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Cash flow sensitivity of cash: when should we use it to measure financial constraints?

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Abstract

Since Almeida et al. (J Financ 59:1777–1804, 2004), there has been a long debate on whether the cash flow sensitivity of cash (CFSC) measures financial constraints. Like all measures of financial constraints, CFSC is not a perfect one. Thus, how to measure financial constraints with CFSC effectively is an important issue. This paper shows that when a firm does not save through external financing, the CFSC can be effectively used to measure financial constraints. However, for firms saving from external financing, CFSC does not effectively measure financial constraints, especially when firms use external funds as substitutes for internal ones. The reason is that CFSC does not only reveal the propensity to save from cash flows but also the internal-external financing relation, which is not necessarily linked to financial constraints. Two identification methods are used to confirm our findings.

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Notes

  1. See, for example, Baum et al. (2011), Chen et al. (2012), Chen and Wang (2012), Erel et al. (2015), Itzkowitz (2015), Meng et al. (2020).

  2. Literature also show a decline and disappearance of the investment-cash flow sensitivity during the 2008 credit crunch (Chen et al. 2012).

  3. Note that to replicate results in Almeida et al. (2004), \(\Delta CASH\) and CF are scaled by current total assets. The estimates of the coefficients do not change significantly if we scale the variables with the total assets at the beginning of the period.

  4. There is much evidence supporting the existence of these economies of scale (Mulligan 1997; Bates et al. 2009). For example, larger firms hold less cash because of economies of scale with the transaction motive.

  5. They extract historical headquarter locations from WRDS SEC Analytics Suite and hand-collect the historical headquarter locations from the Moody’s Manuals (later Mergent Manuals) and Dun & Bradstreet’s Million Dollar Directory (later bought by Mergent)

  6. Fortunately, the University of Notre Dame’s Software Repository for Accounting and Finance provides the augmented 10-X header dataset: https://sraf.nd.edu/data/augmented-10-x-header-data/.

  7. All accounting data are CPI-adjusted into 1971 dollars.

  8. WW index and HP index are measured with the following methods:

    $$\begin{aligned} WW&=-0.091CF-0.062DIVPOS+0.021LEV-0.044SIZE+0.102ISG-0.035SG \\ HP&=-0.737SIZE+0.043SIZE^2-0.040AGE \end{aligned}$$

    where CF is the ratio of cash flow to total assets, LEV is the ratio of long-term debt to total assets, DIVPOS is a dummy indicating positive dividends, SIZE is the natural log of total assets, AGE is the number of years preceding the observation year that the firm has a non-missing stock price on the Compustat file, ISG is the firm’s 3-digit industry sales growth, and SG is the firm sales growth.

  9. KZ index is not included as in Almeida et al. (2004), the financially constrained firms classified with KZ index do not show a positive CFSC.

  10. The financing deficit is defined as the growth in assets less the growth in current liabilities less the growth in retained earnings.

  11. We acknowledge that there is a small proportion of firms that show negative correlations between cash savings and net external financing. Due to the lack of theoretical foundation, we do not consider the situation where the correlation coefficient is strongly negative.

  12. We also calculate the 15-year rolling correlation coefficient between cash savings and external financing to capture time-variant firm heterogeneity. In addition, we use \(\pm 0.2\) as cutoffs to ensure that firms in either group have correlation coefficient estimates that are statistically reliable. Alternative cutoffs are used as robustness checks to alleviate the potential measurement error associated with small sample estimations of the correlation coefficient (See Table 14).

  13. To compute this variable, we exclude firms when the denominator (the sum of cash flow) is negative to ensure that the weight is increasing in the amount of cash flow (Baker and Wurgler 2002).

  14. Detailed definitions of these variables are provided in Appendix E

  15. Many studies show that equity issuance has gradually become a major source of cash savings because of precautionary motives (DeAngelo et al. 2010; McLean 2011; Bolton et al. 2013; Eisfeldt and Muir 2016).

  16. Earnings-based covenants usually specify debt limits as a function of internal funds.

  17. See Appendix A.2 of Lian and Ma (2021) for details about the classification procedures.

  18. The original insight of using the payout ratio to measure financial constraints is built on the notion that the payout policy is a central liquidity management tool (Fazzari et al. 1988). Recent empirical analyses challenge this notion, nonetheless. Almeida et al. (2016), for example, show that stock repurchases are conducted not only to manage liquidity but also to manage earnings-per-share. In particular, the unprecedented increase in stock repurchases over the last 20 years suggests that payout behavior may no longer provide a helpful indicator of constraints (Farre-Mensa et al. 2014).

  19. These measures are obtained from Joel Hasbrouck’s Web site. They are available through 2006, so this reduces the number of observations when we use these measures.

  20. Almeida et al. (2021) reexamine the empirical evidence on the ACW model presented in Almeida et al. (2004) and also find the constraint measure based on the payout ratio yields weak support for the ACW model.

  21. Note that Almeida et al. (2004) focus only on manufacturing firms (SIC: 2000 to 3999). Table 15 shows that our results are robust after using the same filter.

  22. See Heider and Ljungqvist (2015) Appendix A for a list of the relevant tax increases.

  23. Given that tax shields can only benefit firms that have (or expect soon to have) profits to shield from tax, the debt test cannot be applied to chronically loss-making firms. Following Farre-Mensa and Ljungqvist (2016), we excludes firm-years with a zero marginal tax rate. Note that the marginal tax rates data are from Graham (1996a, 1996b). Missing values are filled in as recommended in Graham and Mills (2008).

  24. None of our corporate income tax increases coincides with a bank tax cut.

  25. There are four corporate tax increases that coincide with the lifting of bank branching restriction in the same state: MO (1990), MT (1990), NE (1990), and KS (1992). (See Kerr and Nanda (2009) for a complete list of deregulation events)

  26. In Warusawitharana and Whited (2015), the tax rate on dividends is 35%, and the linear cost is around 5%. Thus lower bound of overvaluation is approximately \(\frac{1}{(1-\tau _d)(1-a)}=160\%\).

  27. For example, Rhodes-Kropf et al. (2005), Hertzel and Li (2010), Fu et al. (2013).

  28. This dataset is available at WRDS website at https://wrds-www.wharton.upenn.edu/pages/get-data/peters-and-taylor-total-q/peters-and-taylor-total-q/.

  29. https://pages.stern.nyu.edu/jhasbrou/Research/GibbsEstimates2006/Liquidity%20estimates%202006.htm.

  30. Data can be found at Havard Dataverse at https://dataverse.harvard.edu/dataset.xhtml?persistentId doi:10.7910/DVN/T9KXMF/.

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** Hu

  • Chinese Academy of Finance and Development, Central University of Finance and Economics, 39 South College Road, Haidian District, Bei**g, 100081, People’s Republic of China

    **-Hu-Aff1">Wei** Hu

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    Appendices

    A numerical example for the availability and cost constraints

    Following Tirole (2010), we consider an entrepreneur has a project. This project requires a fixed investment I, the initial asset is A, where \(A-I<0\). Thus, the firm must borrow. If the project succeeds, the return is \(R>0\). Otherwise, \(R=0\). The probability of success is denoted by p. The entrepreneur can behave or misbehave. The probability of success, \(p=p_H\) if the entrepreneur behaves while \(p=p_L\) if the entrepreneur misbehaves, and \(p_H>p_L\). If the entrepreneur misbehaves, he gets a private benefit G from misbehaving.

    Following Tirole (2010), we assume that borrowers and lenders are risk-neutral. There is no time preference (the discount rate is 0). The loan has zero profit. If the project fails, both the borrower and lender receive 0. If the project succeeds, the two parties share the return R; \(R_b\) goes to borrowers and \(R_l\) goes to the lender.

    1.1 Cost constraint

    The external financing is B,

    $$\begin{aligned} B=I-A \end{aligned}$$

    In the case of costly external financing, an increase in A reduces B. That is,

    $$\begin{aligned} \frac{\partial B}{\partial A}<0 \end{aligned}$$

    1.2 Availability constraint

    Next, we discuss the “availability constraint” through the borrowing capacity. To enable the borrower to behave, the incentive compatibility constraint is:

    $$\begin{aligned} p_HR_b\ge p_LR_b+G \end{aligned}$$

    Thus, the highest income that can be pledged to the lenders without jeopardizing the borrower’s incentives is \(R-\frac{G}{\Delta p}\), where \(\Delta p=(p_H-p_L)\).

    The pledgeable income is,

    $$\begin{aligned} {\mathcal {P}}=p_H \left(R-\frac{G}{\Delta p}\right) \ge I-A=B \end{aligned}$$

    In addition, the pledgeable income should exceed the lenders’ initial outlay. Then we have,

    $$\begin{aligned} A\ge I-p_H \left(R-\frac{G}{\Delta p}\right) \end{aligned}$$

    and, when \(I>0\),

    $$\begin{aligned} \frac{I}{A}\le \frac{I}{I-p_H(R-G/\Delta p)}=k. \end{aligned}$$

    Since \(I>0\) and \(p_H(R-G/\Delta p)<I\), we have \(k>1\). The borrowing should satisfy the following condition,

    $$\begin{aligned} \frac{I}{A}-1=\frac{B}{A}\le =k-1 \Rightarrow B\le (k-1)A. \end{aligned}$$

    The term \((k-1)A\) is the availability constraint. When a borrower faces availability constraints, the borrowing reaches the borrowing capacity. That is,

    $$\begin{aligned} B=(k-1)A \end{aligned}$$

    Thus, in the case of availability constraints, an increase in A increases B. That is

    $$\begin{aligned} \frac{\partial B}{\partial A}=(k-1)>0. \end{aligned}$$

    B Other stylized facts

    See Table 11.

    Table 11 Composition of financially constrained and unconstrained firm-years
    Full size table

    C Robustness tests

    See Tables 12, 13, 14 and 15.

    Table 12 Robustness: mismeasurement of Q corrected by High Order Cumulant estimator
    Full size table
    Table 13 Robustness: mismeasurement of Q corrected by the ‘total q’
    Full size table
    Table 14 Robustness: alternate classification cutoffs
    Full size table
    Table 15 Robustness: manufacturing firms (SICs 2000–3999)
    Full size table

    D Decomposition of market-to-book equity ratio

    A firm’s log market-to-book equity ratio can be decomposed into two items,

    $$\begin{aligned} ln(\frac{ME}{BE}) = ln(\frac{ME}{VE}) + ln(\frac{VE}{BE}) \end{aligned}$$

    Where ME is the observed market value of equity and BE is the book value of equity. VE represents the intrinsic value of equity, which is unobservable.

    To use this decomposition, we must estimate VE. The traditional method of calculating the intrinsic value is usually based on the residual income model (Lee et al. 1999; Dong et al. 2006). However, this model rests on a number of strict assumptions that make it difficult to distinguish between mispricing and growth components clearly. Rhodes-Kropf et al. (2005) relax the residual income model and assume that a firm’s intrinsic value can be expressed as a linear function of accounting variables, which include book equity (BE), net income (NI) and market leverage (MLEV) ratio. The regression is:

    $$\begin{aligned} ln(ME_{it})=\alpha _{0jt}+\alpha _{1jt}ln(BE_{it})+\alpha _{2jt}ln|NI|_{it}+\alpha _{3jt}I_{<0}ln|NI|_{it}+\alpha _{4jt}MLEV_{it}+\varepsilon _{it} \end{aligned}$$

    where, |NI| is the absolute value of net income. \(I_{<0}\) is a dummy variable that is equal to one if net income is negative. The subscript i, j, t stands for firm, industry and time, respectively. As shown above, the parameters are allowed to vary over time and across industries to reflect the variation in investment opportunities across times and industries. Specifically, each year we group firms according to the 12 Fama and French industry classification and run cross-sectional regressions for each industry to estimate the parameters \(\alpha _{jt}\). Like previous studies, the average adjusted \(R^2\) for these regressions exceed \(80 \%\) for almost all industries.Footnote 27 Following Rhodes-Kropf et al. (2005), we get industry-variant parameters \({\overline{\alpha }}_j\) by averaging the \(\alpha _{jt}\) from the annual regressions for each industry. Then the intrinsic value can be expressed as:

    $$\begin{aligned} ln(VE_{it})={\overline{\alpha }}_{0t}+{\overline{\alpha }}_{j}ln(BE_{it})+{\overline{\alpha }}_{2t}ln|NI|_{it}+{\overline{\alpha }}_{3t}I_{<0}ln|NI|_{it}+{\overline{\alpha }}_{4t}MLEV_{it} \end{aligned}$$

    As \(\varepsilon _{it}\) captures the deviation of intrinsic value from observed market value of equity, then \(ln(ME_{it})-ln(VE_{it})\) can be interpreted as the firm-level mispricing at a point of time. Intuitively, if markets know the future growth opportunities, discount rates, and cash flows, \(ln(ME_{it})-ln(VE_{it})\) should equal to zero. If markets make false predictions or do not have information that managers have, then \(ln(ME_{it})-ln(VE_{it})\) will capture the misvaluation component of the market to book equity ratio.

    Definitions of key variables

    Firm-level variables

    • Assets (AT) Book value of total assets (Compustat item at).

    • Capital (K) Net property, plant and equipment (Compustat item ppent).

    • Sales growth (SG) Annual percentage growth in sales (Compustat item sale). It is calculated as sale/l.sale - 1.

    • Market value (M) Market value of total assets (Compustat item prccf \(\times\) csho + at -txdb-ceq).

    • Market equity (ME) Market value of equity (Compustat item prccf\(\times\)csho).

    • Book equity (BE) Book value of equity (Compustat item ceq).

    • Cash holdings (CASH) Cash and cash equivalents (Compustat item che) scaled by total assets.

    • Cash savings (\(\Delta CASH\)) Changes in cash holdings.

    • Cash flow (CF) Firm’s cash flow in a year (Compustat item ib+dp-dvt) scaled by total assets.

    • Tobin’s q (Q) Market value divided by book value of total assets.

    • Total q (\(Q_{tot}\)) New Tobin’s q measure that accounts for intangible capital, provided by Peters and Taylor (2017).Footnote 28

    • EBITDA (EBITDA) Earnings before interest, tax, depreciation and amortization (Compustat item oibdp) scaled by total assets.

    • Net income (loss) (NI) Fiscal income or loss after subtracting expenses and losses from all revenues and gains (Compustat item ni) scaled by total assets.

    • Issuance costs (Cost) We mainly use three measures of issuance costs (Gibbs, Amihud, and Amivest) obtained from Joel Hasbrouck’s website.Footnote 29Gibbs is the Hasbrouck (2009) Bayesian estimate of the basic market-adjusted model adapted from Roll (1984). Amihud is the Amihud (2002) illiquidity measure, which is the absolute value of daily returns divided by daily dollar volume. Amivest is a liquidity measure, which is the amount of volume needed to get a unit change in stock price.

    • Net debt issuance (NDEBT) Net proceeds from debt sales (Compustat item dltis-dltr) scaled by total assets.

    • Net equity issuance (NEQUITY) Net proceeds from equity issues (Compustat item sstk-prstkc) scaled by total assets.

    • Cash flow-based lending (\(Lending^{CF-Based}\)) Cash flow-based lending scaled by total assets.Footnote 30

    • Investment (Investment) Capital expenditure (Compustat item capx) scaled by total assets.

    • R& D (\(R \& D\)) Research and development expense (Compustat item xrd) scaled by total assets.

    • Tangibility (Tangibility) Asset tangibility. It is constructed following Berger et al. (1996) and Almeida and Campello (2007) as 0.715 \(\times\) Receivables (Compustat item rect/at) + 0.547 \(\times\) Inventory (Compustat item invt/at) + 0.535 \(\times\) Capital (Compustat item ppent/at).

    • Long-term book leverage (LEV) Long-term debt (Compustat item dltt) scaled by total assets.

    • Fraction of fixed assets (FixAsset) The ratio of net fixed assets (Compustat item ppent) to total assets.

    • Market leverage (MLEV) Market leverage ratio, which is defined as 1-Market equity/Market value.

    • Cash flow volatility (CFVOL) Cash flow uncertainty proxy. It is constructed following Minton and Schrand (1999) as standard deviation of quarterly cash flow using sample over the previous 6-year period.

    • Mispricing component (Overvaluation) The ratio of market equity to intrinsic value, which is regarded as the mispricing component in market to boot equity ratio. The natural logarithm of the intrinsic value can be expressed as a linear function of observable accounting information, including net income, market leverage and book equity: \(ln(VE_{it})={\overline{\alpha }}_{0t}+{\overline{\alpha }}_{j}BE_{it}+{\overline{\alpha }}_{2t}ln|NI|_{it}+{\overline{\alpha }}_{3t}I_{<0}ln|NI|_{it}+{\overline{\alpha }}_{4t}MLEV_{it}\). We estimate the coefficients following Rhodes-Kropf et al. (2005).

    • Marginal tax rate (MTR) Following Graham et al. (1998), We use after-interest marginal tax rates (variable mtrafter) from John Graha (http://faculty.fuqua.duke.edu/jgraham/taxform.html). Missing values are filled in as recommended in Graham and Mills (2008).

    • Firm-level cash flow sensitivity (\(F-CFSC\)) First, we get residuals \(\varepsilon _{it}\) by regressing cash savings on control variables, including Tobin’s q and size. Then, we define the firm-level cash flow sensitivity as the difference between cash flow weighted-average residuals and simple average residuals. The calculation mainly follow Hovakimian (2009).

    Financial constraint measures

    • Firm size (SIZE) Natural logarithm of the book value of total assets.

    • Payout ratio (DIV) The ratio of total distributions (Compustat item dvt+prstkc) to operating income (Compustat item oibdp).

    • HP index (HP) The variable measures financial constraints. The calculations follow Hadlock and Pierce (2010).

    • WW index (WW) The variable measures financial constraints. The calculations follow Whited and Wu (2006).

    Macro variables

    • Recession dummy (Recession) The recession dummy that is equal to one if six or more of the previous 12 months had declining GDP and zero otherwise.

    • Default spread (Spread) The difference between Moody’s seasoned Aaa and Baa corporate bond yields.

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    Hu, W., Zhang, X. & He, Y. Cash flow sensitivity of cash: when should we use it to measure financial constraints?. Rev Quant Finan Acc 62, 637–682 (2024). https://doi.org/10.1007/s11156-023-01219-3

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