Tobin’s q

Tobin’s q is the ratio of the market value of a firm to the replacement cost of its assets. This statistic can be used to predict investment spending or to control for a firm’s current and future profitability in empirical studies of corporate structure and behavior.

The Motivation for q

A standard tenet of corporate finance is that the retention of earnings to finance expansion raises a stock’s price if the rate of return on these investments, ρ, is larger than shareholders’ required return on their stock, R. For example, an investment that costs $1 million is worth more than $1 million to stockholders if ρ > R. This principle suggests that whether a firm’s stock sells for a premium or a discount relative to the cost of its assets depends on ρ versus R and, further, that a firm’s investment decisions ought to depend on a comparison of ρ with R

The shareholders’ required return is determined in financial markets by shareholders pricing stock to yield an anticipated return that is competitive with comparable investments they might make. This determination of required returns is one of the primary ways in which financial markets affect real economic activity. When interest rates fall, required stock returns decline, making it more likely that ρ > R, so that the profits from prospective investments are sufficient to make these investments attractive for firms that care about their shareholders.

But where do firms (or economic forecasters) see these shareholder required returns? It is straightforward to calculate the yield to maturity on a bond by determining the discount rate that equates the present value of the promised cash flow to the market price. There are no comparable calculations for stocks because the cash flow to investors is unknown. An ingenious alternative, proposed by James Tobin (Brainard and Tobin, 1968; Tobin, 1969), is to look at stock prices. Specifically, Tobin argues that we should look at how financial markets value a firm relative to the replacement cost of the firm’s assets:

(1)

The numerator and denominator of Tobin’s q can either be aggregate market value and replacement cost or, equivalently, price per share and assets per share. If a firm has debts, these can be included in the numerator.

What Determines q?

How can assets be valued in financial markets at other than their replacement cost? Assets are of value to shareholders only to the extent that they generate profits. It matters not at all that a factory cost $1 billion to build if it doesn’t make a dime of profits. For a factory to be worth what it costs shareholders, it must earn the shareholder’s required rate of return.

For a simple example, suppose that a hamburger chain has no debt and pays out all earnings as dividends. Assume also that a new restaurant costs $1 million to build and is expected to earn a constant 20 percent profit (ρ = 0.20), $200,000 a year forever. The value that financial markets place on the $200,000 annual cash flow depends on how highly hamburger earnings are valued. If Treasury bonds yield 5 percent, perhaps stock in risky hamburger restaurants is priced to yield 10 percent (R = 0.10). Because the anticipated dividends are a constant $200,000, the market value of the restaurant is

Valued at $2 million, the $200,000 annual dividend provides stockholders their requisite 10 percent return.

In this case, the market value of the restaurant is twice its construction cost: q = 2. Stockholders welcome this investment, because the use of $1 million in potential dividends to build the restaurant provides $2 million in market value. The underlying reason is that the restaurant’s 20 percent profit rate is larger than the market’s 10 percent required rate of return.

If, on the other hand, shareholders’ required rate of return is 25 percent, then

Now q = 0.8 and the construction of the restaurant will be to the detriment of shareholders. Because the restaurant earns only 20 percent on its cost, the stock must be valued at less than the asset’s cost in order to provide shareholders their 25% required return.

Implications for Investment Decisions

A connection between business investment spending and market value relative to cost was pointed out many years ago by John Maynard Keynes (1936):

[T]he daily revaluations of the Stock Exchange, though they are primarily made to facilitate transfers of old investments between one individual and another, inevitably exert a decisive influence on the rate of current investment. For there is no sense in building up a new enterprise at a cost greater than that at which a similar existing enterprise can be purchased; whilst there is an inducement to spend on a new project what may seem an extravagant sum, if it can be floated on the stock exchange at an immediate profit.

Similarly, Tobin argues that a firm should invest in new buildings and equipment if the stock market will value the project at more than its cost (that is, if the project’s q is greater than 1). If the market value is larger than the cost, shareholders prefer that the firm make this investment rather than distribute its cost as dividends, gladly giving up a dollar of dividends in exchange for a two-dollar increase in the value of their stock. Put more plainly, the appropriate question a firm should ask is whether, if it were to sell shares in its new venture, it could raise enough money to cover the project’s cost. It can if the value of Tobin’s q is larger than 1, but not otherwise. Thus Tobin’s q provides a barometer of the incentives for business investment.

Similarly, the firm should compare the price it can get for selling its existing assets with the value that financial markets place on these assets. If the market value is less than the sale price (q < 1), the firm is worth more dead than alive, and it should sell off its assets and distribute the proceeds either through dividends or share repurchases. A low market value relative to replacement cost may also motivate takeover bids, since an outside group may profit by purchasing enough stock to gain control of a company and then liquidating its assets.

Marginal and Average q

Why don’t firms immediately exploit any differences between market value and replacement costs, thereby causing q to return to 1 instantaneously? Three, sometimes related, explanations involve convex adjustment costs, monopoly rents, and heterogeneous capital (Lucas and Prescott, 1971; Mussa, 1977; Smith, 1981; Hayashi, 1982; Abel, 1983; Erickson and Whited, 2000; Gomes, 2001). A consideration of these issues requires a distinction between average q, the aggregate market value and replacement cost of a firm’s assets, and marginal q, the change in a firm’s market value resulting from a specific investment relative to the cost of that investment.

An observed average q that is greater than 1 might accurately reflect a company’s substantial profits, but further investment may be restrained by convex adjustment costs that cause the marginal q for a large expansion to be less than 1. It might be prohibitively expensive for a hamburger chain to triple its size in a year. A related strand of literature (summarized by Hubbard, 1998) investigates how investment by financially constrained firms may be less sensitive to q and more sensitive to the firm’s cash flow.

Similarly, a firm might earn monopoly rents that cause average q to exceed 1, but have a marginal q that is less than 1 because new investments would erode these rents. A hamburger restaurant with a patented secret formula might not want to open a competing restaurant next door that would lure away customers. The grower of an exotic fruit may not want to flood the market with produce that could only be sold by lowering prices.

Finally, prospective ventures might be quite different from the firm’s existing operations, with different rates of return and with risks that command different required returns. A tobacco company acquires a snack food company; a yogurt maker enters the bottled water market; a software company enters the video game market. In each case, marginal q might be quite different from average q.

A further complication is that observed market values presumably take into account not only existing assets but also future investments anticipated by the market. Suppose, for example, that a firm currently has assets with a replacement cost and market value that both equal $100 million and is planning to make an investment that will cost $20 million and have a market value of $30 million. Average q for the firm’s current assets is 1 and marginal q for this investment is 1.5. If the stock market takes into account this projected investment, the current market value is increased by $10 million (discounted somewhat to the extent the value added will occur in the future and if there is uncertainty about whether the investment will be made.) Thus observed average q reflects both the profitability of the current capital stock and also the perceived profitability of the firm’s future opportunities, overstating the former and understating the latter.

Estimates of q

The book value reported by firms is a rough proxy, a starting point, for estimating the replacement cost of a firm’s assets. Accounting conventions value assets at historical cost, with no adjustments for subsequent cost increases, and depreciate assets according to accounting conventions rather than true economic depreciation. Inflation can cause book values to understate the replacement cost of assets (think of real estate); technological progress can cause the reverse (think of computers). The market value of a firm’s equity is commonly estimated by multiplying the market price of a firm’s stock by the number of shares outstanding; data on the market value of a firm’s preferred stock and debt are not so easily obtained because data bases generally record the book values reported by firms in their balance sheets.

A variety of often complex procedures have been employed to estimate the market value of a firm’s debts and the replacement cost of its assets (Brainard, Shoven, and Weiss, 1980; Lindenberg and Ross, 1981; Lewellen and Badrinath, 1997; Lee and Tompkins, 1999), while other authors argue that more readily available book values provide sufficiently accurate approximations (Chung and Pruitt, 1994; Perfect and Wiles, 1994).

Because of these measurement errors, when q is used as an explanatory variable in a regression model, least squares estimates of the coefficient of q will be biased towards zero and estimates of the coefficients of other explanatory variables may be biased towards zero or away from zero. For example, in a model that uses a firm’s q and current cash flow to predict investment spending, the coefficient of q will be biased downward (toward zero) and the coefficient of cash flow may be biased upward. Erickson and Whited (2000) propose sophisticated estimators to deal with measurement error and obtain relatively large estimates of the relationship between q and investment.

Another issue is whether we should use the market’s valuation or the firm’s internal valuation of prospective investments, since the firm may have better information about the projected cash flows and speculative stock market noise can causes market prices to wander from fundamental values (Blanchard, Rhee, Morck, Shleifer, and Vishny, 1990; Summers, 1993). Several authors have proposed creative ways of estimating marginal q from information available to managers (Abel and Blanchard, 1986; Gilchrist and Himmelberg, 1995) or from stock analysts’ earnings forecasts (Cummins, Hasset, and Oliner, 1999; Bond and Cummins, 2001). Gentry and Mayer (2002) apply the q model to REITs and find that the use of appraised value in place of accounting-based replacement cost increases the estimated empirical relationship between REIT investment and q.

Uses of q

Empirical studies using Tobin’s q initially focused on either explaining q (Lindenberg and Ross, 1981; Salinger, 1984) or using q to predict investment spending (Furstenberg, 1977; Summers, 1981; Hayashi, 1982), but have since broadened to include many issues in corporate finance that hold investment opportunities constant. For example, if we want to use cross-section data to see whether dividend policy affects the value of a firm, we need to control for each firm’s profitability. Thus q has been used in studies of the effects of managerial equity ownership (Morck, Shleifer, and Vishny, 1988; McConnell and Servaes, 1990), the size of a company’s board of directors (Yermack, 1996), corporate diversification (Berger and Ofek, 1995; Rajan, Servaes, and Zingales, 2000); and dividend changes (Lang and Litzenberger, 1989; Denis, Denis, and Sarin, 1994). For similar reasons, Tobin’s q has been used to hold investment opportunities constant while investigating the determinants of capital structure (Titman and Wessels, 1988), leveraged buyouts (Opler and Titman, 1993), and takeovers (Lang, Stulz, and Walkling, 1989; Servaes, 1991).

Tobin’s q will no doubt be used in many other empirical studies of corporate structure and behavior because it circumvents the unresolved issue of how to estimate shareholders’ risk-adjusted required return by looking directly at observable market prices, which incorporate both the cash flow expectations of investors and the required returns they use to discount this anticipated cash flow.

Gary Smith
Fletcher Jones Professor of Economics
Pomona College
Claremont, CA 91711
gsmith@pomona.edu

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