Investment and Cash Flow With Imperfect Capital Markets

Many models of capital market imperfections reach the conclusion that financing an investment project is cheaper with ‘internal’ than with ‘external’ funds. (Internal funds are those that the firm owns, for example, in its bank account; external funds are obtained from outsiders like banks or new investors). For a lucid exposition of an example of models of this kind, see the discussion of financial market imperfections in Romer (2011).

These models tend to be highly specialized, with entrepreneurs who receive exogenously specified endowments of ‘internal’ cash who make a one- or two-period investment decision. This is a striking contrast with the generality of the canonical $ϙ$ model of investment in which optimizing firms make investment decisions that take into account infinite future paths of adjustment costs, marginal products of capital, taxes, and all other features of the environment.

But models with imperfect capital markets are always very clear on who receives what cash, when, and why. In contrast, the power of the $ϙ$ model comes at a high cost: The model has no implications whatsoever for the firm’s decisions about when and how to make payments to shareholders and lenders.

1 Modigliani-Miller

To see this, consider the benchmark discrete time framework qModel without taxes or depreciation, and (as in that handout) assume that the firm issues or repurchases shares to maintain a number of shares $s t$ outstanding equal to the size of the physical capital stock (so $st = kt$ in every period). Suppose we assume that the firm has a ‘dividend policy’: In every period, it pays to each shareholder a dividend equal to the flow of revenues per share.

In this case, the value of all the firm’s shares $st$ (the equity value of the firm) will be

(Notice that because the firm always has $st = kt,$ the value of the firm’s shares defined here $ˆet(st)$ is identical to the value of the firm’s capital $et(kt)$ defined in qModel.)

Now suppose the firm wants to consider deviating from this dividend policy. It issues an extra share in period $t$ , which raises an amount of money equal to the marginal value of capital; it invests the proceeds in the riskless asset, earning return $R$ , then pays out the resulting cash to shareholders in the next period. However, we assume that the firm continues to maximize its value. This modifies the infinite sum to:

The point can be extended to show that the firm can raise an arbitrary amount of money in one period, paying it back in another, or vice versa, without having any effect on its value or its optimal investment plans.

This is an example of the famous theorem by Modigliani and Miller (1958), who showed that under perfect capital markets the value of the firm is identical whether its investment is financed by equity, debt, or any combination of the two.

It is precisely to get around this result that models of imperfect capital markets were invented, since from the beginning many economists did not believe that the result is a plausible description of reality (including, I believe, Modigliani and Miller). Indeed, the existence (and high salaries) of corporate financial officers constitute a proof that the proposition is not true. What remains true, however, is that models of investment that relax the assumption of perfect capital markets are much more difficult to work with and harder to extract implications from than the perfect capital markets versions.

A testable result that generally emerges from these models, however, is that the amount of a firm’s investment depends on the amount of cash the firm has on hand with which to finance that investment.

qModel shows that the $ϙ$ model can be manipulated (abstracting from depreciation, taxes, and other complications) to yield an implication for investment dynamics of approximately the following kind:

2 Testing for the Failure of Modigliani-Miller

The simplest class of imperfect capital markets models is one in which the firm is constrained to pay dividends to shareholders equal to whatever is its flow of cash after subtracting off expenses. But the rate of return that the firm must pay for external funds exceeds the return it can earn on internal funds. Without going into details, the rough implication of this is that an empirical model of the firm’s investment choices should augment (3) with a measure of the funds the firm has in its hands at the time the investment decision is made:

A large literature spurred by the seminal paper of Fazzari, Hubbard, and Petersen (1988) estimates equations like this, and virtually always finds a statistically significant estimate of $ψ 2$ , interpreted as indicating the importance of ‘cash flow’ for investment decisions. There are many criticisms of this literature, and the importance of imperfections in capital markets remains a lively area of debate. My own view is that the most persuasive evidence of large deviations from the benchmark of the MM theorem is the fact that the financial services industry (including corporate CFOs) absorbs a very substantial amount of resources every year. Why would such a large industry exist if the informational problems were easy to solve? The most plausible answer is that it wouldn’t - especially in the internet era, where it would be a trivial matter to match up borrowers and lenders in the absence of informational and enforcement difficulties.

References

FAZZARI, STEPHEN, R. GLENN HUBBARD, AND BRUCE C. PETERSEN (1988): “Financing Constraints and Corporate Investment,” Brookings Papers on Economic Activity, 1988(1), 141–206.

MODIGLIANI, FRANCO, AND MERTON H. MILLER (1958): “The Cost of Capital, Corporation Finance, and the Theory of Investment,” American Economic Review, 48(3), 261–297.

ROMER, DAVID (2011): Advanced Macroeconomics. McGraw-Hill/Irwin, fourth edn.