Cash Flow Patterns as a Proxy for Firm Life Cycle

8/14/2019 Cash Flow Patterns as a Proxy for Firm Life Cycle

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Cash Flow Patterns as a Proxy forFirm Life Cycle

Victoria Dickinson, PhD, CPAE. H. Patterson School of Accountancy

University of Mississippi

Current Draft: November 2010

Correspondence: Victoria Dickinson, University of Mississippi – E.H. Patterson School of Accountancy, Conner 204C,University, MS 38677; Phone: (662) 915-5448; Fax: (662) 915-7483; email: [email protected].

This paper is based on my dissertation at the University of Wisconsin – Madison. I would like to thank the members ofmy committee: Don Hausch, Jed Frees, Holly Skaife, Terry Warfield, and John Wild (Chair), along with Mike Donohoe,Frank Heflin, Ryan LaFond, Matt Magilke, Bill Mayew, Brian Mayhew, Per Olsson, K. Ramesh, Greg Sommers, Jenny

Tucker and Rodrigo Verdi for their helpful discussions and comments. This paper has also benefited from thecomments of conference participants at the American Accounting Association and from workshop participants at theCollege of William and Mary, Florida State University, Miami University, University of Alabama at Birmingham,University of Florida, University of Mississippi, University of Utah, and University of Wisconsin - Madison.

mailto:[email protected]





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Cash Flow Patterns as a Proxy forFirm Life Cycle

Abstract: This paper examines the validity of cash flow patterns as a proxy for firm life cycle. Cash

flow patterns provide a parsimonious, but robust, indicator of firm life cycle stage that is free from

distributional assumptions inherent when using a univariate or composite measure. Life cycle stage

is an important determinant of the level and time series properties of profitability. Return on net

operating assets (RNOA) does not mean-revert (spread of seven percent after five years) when

sorted by life cycle stage which has implications for forecasting growth rates and for determining

forecast horizons. Determinants of future profitability identified in prior literature such as asset

turnover and profit margin are differentially affected by life cycle stage. Furthermore, market

participants undervalue mature firms, specifically those with extreme book-to-market ratios. The

cash flow pattern proxy has numerous applications in forecasting and analysis and is a useful control

variable for future research.



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1. Introduction

Business firms are evolving entities and the path of evolution is determined by internal

factors (e.g., strategy choice, financial resources, and managerial ability) and external factors (e.g.,

competitive environment, macroeconomic factors). Firm life cycles are distinct phases that result

from changes in these factors, many of which arise from strategic activities undertaken by the firm.

Lev and Zarowin (1999) document that: (1) the rate of business change has increased over time, and

(2) the value-relevance of earnings has decreased over time. Taken together, these findings suggest

that a non-earnings-based measure that captures firm life cycle stage would be useful to investors

and creditors. In response, this paper develops and validates a parsimonious proxy for firm life

cycle based on a firm s cash flows patterns.

Capturing life cycle at the firm level (rather than at the individual product or industry level) 1

is a difficult undertaking. The firm is an aggregation of multiple products, each with a distinct

product life cycle stage. Additionally, the firm may compete in multiple industries such that its

product offerings are quite diverse. As a result, firm-level life cycle stage is difficult to assess

because it is a composite of many overlapping, but distinct product life cycle stages.

The economics literature has addressed individual attributes of life cycle theory such as

production behavior (Spence 1977, 1979, 1981; Wernerfelt 1985; Jovanovic and MacDonald 1994),

learning/experience (Spence 1981), investment (Spence 1977, 1979; Jovanovic 1982; and Wernerfelt

1985), entry/exit patterns (Caves 1998), and market share (Wernerfelt 1985). I propose a life cycle

proxy based on accounting information (specifically cash flow patterns) that can be linked to these

constructs from the extant economics literature.

1 The following studies examine the validity of product life cycle for the following industries: German automobilemanufacturers (Brockhoff 1967); pharmaceuticals (Cox 1967); tobacco, food, and personal care products (Polli andCook 1969); household cleansers (Parsons 1975).



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Anthony and Ramesh (1992) was one of the first studies to demonstrate the usefulness of

firm life cycle in explaining market performance. However, their sample period ended before the

Statement of Cash Flows was a required disclosure. Therefore, their life cycle measure relied on a

composite of economic characteristics such as sales growth, dividend payout, capital expenditures,

and firm age. By necessity, their life cycle proxy had to rely on portfolio sorts to draw distinctions

between the life cycle stages. On the other hand, the classification scheme used in this paper is

accomplished by using a firm s operating, investing, and financing cash flows in combination to

assign life cycle stage. The classification methodology is “organic” in that life cycle stage

identification is the result of the firm s performance and allocation of resources , as opposed to

arbitrary assignment.

I use the cash flow patterns proxy to document the economic characteristics and market

behavior of firms within each life cycle stage. Specifically, I validate the cash flow proxy in relation

to competing measures for firm life cycle and find that it is better aligned with the functional form

of firm profitability. Economic theory predicts a nonlinear progression of variables such as

earnings, return on net operating assets (RNOA) 2

, asset turnover (ATO), profit margin (PM), sales

revenue, leverage, dividend payout, size and age across the life cycle continuum which is consistent

with the distribution that results from using cash flow patterns as a life cycle proxy.

Once the descriptive validity of the cash flow pattern proxy for life cycle is established, I

examine which life cycle stages demonstrate persistence in profitability and investigate the inter-

temporal convergence of profitability by life cycle stage. Previous research documents that

profitability measures mean-revert over time (Brooks and Buckmaster 1976; Freeman, Ohlson and

2 RNOA removes the effect of financing from the profitability metric and is measured as operating income divided bynet operating assets (NOA). NOA excludes financial assets from the denominator since they are already valued at fair

value on the balance sheet. NOA also subtracts out operating liabilities from operating assets. This is because operatingliabilities reflect a source of leverage that can increase profitability.



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Penman 1982; Fairfield, Sweeney and Yohn 1996; Fama and French 2000; Nissim and Penman

2001) and understanding the evolution of profitability improves predictability. Conditioning an

inter-temporal analysis by life cycle stage is expected to explain differences in convergence rates

across firms. The results support that prediction. Specifically, RNOA maintains a differential

spread of three to 10 percent between decline and mature firms even after five years. This difference

is economically significant and suggests differences in firm life cycle are an impediment to the mean-

reversion of profitability.

Prior research has demonstrated that changes in future accounting returns (specifically

RNOA) are explained by level and change of current profitability, growth in net operating assets,

and by increases in the asset turnover (ATO) (Fairfield and Yohn 2001). Since firm life cycle stage

differentially explains profitability, including the cash flow pattern proxy for life cycle also provides

significant information about future change in RNOA, and the explanatory power of the cash flow

pattern proxy outperforms alternative life cycle proxies. Furthermore, the explanatory power of

changes in ATO for changes in RNOA is concentrated in the mature life cycle stage. This is

consistent with economic theory that states competitive pressures will drive mature firms to focus

on efficiency and cost containment. Also, Penman and Zhang (2006) find that increases in profit

margin (PM) result in negative future RNOA because those increases are achieved through a

reduction of operating expenses which are not sustainable. Again, this effect is concentrated in the

mature life cycle stage, where product differentiation efforts (which manifest in the PM) have

reached diminishing returns (Oster 1990, Shy 1995).

Considering that life cycle affects non-convergence of profitability over time and that life

cycle differences interact with the determinants of profitability, the next step is to investigate what

role life cycle plays in understanding current firm value and predicting stock returns. The market

does not fully capture information provided by the life cycle proxy such that mature firms earn



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positive excess returns in the year following life cycle stage assignment. This indicates that investors

underestimate the persistence of the elevated profitability of mature firms and instead expect their

profitability to mean-revert to a “normal” level.

Prior literature has found that profitable trading strategies can be developed based on

extreme values of the book-to-market ratio (B/M) where low B/M firms are referred to as glamour

firms and high B/M firms are considered value firms (Fama and French 1992, Lakonishok et. al.

1994). Two common B/M trading strategies (Piotroski 2000, Mohanram 2005) focus on using

fundamental analyses to separate out firms that are undervalued versus those that overvalued among

the glamour/value firms. The fundamental analyses used in this line of research are comprised of

composite scores of numerous metrics (ranging from eight to nine signals for each fundamental

analysis score). The cash flow pattern proxy for life cycle provides a simple and effective way to

identify the “winners” among both B/M extremes using considerably less data. All market results

are robust to consideration of delisting returns and execution issues regarding shorting illiquid

securities.

In summary, this paper presents and validates cash flows patterns as a parsimonious proxy

for identifying firm life cycle stage. This classification is useful in the following contexts: (1) to

better assess growth rates and forecast horizons in valuation models; (2) to better understand how

economic fundamentals affect the level and convergence properties of future profitability; (3) to

identify firms where potential unidentified risk factors and/or market mispricing exist based on

differences in life cycle stage; (4) as a control variable for distinct economic characteristics of the

firm related to firm life cycle that affect firm performance. These contributions benefit equity

investors, creditors, auditors, analysts, regulators, and researchers alike. The remainder of the paper

is organized as follows: Section 2 presents and validates the firm life cycle proxy, Section 3



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demonstrates the usefulness of the proxy in explaining future profitability, Section 4 examines the

market implications of life cycle information for future stock returns, and Section 5 concludes.

2.Is the proposed life cycle classification scheme descriptively more valid?

Gort and Klepper (1982) define five life cycle stages: (1) an introductory stage, where an

innovation is first produced; (2) a growth stage, where the number of producers increases dramatically;

(3) a maturity stage, where the number of producers reaches a maximum; (4) a shake-out stage, where

the number of producers begins to decline; and (5) a decline stage, where there is essentially zero net

entry. I propose that cash flows capture the outcome of these distinct life cycle stages. Livnat and

Zarowin (1990) document that the decomposition of cash flows into operating, investing and

financing activities differentially affects stock returns. Therefore, cash flows capture differences in a

firm s profitability, growth, and risk ; and the combination of those cash flows are mapped into life

cycle theory to derive the life cycle classification used throughout the paper. A survey of economic

theory related to life cycle and the predicted relation to cash flows is summarized in Table 1.

The combination of cash flow patterns represents the firm s resource allocation and

operational capabilities interacted with the firms choice in strategy. Predictions about each cash

flow component can be derived from economic theory which forms the basis for the cash flow

patterns proxy for life cycle. For example, introduction firms lack established customers and suffer

from knowledge deficits about potential revenues and costs, both of which result in negative

operating cash flows (Jovanovic 1982). However, profit margins are maximized during increases in

investment and efficiency (Spence 1977, 1979, 1981; Wernerfelt 1985) which means that operatingcash flows are positive during the growth and maturity stages. Wernerfelt (1985) points out that

declining growth rates will eventually lead to declining prices such that operating cash flows will

decrease (and become negative) as firm enter the decline stage.



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Managerial optimism (Jovanovic 1982) encourages firms to make early investments which

ultimately serve to deter entry into the market by competitors (Spence 1977, 1979, 1981).

Consequently, investing cash flows are negative for introduction and growth firms. While mature

firms decrease investment relative to growth firms, they will invest to maintain capital (Jovanovic

1982, Wernerfelt 1985). If the cost of maintenance increases over time (i.e., rising prices), investing

cash flows are negative for mature firms, although at a lesser magnitude than cash outflows for

introduction and growth firms. Decline firms will liquidate assets in order to service existing debt

and to support operations which results in positive cash flows from investing.

Pecking order theory states that firms initially access bank debt followed by equity later in

their life (Myers 1984, Diamond 1991). Barclay and Smith (1995) demonstrate that growth firms will

access debt that is shorter in duration than mature firms. Taken together, financing cash flows are

positive for introduction and growth firms. However, mature firms will begin to service debt and

distribute cash to shareholders as they exhaust positive net present value investment opportunities,

which results in negative financing cash flows. There is a void in the literature with respect to

whether financing cash flows will be positive or negative for decline firms.3

The combination of a firm s patterns of operating, investing, and financing cash inflows

and outflows provide a firm life cycle mapping at a given point in time. By using the sign (positive

or negative) of the net operating, investing and financing cash flows, eight possible cash flow pattern

combinations exist.4 The eight classifications are collapsed into the five practical life cycle stages

3 Likewise, the literature is silent regarding cash flows for shake-out firms. As a result, shake-out firms classified bydefault if the cash flow patterns do not fall into one of the other theoretically-defined stages. 4 Incorporating the sign and magnitude of the cash flows would likely improve performance of the proxy. However, ifpositive (negative) cash flows were separated into low- and high-positive (negative) cash flows, the number of patterns

would increase to 64, which is less straightforward to connect to economic theory. For that reason, only sign isconsidered.



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(mentioned at the beginning of the section): introduction, growth, mature, shake-out, and decline

based on expected cash flow behaviors from Table 1. 5

A benefit of the cash flow pattern proxy used in this paper, is that it uses the entire financial

information set contained in operating, investing, and financing cash flows rather than a single

metric to determine firm life cycle. As mentioned in the previous section, prior literature uses sorts

on variables such as age, sales growth, capital expenditures, dividend payout or some composite of

these variables to assess life cycle stage (Anthony and Ramesh 1992, Black 1998). The drawback of

these methods, however, is that an ex ante assumption is required regarding the underlying

distribution of life cycle membership. By forming portfolios sorted on a single variable (or a

composite of those sorts), a uniform distribution of life cycle stages across firms is inherently

assumed. Cash flow patterns, on the other hand, are the organic result of a firm s operations and

achieve better congruence with economic theory (i.e., a normal distribution).

Both size and firm age are common proxies for life cycle.6 When size and age are used as a

life cycle proxy, an implicit assumption is that a firm moves monotonically through its life cycle.

This assumption arises because product life cycles are characterized by forward progression from

introduction to decline. However, a firm is a portfolio of multiple products, each at potentially a

different product life cycle stage. Substantial product innovations, expansion into new markets or

5 There are three cash flow types (operating, investing, and financing) and each can take a positive or negative sign whichresults in 23 = 8 possible combinations. The 8 patterns are collapsed into five stages as follows:

6 Recent accounting research that relies on firm size or age to capture life cycle effects includes Bradshaw et al. (2010),Khan and Watts (2009), Caskey and Hanlon (2007), Doyle et al. (2007), Desai et al. (2006), Freeman et al. (2006), Kleinand Marquardt (2006), Wasley and Wu (2006), Bhattacharya et al. (2004), and Chen et al. (2002). An abstract search for“firm age” in SSRN yielded 592 results while a search for “firm size” exceeded the maximum results of 1,000 papers.

1 2 3 4 5 6 7 8

Int roduct ion Growth Mature Shake-Out Shake-Out Shake-Out Decline Decline

Predicted sign Cash flows from operating activities – + + – + + – – Cash flows from investing activities – – – – + + + + Cash flows from financing activities + + – – + – + –



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structural change can cause firms to move across life cycle stages non-sequentially. For that reason,

firm life cycle can be cyclical in nature and the firm s primary goal is to maintain its firm life cycle at

the growth/mature stage where the reward-risk structure is optimized.

Additionally, firms can enter the decline stage from any of the other stages. The

management literature documents a “liability of newness” phenomenon (Stinchcombe 1965 ;

Jovanovich 1982, Freeman, Carroll and Hannan 1983; Amit and Schoemaker 1993), which means

that variation in the level of initial endowments (monetary resources, technological or managerial

capability, etc.) interacts with mortality rates.7 Therefore, firms in the decline stage are likely to

include very young firms that succumb to this high initial mortality rate. Additionally, firm life cycle

differs from firm age because firms of the same age can learn at different rates due to imperfections

in their feedback mechanisms (i.e., accounting quality). All of these factors result in a misalignment

between firm performance and firm age causing life cycle progression to be nonlinear in age. Taken

together, size and age should be maximized during the mature stage due to nonlinearity.

The first step of this paper is to validate whether the life cycle stages based on cash flow

patterns are consistent with economic theory with empirical analysis. Firms listed on the NYSE,

AMEX and NASDAQ exchanges (excluding ADRs) with necessary data on Compustat comprise

the sample. The sample period extends from 1989 (the first year data from the Statement of Cash

Flows was available for all firms) through 2005. Firms with average net operating assets (NOA),

sales revenue, or market value of equity less than $1 million are excluded from the sample because

small denominators skew the profitability metrics used throughout the paper. Similarly, firms with

an absolute book value of equity less than $1 million are excluded from the sample. Firms in the

financial industries are excluded due to the unique nature of their cash flows. Firms with SIC codes

7 For example, Jovanovic (1982) presents an analytical model where firms hazard rates (probability of failure) initiallyincrease in the early life cycle stages.



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greater than 9100 are omitted to ensure only for-profit firms are included in the sample. These

constraints result in a final sample of 48,369 firm-year observations.

If mature firms are stable, then the greatest frequency of observations will be present in this

category, while the lowest frequency of observations will be in the decline stage. Table 2 – Panel A

confirms this prediction with 41 (five) percent of the firms classified as mature (decline). The effect

of firm life cycle on several economic characteristics is tested by regressing each economic

characteristic on indicator variables for life cycle membership, with the intercept capturing the

mature stage. The coefficients on introduction, growth, shake-out and decline are the effect on the

dependent variable relative to the mature stage.

[Insert Table 2 about here]

Economic theory predicts that profitability is maximized in the mature stage and this is

confirmed by the regressions on Earnings per Share ( EPS ) and Return on Net Operating Assets

( RNOA ) (all coefficients except for mature are negative). The components of profitability, profit

margin and asset turnover, are a function of strategy and the competitive environment. For

example, Selling and Stickney (1989) point out that product-differentiating firms focus on research

and development, advertising, and capacity enlargement. These expenditures should result in a

higher profit margin ( PM ), which results confirm is maximized in the mature stage. Selling and

Stickney also indicate that as firms mature, competition becomes more intense and the emphasis

shifts to cost reduction and improved capacity utilization. This means that asset turnover ratios

( ATO ) should increase in the mature stage, which is confirmed by the regression results (the

coefficient for growth firms is negative which indicates that asset turnover in the growth stage is

lower relative to the mature stage). The high level of ATO in the introduction stage may be due to

investments in uncapitalized assets such as research and development and/or operating leases.



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Immediate expensing of these assets result in lower GAAP asset levels, which in turn depress ATO

(and RNOA ) relative to mature stage firms.8

Growth in sales ( GrSALES ) and capital investment ( GrNOA ) should monotonically

decrease across life cycle stages (Spence 1977, 1979, 1981), both of which are verified for

introduction through shake-out. Market-to-book ( MB ) is thought to proxy for both expected future

growth and risk. This suggests that mature firms should possess the lowest relative market-to-book

as compared with the tail observations and the results support this prediction. With respect to other

measures of risk, firms should make greater use of financial leverage ( LEV ) in the growth stage

(Myers 1984, Diamond 1991) and asset beta ( ASSET BETA ) (an unlevered measure of business

risk) should be minimized for mature firms. Dividends ( DIVPAY ) are more likely to be paid by

mature firms due to decreased investment opportunities. The results confirm the above for LEV ,

ASSET BETA and DIVPAY .

Advertising intensity ( ADVINT ) and research and development ( INNOV ) should be

highest for early-stage firms as they build their initial technology. Both variables are highest in the

introduction stage (although decline firms appear to increase their research and development,

perhaps in a turnaround attempt). The number of segments ( SEGMENTS ) is expected to increase

through maturity as growth is executed via product and/or geographical expansion, which the

results confirm. Merger activity ( MERGER ) should be greatest for growth firms as they will likely

be targets for acquisition and results indicate that introduction and growth stages are where the

highest degree of activity takes place. Finally, size ( SIZE ) and age ( AGE ) are maximized for mature

stage firms consistent with life cycle being nonlinear in both of these variables. Cash flow patterns

8 I thank one of this paper s reviewers for providing this insight.



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result in a proxy that is representative of the economic theory underlying the life cycle

phenomenon. 9

The preceding analysis is repeated for life cycle classifications based on Anthony and

Ramesh (1992) (Table 2, Panel B) and age quintiles (Table 2, Panel C). In Anthony and Ramesh

paper, the median values of dividend payout, sales growth, and capital expenditure (scaled by market

value) are computed over a five-year horizon. Those values, along with age are used to assign scores

to each observation.10 Composite scores are used to form five equal-sized portfolios which they

label Growth, Growth/Mature, Mature, Mature/Stagnant, and Stagnant. Similarly, five equal-sized

portfolios are formed on firm age, designated as Young, Mid-Young, Middle, Mid-Old and Old.

In the last column of each panel, Vuong statistics are computed to compare the performance

of the cash flow patterns proxy to the Anthony and Ramesh (hereafter, AR) in Panel B and the age

quintile classifications in Panel C.11 The cash flow patterns proxy significantly outperforms the AR

proxy for EPS, RNOA, PM, GrSALES, GrNOA, INNOV , and MERGER . All results hold for

cash flow patterns versus age with the exception of GrSALES .

Recall that the AR classification is the composite of sorts on sales growth, capital

expenditures, dividend payout, and age. As a result, AR provides better explanatory power for

DIVPAY and AGE (other components of AR s proxy) . AR s measure is also more descriptive of

9 It is possible that the results reported in Table 2 are due to industry effects. If life cycle is actually an industryphenomenon, then a simple industry control would capture the differences across firms. The economics literaturesuggests industry life cycle patterns occur because the rate of innovation and intensity of competition change over theindustry life cycle. However, individual firms life cycle stages may differwithin an industry because innovation is acontinuing process with firms entering and exiting the market throughout the entire industry life cycle. Furthermore, thelife cycle stages of individual firms within an industry vary due to differences in a firm s knowledge acquisition, initialinvestment and re-investment of capital, and adaptability to the competitive environment. All tests throughout thepaper were repeated on industry-adjusted samples based on the Fama French (1997) industry classifications (resultsuntabulated). In each case, the results were consistent with those reported throughout the paper. Therefore, firm lifecycle stage is distinct from industry life cycle. 10 Terciles of low to high dividend payout, high to low sales growth, high to low capital expenditure and young to old age

were given scores of one to three, respectively. The composite scores ranged from three to nine as in Anthony andRamesh (1992).11 A positive (negative) Vuong statistic indicates that the cash flow patterns classification provides a better (worse) fit forexplaining each economic characteristic than does the alternative proxy.



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ATO , MB, SEGMENTS and SIZE. To reconcile the differences in performance between the cash

flow patterns proxy and the AR classification, it should be pointed out that the cash flow patterns

capture the nonlinearity of earnings, RNOA, PM, level of sales (as opposed to sales growth), ATO,

age, etc. across the economically-defined life cycle stages. All of these variables are maximized in the

mature stage (i.e., an inverted-U shaped distribution). If profitability drives market performance,

then the cash flow proxy will be effective in predicting future performance from a profitability and

market perspective. Next, age quintiles outperform the cash flow proxy for the same set of

economic characteristics in which AR provided better explanatory power, which is expected since

age was a component of AR s measure. Since young firm contain both introduction and decline

firms, age provides less detail than the cash flow proxy with respect to low-performing firms.

Having validated the cash flow patterns proxy, in the next section I use the proxy to examine

the inter-temporal behavior of firms conditional on their initial life cycle stages. Survivorship bias is

an issue inherent in this type of analyses. Table 3 – Panel A examines the proportion of firms that

survive for five years subsequent to the initial life cycle identification. To ensure a time span of five

years subsequent to initial identification, a reduced sample from 1989 to 2000 is used (the sample

period ends in 2005).12 In the pooled sample, only 78 percent of firms survive five years ahead.

Possible reasons for absence include merger activity, going private, or bankruptcy. The proportion

of firms that delist for merger or performance-related issues are reported according to their life cycle

stage in the year prior to delisting, and this breakdown is displayed in the last two columns.13

Delisting proportions by life cycle stage are significantly different from a uniform distribution across

life cycle stages (all z-statistics are significant). Over 65 percent of merger activity involves growth

12 Since one-year-ahead profitability is required for tests of explanatory power in Section 3, all firms survive through yeart + 1 by construction. 13 Cash flow data is insufficient for computing life cycle stage in the year in which the delisting takes place. Delistingcodes of 200-299 are categorized as Merger and codes of 500-599 are categorized as performance-related (Beaver,McNichols and Price 2007).



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or mature firms and over 68 percent of performance-related delistings involve introduction or

decline firms.


The survivorship analysis is repeated by life cycle stage for the proportion of firms in

existence relative to the year of life cycle identification and z-statistics are computed on differences

in proportion between each life cycle stage and the pooled sample. The survival rates for mature

(decline) stage firms are significantly higher (lower) than the survival rates for the pooled sample in

all subsequent years. The introduction and growth firms are significantly lower than the pooled

sample for years t + 3 through t + 5.

Table 3 - Panel B examines the transition of firm-observations from one life cycle stage to

another in subsequent periods, again using the reduced sample to ensure five subsequent years from

the initial classification. The shaded portions of the table represent the proportion of firms that

remain in their initial stage in later periods. For example, 60.13 percent of mature firms remain in

the mature stage one year after initial classification. This proportion monotonically decreases to

55.97 percent by year t + 5. Several observations are worth noting from this analysis: (1)

introduction firms are likely to stay in introduction or to move to the growth or mature stage (over

80 percent of observations at end of five years), (2) growth firms are fairly stable but a large

proportion (ranging from 33.11 in year t + 1 and increasing to 43.23 percent by year t + 5) will

move to mature, (3) growth firms are not likely to move to decline (less than four percent are in

decline by year t + 5), (4) mature firms are stable and slightly less than 30 percent transition to

growth over the next five years, (5) movements from mature to decline are unlikely (only two

percent transition to decline during the five subsequent years), (6) a small proportion of decline

firms remain in decline (only 18 percent after five years), but movement to introduction (25 percent

by year 5) or to growth (23 percent), mature (20 percent) or shake-out (12 percent) is also fairly



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common. Taken together, introduction firms tend to improve their position, growth and mature

firms are relatively stable, and decline firms (that survive) have unpredictable outcomes in

subsequent periods.

3. How can life cycle classification help us better understand future profitability?

Previous research documents that profitability measures mean-revert over time (Brooks and

Buckmaster 1976; Freeman, Ohlson and Penman 1982; Fairfield, Sweeney and Yohn 1996; Fama

and French 2000; Nissim and Penman 2001) and understanding the evolution of profitability

improves predictability. Stigler (1963) reported that profitability displayed a strong central tendency

over time, but that the convergence was incomplete. He stated that impediments to complete

convergence stem from disturbances related to shifts in demand, advances in technology, and

macroeconomic factors. Another potential impediment to convergence is differences in firm life

cycle stage.

Nissim and Penman (2001) suggest that truncated forecast horizons can be used if valuation

attributes “settle down” to permanent levels within the forecast horizon. Therefore, understanding

the convergence properties of profitability leads to better decisions with respect to growth rates and

forecast horizons. Specifically, if convergence properties differ across life cycle stages, this

information can be utilized to refine the valuation parameters for subsets of firms according to their

current life cycle stage.


To examine the convergence characteristics of profitability by life cycle stage, Table 4 – Panel A reports the mean of annual median values of RNOA examined over a five-year period

subsequent to the initial life cycle identification period. Pooled RNOA is relatively constant over

time, ranging from 8.30 to 9.12 percent. Likewise, the mature stage is characterized by stable



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profitability with RNOA ranging between 10 and 11 percent. However, the RNOA of both

introduction and decline firms increase monotonically over time.

[Insert Figure 1 about here]

These medians are depicted graphically in Figure 1. Median RNOA by life cycle stage

partially converges by year 3, but the difference in median RNOA between mature firms (10.41

percent) and decline firms (3.26 percent) is quite distinct five years later (difference of 7.15 percent

which is substantial given that the median RNOA for the sample is 9.12 percent at time t). Growth

and shake-out firms have relatively stable RNOA over the subsequent five years but the level is

lower than that of mature firms. Indeed, mature firms maintain a sustainable advantage over the

other life cycle stages while introduction firms earn considerably less even after five years (10.41

percent for mature compared to 5.31 percent for introduction). Therefore, convergence of RNOA

remains incomplete at the end of five years, such that incorporating life cycle stage information will

substantially impact forecasts of future RNOA.

Next, I examine the frequency of RNOA decile membership by life cycle stage in Table 4 –

Panel B. Nissim and Penman (2001, Figure 4(b)) form deciles of RNOA and examine the

convergence of the deciles over five subsequent years to document how RNOA evolves over time.

They report a persistent difference in RNOA between the highest and lowest decile of RNOA after

five years. If those differences were attributable to firm life cycle, we would expect to see an

overrepresentation (underrepresentation) of introduction and decline (mature) firms in the lowest

RNOA deciles. Consistent with these expectations, Panel B shows that nearly two-thirds of

introduction firms (66 percent) and three-fourths of decline firms (78 percent) reside within the

lowest three deciles of RNOA. Comparatively, only 17 percent of mature firms are contained within

the lowest three RNOA deciles. Therefore, a partial explanation for the non-convergence in RNOA

in Nissim and Penman s study is attributable to differences in firm life cycle stage as measured by



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cash flow patterns. Specifically, the mean-reversion of Nissim and Penman s lowest deciles of firms

is largely driven by the improvements in performance experienced by introduction firms and the

decline firms that survive in the future. However, the highest deciles (those shown to decline over-

time in Nissim and Penman) are not overpopulated by any one life cycle stage. Therefore, life cycle

theory better explains the mean-reversion properties of low-profitability firms than of high-

profitability firms.

Given the differences in RNOA by firm life cycle demonstrated in the previous analyses,

information about firm life cycle stage should be useful in explainingfuture profitability. I adapt

Fairfield and Yohn s (2001) model of future profitability to test for the incremental effect of life

cycle stage in explaining one-year-ahead change in RNOA.14 Current profitability (both level and

change in current RNOA) is included in the model because it is known to be serially correlated with

future profitability. The coefficients on current RNOA and ∆RNOA are expected to be negative

since profitability is mean-reverting (Brooks and Buckmaster 1976; Freeman, Ohlson and Penman

1982; Fairfield and Yohn 2001). Future changes in profitability can also occur due to a denominator

effect, or growth in NOA. This growth, captured by GrNOA, is controlled for to ensure that the

changes in future profitability are not driven solely by changes in investment. Prior research has

shown the coefficient on GrNOA to be negative since investment in NOA is subject to diminishing

returns.

RNOA is decomposed into two components: asset turnover ( ATO ) and profit margin ( PM ).

Asset turnover indicates the amount of assets needed to generate sales whereas profit margin

indicates a firm s ability to convert sales into profit. A cost leadership strategy is aimed at improving

the asset turnover, while a product differentiation strategy is oriented toward improving profit

14 Forecasts of future profitability are improved when based upon operating income rather than GAAP net income(Fairfield, Sweeney and Yohn 1996; Nissim and Penman 2001). Therefore excluding the financing portion of the firmfocuses the analysis on the sustainability of operating profitability.



19

margin. Fairfield and Yohn (2001) examine the effect of both levels and changes in ATO and PM

on future change in RNOA. 15 Changes in ATO are indicative of increased efficiency in production

and should represent permanent sources of profitability such that a positive relation with future

profitability is expected (Penman and Zhang 2006, Fairfield and Yohn 2001). Penman and Zhang

(2006) find a negative relation between change in profit margin and future profitability. They

suggest that an increase in PM is derived from a current reduction in operating expenses, which is

not sustainable and thus has negative consequences for future profitability.

Next, I add alternative life cycle proxies (i.e., cash flow patterns, Anthony and Ramesh s

classification, and age quintiles) to determine which classification scheme best explains future

profitability. Thus Model 1 is:

1

4

1

543211

t k

t k

t t t t t t

LC D

PM ATOGrNOA RNOA RNOA RNOA

(1)

Because life cycle stages are captured by indicator variables set to one if the firm-observation

is a member in that stage, the intercept captures either mature firms (for cash flow patterns and the

AR classification) or middle-aged firms (for age quintiles).16 The results of estimating Model 1 are

reported in Table 5. All standard errors reported throughout the analyses are robust with respect to

firm and year clustering. All of the profitability coefficients are significant (with the exception of

change in PM) and are in the predicted direction. For ease of comparison, all of the life cycle

coefficients are reported as the total effect (intercept + D k ) but the t-statistics pertain to the

incremental difference between the each life cycle stage and the mature/mature/old stage.


15 They report that current levels of ATO and PM are not informative in forecasting one-year-ahead change inRNOA but that change in ATO is positively related to one-year-ahead change inRNOA . 16 The following alignments were made across classification schemes (cash flow patterns/AR/age quintiles):Introduction/Growth/Young, Growth/Growth-Mature/Mid-Young, Mature/Mature/Middle, Shake-Out/Mature-Stagnant/Mid-Old, and Decline/Stagnant/Old.



20

All cash flow pattern life cycle stage coefficients are significant with the mature stage

representing positive future change in profitability (t = 14.89). For brevity, only the cash flow

pattern life cycle stage names are used in Table 5, but I will include the alternative name in

parentheses when discussing the results for the AR and age quintile classifications. In the AR

classification, only the introduction (growth) stage was significantly and negatively related to future

change in profitability. Significant positive associations with future profitability are found for the

shake-out (mature/stagnant) and decline (stagnant) stages, which is counter to theory and intuition.

All age quintile life cycle stages, with the exception of mature (middle-aged), have a significant

association with one-year-ahead change in profitability, but again, the sign of the effect is counter to

economic theory. Therefore, life cycle stage as measured by cash flow patterns is most consistent

with theoretical expectations of future profitability. As a final check, Vuong statistics test the

validity of pairwise comparisons of the models for explaining∆RNOA t+1 and the cash flow pattern

classification outperforms both the AR classification (z = 4.19) and the age quintile classification (z

= 3.89).

Recalling that Fairfield and Yohn (2001) found ∆ATO to be informative for explaining

future profitability, economic theory suggests that mature firms should benefit the most from

improvements in efficiency (Spence 1977, 1977, 1981; Wernerfelt 1985). This occurs because

mature firms generate higher-than-normal profits, which attracts competition from other firms.

Thus, to continue to maintain profitability, mature firms need to refocus their operations on cost

containment and production efficiency. Selling and Stickney (1989) suggest that operational gains in

efficiency are reflected in improvements in ATO . Therefore, I predict that the explanatory power of

∆ATO for future profitability will be concentrated in mature firms (i.e., a positive coefficient on an

interaction term, Mature × ∆ATO ).



22

PM are not associated with increases in future RNOA for growth firms in any life cycle

classification.17 However, consistent with predictions, the negative relation between changes in PM

and future profitability documented in Penman and Zhang (2006) is concentrated in the mature

stage for both the cash flow patterns and AR classifications.

Finally, Vuong tests of pairwise performance comparison indicate that the cash flow pattern

proxy outperforms the AR classification (z = 2.04) and slightly outperforms the age quintile

classification (z = 1.67) once the ATO and PM interactions are considered. Given the fact that both

the AR and age quintile classifications outperformed cash flow patterns when explaining ATO

(Table 2), it follows that the performance of cash flow patterns would decline once the ∆ATO

interaction was included. Given the results of this analysis and the parsimony in computing the cash

flow pattern proxy relative to the AR classification, the cash flow patterns proxy better provides a

more tractable firm life cycle measure. Age is a parsimonious proxy, but young firms can be

distressed (Stinchcombe 1965; Jovanovich 1982; Freeman, Carroll and Hannan 1983; Amit and

Schoemaker 1993 ). While the “Old” classification may capture maturity, age does not provide a

distinct separation of introduction versus decline firms among the “Young” classification.

Cash outflows for research and development are included in the Statement of Cash Flows as

operating activities, but they are more representative of investing cash flows. For this reason, in an

untabulated analysis, the cash flow patterns specification for all analyses throughout the paper was

re-estimated with research and development reclassified as investing cash flows with no substantial

change in results from the results presented in the paper.

17 Some economics research claims that the benefits of product differentiation techniques such as advertising andmarketing are difficult to capture at the individual firm level because advertising partly serves to increase demand for theentire market (Oster 1990, Shy 1995), i.e. there is a free-rider effect. Additionally, gains in innovation are difficult tocapture due to the mobility of labor among competing firms (Porter 1980, Jovanovic and Nyarko 1995). These factorscould mitigate the ability of product differentiation efforts to result in persistent increases in profitability.



23

4. What is the role of life cycle classification in understanding current firm value and predicting future stock returns?

In previous sections, I have demonstrated that cash flow patterns provide a reliable and

parsimonious proxy for firm life cycle. Given the superior profitability of mature stage firms, thislife cycle attribute should be associated with higher buy-and-hold stock returns in future periods

conditional on a mature life cycle signal in the current period. Since the majority of firms are in the

mature stage at any given point (41.18 percent of the sample), investing upon seeing a mature life

cycle signal is easily implementable by all types of investors.

To examine whether investors recognize the persistent profitability of mature stage firms, I

examine 12-month buy-and-hold size-adjusted returns18 computed by subtracting the appropriate

market capitalization decile return (from the CRSP database) from a firm s raw return. Size-adjusted

returns are accumulated from the beginning of the fifth month of year t + 1 through the fourth

month of the second year following the life cycle stage signal (t + 2). This allows market

participants to assess life cycle stage based on the published financial statement data prior to

portfolio formation. Additionally, delisting returns are used when they are included in the CRSP

database and delisted firms without a corresponding delisting return are assumed to have a return of

zero (Piotroski 2000) unless the delisting occurred due to performance-related reasons in which case

the missing delisting return was set to -100.00 percent.19

The independent variables used in the returns regression are earnings per share scaled by

stock pricet-1 ( X/P ) and change in earnings ( ∆X/P ) because both earnings levels and changes have

significant explanatory power for annual stock returns (Easton and Harris 1991). Prior research has

18 The results are invariant in all analyses for replacing size-adjusted returns with market-adjusted returns.19 Prior research has used -30.00 percent for NYSE and AMEX firms (Shumway 1997, Mohanram 2004) and -55.00percent for NASDAQ firms (Shumway and Warther 1999) that are delisted for performance. Sloan (1996) uses -100.00percent for performance-related delistings. Since missing delisting returns for mergers are likely to be understated whensetting to zero, I make no upward correction for merger-related missing returns to bias against finding results.



25

French attribute this result to risk due to the fact that high B/M firms may be closer to default. By

contrast, Lakonishok et al. attribute the B/M effect to mispricing such that investors are overly

optimistic about low B/M stocks (glamour firms) and pessimistic about value stocks (high B/M).

Piotroski (2000) and Mohanram (2005) investigate whether fundamental analysis can be used to

separate the “winners” from the “losers” at the two extremes of the B/M spectrum.

Piotroski develops an FSCORE based on nine binary variables (i.e., earnings versus loss,

increasing ROA, positive cash flows, cash flows greater than net income, increasing operating

margin, increasing asset turnover, decreasing leverage, increasing current ratio, and non-issuance of

equity) for value firms. Mohanram develops a GSCORE based on eight signals (i.e., ROA and cash

flows greater than median for other low B/M firms in the same industry, cash flows greater than net

income, lower earnings and sales growth variability than for other low B/M firms in industry, and

research and development, advertising intensity and capital expenditures all greater than other low

B/M in the same industry) for glamour firms. In both cases, partitioning on the respective

composite scores can identify firms where significant excess returns can be earned based on the ex

ante signal (FSCORE or GSCORE, along with the identification of low or high B/M). In

Piotroski s study, high B/M firms with the highest FSCORE earned mean market-adjusted returns

of 13.4 percent while high B/M firms with the lowest FSCORE earned -9.6 percent. Mohanram

found that low B/M firms with the highest GSCORE earned a mean size-adjusted return of 3.1

percent while the lowest GSCORE among low book/market firms earned -17.5 percent in the year

after portfolio formation.

It is possible that life cycle information (measured parsimoniously by cash flow patterns) can

effectively detect the upside of both the value and glamour trading strategies demonstrated in

Piotroski s and Mohanram s studies. Since most of the variables that comprised the FSCORE and

GSCORE are related to life cycle, especially as measured by cash flow patterns, the proxy used in



26

this paper may capture the essence of what makes the composite scores effective in predicting future

returns. Combining the B/M screen with the mature life cycle stage screen may identify firms that

comprised the long portion of the two B/M strategies. Furthermore, by restricting the B/M screen

to only mature firms, the necessity to short some firms is eliminated which makes the strategy highly

implementable for all types of investors.

Since market participants have access to more information than what is captured by the

accounting system, a high market value relative to book value (resulting in low B/M) may be

reflective of future product development. In other words, mature firms that have low B/M ratios

(mature-glamour firms) may be on the cusp of recycling back to the growth life cycle stage in future

periods due to new product or market expansions. If the new development is successful, those

firms should enjoy increasing profitability as the new development matures.

Conversely, a low market value relative to book value (high B/M) is indicative of market

inattention or neglect by information intermediaries such as analysts. When high B/M firms are also

mature (mature-value firms), the risk of distress is much lower than stocks that are avoided due to

anticipation of poor performance. It has been demonstrated that these types of value stocks are

undervalued by the market which may result in a positive reaction when the market realizes their

profitability did not mean-revert to lower expectations. Therefore, Model 3 examines whether

interacting the mature life cycle stage with alternatively the lowest and highest quintiles of B/M

results in positive size-adjusted returns in the year following the mature and B/M signal:

1,,10

,9,8,7,6

,5,4,3,2,101,

)/()/(

/)/(//

t it i

t it it it i

t it it it it it i

M HighB Mature M LowB Mature Mature BetaSize

M B Loss P X Loss P X P X RET

(4)

Results show that the interactions between Mature and both the lowest and highest quintiles

of B/M generate positive size-adjusted returns in the year after portfolio formation (t = 3.05 and t =

2.16, respectively). Overall, the mispricing based on extreme values of B/M demonstrated in prior



27

research is likely to be more severe among mature firms, consistent with the market not recognizing

the level and persistence of RNOA in these firms. Furthermore, there are ample observations in the

Mature-Low B/M quintile portfolio (ranging from 104 firms in 2000 to 256 firms in 2003) and in

the Mature-High B/M quintile portfolio (ranging from 180 firms in 1989 to 295 firms in 2002) to

comprise an economically meaningful investment portfolio to exploit this mispricing in any given

year.

5. Conclusion

This paper develops and validates the use of cash flow patterns as an effective and

parsimonious proxy for firm life cycle. Several performance measures and firm characteristics such

as profitability, market performance, size, and age are nonlinearly related to firm life cycle. For that

reason, univariate sorts on these performance measures result in an inappropriate assignment of life

cycle stages such that the lowest portfolios are populated with both introduction and decline firms,

which have differential implications for future performance. More importantly, a simple sort on

univariate measures makes a distributional assumption of uniformity that is not supported by

economic theory.

The paper first validates the life cycle proxy according to economic theory and then

examines how cash flow patterns capture the economic concept of life cycle relative to proxies used

in past research (i.e., Anthony and Ramesh s metric and firm age). Next, the persistence of

profitability, measured by return on net operating assets (RNOA) is examined by life cycle stage.

Convergence rates and the patterns of mean-reversion of future profitability are shown to differ bylife cycle stage. Specifically, the spread in RNOA is three to 10 percent between mature and decline

firms five years subsequent to portfolio formation (based on life cycle identification). This spread of

seven percent is economically significant given that the median RNOA for the sample is 8.61



28

percent. The valuation and forecasting implications are that growth rates and forecast horizons

should be conditioned on information pertaining to the firm s current life cycle stage.

Additionally, past research on the decomposition of RNOA has shown that change in asset

turnover is an important driver of future changes in RNOA (Fairfield and Yohn 2001) but that

improvements in future profitability due to increases in profit margin are not sustainable (Penman

and Zhang 2006). Both of these results are primarily concentrated in mature firms. Increases in

operational efficiency are critical for mature firms due to increased competition that is attracted to

the superior profits earned by mature firms. At the same time, diminishing returns to product

differentiation efforts appear to be evident among those same firms.

Finally, the market valuation consequences of life cycle (as captured by cash flow patterns)

are investigated and it is demonstrated that positive future excess returns can be earned for firms

that fall into the mature category. Furthermore, life cycle adds crucial fundamental information to

separate out the “winners” from the “losers” at both extremes of the book/market spectrum (i.e.,

glamour and value firms). The cash flow pattern proxy captures information priced by the market in

a more efficient manner than the fundamental signals used in previous trading strategies which

require the computation of composite scores based on numerous metrics.

In summary, this paper uses basic accounting information to capture the construct of firm

life cycle which embodies differences in resources, rates of investment, obsolescence rates, learning

and experience curves, adaptation, product-differentiation, and production efficiencies. The cash

flow pattern proxy for life cycle stage outperforms other proxies used in extant research including

age, and better explains future profitability (both in rates of return and stock returns) given its

foundation in economic theory.



29

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33

Table 1Economic Links to Cash Flow Patterns

Cash Flow Type Introduction Growth Mature Shake-Out Decline

Operating

Firms enter market with

knowledge deficit aboutpotential revenues andcosts (Jovanovic 1982)

( ) Cash Flows

Profit margins aremaximized during

period of greatestinvestment (Spence1977, 1979, 1981)

(+) Cash Flows

Efficiency maximizedthrough increased

knowledge of

operations (Spence1977, 1979, 1981; Wernerfelt 1985)

(+) Cash Flows

Declining growth rateslead to declining prices

(Wernerfelt 1985)

Routines of establishedfirms hinder competitiveflexibility (Hannan and

Freeman 1984)

(+/ ) Cash Flows

Declining growth rates

lead to declining prices(Wernerfelt 1985)

( ) Cash Flows

Investing

Managerial optimismdrives investment(Jovanovic 1982)

Firms make early largeinvestments to deterentry (Spence 1977,

1979, 1981)

( ) Cash Flows

Firms make early largeinvestments to deterentry (Spence 1977,

1979, 1981)

( ) Cash Flows

Obsolescenceincreases relative tonew investment as

firms mature(Jovanovic 1982,

Wernerfelt 1985)

( ) Cash Flows

Void in theory

(+/ ) Cash Flows

Liquidation of assetsto service debt

(+) Cash Flows

Financing

Pecking order theorystates firms will accessbank debt then equity

(Myers 1984, Diamond1991); Growth firms will issue short-term

debt (Barclay and Smith1995)

(+) Cash Flows

Pecking order theorystates firms will accessbank debt then equity

(Myers 1984, Diamond1991); Growth firms will issue short-term

debt (Barclay and Smith1995)

(+) Cash Flows

Focus shifts fromacquiring financing to

servicing debt anddistributing excess

funds to shareholders;Mature firms will issue

longer term debt(Barclay and Smith

1995)( ) Cash Flows

Void in theory

( +/ ) Cash Flows

Focus on debtrepayment and/or

renegotiation of debt

(+/ ) Cash Flows



34

Table 2Effect of Life Cycle Classification on Economic Characteristics

Panel A – Life Cycle Stages defined by Cash Flow Patterns

Pooled Introduction Growth Mature Shake-

OutDecline

N 48,369 5,752 16,423 19,920 3,861 2,413

% of total N 100.00% 11.89% 33.95% 41.18% 7.98% 4.99%

Dependent Variable Mean Coefficients (relative to Mature)

( t-statistic ) Adj.

R 2

EPS 0.61 -1.490( -69.11 )

-0.355( -24.00 )

1.122( 110.12 )

-0.713( -24.88 )

-1.820( -57.00 ) .1317

RNOA 8.61% -0.692( -46.03 )

-0.012( -4.15 )

0.133( 77.51 )

-0.146( -14.20 )

-1.078( -37.74 ) .2156

PM 4.57% -0.509( -42.10 )

-0.012( -7.39 )

0.059( 74.63 )

-0.099( -14.78 )

-0.782( -34.50 ) .2062

ATO 1.95 0.085( 2.07 ) -0.056( -2.11 ) 2.673( 151.06 ) 0.101( 1.98 ) -0.075( -1.20 ) .0003

GrSALES 9.97% 0.345( 31.95 )

0.180( 44.95 )

0.101( 55.40 )

-0.021( -3.00 )

0.125( 8.17 ) .0629

GrNOA 7.28% 0.549( 31.23 )

0.365( 48.45 )

0.062( 20.15 )

-0.013( -0.97 )

0.167( 6.60 ) .0611

MB 1.91 0.523( 9.81 )

0.263( 8.92 )

2.615( 133.65 )

-0.375( -7.75 )

0.216( 2.80 ) .0058

LEV 0.19 -0.155( -7.46 )

0.078( 5.81 )

0.421( 48.35 )

-0.159( -6.30 )

-0.541( -18.52 ) .0117

ASSET BETA 0.73 0.611( 14.50 )

0.301( 15.10 )

0.783( 67.77 )

0.338( 8.29 )

0.897( 12.95 ) .0132

DIVPAY 15.38% -0.194( -46.76 ) -0.087( -20.19 ) 0.217( 69.40 ) -0.076( -9.66 ) -0.191( -33.16 ) .0295

ADVINT 0.98% 0.002( 4.19 )

-0.002( -8.94 )

0.010( 56.23 )

0.000( 0.38 )

0.001( 0.91 ) .0028

INNOV 4.97% 0.136( 27.41 )

0.012( 16.16 )

0.016( 47.64 )

0.033( 12.93 )

0.258( 25.86 ) .1142

SEGMENTS 2.59 -0.802( -31.05 )

-0.238( -10.82 )

2.803( 184.55 )

-0.056( -1.46 )

-0.705( -18.26 ) .0183

MERGER 17.70% 0.079( 13.83 )

0.163( 39.02 )

0.117( 51.27 )

-0.014( -2.65 )

0.014( 1.93 ) .0381

SIZE 5.39 -1.338( -51.76 )

-0.064( -3.10 )

5.816( 386.40 )

-0.677( -18.71 )

-1.366( -38.93 ) .0631

AGE 10.43-10.540( -59.61 )

-5.538( -33.40 )

19.663( 161.72 )

-3.089( -11.16 )

-9.184( -35.69 ) .0571



35

Table 2 - ContinuedEffect of Life Cycle Classification on Economic Characteristics

Panel B – Life Cycle Stages defined by Anthony and Ramesh ClassificationGrowth Gr/Mat Mature Mat/Stag Stagnant

N 8,169 7,135 7,814 7,640 11,527 CF Patt.% of total N 19.32% 16.87% 18.48% 18.07% 27.26% over AR

Dependent Variable

Coefficients (relative to Mature)( t-statistic )

Adj.R 2

VuongStatistic

EPS -0.381( -20.02 )

-0.093( -4.51 )

0.491( 38.84 )

0.230( 10.65 )

0.956( 49.11 ) .0909 6.28

RNOA -0.089( -7.50 )

0.044( 4.26 )

-0.066( -9.71 )

0.091( 10.19 )

0.172( 24.39 ) .1778 37.27

PM -0.073( -8.32 )

0.024( 3.08 )

-0.090( -18.48 )

0.074( 11.16 )

0.148( 29.12 ) .0231 36.51

ATO -0.047

( -1.17 )

-0.110

( -2.65 )

2.865

( 114.94 )

-0.185

( -4.68 )

-0.605

( -19.22 ).0077 -9.33

GrSALES 0.030( 3.78 )

-0.093( -12.73 )

0.295( 55.45 )

-0.175( -26.36 )

-0.215( -37.30 ) .0415 4.11

GrNOA 0.009( 0.64 )

-0.131( -9.32 )

0.384( 41.77 )

-0.248( -21.25 )

-0.290( -29.09 ) .0228 13.32

MB 0.482( 10.53 )

0.130( 2.84 )

2.776( 107.17 )

-0.433( -10.83 )

-0.252( -7.19 ) .0096 -5.15

LEV -0.177( -9.35 )

-0.500( -2.41 )

0.362( 29.88 )

0.084( 4.28 )

0.215( 13.70 ) .0097 1.54

ASSET BETA 0.348( 9.54 )

-0.021( -0.62 )

1.150( 56.70 )

-0.304( -10.06 )

-0.537( -23.08 ) .0186 -3.19

DIVPAY -0.087( -26.22 )

-0.062( -15.92 )

0.098( 32.96 )

0.040( 7.42 )

0.284( 48.65 ) .1193 -26.77

ADVINT -0.000( -0.95 )

-0.001( -2.73 )

0.011( 46.84 )

-0.003( -7.40 )

-0.001( -3.62 ) .0011 1.61

INNOV 0.029( 8.09 )

-0.005( -1.58 )

0.064( 33.01 )

-0.025( -9.56 )

-0.052( -26.15 ) .0190 19.41

SEGMENTS -0.350( -15.62 )

0.044( 1.64 )

2.253( 147.81 )

0.575( 20.20 )

1.259( 46.68 ) .0846 -25.39

MERGER 0.052( 8.99 )

0.012( 2.12 )

0.191( 57.21 )

-0.044( -8.39 )

-0.056( -12.27 ) .0097 12.68

SIZE -0.058( -2.39 )

0.177( 6.39 )

5.109( 322.12 )

0.264( 9.50 )

1.447( 58.38 ) .0883 -9.45

AGE -5.167( -55.49 )

-1.547( -14.18 )

9.996( 113.88 )

8.478( 50.29 )

23.460( 130.49 ) .4676 -104.03



36


Panel C – Life Cycle Stages defined by Age Quintiles Young Mid/Young Middle Mid/Old Old

N 9,705 9,647 9,641 9,725 9,651 CF Patt.% of total N 20.06% 19.94% 19.93% 20.11% 19.95% over Age

Dependent Variable

Coefficients (relative to Mature)( t-statistic )

Adj.R 2

VuongStatistic

EPS -0.336( -16.39 )

-0.177( -8.76 )

0.500( 34.54 )

0.260( 12.84 )

1.048( 45.03 ) .1001 6.98

RNOA -0.212( -17.04 )

-0.064( -6.40 )

-0.007( -1.14 )

0.073( 9.45 )

0.118( 17.47 ) .0296 36.30

PM -0.157( -17.06 )

-0.047( -6.07 )

-0.051( -10.22 )

0.063( 10.74 )

0.113( 22.13 ) .0346 35.74

ATO 0.397

( 9.15 )

0.162

( 3.97 )

2.663

( 97.58 )

-0.094

( -2.50 )

-0.390

( -11.18 ).0093 -8.57

GrSALES 0.238( 27.20 )

0.034( 4.96 )

0.188( 40.77 )

-0.065( -11.50 )

-0.102( -19.30 ) .0599 -1.34

GrNOA 0.355( 22.78 )

0.049( 4.15 )

0.213( 27.84 )

-0.056( -5.63 )

-0.118( -13.35 ) .0368 7.11

MB 0.510( 10.61 )

0.116( 2.54 )

2.732( 88.05 )

-0.258( -6.37 )

-0.176( -4.24 ) .0080 -2.05

LEV -0.099( -4.72 )

-0.044( -2.16 )

0.336( 23.43 )

0.046( 2.51 )

0.322( 17.09 ) .0122 1.19

ASSET BETA 0.488( 12.99 )

0.138( 3.99 )

1.033( 44.62 )

-0.175( -5.79 )

-0.408( -15.36 ) .0183 -1.27

DIVPAY -0.018( -3.74 )

-0.027( -6.05 )

0.089( 26.53 )

0.078( 14.69 )

0.249( 39.40 ) .0682 -14.51

ADVINT 0.002( 6.15 )

0.000( 0.84 )

0.009( 37.71 )

-0.002( -6.46 )

0.000( 1.30 ) .0032 -1.39

INNOV 0.050( 13.89 )

0.016( 5.09 )

0.051( 26.00 )

-0.019( -7.87 )

-0.041( -20.66 ) .0243 19.33

SEGMENTS -0.350( -15.62 )

-0.152( -5.77 )

2.314( 123.48 )

0.415( 15.05 )

1.533( 48.08 ) .0846 -30.89

MERGER 0.083( 13.82 )

0.023( 4.09 )

0.173( 43.87 )

-0.017( -3.11 )

-0.038( -7.20 ) .0115 11.71

SIZE 0.026( 0.98 )

-0.079( -2.91 )

5.175( 264.35 )

0.187( 6.60 )

1.685( 58.01 ) .1110 -12.92

AGE -8.167( -292.82 )

-4.681( -158.23 )

10.454( 421.39 )

9.016( 192.31 )

30.652( 192.72 ) .7932 -221.89



37


For the sample period 1989 to 2005. Means presented in Panel A are the means of annual medians except for total number ofobservations, dividend payout ratio, advertising, innovation, number of segments, and mergers which are annual means. The

explanatory power of each life cycle classification is tested by regression each dependent variable on indicator variables for each lifecycle stage except for Mature (Middle) which is captured in the intercept. This means that the regression coefficients capture theeffect of each life cycle stage relative to maturity. Robust standard errors are clustered by firm and year. Coefficients significant at the0.05 level or better are designated in bold. Vuong statistics report the explanatory power of the Cash Flow Pattern classification over

Anthony and Ramesh s ( Age Quintiles) classification in Panel B (Panel C). Dependent variables are measured as follows: Earningsper share ( EPS ) is measured before extraordinary items (#58). Return on net operating assets ( RNOA ) = Operating Income(OI t )/Average Net Operating Assets (NOA). Profit margin ( PM ) = Operating Income (OI)/Net sales (#12). Asset Turnover ( ATO )= Net Sales)/Average Net Operating Assets (NOA). Growth in Sales ( GrSALES ) is defined as (Net Sales/Lagged Net Sales t ) – 1.Growth in NOA ( GrNOA ) is defined as (NOA/NOA) – 1. Market-to-Book ( MB) = Market Value of Equity/Book Value of Equity(#60). Leverage ( LEV ) = Net Financial Obligation/Common Equity (#60). ASSET BETA is the mean market model beta from aregression of daily raw returns on the value-weighted market return over the prior 250 days adjusted for leverage. Dividend PayoutRatio ( DIVPAY) = Common dividends (#21)/Net Income (#172). Advertising Intensity ( ADVINT) is Advertising Expense (#15)/Net Sales (#12), Innovation ( INNOV) is [R&D (#46) plus Amortization Expense (#65)/Net Sales (#12)]. SEGMENT is thenumber of segments reported in the Compustat segment files. MERGER is the percentage of firms that have „AA codes inCompustat (AFTNT1). SIZE is the log of market value of equity. AGE is defined as the log of the number of years since the firm s

first appearance in the CRSP database. All variables are winsorized at the 1st and 99th

percentiles to mitigate the influence of extreme values.



38

Table 3Survival Rate and Transition Matrix Analyses

Panel A – Proportion of firms that survive beyond portfolio formation periodN = 33,088

Stage atPortfolio

Formation t+1 t+2 t+3 t+4 t+5

%DelistedMerger

%Delisted

Perf.Pooled 100.00% 93.45% 87.74% 82.77% 78.15%

Introduction 100.00 93.11 86.70 81.36 76.44 15.30 41.53z-stat - 0.796 1.887 2.230 2.477 4.615 15.008

Growth 100.00 92.98 86.84 81.53 76.95 32.04 11.98z-stat - 1.732 2.518 3.020 2.677 9.640 6.858

Mature 100.00 94.26 89.20 84.75 80.33 33.79 7.78z-stat - 3.233 4.401 5.179 5.198 10.382 10.891

Shake-Out 100.00 92.82 87.17 82.07 76.59 10.87 11.68z-stat - 1.161 0.790 0.849 1.760 8.753 7.820

Decline 100.00 91.74 85.42 79.45 75.14 8.01 27.03z-stat - 2.459 2.536 3.167 2.624 12.186 5.183

Base years range from 1989 to 2000 so that five subsequent years are available for each observation (sample period extends to 2005).Z-statistics (in italics below the proportion) from a test of equal proportions is computed for each life cycle stage relative to thepooled sample for the years subsequent to life cycle identification; and for each stage relative to a uniform distribution for thedelisting categories. Z-Statistics in bold indicate a significant difference in proportions at 0.05 significance level or better. Delistingdata was extracted from the CRSP Event database and was computed for all observations with adequate cash flow data to computethe life cycle stage in the year prior to delisting. CRSP categorizes delistings as follows: 200-299 are mergers and 500-599 aredropped securities due to performance. The proportion of delistings due to mergers (inadequate performance) is computed by lifecycle stage and reported in the second to the last (last) column.



39

Table 3 ContinuedSurvival Rate and Transition Matrix Analyses

Panel B – Transition Matrix: Proportion of observations in each life cycle stage in years subsequentto portfolio formationN = 33,088

Stage atPortfolio

Formation

Stage inFuturePeriod t+1 t+2 t+3 t+4 t+5

Introduction Introduction 36.93 30.11 27.48 26.21 23.66Growth 22.46 23.64 25.75 27.58 27.73Mature 19.72 23.80 25.33 27.26 29.13

Shake-Out 8.28 8.82 8.50 8.04 8.43Decline 12.61 13.62 12.94 10.90 11.07

Growth Introduction 7.71 6.84 6.30 6.26 5.89Growth 51.39 45.06 42.47 40.92 38.66Mature 33.11 38.27 40.71 41.82 43.23


Mature Introduction 4.44 5.07 5.24 5.10 4.98Growth 27.68 29.07 28.42 28.58 28.85Mature 60.13 57.02 56.63 56.13 55.97


Shake-Out Introduction 10.07 9.53 10.02 10.26 9.35Growth 22.99 25.30 26.62 25.46 28.17Mature 41.57 41.80 42.89 43.85 43.72

Shake-Out 18.41 16.09 14.07 13.31 12.78Decline 6.96 7.28 6.39 7.11 5.98Decline Introduction 28.18 29.04 28.91 26.23 25.83

Growth 14.16 17.03 20.24 19.69 23.36Mature 16.78 18.76 19.39 22.50 20.31


Base years range from 1989 to 2000 so that five subsequent years are available for each observation (sample period extends to 2005).For each life cycle stage at the time of portfolio formation (year t), this table reports the proportion of surviving firms by life cyclestage for each year subsequent to life cycle identification.



40

Table 4 Analysis of Return on Net Operating Assets (RNOA) by Life Cycle Stage

Panel A – Inter-temporal Analysis of Median RNOA by Life Cycle Stage

Pooled Introduction Growth Mature Shake-

OutDecline

N 33,088 4,121 11,742 13,424 2,409 1,392

% of total N 100.00% 12.45% 35.49% 40.57% 7.28% 4.21%

Year Relative toFormation

t 9.12% -4.18% 9.54% 11.01% 8.26% -16.30%

t + 1 8.53% -1.75% 8.38% 10.74% 7.85% -9.08%

t + 2 8.30% 1.30% 7.86% 10.34% 7.96% -4.86%

t + 3 8.43% 3.15% 7.84% 10.27% 8.37% 0.30%

t + 4 8.71% 4.56% 8.03% 10.50% 8.60% 0.59%

t + 5 8.93% 5.31% 8.19% 10.41% 9.45% 3.26%

Panel B – Proportion of Life Cycle Stage by RNOA Decile Membership

Pooled Introduction Growth Mature Shake-Out Decline

N 48,369 5,752 16,423 19,920 3,861 2,413

% of total N 100.00% 11.89% 33.95% 41.18% 7.98% 4.99%

RNOA Decile

Lowest 35.95% 3.57% 2.44% 12.04% 50.73%

2 19.66% 8.32% 6.57% 14.69% 19.31%

3 10.57% 10.97% 8.92% 12.04% 7.67%

4 7.09% 11.54% 10.48% 8.70% 4.68%

5 5.49% 11.70% 11.31% 7.10% 2.86%

6 5.09% 11.37% 11.71% 7.46% 2.49%

7 5.18% 10.91% 12.08% 7.80% 1.82%

8 4.73% 9.89% 12.86% 7.93% 2.98%

9 3.76% 10.13% 12.73% 9.35% 2.69%

Highest 2.47% 11.59% 10.90% 12.90% 4.77%

Total 100.00% 100.00% 100.00% 100.00% 100.00% Likelihood Ratio Chi-Square: 11,311.17 (<.0001)



41

Table 4 - Continued Analysis of Return on Net Operating Assets (RNOA) by Life Cycle Stage

The sample period is 1989 to 2000 for Panel A and from 1989 to 2005 for Panel B. Panel A requires five subsequent years toportfolio formation to ensure that the results are not affected by a truncated time period. Return on net operating assets ( RNOA ) is

the mean of the annual medians and is measured as Operating Income (OI t )/Average Net Operating Assets (NOA). In Panel B, lifecycle stage membership is analyzed as a proportion of RNOA decile membership. A test of equal proportions across RNOA decilesby life cycle stage was rejected with a Likelihood Ratio Chi-Square of 11,311.17 (<0.0001).



43

Table 5 ContinuedExplanatory Power of Life Cycle Stages for Future Change in RNOA

For the sample period 1989 to 2005. Robust standard errors are clustered by firm and year. The dependent variable is ∆RNOA t+1 . The coefficients are the total effect (the main effect plus the incremental effect for each life cycle stage). The t -statistics pertain to whether the mature stage coefficients are different from zero or whether the other life cycle coefficients are statistically different fromthe mature stage coefficient.

The following alignments were made across classification schemes (cash flow patterns/AR/age quintiles):Introduction/Growth/Young, Growth/Growth-Mature/Mid-Young, Mature/Mature/Middle, Shake-Out/Mature-Stagnant/Mid-Old, and Decline/Stagnant/Old.Return on net operating assets (RNOA) = Operating Income (OIt)/Average Net Operating Assets (NOA). Growth in NOA(GrNOA) is defined as (NOA/Lagged NOA) – 1. Asset turnover (ATO) = Net sales (Compustat #12)/Average Net Operating

Assets (NOA). Profit margin ( PM ) = Operating Income (OI)/Net sales (#12). All variables are winsorized at the 1st and 99 th percentiles to mitigate the influence of extreme values.



44

Table 6Buy-and-Hold Annual Size-Adjusted Returns to Life Cycle Strategy

n = 46,226

Variable Predicted Sign Model 1 Model 2 Model 3

Intercept +/ 0.020(4.30)

0.005(0.86)

0.005(0.94)

X/P + 0.219(4.13)

0.202(3.80)

0.208(3.90)

∆X/P + 0.045(5.25)

0.042(4.94)

0.043(4.97)

Loss +/ 0.068(6.77)

0.075(7.40)

0.075(7.31)

X/P × Loss -0.239(-4.31)

-0.222(-4.01)

-0.227(-4.09)

B/M + 0.197(12.97)

0.194(12.76)

0.191(12.06)

Size -0.039(-7.08)

-0.037(-6.78)

-0.037(-6.72)

Beta + 0.022(3.68)

0.023(3.78)

0.023(3.83)

Mature + 0.033(6.60)

0.024(4.26)

Mature × Low B/M + 0.028(3.05)

Mature × High B/M + 0.022

(2.16) Adj. R-sq. 1.15% 1.23% 1.25%

For the sample period 1989 to 2005. Robust standard errors are clustered by firm and year. This table presents 12-month buy-and-hold size-adjusted returns accumulated from the beginning of the fifth month of year t + 1 through the fourth month of year t + 2.Portfolio formation is based on life cycle stage or book-to-market ratio at the end of year t. Delisting returns are used when includedin the CRSP database. Delisted firms without a corresponding delisting return are assumed to have a return of -100 percent in thedelisting period when delisted for performance-related reasons (Delisting codes between 200 and 299); zero percent otherwise.Earning/Price ( X/P ) are earnings per share before extraordinary items scaled by beginning of the year stock price. Loss is anindicator variable set to one if earnings are negative in the current year. Book-to-Market ( B/M) = [Book Value of Equity (#60) /Market Value of Equity] scaled by beginning of the year stock price. SIZE is the log of market value of equity scaled by beginning ofthe year stock price. BETA is the mean market model beta from a regression of daily raw returns on the value-weighted marketreturn over the prior 250 days scaled by beginning of the year stock price. MATURE is an indicator variable set to one if theobservation is in the mature category (based on cash flow patterns) at the end of the year. Low (High) B/M is the lowest (highest)quintile of the B/M ratio at the end of the year. All variables are winsorized at the 1st and 99 th percentiles to mitigate the influence ofextreme values.



Figure 1Convergence Analysis - Future RNOA by Life Cycle Stage

N=33,088

For the sample period 1989 to 2000. Life cycle stage is determined at time zero and median RNOA for each stage is computed forthe five subsequent years.

-20.00%

-15.00%

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

0 1 2 3 4 5

M e d i a n

R N O

A

Year Relative to Portfolio Formation Year

Introduction Growth Mature Shake Out Decline

Cash Flow Patterns as a Proxy for Firm Life Cycle

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