Modigliani and Miller's Irrelevancy Propositions

Much of early financial economics considered what possible causes could and could not have an effect on the rational behaviours of individuals and firms in well-functioning markets. A number of ‘irrelevance’ and ‘separation’ theories followed where things that were intuitively believed to be important in matters such as corporate financial structure, corporate investment policy or individuals’ portfolio composition were shown to be theoretically irrelevant to all or specific parts of a rational decision-making process. An early and important example of such a theory was provided by the Yale economics professor Irving Fisher in his seminal 1930 book The Theory of Interest.[1] Fisher substantially pre-dates the recognised classic period of financial economics that started in the 1950s—The Theory of Interest arguably provides a bridge from macroeconomics to the fledgling discipline of financial economics (that is, to the formal and rigorous economic treatment of the fields of investment and finance).

For financial economists, Fisher’s book is best remembered for what has become known as Fisher’s Separation Theorem. This theory states that a firm’s value is maximised when it chooses to invest in projects that generate cashflow streams with positive expected present values when discounted using market discount rates. This may appear as an unremarkable statement—but the key point was that the choice of discount rate should be determined only by the market’s required return and should be independent of the particular risk and timing preferences of the firm’s specific set of shareholders. These preferences are irrelevant to the shareholder’s own wealth because, in well-functioning markets, shareholders would be able to take actions (buying stock, selling stock, borrowing, lending) that would deliver to them whatever risk and timing preferences they wanted, whilst preserving the value created by the firm’s investment decisions. Hence, all shareholders’ wealth would be maximised when the firm chose to invest to maximise the present value at market discount rates, even if it resulted in a risk or income timing profile that was not desired by some, or even all, of the firm’s actual shareholders. The firm’s optimal choice of investments was therefore separate from the risk and income-timing preferences of its shareholders.

Fisher was not the only US economist of the 1930s who was focused on corporate investment theory and the valuation of the firm. In 1938, John Burr Williams published his Harvard doctoral thesis, The Theory of Investment Value.2 According to Mark Rubinstein, the eminent late twentieth century financial economist and occasional historian, Williams’s book ‘contains what is probably the first exposition of the Modigliani—Miller (1958) proposition on the irrelevancy of capital structure’.[2] [3] This principle is set out by Williams in his Law of Conservation of Investment Value:

If the investment value of an enterprise as a whole is by definition the present worth of all its future distributions to security holders, whether on interest or dividend account, then this value in no [way] depends on what the company’s capitalization [financial structure] is.[4]

Thus Williams’s Law of Conservation of Investment Value said that the total value of the firm was determined by the cashflows its assets generate, and this was not affected by how those cashflows were split up and packaged into various forms of securities such as equities and debt. Williams never set out formally to prove his law: his justification was based on rhetorical persuasion rather than a rigorous demonstration deduced from a set of stated axioms. He reasoned that, ‘Clearly if a single individual or single institutional investor owned all the bonds, stocks and warrants issued by a corporation, it would not matter to this investor what the company’s capitalization was’.[4] Some 20 years later, Modigliani-Miller’s famous paper was published in which Williams’s argument was developed using a more formal economics.[6] Indeed, the Modigliani-Miller paper was arguably as important to financial economics for how it influenced the way in which its theories would be developed as for its specific content. In particular, Modigliani-Miller pioneered the formal use of no-arbitrage as a way of proving a financial theory. That is, the proof was based on the demonstration that if the theory did not hold, an arbitrage would exist such that some investors would be able to make limitless riskless profits at the expense of others: if it was an assumption of wellfunctioning markets that such opportunities do not exist, then the theory must hold in such a market. Virtually every notable theory of financial economics published ever since has used a no-arbitrage argument in its formulation. Modigliani-Miller’s version of Williams’s Law was given in their famous Proposition I:

The market value of any firm is independent of its capital structure ... the average cost of capital to any firm is completely independent of its capital structure and is equal to the capitalization rate of a pure [unleveraged] equity stream of its class.[7]

Modigliani-Miller’s no-arbitrage argument was built on the assumption that a group of firms in a given ‘class’ had perfectly correlated underlying assets. From this assumption, it was possible to show that different segments of the capital structure of the different firms in the class could be bought or sold to create an arbitrage if Proposition I did not hold. This is, of course, a somewhat artificial and theoretical arbitrage argument—in reality there are not many groups of firms with perfectly correlated assets—but it provided their argument with a new economic rigour. Like Williams’s Law of Conservation of Investment Value, Proposition I said that the total size of the pie (the value of the firm) does not depend, in a well-functioning capital market, on how you split up the pie (between shareholders and bondholders and any other form of security holders). In essence, if we assume that the firm’s asset cashflow is independent of its capital structure choice, then this is really only saying that present values are additive. For example, in a simple single-timestep model where the firm’s (uncertain) asset cashflow X, is paid at the end of the period, and a debt of amount D is due to bond holders at this time, the respective pay-outs are:

The sum of the pay-outs is always X and the present value of the sum of the pay-outs is not a function of the choice of value for D. Proposition I also said that the choice of capital structure had no impact on the firm’s total cost of capital (and hence on corporate investment choices): the cost of capital was solely a function of the riskiness of the investments that the firm made (the asset side of the corporate balance sheet), and this was not altered by the firm’s capital structure (the liability side of the corporate balance sheet). In a similar vein to Fisher’s argument, Modigliani—Miller said firms create value through the investments they make; these investments should be discounted at market discount rates commensurate with the risk of the investments; the firm’s capital structure and the individual preferences of their capital owners were both irrelevant to these choices and values. The behaviour of the firm’s cost of capital as a function of the level of debt in the capital structure according to Proposition I can be summarised by Fig. 4.1 below.

The cost of capital is constant across the choice of capital structure, and is therefore always equal to the cost of capital of a pure equity (unleveraged, zero debt) firm. As debt is introduced into the capital structure, three things happen that have a collectively offsetting impact on the firm’s weighted-average cost of capital: the value of debt as a proportion of total assets increases; the expected

Cost of capital and capital structure example

Fig. 4.1 Cost of capital and capital structure example (Modigliani-Miller proposition I) return on debt increases (starting from the risk-free rate); and the expected return on equities increases (starting from the cost of capital of an unleveraged firm). In the limit, very high debt levels make default increasingly more likely and debt accordingly behaves more and more like (unleveraged) equity.

Modigliani-Miller did not say anything about how to value the respective shareholder and bondholder claims, or how the expected return on equities and debt specifically behaved. Their valuation statements were only relative: the sum of their pay-outs was not a function of the choice of D and the firm’s cost of capital was not a function of D. Absolute statements about the valuation of equities and debt would require a specification for the stochastic process driving the underlying assets of the firm (and a theory of valuation of contingent claims that did not yet exist). Modigliani-Miller showed that these relative properties must hold true for any stochastic process that drives the asset values of the firm, and this had major ramifications for how management can and cannot create value for the firm’s capital providers (in perfect market conditions).

Whilst their theory could be derived from a relatively simple arbitrage argument and could be shown to ultimately be a simple expression of the additivity of present values, it still ran counter to perceived wisdom—which was that firms should prefer to use debt rather than equity until required bond returns became prohibitive. Modigliani-Miller recognised that their assumption of perfect markets was a ‘drastic simplification’, and that real-life complexities may have an impact on optimal financial structure. Their paper prompted decades of further academic research into how market imperfections such as taxation,[8] bankruptcy costs,[9] management agency costs[10] and informationsignalling[11] could make capital structure relevant to firm value. But their theory showed what did not matter: whilst expected equity returns would be enhanced through debt financing, this only systematically increased the riskiness of the equity return. Raising debt merely geared up equity returns in a way that individual shareholders could choose to do (or undo) with their own borrowing and lending (rather like in Fisher’s Separation Theorem).

Modigliani and Miller published a second jointly-authored paper[12] in 1961 that provided the equivalent irrelevancy theorem for corporate dividend policy: in perfect capital markets, changes in dividend policy could not have an effect on the overall return earned on a firm’s equity, all other things being equal. Again their argument was that all value was determined on the asset side of the corporate balance sheet—whether firms chose to finance that investment through retained earnings or new equity issuance or other forms of capital raising was irrelevant to the economics of the value. Again they recognised that the theory was an abstraction—for example, in real life, dividend decisions were likely to have important informational content for shareholders —but they once again highlighted that where these decisions did matter, it was because of market imperfections or limitations rather than the fundamental economics. Miller-Modigliani were aware that what they were saying was beguilingly simple:

Like many other propositions in economics, the irrelevance of dividend policy is “obvious once you think about it”. It is, after all, merely one more instance of the general principle that there are no “financial illusions” in a rational and perfect economic environment. Values there are determined solely by “real” considerations — in this case the earning power of the firm’s assets and its investment policy — and not by how the fruits of the earning power are “packaged” for distribution.[13]

And yet, it is not difficult to find examples of twentieth-century economists whose thinking on this topic was woolly at best. Recall Edgar Lawrence Smith’s argument that US corporations’ practice of retaining and reinvesting a significant portion of their earnings was a vital factor in the ability of equities to so strongly out-perform corporate bonds. Smith was not a substantial economist, but his views were endorsed by John Maynard Keynes, arguably the most influential economist of the century. In reviewing Smith’s book, Keynes wrote of Smith’s corporate-dividend-policy-as-explanation-of-equity-outperformance argument: ‘I have kept until last what is perhaps Mr Smith’s most important, and certainly his most novel, point. Well-managed industrial companies do not, as a rule, distribute to the shareholders the whole of their earned profits.’[14] Miller and Modigliani brought a clarity to what matters—or rather to what should not matter—for capital structure, dividend policy and corporate investment policy. They did so by introducing a new formal rigour to the embryonic discipline of financial economics, profoundly influencing its subsequent practice. Franco Modigliani and Merton Miller received the Nobel Prize in Economic Sciences in 1985 and 1990 respectively, both in part for their two jointly written papers.

  • [1] Fisher (1930).
  • [2] Williams (1938).
  • [3] Rubinstein (2006), p. 79.
  • [4] Williams (1938), p. 72.
  • [5] Williams (1938), p. 72.
  • [6] Modigliani—Miller (1958).
  • [7] Modigliani-Miller (1958), pp. 268-69.
  • [8] Miller (1977).
  • [9] Stiglitz (1972).
  • [10] Jensen and Meckling (1976).
  • [11] Ross (1977).
  • [12] Miller and Modigliani (1961).
  • [13] Miller and Modigliani (1961), p. 414.
  • [14] Keynes (1983), p. 250.
 
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