

2 4

3 11

1 1

3 10

1 3

3 8

0 0

2 7

Number of Significant Coefficients with the hypothesized relationship to the rate of return FCFE or NI • Non-overlapping Five Year Windows • Overlapping Five Year Windows ln SIZE • Non-overlapping Five Year Windows • Overlapping Five Year Windows B/M • Non-overlapping Five Year Windows • Overlapping Five Year Windows Number of R2 >.20 • Non-overlapping Five Year Windows • Overlapping Five Year Windows Number of R2 >.30 • Non-overlapping Five Year Windows • Overlapping Five Year Windows Number of R2 >.40 • Non-overlapping Five Year Windows • Overlapping Five Year Windows Sample Size a

b

1 0 5 2 (881 to 1034)

0 0 1 0 (166 to 365)

1+ significant FCFE coefficients with the correct positive relationship with the rate of return (r). 10- significant ln Size coefficients with the correct negative relationship with the rate of return (r).

Table 13 Number of Coefficients That were Significant at the .05 Level U.S. FCFE 7 4 15

NI 9 4 15

Statistics are in Table Number Number of Five Year Non-overlapping Windows Number of Five Year Overlapping Windows Number of Significant Intercepts 2 3 • Non-overlapping Five Year Windows 9 8 • Overlapping Five Year Windows Number of Significant Positive Intercepts 2 2 • Non-overlaping Five Year Windows 9 8 • Overlapping Five Year Windows Number of Significant Coefficients with the hypothesized relationship to the rate of return NOF Non-overlapping Five Year Windows 4+a NOF Overlapping Five Year Windows 14+ NIF Non-overlapping Five Year Windows 2-b NIF Overlapping Five Year Windows 6WCF Non-overlapping Five Year Windows 2WCF Overlapping Five Year Windows 11PFDDIV Non-overlapping Five Year Windows 1+ PFDDIV Overlapping FiveYear Windows 4+ LTD Non-Overlapping Five Year Windows 3+ LTD Overlapping Five Year Windows 9+ ln Size Non-Overlapping Five Year Windows 2ln Size Overlapping Five Year Windows 8B to M Non-overlapping Five Year Windows 3+ B to M Overlapping Five Year Windows 9+ NOCF Non-overlapping Five Year Windows 4+ NOCF Overlapping Five Year Windows 15+ ACCF Non-overlapping Five Year Window 4+ ACCF Overlapping Five Year Window 15+ Number of R2 >.20 13 12 2 Number of R >.30 8 8 Number of R2 >.40 6 5 Sample Size (881 to 1034) a

Japanese FCFE NI 8 10 3 3 10 10 2 9

3 9

1 4

1 4

2+ 9+ 0-c 000NA NA 0+ 1+ 152+ 5+

8 2

4+ 15+ 4+ 15+ 10 6

(166 to 365)

4+ means there were four significant NOF coefficients and they were positively related to the rates of return (r) on the common stock as hypothesized. This format is used throughout the remainder of the Table. b 2-indicates two of the significant NIF coefficients were negatively related to the rates of return (r) as hypothesized. This format is used throughout the remainder of the Table. c 0- means none of the NIF coefficients had a significant negative relationship to the rates of return (r) as hypothesized. This format is used throughout the remainder of the Table.