A Quick Overview of the “q Theory” of Investment

Tobin’s q is defined as the ratio of market value to replacement value for a firm’s capital.

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The market value in the numerator reflects the profitability to the firm of one additional unit of capital.  The replacement cost in the denominator can be thought of either as the cost of acquiring new capital or the price earned by selling existing capital.

If q>1, then the additional profit a firm could expect from one more unit of capital (equipment, buildings, etc) is greater than its replacement/acquisition cost.  The firm should increase its capital stock.

If q<1, then the additional profit would be less than the acquisition cost.  We assume diminishing marginal productivity of capital, so this also means that the last unit of capital the firm acquired is producing less for the firm than its market value.  The firm should reduce its capital stock (sell equipment, etc).

In both cases, diminishing marginal utility means q should tend toward 1.  If q>1 and a firm acquires more capital, average productivity will decrease until the market value of the next machine will equal the acquisition costs.  Firms are indifferent to paying $1 for $1 worth of equipment.  If q<1 and the firm sells capital, average productivity will rise until the market value of the remaining capital equals the replacement/sales price.  Firms are also indifferent to selling $1 worth of equipment for $1.

In q theory, a firm acts to maximize the present value of its after-tax net receipts.  A firm’s investment level is a function of its marginal q.  For the specifics of the theoretical model, and for the explicit relationship between marginal q and average q, see “Tobin’s Marginal q and Average q:  A Neoclassical Interpretation,” (Hayashi 1982).

Marginal q refers to the market-value-to-replacement-cost ratio of the next unit acquired.  This cannot actually be observed.  What can be observed is the firm’s average q, or the ratio of market value to acquisition cost for the firm’s entire existing capital stock.

Dynamic Agency and the q Theory of Investment

DeMarzo, Peter M., Michael J. Fishman, Zhiguo He, and Neng Wang, 2012, “Dynamic Agency and the q Theory of Investment,” The Journal of Finance, Vol. 67, No. 6 (2012), 2295-2340.

Purpose:  To introduce an agency problem into the standard q theory of investment; to show that cash flow is not the best predictor of investment.

Motivation:  A large body of literature uses cash flow to predict firm investment levels.  This paper argues that a better proxy is “financial slack,” which is directly related to the agency problem.

Model:

  • Productivity is a Brownian motion, and the agent controls the drift but not the volatility.
  • w = W/K is the agent’s total expected payoff per unit of capital, and must be high enough to incentivize the agent to maximize productivity.
  • The level of w depends on λ, σ, and historical firm profitability.
    • λ is a measure of the extent of the agency problem.
    • σ is the volatility of firm productivity.
    • Past productivity raises or lowers w, and the agent loses his job when w = 0.
    • A portion of w is deferred, giving the agent a stake in continued firm success.
  • Investor’s expected payoff per unit of capital, p(w), is a function of how much they pay the agent.
  • Average q is total firm value per unit of capital stock, or qa = p(w) + w.
  • Marginal q, or qm = p(w)wp’(w).
    • Firms invest when marginal q is less than 1, so investment is a function of w. It follows that investment depends upon λ, σ, and past firm performance.
  • “Financial slack” equals w/λ, and is the largest productivity shock the firm can suffer without changing agents.
  • The agent accumulates cash and available credit equal to the firm’s “financial slack,” then distributes excess income to shareholders.

Conclusions:

  • Financial slack is a better predictor of investment than cash flow.
  • Average q is higher than marginal q because an increase in capital stock K reduces w, and hence reduces the agent’s [historically determined] incentives to maximize productivity.
  • Financial slack and profitability are substitutes in determining average q.
  • When the firm is profitable, w rises, the agent’s incentives grow, and return on investment increases.
    • Investment is serially correlated.
  • The cost of incentivizing the agent leads to underinvestment in every state of the world.

Why do U.S. Firms Hold So Much More Cash than They Used To?

Bates, Thomas W., Kathleen M. Kahle, and René M. Stulz, 2009, “Why Do U.S. Firms Hold So Much More Cash than They Used To?” Journal of Finance, Vol 64, No. 5 (2009), 1985-2021.

Purpose:  To document the increase in U.S. firms’ cash holdings from 1980-2006 and investigate its causes.

Motivation:  U.S. firms in 2006 hold twice as much cash (as a percentage of assets) than they did in 1980.  The average firm in 2006 has enough cash on hand to pay off all its debts.  This cash buildup has excited considerable popular attention.

Findings:

  • Firms of all sizes have a much higher cash-to-asset ratio in 2006 than in 1980.
  • This also holds for firms with no foreign income, so repatriation taxes do not explain it.
  • Cash buildup is observed in firms that do not pay dividends, but not in dividend-payers.
  • Firms whose idiosyncratic risk increased saw more growth in cash holdings.
    • Firms in industries that grew riskier
    • Younger firms (with more recent IPOs)
  • As the increase in idiosyncratic risk has reversed in recent years, cash holdings have declined slightly.

Data/Methods:

  • Data is a sample of 13,599 U.S.-based, nonfinancial, non-utility firms with positive sales and positive assets, over the period 1980-2006 (from WRDS merged CRSP/Compustat database).
  • Look at descriptive statistics of the average cash ratios, with the data segmented by size, industry risk, year of IPO, dividends paid, and net income.
  • Ask whether firms’ cash demand curve shifted or whether firms moved along the curve.
    • Regress cash-to-assets ratio on several firm characteristics (R&D expenditures, size, etc).
  • Connect the rising cash levels to specific firm characteristics.
    • Use Fama-Macbeth regressions with 1980s data to predict cash holdings, based on several firm characteristics, in the 1990s and 2000s.
    • Compare prediction to actual holdings.
  • Examine whether increased cash holdings is due to agency problems.
    • Compare yearly average cash for quintiles based on the GIM index of management entrenchment.

Conclusions:

  • Firms whose cash holdings increased the most are newer, do not pay dividends, and are in industries that have become riskier since 1980.
  • Cash holdings rose because inventories fell, R&D expenses increased, capital expenditures fell, and cash flow risk increased.
  • Cash holdings did not increase more quickly for firms with entrenched management.

Do Acquisitions Relieve Target Firms’ Financial Constraints?

Erel, Isil, Yeejin Jang, and Michael S. Weisbach, “Do Acquisitions Relieve Target Firms’ Financial Constraints?” Journal of Finance, forthcoming as of Aug 2014

Purpose:  To ask whether a target company’s access to capital improves after an acquisition.

Motivation:  Managers often cite, as an argument for acquisition, the ability of the acquirer to finance the target company’s investment opportunities.  It is implicitly claimed that the target is financially constrained, but will be less constrained after the takeover.

Findings:  Takeover targets do seem to be financially constrained, and the constraints weaken after acquisition.  Cash holdings in the targets decline by 1.5%, investment levels increase, the sensitivity of cash to cash flow falls from 10.4% to zero, and cash flow sensitivity of investment also falls.  These effects are significant only for independent targets, which were more likely to be financially constrained than targets who were subsidiaries.  In a similar vein, the effects are strongest for the smallest tercile of target firms.

Data/Methods:  Post-acquisition financial data on U.S. companies is not publicly available, but most European countries require subsidiaries to publicly release such information.  The data comprises before-and-after data for 5,187 European companies who were acquired during the period 2001-2008.

  • Measure before-and-after cash policies of the target
    • Cash levels
    • Cash flow sensitivity of cash
    • Cash flow sensitivity of assets
  • Measure before-and-after investment policies of the target
    • Cash flow sensitivity of investments
  • Measure sensitivity of cash in [former] target to cash flows
    • In whole acquiring firm (including former target)
    • In all other departments of acquirer (not including former target)
  • Compare acquisition effects for targets of different size and sales growth, holding acquirer constant
  • Verify whether any effects are observed for firms very similar to the targets, but which were not acquired

Conclusions:  After firms are acquired, they tend to reduce cash holdings and increase investment, and their cash flow sensitivities of both cash and investment decline.  These changes in cash and investment policy are most notable in very small, independent targets and are much less significant for larger firms or subsidiary firms that are acquired.  There are no significant effects for firms that were not acquired, but were comparable to target firms.  These results suggest that financial constraints relax or disappear post-acquisition, especially for the firms most likely to be constrained.  It appears unlikely that this phenomenon is due to the other departments of the acquirer cross-subsidizing the former target’s investments; the easing of financial constraint is probably due to the target becoming part of a larger firm.

Corporate Finance Over the Past 25 Years

Brennan, Michael J., 1995, “Corporate Finance Over the Past 25 Years,” Financial Management, Vol. 24, No. 2, Summer 1995, 9-22.

Purpose:  To review the development of corporate finance research over the period 1970-1995.

Four Chief Developments:

  • One development has relaxed the constraints of the classical MM (Modigliani-Miller) paradigm.
    • The MM theories about dividends and capital structure take firm cash flows as given, and study how the distribution of that income affects its total value.
    • Analysis later shifted to asking how the structure of claims against the cash flow affects the flow itself, which led to studies of the several types of securities issue.
    • Research in 1970 examined the overall corporation; in 1995, it looks more at specific events or transaction types, such as IPOs, takeovers, repurchases of equity, etc.
  • Another development recognizes that managers are not perfect agents (the agency problem).
    • Newly recognized facets of agents’ opportunities and preferences include their information endowments, their discretionary powers, the nature of the incentives embodied in their contracts, their non-financial compensation (perquisites, reputation, power, etc.), and aversion to effort.
  • A third development has replaced the traditional assumption of actors as price-takers with analyses of games under incomplete information. Analysis has begun to move away from discounted cash-flow modeling, and toward techniques similar to those used in pricing options.
  • A fourth development has realigned the aims of argument:
    • Scholars in 1970 were concerned with the implications of the structure of institutions. Their counterparts in 1995 are more interested in institutional structures as responses to specific problems, and in either defending the structures or proposing new ones.

 

Other Trends:

  • In 1970, bankruptcy was largely ignored, held as synonymous with liquidation, or treated as a cost to offset the tax savings of debt in determining optimal capital structure. Research in 1995 separates direct from indirect bankruptcy costs (and recognizes the latter as substantial); distinguishes between reorganization, bankruptcy, and liquidation; and examines the connection between bankruptcy laws and efficient liquidation.
  • A general trend in corporate finance has been a move away from efforts to prescribe how financial decisions ought to be made, and toward descriptions or explanations of how and why actual decisions are made.

 Unexplored Territory:

As of 1995, little attention had been given to the analysis of knowledge-based firms whose most important capital is autonomous employees (corporate finance research of the past generally assumed that firms relied on physical capital), or to the implications of increased globalization on corporate financial decisions and structures.

The Cash Flow Sensitivity of Cash

Almeida, Heitor, Murillo Campello, and Michael S. Weisbach, 2004, “The Cash Flow Sensitivity of Cash,” The Journal of Finance 59 (4), 1777-1804.

Purpose:  This paper develops a model of a firm’s demand for liquidity, and uses the model to obtain a new measurement of how important financial constraints are in affecting corporate policy.

Theory:  For financially constrained firms, or for firms that expect financial constraints in the future, higher cash flows should lead to more cash on the balance sheet.  For unconstrained firms that do not expect future constraints, the level of cash flows and the amount of cash on the balance sheet should be unrelated.  If this “cash flow sensitivity of cash” can be shown to be correlated with proxies for financial constraint, it will be a useful indicator of the influence of such constraints on firm behavior.

Motivation:  The effects of financial constraints on firm behavior and firms’ financial management are two topics usually studied separately, though they are closely linked.  Most previous literature regarding this link discusses the connection between financial constraints and firm investment demand.  There is a robust debate around this, with no clear consensus on what the empirical evidence means.  One complication with the literature is that current investment demand is correlated with future investment demand (since current investments impact cash flow).  Cash balances are not inherently linked to cash flows, and so are unrelated to future investment demand.  Therefore, the link between cash balances and financial constraints is less problematic to measure.

Empirical Evidence:  Using a large sample of manufacturing firms from 1971-2000, divide firms into subgroups on proxies for financial constraint.  Measure the cash flow sensitivity of cash for each group.

Conclusions:

  • Firms exhibiting proxies for financial constraint hold 15% of assets as cash, compared to only 8-9% for firms that are not under [proxied] financial constraint
  • For 4 of the 5 financial constraint proxies, the firms expected to be constrained have the higher cash sensitivity to cash flows
  • Cash flow sensitivity of cash is a useful method for identifying financially constrained firms

Measuring investment distortions arising from stockholder-bondholder conflicts

Parrino, Robert, and Michael S. Weisbach, 1999, “Measuring investment distortions arising from stockholder-bondholder conflicts,” The Journal of Financial Economics 53, 3-42.

Purpose:  This paper calculates the expected wealth transfer between stock- and bondholders occurring when a firm begins a new project.  It also estimates how stockholder-bondholder conflict impacts investment decisions, and whether it can explain cross-sectional variation in capital structure.

Findings:

  • There will be underinvestment when the firm is faced with safe projects.
    • Stockholders demand a higher return than the CAPM rate.
      • This effect is stronger for high-leverage firms.
    • Safe projects with low returns benefit bondholders at the expense of equity holders.
  • There will be overinvestment when the firm is faced with risky projects.
    • Stockholders are willing to gamble, and will even invest in negative NPV projects if the potential payoff is high.
      • This effect is also stronger for high-leverage firms.
    • Risky projects with negative expected (but high potential) payoffs benefit equity holders at the expense of bondholders.
  • Longer debt duration is vulnerable to larger agency problems
  • Lower marginal tax rates lead to slightly larger distortions
  • The stockholder-bondholder conflict does exist and there do seem to be empirical investment distortions, but these distortions are too small to be useful in explaining most firms’ capital structure decisions.
    • The distortion is only 0.14% for a firm with 20% debt-to-capital ratio, compared with a 3% noise factor in measuring cost of capital

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Motivation:  Managers seek to maximize shareholder value, not necessarily firm value.  The “underinvestment problem” is when managers avoid a positive NPV project that would increase firm value but would lower stockholder value.  The “overinvestment problem” is when managers undertake a negative NPV project that lowers firm value but raises stockholder value.  These agency problems have been widely discussed in the literature for decades, but there is no consensus on their magnitude or on how important they really are.

Data/Methods:  Use numerical simulations to estimate the impact of debt on the investment decisions of a levered firm whose managers seek only to maximize stockholder value.  Compute the stockholder-bondholder wealth transfer accompanying projects with known characteristics.

  • Compustat data for firms from 1981-1995
  • Monte Carlo:  Assume a firm with known cash flows following a random walk without drift for 30 years, after which cash flows are static.  Assume a project financed entirely with equity, whose cash flows similarly follow a random walk without drift for 30 years.  Assume a correlation of 0.5 between firm and project cash flows, run the simulation 5,000 times, and compute the ex ante value of debt and equity each time.
    • Value of debt is the sum of discounted future cash flows to bondholders.
    • Value of equity is the discounted cash flows to stockholders plus a terminal value.

Conclusions:  Distortions in stockholder-bondholder required investment returns vary along several dimensions.  However, for the typical firm they are much smaller than the noise in cost-of-capital measurement.  The effect exists but is too small to explain cross-sectional variation in capital structure.

Investment and Financing Constraints: Evidence from the Funding of Corporate Pension Plans

Rauh, Joshua 2006, “Investment and Financing Constraints: Evidence from the Funding of Corporate Pension Plans,” The Journal of Finance 61 (1), 33-71.

Purpose:   This paper evaluates the dependence of corporate investing on internal financial resources, using mandatory defined-benefit contributions (MCs) as an instrument for internal resources.

Findings:  Capital expenditures fall by $0.60-$0.70 for $1 in mandatory pension contributions (MCs).  The size of this coefficient is inversely related to credit rating, and is clearest among firms with observable financial constraints.

Motivation:  The Miller-Modigliani model predicts that internal financing and external financing are perfect substitutes.  However, with taxes, agency costs, and asymmetric information, internal financing may be less expensive.  If so, then financial constraints should cause a drop in investment in capital or R&D (internal “financing”).  Previous research observes firms’ response to exogenous funding shocks in small samples.  This paper uses a much larger sample and an instrument for exogenous funding shocks.  There is also a prior debate about the correlation between investment and cash flow, which this paper also addresses

Data/Methods:

  • Data:  1,522 Compustat firms making DB contributions between 1990 and 1998 (8,030 firm years)
  • Define cash flow as net income plus depreciation/amortization plus pension expense minus pension plan contribution from IRS forms 5500, since pension expense does not equal cash contribution
  • Regress investment on cash flow and pension contribution variables
  • DB pension funding may be endogenous to the firm’s investing opportunities
    • Overcome endogeneity by looking at contributions to funds around the underfunded threshold
    • Identifying assumption is that the relationship between unobserved investment opportunities and funding status is not the same as that between funding status and required contributions.
  • Separate MCs into unexpected and “predictable”
    • Use predictable, unexpected, and both contribution types as independent variables
  • Divide the sample along several observable dimensions (firm age, credit rating, etc)
    • Run the baseline regression (investment on MCs) on each division
  • Look at whether MCs in one period affect investment in surrounding periods
  • Look at whether MCs in constrained firms leads to higher investment in non-constrained firms

Conclusions:

  • Capital expenditures decrease $0.60 for $1 in MCs, which is 4-7x the magnitude of the effect of cash flows
  • MCs also have marginal effects on acquisitions and dividends, but not on borrowing
  • Unexpected and predictable MCs each account for equal portions of the variance in total MCs
  • Firms that do not sponsor defined benefit (DB) plans take up about 12% of the capital expenditure slack that constrained DB firms leave on the table when MCs are high

Enjoying the Quiet Life? –commentary

This paper uses a clever check for reverse causality.  The authors find that for firms whose incorporating state adopts anti-takeover laws in the preceding twelve months, wages rise and productivity falls.  The reverse causality story is that rising wages (perhaps due to union pressure) and falling productivity threaten firms in a certain state, and therefore make that state more likely to enact anti-takeover laws.  The authors’ story depends on causality in the right direction.

The paper’s main tests use a binary variable BC to indicate whether a firm’s incorporating state enacted anti-takeover laws in the prior 12 months.  The coefficients on BC in the several regressions are the paper’s main findings.

In the reverse-causality check, the authors replace BC with four dummy variables:

  • Before-1 for firms incorporated in states that had not yet passed legislation but would do so in the next 12 months
  • Before0 for firms incorporated in states that had passed legislation in the prior 12 months
  • After 1 for firms incorporated in states that had passed legislation between 12 and 24 months prior
  • After2+ for firms incorporated in states that had passed legislation two or more years previously

Significant coefficients on Before-1 would have suggested that legislation was passed in response to an already-changing business environment.

Before0 was the variable of primary interest.

Small and Insignificant coefficients on After 1 and After2+ would have suggested that the effects of legislation were short-lived and therefore economically much less interesting.

In this case, the coefficients on Before-1 were small and statistically insignificant, ruling out the reverse causality.  The coefficients on After 1 and After2+ were significant and even larger than the coefficients on Before0, strengthening support for the authors’ story since their reported effects of anti-takeover laws continued to grow in the longer term.