Marginal q, Tobin's q, cash flow, and investment.

• Author: Gugler, Klaus

1. Introduction

   Cash flow has always been somewhat of a puzzle in the literature on the determinants of investment. In a strictly neoclassical world, cash flow does not belong in an investment equation, and yet empirical studies dating back over 40 years almost invariably find that cash flow and investment are positively related. (1) A variety of hypotheses have been put forward to account for this empirical regularity including the existence of transaction costs, agency problems, and asymmetric information. (2) This paper provides tests of the latter two hypotheses using a sample of 560 U.S. companies over the period 1977 to 1996.

   Under the asymmetric information (AI) hypothesis firms with attractive investment opportunities may be unable to finance them because of inadequate internal cash flows and because the cost of external funds is too high due to the capital market's ignorance of the firm's investment opportunities. (3) Thus, only firms with large cash flows can finance their attractive investment opportunities, and the puzzle of the relationship between cash flow and investment is resolved. To test this hypothesis, we need to identify those firms that may be subject to AI problems. The very nature of AI makes it difficult if not impossible to cleanly identify firms in this situation. If a researcher can identify a firm with attractive investment opportunities and cash constraints, why can the market not do so? Previous studies have used size, level of dividends, age, concentration of share ownership, and extent of cross-shareholdings to identify firms that are possibly subject to AI problems. (4) Although the capital market may have difficulty judging the investment opportunities of small firms, this in itself need not imply that the firm has attractive investment opportunities or that its cash flows are inadequate to finance them, if it does. Similar criticisms can be lodged against the other characteristics used to identify firms subject to AI problems. (5) One of this article's contributions is to use a characteristic of firms that better identifies whether they suffer from AI problems.

   The AI hypothesis assumes that the firm's managers seek to maximize their shareholders' wealth but are prevented by a shortage of cash from undertaking investments with expected returns above the firm's cost of capital. Any firm caught in this predicament should, therefore, have a return on its investment, r, that is greater than its cost of capital, i. Our procedure for identifying firms subject to such cash constraints is thus to estimate the ratio r/i for each firm over our sample period and to categorize any firm for which this r/i > 1 as possibly cash constrained. (6)

   The agency hypothesis links investment to cash flows by assuming that managers obtain financial and psychological gains from managing a large and growing firm and thus invest beyond the point that maximizes shareholder wealth. (7) When this occurs, a company's returns on investment will be less than its cost of capital. Accordingly we identify firms for which r/i

   Both the AI and MD hypotheses treat cash flow as a measure of financial constraints. It is possible, however, that current cash flows merely proxy for the profitability of future sales. Thus, in testing for the importance of cash flows as a source of capital it is necessary to control for the investment opportunities of firms (Chirinko and Schaller 1995, p. 528). Many studies have used Tobin's q as such a control. Tobin's q reflects the average return on a company's capital, but what is relevant for investment is the marginal return on capital. What is needed, therefore, is an estimate of marginal q. The existing literature has continued to use measures of average q, even though the conditions under which it equals marginal q are quite stringent (e.g., constant returns to scale, perfect competition in all product markets). (8) When firms operate in imperfectly competitive markets, some earn rents, and these rents are capitalized in their market values. Differences in average qs may be dominated by differences in inframarginal returns on capital and, thus, may be poor predictors of investment. An important contribution of this paper is to replace Tobin's average q as a control for the investment opportunities of firms with the theoretically appropriate marginal q. (9) Throughout the paper we use qa to represent average q and qm to represent marginal q.

   Although qa is likely to be a poor proxy for the investment opportunities of a company, it can be a good indicator of the presence of asymmetric information for firms with r greater than i. The higher qa is, the cheaper it should be for firms to raise funds by, say, issuing equity, and the less important cash flow should be as a constraint on investment. We thus predict for firms that are likely to suffer from AI problems that the less responsive their investment is to cash flow differences, the higher their qas are.

   Tobin's q also figures in our tests of the MD hypothesis. The chief constraint on managers' exercising their discretion over the allocation of a firm's cash flows is the threat of a takeover and dismissal should the firm's share price fall too low. The higher the firm's share price is, therefore, the greater the freedom managers have to overinvest. We thus predict for the sample of firms that is likely to suffer from agency problems that the more responsive their investment is to cash flow differences, the higher their Tobin's qs are.

   We see the three main contributions of this paper as follows: First, to estimate a marginal q and use it to separate the population of firms into those that are likely to fit the AI and MD hypotheses. Second, to use marginal q to control for investment opportunities so that cash flows' effect is limited to its role as a source of liquidity. Third, to use qa not as a control for investment opportunities as in other studies but as a measure of the cost of external finance for firms potentially subject to cash flow constraints and as a measure of the tightness of the takeover constraint for firms potentially suffering from agency problems. As already stressed, our use of both marginal and average q is new to the literature. Only Kathuria and Mueller (1995) have estimated a marginal q and used it to separate firms into different subsamples as we do. They did not employ marginal q to control for the investment opportunities of the firm, however, nor did they use Tobin's q in the way we do to discriminate between the two hypotheses.

   A fourth contribution of the paper will be to see whether the merger wave of the late 1980s, which included many hostile takeovers, tightened the takeover constraint on managers and led to a reduction in their discretion to invest internal cash flows for the purpose of pursuing growth. The wave of spin-offs in the early 1990s, the emphasis on "downsizing" and "returning to core competences," and the renewed interest in "shareholder value" as evidenced by share buy backs are all consistent with the hypothesis that the existence and/or exercise of managerial discretion declined during the late 1980s and 1990s. (10) We find no evidence in support of this hypothesis, however.

   We proceed as follows. Section 1 reviews various theoretical arguments for including qa and cash flow in an investment equation. In it we also explain the methodology for calculating marginal q. In section 2 we briefly describe the data set and the procedures used to make the estimates. The results are presented in section 3, and conclusions are drawn in the final section.

2. Theoretical Issues

   The Calculation of Marginal q

   The arguments for putting Tobin's q in an investment equation rest on the assumptions of perfect competition, constant returns to scale, and that firms are price takers, which imply that the marginal and average returns on capital ale equal to each other and to a firm's cost of capital. (11) When firms are not price takers and markets are imperfectly competitive, however, marginal and average returns on capital do not coincide and equilibria may exist in which a firm's average return on capital differs from its marginal return. The same level of investment may be optimal for a monopolist as for a competitive firm even though the monopolist's profits on existing assets, and hence qa, are much larger than for the competitive firm. To predict the investments of these two companies more accurately, we need a measure of their marginal returns on capital relative to their costs of capital, which we now derive. (12)

   Let It be a firm's investment in period t, [C.sub.t + j] the cash flow this investment generates in t + j, and [i.sub.t] the firm's cost of capital in t. Then the present value of this investment is

   (1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

   We shall assume capital market efficiency and, thus. that the capital market makes an unbiased estimate of the present value, P[V.sub.t], of any investment [I.sub.t] in t. We can then take the market's estimate of P[V.sub.t] and the investment [I.sub.t], that created it and calculate the ratio of a pseudo-permanent return [r.sub.t] on [I.sub.t] to [i.sub.t]

   (2) P[V.sub.t] = [I.sub.t][r.sub.t]/i[sub.t] = [qm.sub.t][I.sub.t]

   If the firm had invested the same amount It in a project that produced a permanent return [r.sub.t], this project would have yielded the exact same present value as the one actually undertaken. The ratio of [r.sub.t] to [i.sub.t] is the key statistic in our analysis, If a firm maximizes shareholder wealth, then it undertakes no investments for which [qm.sub.t]

   The market value of the firm at the end of period t can be defined as

   (3) [M.sub.t] = [M.sub.t-1] + P[V.sub.t] - [[delta].sub.t][M.sub.t-1] + [[mu].sub.t],

   where [[delta].sub.t] is the depreciation rate for the firm's total capital and [[mu].sub.t], the market's error in evaluating [M.sub.t]. Substituting from Equation 2 into Equation 3 and...