The Value Relevance of Earningsand the Prediction of Future Cash Flows

Oliver KimUniversity of Maryland

Steve C. Lim Taewoo ParkTexas Christian University University of Maryland

December 2005Very Preliminary

AbstractIn this paper we test the validity of the prediction test of future cash

flows as a substitute for the test of value relevance of earnings. We theo-retically show that the R2 of the cash flows prediction regression is conta-minated by (1) the relative presence of noise in future cash flows (2) therelative presence of noise in the covariance between future cash flows andcurrent earnings. We test if either of the above two factors contribute tothe result of Kim and Kross (2005) that the ability of earnings to predictone-year-ahead cash flows has increased over the recent decades, in con-trast to the evidence of decreasing value relevance of earnings presentedby others. We find empirical evidence that both factors contributed totheir result. From the significant presence of noise in cash flows (97%) andalso in the covariance (87%), we conclude that the cash flows predictiontest is a poor substitute for the test of value relevance of earnings, andperhaps of other accounting numbers as well.

1 Introduction

The purpose of this paper is to examine the implication of the prediction test of

immediate future cash flows by current earnings on the value-relevance of earnings.

We attempt to assess two seemingly conflicting views of cash flows manifested in

the existing literature. On the one hand, we have long adopted accrual accounting

over cash accounting, and archival evidence clearly shows that stock returns are more

closely associated with earnings than cash flows.1 On the other hand, the usefulness

of an accounting number is often gauged by its ability to predict future cash flows.2

Despite the appearance of a possible conflict between the two views, return association

tests and cash flows prediction tests have been used as the two most prominent tests

of the usefulness of an accounting number.

A recent paper by Kim and Kross (2005), however, brings the conflict to the

surface. They show that the ability of current earnings to predict one-year-ahead cash

flows has significantly increased over recent decades. Combined with the evidence of

deteriorating association between earnings and stock returns over the same recent

decades provided by Francis and Schipper (1999) and others, the two sets of results

beg for an explanation why value relevance and cash flows prediction diverge for

earnings. Kim and Kross (2005) describe it well: “If stock price is the present value

of future cash flows, the deterioration in the association between accounting earnings

and stock prices implies a growing inability of accounting numbers to forecast future

cash flows, but that is not what we find.”

The theoretical foundation for value-relevance tests is firmly established in the

1 For example, Dechow (1994) shows that earnings explain 16.2% of the variation in annual returnswhile cash flows from operations explain only 3.2%.2 This literature includes Finger (1994), Dechow, Kothari and Watts (1998), (and) Barth, Cramand Nelson (2001), and Kelly, Shores, and Tong (2003).

1

literature. For example, Kim and Verrecchia (1991) show in a short-window setting

that if a significant fraction of investors use certain information in their investment

decisions, the information will be impounded into the equilibrium price. Therefore,

an association of certain information with stock price or its change can be considered

as evidence that the information is used by investors. In a long-window setting, an

association with return indicates that either the information was used by the market

or at least the information reflects the beliefs of the market participants.

In contrast, the theoretical foundation for cash flows prediction tests is rather

weak. Investors as well as creditors are clearly concerned about a firm’s future cash

flows, and this is reflected in the concept statement of the Financial Accounting Stan-

dard Board that a primary objective of financial reporting is to provide information to

help investors, creditors, and others assess the amount and timing of prospective cash

flows (FASB 1978, 37-39). The problem is, however, that “prospective cash flows”

are elusive and difficult to pinpoint, because the term literally means all prospective

flows of cash. A researcher who wants to find a number that represents “prospective

cash flows” other than from the market (i.e., from the security price and its change)

encounters many problems. First, he has to choose a subset of cash flows among the

long cash flows series. Second, if cash flows of multiple years are chosen, he must de-

termine what weights to assign to cash flows of different years when combining them.

Third, observed cash flows of a particular period may contain period noise that cancel

one another across multiple periods and is thus ignored or discounted by the users of

accounting information. The above three problems are closely interrelated and must

be dealt with simultaneously.

For simplicity, most existing studies of cash flows prediction concentrate on a

small number of immediate future years’ cash flows, and a majority including Kim and

2

Kross (2005) on one-year-ahead cash flows. This practice ignores the first problem and

bypasses the second problem above, and has been accepted as a practical approach

in the literature.3 This study also investigates the prediction of one-year-ahead cash

flows by current earnings and, as a result, concentrate on the third problem above.

That is, one-year-ahead cash flows may be a very noisy proxy for “all prospective

cash flows” because they contain significant value-irrelevant noise.

The purpose of this paper is to resolve the conflict between result of decreasing

value-relevance of earnings and the result of increasing ability of earnings to predict

future cash flows focusing on noise in cash flows (and in earnings). We first develop a

theoretical model of stock returns, earnings, and cash flows in which earnings and cash

flows each consists of two additive components, value-relevant component and value-

irrelevant noise. As a result, all the variances and (contemporaneous and lagged)

covariances among returns, earnings, and cash flows also consist of the value-driven

portion and the noise-driven portion. We then define the value-relevance of earnings

and cash flows as the percentages of the value-driven portions in the variances. Simi-

larly, the value-relevance of predicting one-year-ahead cash flows by current earnings

is defined as the percentage of the value-driven portion in their covariance.

We then express the R2 of the return-earnings regression and the R2 of the cash

flows prediction regression as the value relevance of earnings contaminated by noise.

While the former is depressed by the presence of market noise, the latter is depressed

by the presence of noise in cash flows and also boosted by the presence of noise

in the covariance between one-year-ahead cash flows and current earnings. We test

hypotheses that the two factors contribute to the result of improving cash prediction

by earnings.

3 A notable related study is Dechow and Dicheve (2002) who consider past, current, and future cashflows, in their definition of earnings quality.

3

Our empirical results show that both of the above factors contributed to the

observation of Kim and Kross (2005). Based on our results, we conclude that the

cash flows prediction test is a poor substitute for the test of value relevance of an

accounting variable.

The paper is organized as follows. Section 2 present the model and section 3

analyzes the differences between the R2’s of the return-earnings regression and the

cash flows prediction regression and develops the two hypotheses. In section 4 we

develop value relevance measures and present empirical results in section 5. Section

6 concludes.

2 A Model of Return, Earnings, and Cash Flows

In order to analyze the differences between the value-relevance test and the cash

flows prediction test, we develop a model of return, earnings, and cash flows in which

all three variables are noisy. We first use an equation that expresses stock returns

consiting of two components. The first component reflects the change in the market’s

assessment of the value of the firm (i.e., in the market’s expectation of all future

payoffs by the firm) and the second component is unrelated to it. We assume that

the two components are additive and independent of each other. That is:

Rt = Xt + δt (1)

for all t, where Rt is the year t stock return, Xt is the value-related return, and δt is

value-irrelevant return which we call market noise. Given equation (1) and the fact

that returns are serially independent, we assume that Xt is serially independent and

normally distributed with variance v.

4

We specify earnings and cash flows in relation to equation (1) as:

Et = α1Xt + α2Xt−1 + εt (2)

and

Ct = β1Xt + β2Xt−1 + γt, (3)

where εt and γt are normally distributed independently of Xt’s and δt’s. In equa-

tions (2) and (3) earnings and cash flows are similarly characterized with different

parameters and are each decomposed into three components. The first components,

α1Xt and β1Xt, are priced in the same year and the second components, α2Xt−1 and

β2Xt−1, are priced in earlier years.4 The third components, εt and γt, are those that

are not priced in any year. The three components are mutually independent.

The second component is what is priced earlier than this year, and is due to the

fact that earnings and cash flows are not completely timely (Collins et al. 1994). This

untimeliness of an accounting measure is inevitable in order to guarantee a certain

degree of objectivity to the measure. For earnings, revenues are recognized when

earned and realizable and expenses are recognized when the matching revenues are

recognized. For cash flows, the criterion is the receipt and payment of cash. On the

contrary, the stock price responds to the expectations of future earnings and cash

flows. For example, consider a company that developed a promising new product

during a year. Stock price goes up reflecting the market’s expectation of increased

future earnings and cash flows due to the new product. However, earnings does

not increase until the firm manufactures and sells the product. Earnings may even

decrease in the current year due to the development costs of the new product that

4 Earnings and cash flows information is impounded into price more than one year early. However,we only consider year t − 1 to make things simple here. Combining years t − 2, t − 3, and t − 4generate qualitatively similar theoretical and empirical results.

5

are expensed. Also, cash flows generally reflects the sales even later than earnings

when cash is collected for the sales.

While (the lack of) timeliness concerns about how swiftly an accounting number

reflects information being incorporated in stock price, the other source of the imper-

fection of earnings and cash flows that is the focus of this paper is the components that

are never impounded into stock price, i.e., εt and γt. In this paper we consider these

portions as the components of earnings and cash flows that are not used by investors.

In this sense we will call εt and γt earnings noise and cash flows noise, respectively.

This period noise reflects the period fluctuations of earnings and cash flows that are

not priced because the fluctuations of different periods cancel each other out. Under

the current accounting system, this period noise reverses over time. In other words, if

earnings (or cash flows) of many consecutive periods are added up, the noise signifi-

cantly diminishes. While the reversal of the period noise automatically gives a degree

of negative autocorrelation, it is also possible that the direction of intended (e.g.,

income management) or unintended (e.g., ones due to applying a certain accounting

rules such as a decreasing-charge depreciation method) period noise may persist over

multiple years, giving a degree of positive autocorrelation. It is also reasonable to

assume that certain noise affects both earnings and cash flows, either in the same

year or with a lag. The magnitudes of the noise in earnings and cash flows, εt and

γt, , i.e., V ar(εt) and V ar(γt), and their auto- and cross-covariances, Cov(εt, εt−1),

Cov(γt, γt−1), Cov(εt, γt), Cov(εt, γt−1), and Cov(γt, εt−1), seem largely an empirical

issue and we do not make any assumption about their magnitudes at this point.

6

3 Value Relevance and Cash Flows Prediction

3.1 The Theoretical Differences

In this section we analyze the differences between the value-relevance test and the

cash flows prediction test using the model of section 2. The (theoretical value of the)

R2 of the contemporaneous return-earnings regression can be written as:

R2(Rt, Et) =[Cov(Rt, Et)]

2

V ar(Rt) · V ar(Et)

=(α1v)

2

[v + V ar(δt)] [(α21 + α22)v + V ar(εt)]

=v

v + V ar(δt)· α

21v

(α21 + α22)v + V ar(εt)

= V RR · V REcur. (4)

In the third expression of equation (4) the R2 is expressed as the product of two

terms. The first term, vv+V ar(δt)

, is the percentage of the value-related variance in

the variance of return and is directly affected by the relative presence of market

noise. This second term, α21v

(α21+α22)v+V ar(εt)

, is the percentage of the variance of the

component of earnings directly related to current return, i.e., the variance of α1Xt, in

the total variance of earnings. We will call this ratio the value-relevance of earnings

with respect to current return, denoted by V REcur. The two terms above are not

separately observable, and the R2 can be considered as a noisy measure of the value-

relevance of earnings depressed by vv+V ar(δt)

.5

We now write theR2 of the cash flows prediction regression and relate it to V REcur5 The regression coefficient, i.e., the earnings response coefficient, can be expressed as

α1v(α21+α

22)v+V ar(εt)

, which is different from the second term because α1 is not squared.

7

as follows:

R2(Ct+1, Et) =[Cov(Ct+1, Et)]

2

V ar(Ct+1) · V ar(Et)

=

£α1β2v + Cov(γt+1, εt)

¤2£¡β21 + β

22

¢v + V ar(γt+1)

¤[(α21 + α

22)v + V ar(εt)]

=[α1β2v]

2

[(α21 + α22)v + V ar(εt)]

£¡β21 + β

22

¢v + V ar(γt+1)

¤·∙α1β2v + Cov(γt+1, εt)

α1β2v

¸2=

α21v

(α21 + α22)v + V ar(εt)

· β22v¡

β21 + β22

¢v + V ar(γt+1)

·∙α1β2v + Cov(γt+1, εt)

α1β2v

¸2≡ V REcur · V RClag ·

1

(%V PCE)2. (5)

Equation (5) expresses the R2 of the cash flows prediction regression as the value-

relevance of earnings with respect to current return, V REcur, multiplied by two fac-

tors. The first factor is the value-relevance of cash flows with respect to lagged return,

i.e., V RClag =β22v

(β21+β22)v+V ar(γt+1)that depresses the measure. The second factor is the

squared inverse of the percentage of value-driven portion in Cov(Ct+1, Et), denoted

by , i.e., %V PCE, that boosts the measure because%V PCE ≡ α1β2vα1β2v+Cov(γt+1,εt)

< 1.

To summarize the implications of equations (4) and (5), while the R2 of the

contemporaneous return-earnings regression measures V REcur with market noise, the

R2 of the cash flows prediction regression measures V REcur with noise in one-year-

ahead cash flows and also with noise in the covariance between one-year-ahead cash

flows and current earnings.

8

3.2 The Observed Trends and Hypotheses Development

The analysis of last subsection enables us to track the sources of the discrepancy be-

tween the decreasing value relevance of earnings and the increasing ability of earnings

to predict one-year-ahead cash flows. This can occur if either or both of the following

have occurred. We divide the two factors into the following two hypotheses:

Hypothesis 1: The value-relevance of cash flows with respect to lagged return,

i.e., V RClag, has increased over the recent decades.

Hypothesis 2: The percentage of the value-driven portion in the covariance

between current earnings and one-year-ahead cash flows, i.e., %V PCE, has decreased

over the recent decades.

The above two hypotheses, if they can be tested, would generate valuable insights on

the usefulness of the cash flows prediction tests. However, variances and covariances

are always observed as the sums of value-driven and noise-driven portions, and there

is no easy way to separate them. The next section is devoted to developing measures

of V REcur, V RClag, and %V PCE in order to test hypotheses 1 and 2.

4 Measures of Value Relevance

4.1 Measuring the Percentage of the Value-Driven Varianceand Covariance

The value-relevance of a periodic performance measure such as earnings and cash

flows is understood in this paper as the degree to which the measure reflects the

firm’s value. We first write their variances as:

V ar(Et) =¡α21 + α

22

¢v + V ar(εt), V ar(Ct) =

¡β21 + β

22

¢v + V ar(γt).

9

The value-relevance of earnings, denoted by V RE, and the value-relevance of cash

flows, denoted by V RC, are each defined as:

V RE ≡ (α21 + α

22) v

(α21 + α22) v + V ar(εt)

, V RC ≡¡β21 + β

22

¢v¡

β21 + β22

¢v + V ar(γt)

.

In the above definition, the value-driven portion comes not only from the timely

contemporaneous association, but also from the delayed lagged association between

value and the performance measure. The definition is also similar to the concept

of signal-to-noise ratio, which is defined as the value-driven variance divided by the

noise-driven variance.6

We also define the value-relevance of earnings and cash flows with respect to either

the current return or lagged return. For example, the value-relevance of earnings with

respect to current return, denoted by V REcur, is defined by:

V REcur ≡α21v

(α21 + α22) v + V ar(εt)

,

and the value-relevance of cash flows with respect to one-year lagged return, denoted

by V RClag, is defined by:

V RClag ≡β22v¡

β21 + β22

¢v + V ar(γt)

.

Though the above definitions of value-relevance are natural, there is usually a

problem with measuring them because a firm’s value or its change (Xt) is rarely

observed separate from market noise (δt). The problem is illustrated below in the

attempt to compute the value-relevance of earnings and cash flows. Given a sample,

we first use the fact that the covariances between return and current or one-year-ahead

6 There is a one-to-one relation between the two, which can be written as SNR = V R1−V R or, wquiv-alently, as V R = SNR1+SNR .

10

earnings or cash flows can be measured and take the following simple forms:

Cov(∆Pt, Et) = α1v, Cov(∆Pt, Et+1) = α2v,

Cov(∆Pt, Ct) = β1v, Cov(∆Pt, Ct+1) = β2v. (6)

Using equation (6), parameters α2, β1, and β2 can be converted to a multiple of α1:

α2 =Cov(∆Pt, Et+1)

Cov(∆Pt, Et)·α1, β1 =

Cov(∆Pt, Ct)

Cov(∆Pt, Et)·α1, β2 =

Cov(∆Pt, Ct+1)

Cov(∆Pt, Et)·α1. (7)

Equation (7) allows us to write the variances of earnings and cash flows as follows:

V ar(Et) =

"1 +

µCov(∆Pt, Et+1)

Cov(∆Pt, Et)

¶2#α21v + V ar(εt), (8)

V ar(Ct) =

"µCov(∆Pt, Ct)

Cov(∆Pt, Et)

¶2+

µCov(∆Pt, Ct+1)

Cov(∆Pt, Et)

¶2#α21v + V ar(γt). (9)

We can also express the covariance between one-year-ahead cash flows and current

earnings as follows using equation (7):

Cov(Ct+1, Et) = α1β2v + Cov(γt+1, εt)

=Cov(∆Pt, Ct+1)

Cov(∆Pt, Et)· α21v + Cov(γt+1, εt), (10)

The percentage of value-driven portion in the above covariance, denoted by%V PCE,

can be written as:

%V PCE ≡ α1β2vα1β2v + Cov(γt+1, εt)

=

Cov(∆Pt,Ct+1)Cov(∆Pt,Et)

· α21vCov(∆Pt,Ct+1)Cov(∆Pt,Et)

· α21v + Cov(γt+1, εt). (11)

We can similarly define %V PEE, %V PEC, and %V PCC for other covariances in

the predictions of earnings by earnings, earnings by cash flows, and cash flows by

cash flows, respectively.

Equations (8), (9), and (10) indicate that for any given number of equations for

variances and covariances of earnings and cash flows and their observed values, we

11

have one more unknowns, namely, α21v, in addition to the variances and covariances

of noise in earnings and cash flows. Our approach here is not to impose any strong

assumptions about the relations between earnings and cash flows noise and increase

the number of equations or reduce the number of unknowns. Instead, we attempt to

investigate their upper bounds.

4.2 Procedure of Computing Value Relevance Measures

We seek to obtain a sufficiently tight upper bound for α21v that would in turn generate

sufficiently tight upper bounds for V REcur, V RClag, and %V PCE in equations (8),

(9), and (10). Then, they can be used as reasonable proxies for V REcur, V RClag,

and %V PCE themselves, respectively. An upper bound for α21v is chosen for each

year in the following way.

First, we assume that the value-relevance of return, V RR = vv+V ar(δt)

, stay the

same for different years, since the extent of market noise is not observable. Under

this assumption, the R2 of the regression of current earnings on current and lagged

returns is proportional to the value-relevance of earnings, V RE.

Second, we seek the maximum R2 of the above regression among all years and

assign V RE = 100% to the year and assign V RE of other years proportionally to

the R2 of the above regression. By doing this, we ensure that V RE of any given year

does not exceed 100%. This value of V RE for any given year can be understood as

the upper bound.

Third, once V RE is computed for each year, α21v can be solved from:

V RE ≡

∙1 +

³Cov(∆Pt,Et+1)Cov(∆Pt,Et)

´2¸α21v

V ar(Et), (12)

which is obtained from equation (8).

12

Fourth, compute V REcur, V RClag, and %V PCE by using equation (8), (9), and

(10).

5 Data and Empirical Results

5.1 Data

Our sample includes all non-financial firms (excluding firms with SIC 6000s), of which

accounting and return data are available from the CRSP and Compustat from 1970

through 2002. We follow the data screening procedure of Kim and Kross (2005).

Sample firms should have information on stock returns of the test period, and ac-

counting income, cash flow and asset amount up to next two years. After eliminating

top and bottom 1% of distribution of earnings, cash flows and returns, we analyze to-

tal 98,149 observations over 33 years. Following Kim and Kross (2005), and Dechow,

Kothari and Watts (1998), we define cash flows such that

CFO = Operating Income before Depreciation− Interest Expense (13)

+ Interest Revenue− Taxes−∆WC,

where ∆WC is the change in accounts receivable, inventory, other current assets

from year t − 1 to year t, minus change in accounts payable, taxes payable, other

current liabilities and deferred taxes from year t− 1 to year t. And E(Earnings) is

CFO + ∆WC − Depreciation. All variables are deflated by average assets. Stock

returns of period t is the compounded monthly return from the 4th month of year t

through the end of the third month after the fiscal year end.

13

5.2 Empirical Results

Table 4 gives the values of α21v, V REcur, V RClag, and %V PCE for all years from

1970 to 2002. First, the results support both hypotheses 1 and 2. In other words,

the increase in the R2 of the cash flows prediction by current earnings has increased

due both to an increase in V RClag (V REcur) and to a decrease in %V PCE.

Once we have seen the evidence that the decreasing value relevance of earnings

and improving prediction of one-year-ahead cash flows by earnings are caused by

the two factors, V REcur and %V PCE, a more interesting issue is the implications of

these results on the validity of the cash flows prediction test as a test of the usefulness

of an accounting number. Our answer is ‘No’ based on Table 4. Note from equation

(5) that:

R2(Ct+1, Et) = V REcur · V RClag ·1

(%V PCE)2.

The average value of V RClag for 33 years is only 3.01% which means that on average

96.9% of the variance in one-year-ahead cash flows is due to value-irrelevant noise.

Given the mean V REcur of 15.35%, an immediately question that arises is “how can

one use earnings to predict future cash flows, a less value-relevant periodic perfor-

mance measure, and expect to generate any information about the value-relevance of

earnings?”

The mean value of %V PCE is 12.88%. This means that 87.12% of the covariance

between one-year-ahead cash flows and current earnings is driven by noise, which

further muddles the interpretation of the cash flows prediction test results.

It is interesting to see that the value-relevance earnings is in general decreasing,

while the value-relevance of cash flows is increasing. The value-relevance gap between

the two measures is thus narrowing, but the gap still remains wide.

14

Another notable result is that the percentage of the value-driven portion is much

greater (on average 23.31% and 27.05% for earnings predictions versus for cash flows

predictions). This implies that earnings prediction results are more closely related to

value than cash flows prediction results.

6 Conclusion

In this paper we examine the sources of the discrepancy between decreasing value

relevance of earnings and increasing ability of earnings to predict one-year-ahead

cash flows. Our results cast doubts on the validity of using cash flows prediction

tests as tests of the value-relevance or usefulness of an accounting number, method,

or practice. Simply resorting to the FASB concept statement does not seem adequate

because “future cash flows” in the statement means an appropriately discounted sum

of all future cash flows without errors, and not cash flows of a particular period or

periods which include only a fraction of future cash flows with significant noise. The

noise in cash flows (and any periodic performance measure such as earnings) arises

from fluctuations of cash flows that even out over multiple periods and thus are not

priced. For example, a bird in hand does not count if a bird this year implies one less

bird next year. Also, why do we regress to cash flows after having evolved from cash

flows to earnings long time ago?

Our analysis is limited in many ways. For example, we concentrate on one-year-

ahead cash flows, and do not provide guidance as to how to choose and combine

multiple periods’ cash flows.

One caveat is that our criticism of the cash flows prediction literature should

in no way be construed as a statement that cash flow information is not useful to

investors and creditors. Cash flows are in general a good source of information that

15

is complementary to information that can be extracted from earnings (e.g., DeFond

and Hung 2003). Moreover, much of the noise in cash flows may be removed by

observing the components of cash flows or other information such as footnotes and

newspaper articles. We are just cautioning against the use of cash flows tests as tests

of usefulness without qualifications.

16

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[16] Ryan, S.G. and P.A. Zarowin. "Why Has the Contemporaneous Linear Returns-Earnings Relation Declined?" The Accounting Review 78 (2003): 523-553.

[17] Zach, Tzachi. "Predicting future cash flows: Current earnings or current cashflows?" Working Paper (Washington University) 2001.

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Table 1 Descriptive Statistics

Variables Mean Std. Dev. Median C 5.01 12.64 6.81 E 1.70 11.39 3.75 R 11.53 53.43 4.08 The sample includes 98,149 firm observations during 1970 through 2002. C is the cash flow from operations such that C = operating income before depreciation - interest expense + interest revenue – taxes - ∆WC, where ∆WC = changes in accounts receivable, inventory, other current assets from year t-1 to year t, minus changes in accounts payable, taxes payable, other current liabilities and deferred taxes from year t-1 to year t. E is earnings such that E = C + ∆WC - Depreciation. All variables are at percentage, deflated by average assets. R is the compounded monthly return at percentage from the fourth month of the fiscal year through the end of the third month after the fiscal year end.

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Table 2 Trends of the R2 from return and cash flows prediction regressions

(1) Earnings - Return Model : 0 1t t tE Rα α ε= + + (2) Earnings - Return Model : 0 1 2 1t t t tE R Rα α α ε−= + + + (3) Cash Flow - Return Model : 0 1 2 1t t t tC R Rβ β β γ−= + + + (4) Cash Flow Forecasting Model : 1 0 1t t tC Eδ δ ϕ+ = + +

Model 1 Model 2 Model 3 Model 41970 8.67 31.44 6.21 5.871971 13.93 26.78 6.79 4.631972 7.29 17.70 3.63 3.351973 3.05 12.82 6.94 3.161974 7.60 14.52 7.43 5.231975 6.10 14.70 6.99 9.241976 3.53 10.67 2.67 6.411977 4.59 9.11 3.12 10.761978 4.13 8.41 0.72 10.451979 3.80 5.83 2.17 12.801980 6.15 9.05 2.13 15.061981 7.55 13.96 2.83 18.581982 4.71 14.84 2.90 24.771983 2.63 9.29 1.30 19.571984 12.99 14.99 8.05 25.391985 11.26 19.05 7.99 23.941986 5.86 13.23 3.18 21.981987 4.23 6.79 2.66 24.831988 8.91 11.20 4.23 28.791989 10.06 14.40 5.93 28.541990 6.11 10.32 2.82 33.551991 2.42 6.96 0.35 34.121992 3.93 3.93 3.77 35.871993 2.31 3.61 0.56 40.291994 6.93 7.88 4.54 40.291995 1.27 7.95 2.06 38.701996 5.62 5.99 3.93 42.621997 7.91 10.29 5.30 43.591998 2.27 6.33 3.01 38.631999 0.61 1.05 0.36 43.812000 9.16 9.87 7.36 45.702001 3.93 10.70 6.08 49.622002 10.02 14.41 10.27 56.68

Average R2 6.05 11.46 4.19 25.66

% point change per year -0.05 -0.34 0.01 1.58t-value -0.75 -3.49 0.16 30.56

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The table reports percentage R2’s from the return regression models and the cash forecasting model. Each yearly regression includes observations of which the fiscal year ends during the specific calendar year. C is the cash flow from operations such that C = operating income before depreciation - interest expense + interest revenue – taxes - ∆WC, where ∆WC = changes in accounts receivable, inventory, other current assets from year t-1 to year t, minus changes in accounts payable, taxes payable, other current liabilities and deferred taxes from year t-1 to year t. E is earnings such that E = C + ∆WC - Depreciation. All variables are at percentage, deflated by average assets. R is the compounded monthly return at percentage from the fourth month of the fiscal year through the end of the third month after the fiscal year end. The last two rows report the slope coefficients (% point change per year) and t-values from the trend regression of the model 2 0 1t t tR Yearθ θ σ= + + . In the trend regression, the year of 1999 is excluded because the stock return is unusually negatively correlated with earnings or cash flows of the year.

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Table 3 Variance, Covariance and R square over time

Panel A : Earnings and Cash Flows

1970-1986 1987-2002 Later/Earlier Ratio

Var(Et) 55.00 163.29 2.97

Var(Ct) 36.52 111.66 3.06

Cov(Et+1, Et) 42.53 128.49 3.02

Cov(Ct+1, Ct) 36.52 111.66 3.06

Cov(Et, Ct) 41.20 136.06 3.30

Cov(Et+1, Ct) 36.62 115.01 3.14

Cov(Ct+1, Et) 27.78 108.86 3.92

Panel B : Stock Returns

1970-1986 1987-2002 Later/Earlier Ratio

Var(Rt) 21.15 26.71 1.26

Cov(Rt, Et) 82.01 148.14 1.81

Cov(Rt, Ct) 79.85 120.24 1.51

Cov(Rt, Et+1) 101.10 166.70 1.65

Cov(Rt, Ct+1) 27.06 78.88 2.92

Panel C : Regression R squares

1970-1986 1987-2002 Later/Earlier Ratio

R2(Et, Rt) 6.49 5.68 0.88

R2(Ct+1, Rt) 0.85 1.88 2.22

R2(Et, Rt and Rt-1) 14.57 8.99 0.62

R2(Ct+1, Et) 12.45 37.74 3.03

The table reports the averages of annual variances(Var), covariances(Cov) and regression R squares(R2) over the earlier 16 years (1970-1985) and the later 16 years (1986-2002, except for 1999). The year of 1999 is excluded because the stock return is unusually negatively correlated with earnings or cash flows of the year. C is the cash flow from operations such that C = operating income before

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depreciation - interest expense + interest revenue – taxes - ∆WC, where ∆WC = changes in accounts receivable, inventory, other current assets from year t-1 to year t, minus changes in accounts payable, taxes payable, other current liabilities and deferred taxes from year t-1 to year t. E is earnings such that E = C + ∆WC - Depreciation. All variables are at percentage, deflated by average assets. R is the compounded monthly return at percentage from the fourth month of the fiscal year through the end of the third month after the fiscal year end. The last column reports the ratio of later period average over that of earlier period.

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Table 4 Trends of Key Value Relevance Measures

Percent Value-driven

Year α12ν VREcur VRClag PEE PEC PCE PCC1970 8.72 35.33 7.04 64.02 118.01 64.02 44.99 1971 14.34 48.19 0.09 63.97 59.79 9.97 3.73 1972 5.26 22.20 1.85 35.20 53.40 34.54 13.31 1973 1.57 6.66 12.41 19.99 57.44 49.15 37.51 1974 5.84 19.43 0.70 32.46 57.88 16.92 19.20 1975 7.08 19.73 0.45 31.16 51.57 9.95 13.55 1976 5.84 16.08 0.02 22.77 32.78 0.41 0.39 1977 4.35 12.31 0.70 18.59 27.43 9.20 6.34 1978 3.61 10.07 0.05 15.40 11.12 0.40 0.29 1979 2.82 6.00 0.07 10.45 12.59 1.80 1.18 1980 7.07 12.17 0.23 18.84 17.39 4.13 2.86 1981 11.26 16.70 1.18 26.63 22.93 10.38 7.14 1982 14.59 14.60 0.45 28.42 24.58 5.06 3.57 1983 11.78 13.19 0.05 17.91 15.74 0.39 0.35 1984 24.58 21.32 6.33 31.59 36.27 24.27 22.41 1985 30.76 24.07 5.11 37.82 34.53 22.80 16.96 1986 30.04 22.26 1.60 31.42 25.86 13.54 9.19 1987 12.72 9.78 1.69 13.57 13.38 8.03 6.39 1988 28.52 19.07 3.31 22.99 20.69 14.85 11.19 1989 30.78 22.83 2.48 29.92 28.06 14.21 11.28 1990 19.55 15.02 0.94 22.10 15.93 6.90 4.31 1991 12.46 10.61 1.36 14.04 3.77 0.46 0.37 1992 5.19 4.43 0.90 7.24 7.25 3.30 2.73 1993 6.85 4.46 0.55 6.61 4.43 2.40 1.35 1994 17.57 10.36 3.19 15.77 16.13 9.10 7.87 1995 14.11 8.41 0.17 15.15 11.00 0.40 0.35 1996 14.26 8.13 2.95 11.55 11.33 7.34 6.36 1997 25.40 13.67 7.24 19.11 18.93 14.86 12.71 1998 15.51 8.20 2.03 12.96 12.03 6.41 5.28 1999 3.99 2.26 4.34 1.90 1.47 4.69 3.36 2000 33.88 14.86 6.26 20.17 18.75 14.53 12.84 2001 30.20 13.02 8.17 20.87 20.91 14.86 13.82 2002 41.80 21.16 15.59 28.48 29.34 25.79 24.52

Average 15.22 15.35 3.01 23.31 27.05 12.88 9.93

% changes per year 0.724 -0.400 0.123 -0.735 -1.550 -0.474 -0.241 t-value 4.540 -2.560 1.780 -3.400 -4.640 -1.840 -1.220

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The table reports trends of key value relevance measures at percentage.

2 2 2 2 21 max 1( ) ( ) (1 ( , ) ( , ) )t t t t tR R Var E Cov R E Cov R Eα ν += × + ,

21 ( )cur tVRE Var Eα ν= ,

2 2 21 1 1( ( , ) ( , ) ) ( )lag t t t t tVRC Cov R C Cov R E Var Cα ν+ += × ,

21 1 1( ( , ) ( , )) ( , )t t t t t tPEE Cov R E Cov R E Cov E Eα ν+ += × ,

21 1 1( ( , ) ( , )) ( ( , ) ( , )) ( , )t t t t t t t t t tPEC Cov R C Cov R E Cov R E Cov R E Cov E Cα ν+ += × × ,

21 1 1( ( , ) ( , )) ( ( , ) ( , )) ( , )t t t t t t t t t tPCE Cov R E Cov R C Cov R C Cov R C Cov C Eα ν+ += × × ,

21 1 1( ( , ) ( , )) ( , )t t t t t tPCC Cov R C Cov R C Cov C Cα ν+ += × ,

where R2 is the R squares from the yearly regression of 0 1 2 1t t t tE R Rα α α ε−= + + + , and R2

max is the maximum R2 from the above yearly regression over 33 years. Var( ) and Cov( ) represent the variance or covariance. C is the cash flow from operations such that C = operating income before depreciation - interest expense + interest revenue – taxes - ∆WC, where ∆WC = changes in accounts receivable, inventory, other current assets from year t-1 to year t, minus changes in accounts payable, taxes payable, other current liabilities and deferred taxes from year t-1 to year t. E is earnings such that E = C + ∆WC - Depreciation. All variables are at percentage, deflated by average assets. R is the compounded monthly return at percentage from the fourth month of the fiscal year through the end of the third month after the fiscal year end. The last two rows report the slope coefficients (% changes per year) and t-values from the trend regression of the model 0 1t t tMeasures Yearθ θ σ= + + . In the trend regression, the year of 1999 is excluded because the stock return is unusually negatively correlated with earnings or cash flows of the year.