Wacky WACC and the cost of capital

WAAC is an acronym widely used in corporate finance which stands for Weighted Average Cost of Capital. It is often identified (confused) as the marginal cost of capital or the rate of return required by a firm. In discounted cash flow models, WACC is used as a discount rate to evaluate investment projects or to value companies.

There are several controversies regarding the way it should be computed (e.g. see Fernandez, 2011) but I do not address them here. I shall focus on its abusive identification with a true definition of the cost of capital. Indeed, the WACC is neither a cost nor a required return, but an weighted average of both.

Initially, finance theory discussed the concept of the cost of capital in the context of how to fix the rates of public utilities, in order to recover the costs of investment, their replacement costs, their financing costs and any other costs. In corporate finance, it originates from the valuation of investments, and can be regarded either as a discount rate or a multiple used to obtain the present value of expected future net cash flows.

So, what is the appropriate discount rate? Since different investors may use different valuations for different objectives, there is no single rate derived independently of specific markets and circumstances (e.g. Somers, 1971, even argues that “appropriate discount rates are not only project-specific, they are project-unique”).

Nevertheless, modern corporate finance, has been dominated by a specific choice that is consistent with the model of the irrelevance of capital structure and dividend policy. At the theoretical level, the modern school of finance (Modigliani and Miller 1958) postulated that the cost of capital, measured as the market rate of return, is a perfectly definite quantity not subject to manipulation through capitalization or dividend policies.

On the contrary the old school of finance (Durand 1952 and 1966), regards the cost of capital as too nebulous and elusive to play a key role in financial policy. I shall argue that the “old school” argument is more reasonable and does not introduce an unnecessary bias in favor of managerial capitalism.

From an empirical point of view the approach followed by the modern theory of finance may be dismissed on the grounds that a valuation based merely on a small share of total financing – traded debt and common stock – is necessarily unreliable. In fact, that was the argument for its dismissal by its first proponent (William, 1938).

Nonetheless, from a theoretical point of view, it could still be useful. However, it happens that its theoretical value is also limited, even at the mathematical level, despite its straightforward mathematical definition.

Weighted averages must be meaningful. For instance, one may calculate the weighted average cost of a piece of fruit in two baskets by summing the average price of each basket multiplied by the percentage of fruits it contains, regardless of whether both baskets contain apples or one has apples and the other has pears.

However, for most purposes one is only interested in averaging close substitutes, e. g. apples with apples or apples with pears, not baskets with a mix of completely different fruits. Likewise, with various sources of funding one must ascertain if they are really close substitutes beyond a narrow range within the capital structure.

So, for a start, one may consider weird a metric like WACC that averages two distinct terms - the cost of debt, which is indeed clearly perceived as a cost and easily measureable, and the required return on equity, which is not unquestionably defined or easily perceived as a cost in an accounting sense but as a potential gain that needs to be estimated. This mix up is reasonable if presented as an expedient or academic exercise but not as a scientific foundation for investment decisions made by different agents.

It is true that seen from an investor perspective exchange-traded debt and equity issued by a firm look like two substitute financing instruments suitable for arbitrage. However, debt and equity financing are not identical or sufficiently similar instruments to be considered perfect substitutes for controlling shareholders or for pure arbitrage. They may be sufficiently correlated for statistical arbitrage but that is not enough to combine them in the same basket. Let me show why by explaining first why the return on equity cannot be considered truly a cost like debt.

Imagine a business run by Mr. Management and funded by Mr. Supplier, Mr. Creditor and Mr. Stockholder. From time to time Mr. Management organizes a tender to finance the firm´s funding needs and asks suppliers, debt providers and stockholders to bid. Mr. Supplier would have to compete with other suppliers to offer better payment terms for the amounts procured. Similarly, Mr. Creditor needs to outbid other debt providers and Mr. Stockholder would need to beat other equity investors.

It is obvious that the tender would have to offer investors different terms for different types of funding. For suppliers, other than business preference, the firm may not offer any explicit consideration for deferred payment. To creditors it offers to pay interest in cash or kind. To stockholders it offers a payment in kind by giving them part ownership in the company.

Suppliers, creditors and shareholders bid for the three types of funding would depend on the respective consideration and the seniority of their claims on the firm’s assets. Stockholders are the last in terms of seniority and the cost of funding (the return demanded) declines as the seniority of the claims increases.

Now, imagine that Mr. Management has a fiduciary duty to minimize net working capital, the cash conversion cycle and funding costs. So, he must bargain hard payment terms and fund as much as possible from the cheapest source of funding. The first two suppliers of finance are easy to bargain independently, but not so with stockholders.

Stockholders pose a special challenge since they should be able to bid for how much they wish to plowback into the business and the possibility of providing additional financing. Indeed, Mr. Management would need to make sure that the value of the stock owned by their existing shareholders would not be reduced by the ownership dilution of their holdings. That is the new capital would need to earn enough to meet the current owners required rate of return plus any dilution costs.

When Mr. Management is also the majority owner of the company this paradox is easily solved by treating the other shareholders as junior partners. However, this is not the case for firms operating under managerial capitalism. In such firms, the directors’ ownership is small or inexistent making them simply agents of other stockholders. These, in general, have only small stakes. Indeed, their capital dispersion may be so high that managers are able to select shareholders rather the other way around, creating serious agency problems when choosing different sources of funding and defining objectives.

So, the key issue is whether firms should leave the amount of equity (including retained earnings) as a residual source of financing after exhausting all other funding sources or instead should the shareholders decide how much they wish to fund the business and let the others with the residual to be funded through other sources?

Traditionally, textbooks avoid this question by assuming that shareholders can attain their objectives in terms of capital structure through homemade leverage, leaving the firm to invest up to the point where its marginal return equals the marginal cost of capital.

But then, the capital structure and the marginal cost of capital cannot be determined separately when both depend on the same determinants (lenders mark-ups and risk aversion) and leverage has simultaneously contractionary and expansionary effects on investment (Marques-Mendes and Mheica, 2006).

For a simple illustration of the kind of confusions caused by the cost of capital theory consider the valuation of two unlevered companies with the same cash flow. Imagine that they are quoted in the same market and one of them is seen as outperforming and the other as lagging the market, so that the first appreciates more than the market while it rises and falls less when it declines and the opposite happens with the second company. For instance, assuming that when the market declines at a rate of 2% the first company declines at 1% and the second at 3%, and the opposite happens during rising markets, the average betas would be 1.09 and 0.93, respectively. Assuming further that the risk free rate and equity risk premium are 4 and 6%, respectively, the second company would be worth more 10% than the first company. So, using the popular CAPM model to estimate the required rate of return, the first company would have a higher beta and therefore a higher rate of return. However, assuming that it is the true cost of capital, this would mean that investors would value more the second company which is the opposite of what they are doing.

The reasons why such an obscuring theory achieved such popularity among academics and professionals were already given in another post. So, I will conclude by recalling how a reasonable minor departure from profiting maximization was seized by special interest groups on the basis of a somewhat wacky theory.