Problems with Tobin’s Q

Tobin’s Q remains the most-used proxy of “investment opportunities” in financial economics.  Economists typically assume that firms face constant returns to scale, in which case marginal Q and average Q are equal.  Average Q is calculated as the ratio of a firms’ market value to the book value of its assets.

Problem #1: Book value is a poor proxy for replacement cost.  What Q really tries to measure is how much additional future cash flow each additional $1 of investment will produce.  Consider two firms whose only asset is a building, and who each have expected discounted future cash flows (market value) of $1 million.  Firm X bought its building 40 years ago for $1,000, while Firm Y bought its building (which is identical to X’s building) last year for $10,000.  If each firm invests another $1,000, what will happen to their market value?

  • Tobin’s Q calculates that Firm X tends to produce $1,000 of market value per dollar of assets, and so it assumes that Firm X’s market value will increase by $1 million (double its current value).  It implicitly assumes that X can get another building for just $1,000.
  • Likewise, Q calculates that Firm Y will only get one-tenth of a new building, so its market value will only rise by $100,000.
  • This is a well-known problem with Q.  Most researchers either ignore it completely, assuming insignificant differences between firms in asset age, or else try to control for industry and age, assuming that all firms of a certain age within a certain industry group have close-to-identical assets.

Problem #2: market value of the firm (not just of the equity)

  • Another well-known problem surfaces in calculating the numerator of Tobin’s Q, or the market value of the firm.  The market value of a public firm’s equity is a simple matter, but the market value of a firm’s debt is more complicated.  Few firms have publicly-traded debt.
  • About the best anybody does is to simply use the book value of the company’s debt and assume that measurement errors are not correlated with anything important.

Problem #3: forward-looking asset prices

  • The numerator of Tobin’s Q includes the market value of a firm’s equity, which is a forward-looking number that is partially based on investor’s expectations regarding the firm’s future investment.
  • This is mostly a problem when attempting to establish a strong link between Tobin’s Q (“investment opportunities”) and actual investment.
  • Consider two otherwise identical firms in separate parts of the country.  Firm L operates in a labor market that is not expected to have any growth in wages in the future, while Firm K operates in a labor market that is expected to have high wage growth.  Investors expect that Firm L will maximize future revenues by only investing (capx) what is needed to replace worn-out machinery.  Investors expect that Firm K will maximize revenues by replacing worn-out machinery and also replacing labor with capital as wages rise relative to rental rates.
  • The firms will differ in their realized and even in their predicted investment, while Tobin’s Q will not necessarily differ between them.

Why Does Capital No Longer Flow to the Industries with the Best Growth Opportunities?

Dong Lee, Han Shin, and René Stulz, 2016 working paper

Industries with the highest average Tobin’s q get more net funding from investors (both debt and equity investors), consistent with properly-functioning capital markets, until the mid-1990s.  Since that time, the industries with the highest q receive less net funding.  There does not appear to have been any breakdown in the efficiency of corporate debt markets.  The findings are driven by high-q industries, which have reduced investment and increased share buybacks.

Methods and Findings:

  • Use the Fama-French 48 industries
  • drop financial and utility firms, as well as regulated industries (per Barclay and Smith (1995))
  • calculate Tobin’s q as the ratio of the market value of industry assets to the book value of industry assets
    • numerator: AT-CEQ-TXDITC + (PRC*SHROUT)
      • assets minus common equity minus deferred tax credit + market cap
    • denominator: AT (total assets)
  • Measure industry funding rate as the sum of net debt issuance (long-term debt) and net equity issuance
  • Firms in the top-funding quintile should have higher q (they don’t)
    • double check that high-funding industries are high-investment industries
  • Measure the cross-sectional correlation between funding rate and q
    • the correlation is mostly positive before 1995, and mostly negative after
  • Examine whether the q-differential between firms assigned to the lowest- and high-funding quintiles at time t=0 disappears over the future, consistent with limited investment opportunities and efficient markets
    • The q of industries in the low-funding quintile converges to the q of industries assigned to the highest-funding quintile over the next 1-5 years.
    • The q of high-funding industries, however, does not fall
  • Compare the high- and low-funding industries along three measures of growth
    • investment (capital expenditures) – high-funding industries also have higher investment, but this difference falls over the five years following assignment to funding quintiles
    • change in number of firms – high-funding industries see greater growth in the number of firms
    • growth in assets – high-funding industries see greater asset growth over the five years following assignment to funding quintiles
      • However, it is not the case that the low-funding indutries are simply financially constrained, since they have higher dividend payout rates at the time of quintile assignment.
  • Regress funding rate on q and cash flow
    • the coefficient on q is significant for the sample period ending in 1996, but insignificant both for the post-1996 sample and for the whole 1971-2014 sample.

Comments

  • This was an interesting read, and it addresses a fundamental economic question that perhaps not enough people are talking about:  do capital markets (still) work?
  • Since about the year 2000, firms have been returning funds to investors in the aggregate.  This matches with an essay I read just this morning by Minneapolis Fed president Neel Kashkari, that cites lack of innovation as a possible explanation for the U.S. (and the world) economy’s anemic recovery from the last crisis.  If businesses no longer have anything important to work on, they shouldn’t invest.  Lee, Shin, and Stulz (this paper) find that it is high-q firms with high cash flows that are returning money through stock repurchases.
  • The paper is long on puzzles and short on solutions, but makes an effort to direct the path for future research.
  • This paper relies heavily on a measure of Tobin’s q, standard in corporate finance, which is, roughly, enterprise value divided by book assets.
    • AT-CEQ-TXDITC is supposed to measure the book value of long-term debt.
    • This is not a good measure, and everybody knows it, and everybody still keeps using it!
      • What about a company with home-grown intellectual property?  Consider a firm with one asset – a patent on a new drug.  No buildings, no equipment, not even a stapler – just a patent.  The firm has a market value of $1 million.  The firm’s Tobin’s q, according to the standard measure, is infinity.  Should the firm keep investing?  Now suppose the patent cost $10 million in R&D expense to develop.  Was it worth it? Should the firm keep investing?
      • What about cases where (conservative) accounting depreciation and economic depreciation don’t line up? Consider a firm whose only assets are a plot of land purchased in 1900 for $10,000 and a warehouse built in 1975 (>40 years ago), for total book assets of $10,000.  Now consider another firm with an identical plot of land purchased in 2000 for $1 million, and a warehouse that serves the same purpose but was built in 2010, for total book assets of >$1 million.  Which firm has higher q, by the standard measure?  Which firm has the best investing opportunities?
  • Now, maybe the examples contrived above are too far from reality to be useful. Maybe conservative accounting valuation of assets is just as good today as ever.  But I’m not convinced.  I think today’s economy relies more on assets that are likely to have zero or low book value than in the past.
  • Even when some of these home-grown intangibles are sold and thereby acquire a book value, the most likely scenario is one where the company owning the assets is acquired, and the companies’ investment bankers use comparable transactions to try and assign a price tag to such assets as “trademark,” “customer loyalty,” “research database,” etc.  This is not a neat process, and intuitively should be even harder in a service-based economy than in the manufacturing economy that prevailed in prior decades.

Questions

  • Is the ratio of goodwill to book value higher now than in the past?  This would be consistent with conservative accountants systematically undervaluing acquired assets and with this undervaluing getting worse.  However, it would also be consistent with the value of private control benefits and, hence, with deteriorating corporate governance.  This is probably not the case, but would not be too difficult to analyze.
  • How to the “high-q” and “low-q” industries compare on R&D, on advertising expenses, on customer loyalty?
  • Finally, why do the analysis at the industry level?  Are all firms in industry 11 (Healthcare Services) or in industry 35 (Computers) supposed to have approximately similar, or even tightly correlated, investment opportunities?  Taking industry averages masks potentially large intra-industry heterogeneity.  It would be interesting to see if the high-q industries are pulled up by outliers, or vice-versa.

Takeaway: If you use the traditional measure of Tobin’s q, equity markets no longer allocate capital to the most efficient industries.  This measure of Tobin’s q is potentially problematic, and I see this paper as much as an indictment of the measure of q as of the efficiency of the equity markets.

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.

Untitled

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.