A FRAMEWORK FOR CASH-FLOW PREDICTIONS
By
Kenneth S. Lorek*
February 27, 2012
*The W. A. Franke College of Business
Northern Arizona University
PO Box 15066
Flagstaff, AZ 86011-5066
928-523-7406
Ken.Lorek@nau.edu
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A FRAMEWORK FOR CASH-FLOW PREDICTIONS
Abstract
I provide a synthesis of recent academic research on statistically-based quarterly cash-flow
prediction models which should be of interest to financial analysts interested in generating multi-stepahead cash-flow predictions. New descriptive evidence (Lorek and Willinger 2008, 2011) underscores
that quarterly cash-flow from operations (CFO) exhibit both quarter-to-quarter (adjacent) and quarterby-quarter (seasonal) autocorrelations in marked contrast to earlier work (Lorek, Schaefer and Willinger
1993) that portrayed a substantially simpler autocorrelation pattern. This new descriptive evidence
results in the identification of the (100) X (011) ARIMA model as a candidate, statistically-based
quarterly CFO prediction model. Use of this model results in superior short-term as well as long-term
quarterly CFO predictions relative to other statistically-based CFO prediction models that have been
championed in the academic literature. I also provide a forecasting schema by which statistically-based
projections of CFO might be combined with macroeconomic, industry, and firm-specific information
garnered by analysts via fundamental financial financial analysis.
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A FRAMEWORK FOR CASH-FLOW PREDICTIONS
While analysts’ forecasts of annual and quarterly EPS have been well documented, their
participation in cash-flow forecasts has been more contextual and a relatively recent phenomenon. In
fact, short-run (i.e., one to four quarters ahead) cash-flow forecasts attributed to analysts have become
relatively commonplace (Givoly et al. 2009), however, long-run forecasts (i.e., five to n-quarters ahead)
of cash flow from operations (CFO) are currently virtually non-existent. Nevertheless, multi-step-ahead
quarterly CFO predictions are crucial inputs necessary for firm valuations using discounted cash flow
methodologies ( e.g., Lundholm and Sloan 2007, Palepu and Healy 2008, and Penman 2007). Without
them, investors and analysts must resort to cruder “back of the envelope” valuation techniques
employing net earnings as proxies for CFO in conjunction with industry multiples rather than
conceptually superior alternatives.
First, I summarize recent descriptive and predictive research findings pertaining to the timeseries properties and predictive ability of quarterly CFO data . Then, I explain precisely how this new
evidence has resulted in the refinement of extant statistically-based quarterly CFO prediction models.
Finally, I suggest a framework by which CFO predictions from statistically-based ARIMA models might be
combined with macroeconomic, industry, and firm-specific information garnered by sell-side analysts via
fundamental financial analysis. Subsequent sections include: (1) an overview of analyst involvement
with CFO forecasts, (2) presentation of new descriptive evidence on the time-series properties of
quarterly CFO, (3) an overview of academic research refining extant statistically-based quarterly CFO
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prediction models, and (4) explication of a framework by which statistically-based projections of CFO
might be combined with projections of CFO attributed to analysts.
ANALYST INVOLVEMENT
Givoly et al. (2009) provide evidence of increasing analyst involvement with short-run annual
CFO forecasts. They refer to CFO forecasts as an emerging new product and provide descriptive
evidence that short-run CFO forecasts are currently produced for about 60 percent of firms for which
earnings-per-share (EPS) forecasts are generated. DeFond and Hung (2003) suggest that CFO forecasts
are demanded by investors and supplied by analysts in settings where earnings are perceived to be of
low quality. In addition, Givoly et al. speculate that investors are increasingly concerned about the
inherent shortcomings of accrual accounting such as its subjectivity and susceptibility to earnings
management. While long-run CFO forecasts are required by analysts and investors as inputs to firm
valuations using discounted cash flow methodologies, Lorek and Willinger (2011) speculate that
analysts’ reluctance to provide such forecasts may be due to several factors: (1) inherent variability of
the CFO series vis-à-vis the smoother EPS series making accuracy considerably more difficult, (2)
reputational effects when forecasts errors are subject to scrutiny by the investment community, and (3)
the primacy of EPS versus CFO in the financial press. Given the apparent unavailability of long-run CFO
forecasts, investors are forced to substitute EPS forecasts and price-earnings multiples as proxies for
more comprehensive valuation methodologies using CFO data and discounted cash flows. In fact, Liu,
Nissim and Thomas (2007) state that industry multiples are used often in practice as “quick and dirty”
valuations. The theoretical propriety of discounted cash flow valuation methodologies, however, is
underscored by numerous writers of financial statement analysis texts (e.g., Lundholm and Sloan, 2007,
Palepu and Healy, 2008, and Penman, 2007).
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RECENT DESCRIPTIVE EVIDENCE
Lorek and Willinger (2008, 2011) have recently re-examined the time-series properties and
predictive ability of quarterly CFO reported in accordance with SFAS No. 95. Their sample
autocorrelations of quarterly CFO data reveal significant quarter-to-quarter (adjacent) and quarter-toquarter (seasonal) autocorrelations. This dual process characterization results in their identification of
the (100) X (011) univariate ARIMA model as the expectation model of choice for quarterly CFO data.i
Interestingly, this model was originally proposed by Brown and Rozeff (1979) several decades ago as a
premier, statistically-based predictive model for quarterly EPS. While Lorek and Willinger (2011)
document the descriptive fit of the (100) X (011) ARIMA model on quarterly CFO data, they also provide
additional descriptive evidence that the autoregressive and seasonal moving-average parameters in
their models are systematically smaller for quarterly CFO data than for quarterly EPS data. This suggests
that the accrual process via its myriad assumptions pertaining to depreciation, amortization, and
inventory flows appears to induce incremental autocorrelation in the EPS stream vis-à-vis the more
pristine CFO series. This new evidence is also consistent with the notion that CFO data are more highly
variant and more difficult to predict than EPS data, perhaps justifying the reluctance of analysts to
provide long-term CFO predictions.
RECENT PREDICTIVE EVIDENCE
Academics have studied the time-series properties of quarterly CFO data extensively with the
hope of identifying efficient statistically-based quarterly CFO prediction models. While progress in
model refinement has been attained, methodological issues pertaining to such things as the appropriate
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proxy for CFO, model estimation procedures (cross-sectional versus time-series) and model type
(univariate versus multivariate) needed to be thoroughly examined.
Wilson (1986, 1987) and Bernard and Stober (1989) developed a complex disaggregated-accrual
regression-based model to predict quarterly CFO. It was multivariate in nature and employed
contemporaneous and lagged values of numerous accrual-based and cash-flow variables. Specifically,
they employed a vector of 15 independent variables for each firm in the cross-section. Briefly, these
independent variables are comprised of current and lagged values of sales revenues, net earnings, CFO,
current and noncurrent accruals, and the most recent annual capital expenditures (e.g., Wilson 1986,
1987; Bernard and Stober, 1989). They estimated this model cross-sectionally forcing firm-specific
parameters to be the same across firms and time. Their rationale for doing so was to increase sample
size by not requiring a long time-series of financial data to operationalize their model thus increasing the
power of their statistical tests. While their model outpredicted several naïve benchmark models, Neil
et al. (1991), however, criticized their approach because it used contemporaneous independent
variables to predict CFO. That is, future values of accrual-based variables were employed to help predict
future values of CFO making the model inoperational in a true ex-ante fashion. Unfortunately, this
methodological feature precluded its utilization in real-world settings faced by analsyts.
Concerned by the data requirements and complexity of the regression-based models attributed
to Wilson and Bernard and Stober, Lorek, Schaefer and Willinger (1993) developed a univariate seasonal
autoregressive (SAR) ARIMA model, (100) X (000) in Box-Jenkins notation (See Appendix). This model
had three important differences from the approach discussed above. First, it was parsimonious only
employing past values of CFO to predict future values of CFO unlike employing a set of fifteen
independent variables as in Wilson’s model. Second, it was operational in the sense that it only
employed lagged, publicly available CFO data to predict future CFO data. Third, it was estimated in a
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time-series manner rather than cross-sectionally allowing each sample firm’s data to determine the
parameters of the model. Lorek et al. provide evidence that the SAR ARIMA model significantly
outpredicted the cross-sectional regression models attributed to Wilson and Bernard and Stober.
The next advancement in statistically-based quarterly cash flow modeling is attributed to Lorek
and Willinger (1996) who developed a multivariate time-series regression model (MULT) (See Appendix).
Basically, the MULT model employs lagged values of CFO, operating income, receivables, payables, and
inventory, while also allowing for firm-specific parameter estimation. Considerably more complex than
the SAR ARIMA model discussed above, it was more parsimonious than the Wilson cross-sectional
regression model. Because Lorek and Willinger estimated MULT on a time-series basis, firm-specific
parameters were estimated. They provide predictive evidence that MULT generated one-step-ahead
quarterly CFO forecasts that were significantly more accurate than the SAR ARIMA model or Wilson’s
cross-sectional regression model.
All aforementioned empirical works were conducted on a proxy series for quarterly CFO
compiled via algorithms that added back non-cash expenses like depreciation and amortization to net
income due to the unavailability of reported CFO data. SFAS No. 95 was promulgated in 1988
mandating that all listed firms report a cash-flow statement displaying CFO effective for fiscal years
ending after July 15, 1988. Unfortunately, Hribar and Collins (2002) provide evidence that the
algorithmic CFO series employed in earlier work was not highly correlated with the CFO series reported
in accordance with SFAS No. 95 reporting standards perhaps casting doubt upon the external validity of
previous findings. This motivated researchers to reassess the time-series properties and predictive
ability of quarterly CFO data using CFO data reported in accordance with SFAS No. 95.
Lorek and Willinger (2008) examined the time-series properties of quarterly CFO reported in
accordance with SFAS No. 95 rather than the algorithmic proxy employed in previous studies. They
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provide descriptive evidence that the time-series properties of the quarterly CFO series are at variance
with studies that employed an algorithmic proxy for CFO, consistent with the evidence of Hribar and
Collins (2002). Specifically, quarterly CFOs are not purely seasonal which is what Lorek, Schaefer, and
Willinger (1993) reported in their examination of the proxy quarterly CFO series. Reported quarterly
CFO exhibit both quarter-to-quarter (adjacent) and quarter-by-quarter (seasonal) autocorrelations
substantially different than the purely seasonal characteristics reported by Lorek, Schaefer, and
Willinger (1993). This led Lorek and Willinger (2008) to identify the (100) X (011) Brown-Rozeff ARIMA
model as a candidate model for quarterly CFOs (See Appendix). Unlike the SAR ARIMA model, this
ARIMA model is considerably more complex containing an autoregressive parameter, seasonal
differencing, and a seasonal moving-average parameter. Lorek and Willinger (2008) provide evidence
that the (100) X (011) ARIMA model provides significantly more accurate one-quarter-ahead predictions
of CFO than all of the aforementioned statistically-based, quarterly CFO prediction models that we have
discussed previously.
Lorek and Willinger (2011) substantiated the descriptive findings of their earlier work and
provided empirical evidence demonstrating the superior predictive performance of the (100) X (011)
ARIMA model in one thru twenty quarter-ahead CFO predictions. This recent evidence is particularly
salient to investors and analysts since it is not confined to short-term CFO predictions but also applies to
longer-term predictions necessary for firm valuations. Another empirical finding of Lorek and Willinger
pertained to relatively smaller parameter values for the CFO models versus corresponding earningsbased models. This suggests that CFO data exhibit lower levels of autocorrelation than EPS data and is
consistent with the notion that the historical cost model injects increased levels of autocorrelation into
the EPS series via such mechanisms as depreciation, amortization, and inventory costing methods.
Likewise, the smoothing of the earnings series via these processes inherent in historical cost may
contribute to the increased accuracy of EPS projections versus CFO projections.
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A FRAMEWORK FOR CFO PREDICTIONS
Figure 1 displays a proposed framework by which statistically-based CFO forecasts generated by
the (100) X (011) ARIMA model may be combined with qualitative adjustments through the use of
fundamental financial analysis. That is, this combinational framework uses statistically-based CFO
forecasts as a starting point but fine-tunes them via macroeconomic, industry, and firm-specific
adjustments. The univariate ARIMA CFO forecasts may be viewed as a steady-state extrapolation of
past, firm-specific CFO time-series behavior. Analysts’ expertise on the economy, competitor firms, and
information on recent product developments and/or marketing strategies could then be used to refine
the purely statistically-based CFO forecast upwards or downwards. This framework has several
characteristics that are appealing. First, it is anchored by statistically-based CFO forecasts derived from
the (100) X (011) ARIMA model which has considerable empirical support in the academic literature.
Since identifying an ARIMA model structure may be bypassed, estimating the (100) X (011) ARIMA
model is no more complicated than estimating parameters using OLS regression.ii Second, rather than
viewing statistically-based forecasts as the end product, it provides a vehicle by which qualitative factors
might be incorporated into the CFO forecast. Third, and most importantly, it makes explicit not only the
amount of the CFO forecast adjustment but also the rationale of the analyst - both of which will be
subject to the scrutiny of the investment community. This combination of quantitative and qualitative
forecasting factors should enable users to better understand the sources of CFO forecast accuracy
and/or error and represents a conceptually appealing union of quantitative and qualitative forecasting
methodologies.
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Figure 1
Comprehensive CFO Forecasting Schema
Preliminary
Univariate
(100) X (011)
ARIMA CFO
Forecast
Qualitative
Fine-Tuning
Adjustments
Attributed to
Analysts
Final CFO
Forecast
CONCLUDING REMARKS
We provide a detailed overview of relatively new descriptive evidence pertaining to the timeseries properties of quarterly CFO which may be of interest to analysts interested in CFO forecasting.
This evidence suggests that quarterly CFO exhibit quarter-to-quarter (adjacent) and quarter-by-quarter
(seasonal) autocorrelations leading Lorek and Willinger (2008, 2011) to identify the (100) X (011) BrownRozeff ARIMA model as the best statistically-based CFO prediction model. While analysts’ involvement
with short-run CFO forecasts is increasing (Givoly et al., 2009), long-run CFO forecasts attributed to
analysts are still virtually non-existent. Yet, analysts and investors require these long-run CFO forecasts
to operationalize discounted cash flow valuation models. In an effort to further the availability of longrun CFO forecasts, we propose a forecasting schema which combines the statistical power of the (100) X
(011) ARIMA model with information garnered by analysts using fundamental financial analysis.
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REFERENCES
Bernard, V. and T. L. Stober. 1989. The timing, amount, and nature of information reflected in
cash flows and accruals. The Accounting Review 64: 624-652.
Brown, L. D. and M. S. Rozeff. 1979. Univariate time-series models of quarterly accounting
earnings per share: A proposed model. Journal of Accounting Research 7: 179-189.
DeFond, M. L. and M. Hung. 2003. An empirical analysis of analysts’ cash flow forecasts.
Journal of Accounting and Economics 35: 73-100.
Givoly, D., C. Hayn, and R. Lehavy. 2009. The quality of analysts’ cash-flow forecasts. The
Accounting Review 84: 1877-1911.
Hribar, P. and D. W. Collins. 2002. Errors in estimating accruals: Implications for empirical
research. Journal of Accounting Research 40: 105-134.
Liu, J. D. Nissim, and J. Thomas. 2007. Is Cash flow king in valuations? Financial Analysts
Journal 63: 56-68.
Lorek, K. S., T. F. Schaefer, and G. L. Willinger. 1993. Time-series properties and predictive
ability of funds flow variables. The Accounting Review 68: 151-163.
Lorek, K. S. and G. L. Willinger. 1996. A multivariate time-series prediction model for cashflow data. The Accounting Review 71: 81-101.
Lorek, K. S. and G. L. Willinger. 2008. Time-series properties and predictive ability of quarterly
cash flows. Advances in Accounting 24: 65-71.
Lorek, K. S. and G. L. Willinger. 2011. Multi-step-ahead quarterly cash-flow prediction models.
Accounting Horizons 25: 71-86.
Lundholm, R. and R. Sloan. 2007. Equity Valuation and Analysis. 2nd. ed. McGraw-Hill.
Neill, J. D., T. F. Schaefer, P. R. Bahnson, and M. E. Bradbury. 1991. The usefulness of cash
cash flow data: A review and synthesis. Journal of Accounting Literature 10: 117-150.
Palepu, K. G. and P. M. Healy. 2008. Business Analysis & Valuation. 4th ed. Southwestern
College Publishing.
Penman, S. H. 2007. Financial Statement Analysis & Security Valuation. 3rd. ed. McGraw-Hill.
Wilson, G. P. 1986. The relative information content of accruals and cash flows: Combined evidence
At the earnings announcement and the annual report release date. Journal of Accounting
Research 24 (Supplement): 165-200.
Wilson, G. P. 1987. The Incremental information content of the accrual and funds components
of earnings after controlling for earnings. The Accounting Review 62: 293-322.
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APPENDIX
STATISTICALLY-BASED QUARTERLY CFO PREDICTION MODELS
MULT:
CFOt = a + b1 CFOt-1 + b2 CFOt-4 + b3 OIBDt-1 + b4 OIBDt-4 +
b5 RECt-1 + b6 INVt-1 + b7 PAYt-1 + at
(1)
where OIBD is operating income before depreciation, REC is accounts receivable, INV is inventory, PAY is
accounts payable, and at is a current disturbance term.
SAR ARIMA MODEL:
(000) x (100)
CFOt = φ CFOt-4 + at
(2)
BROWN-ROZEFF ARIMA MODEL:
(100) x (011)
CFOt = CFOt-4 + φ1 (CFOt -1 - CFOt-5) + at - Ө1 (at-4 )
(3)
where:
CFOt
= operating cash flows at time t
φ1 = autoregressive parameter
Ө1 = seasonal moving-average parameter
at = current disturbance term
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Endnotes
I employ the (pdq) X (PDQ) notation where: p (P) = number of regular (seasonal)
autoregressive parameters, d (D) = number of consecutive (seasonal) differences, and q (Q) =
number of regular (seasonal) moving-average parameters.
i
ii
User-friendly ARIMA subroutines are currently available in SAS and SPSS.
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