42

It seems churlish to discredit cost of capital when practice and theory remain loud in its praise. Tim Ogier and colleagues' Real Cost of Capital has penetrated boardrooms while Seth Armitage's Cost of Capital graces business schools worldwide. Cost of capital is no doubt significant in principle as a neat criterion for checking out the value of our equity, bonds, corporate plans and acquisition targets. The trouble is that we can't define or measure it within useful bounds.

In particular:

•   The favoured definition - weighted average cost of capital (WACC) - is impoverished. Even an extended definition may not reflect what actually matters to investors.

•   We can't measure the parameters of any definition with useful accuracy.

•   Attempts to adapt a general cost of capital to the individual company and then to individual projects merely compound basic unrealities.

•   If we seek wisdom in practice we find managers behaving in an untutored, inconsistent and incomplete way.

Cost of capital is typically defined as shown in Figure 1.

This extensively used yardstick is impoverished. It is restricted to paid-up capital in place and fails to allow for contingent capital. Prakash Shimpi, managing principal (US) for Swiss Re New Markets, proposes total average cost of capital (TACC) towards a solution. TACC includes insurance, letters of credit and financial derivatives. Management's objective becomes cost minimisation over all capital resources, not just paid-up capital: TACC recognises that risk is allocated across all resources. With insurance, for example, TACC is defined as shown in Figure 2.

Insurance assumes the risk that would otherwise have to be borne by an additional cushion of risk-bearing equity. It is accordingly a substitute for further retention of earnings, a rights issue or a public offering.

The value of the insurance is the avoided equity and its cost is the annual insurance premium.

Do the parameters of our definitions express what matters to investors?

Most managers of listed companies compute cost of capital using WACC and the capital asset pricing model (CAPM). CAPM emphasises systematic risk expressed as beta ($). Beta measures the responsiveness of a company's returns to those of the market as a whole. The market itself has a beta of 1. Expected return becomes:

E(Rj) = Rf + $j (E(Rm) - Rf)

E(Rj) and E(Rm) are the expected returns to investment j and the market respectively; Rf is the risk free rate, and $j is the beta of investment j.

But what if beta fails to express investors' rational preferences however efficiently markets assimilate economic information? Academics Eugene Fama and Kenneth French (FF) argue that beta is not nearly as explicative as company size and the book value/market value ratio. This may be because rational investors require more from small companies and from companies with a high book/market ratio as compensation for risk. Alternatively, FF's findings may result from biased data, chance results or misspecification of the market portfolio.

A third possibility is that beta may fail to tell what matters to investors because investors are irrational and markets are inefficient. Indeed, the most powerful recent challenge to WACC and CAPM comes from behavioural finance. Behaviouralists visualise a world that is significantly influenced by irrational behaviour and in which investors fall back on false simplifications (cognitive heuristics) to reduce decisions to manageable proportions.

Investors extrapolate growth patterns, sometimes over-react and sometimes under-react. They indulge in mental accounting and manage different parts of their portfolio inconsistently. The result is that market prices do not reflect an economically rational cost of capital whether defined as WACC, TACC or otherwise.

However, the biggest problem is not that the definition of WACC is impoverished and that we can't be sure that it reflects investors' demands. This is bad enough. But the most glaring weakness of cost of capital computations is that we simply can't measure cost of capital's parameters within meaningful bounds.

Beta provides a dramatic example. Pablo Fernandez, PricewaterhouseCoopers professor of corporate finance at the IESE Business School, Madrid, recently calculated the betas of nearly 4,000 companies using 60 monthly returns for each day of December 2001 and January 2002. The maximum beta of any given company was, on average 15.7 times its minimum beta. This is devastating, given the importance of beta in arriving at required returns. Worse, even small differences in required returns have large impacts on valuation.

For example, Harvard researchers found that dropping the discount rate by only 0.4% from 12% to 11.6% increased Vodaphone's estimated value by 15% or £13.4bn. Taken together with the fact that recent published estimates for the average cost of equity capital range from zero to 7%, what is the practical value of a cost of capital estimate? Difficulties are only compounded in the case of international enterprises, public sector corporations and unlisted companies.

Even if a corporate cost of capital could be meaningfully computed it would fail to distinguish among the corporate, strategic and tactical levels of decision-making. Rates need to reflect distinctive opportunities at each level.

If we seek wisdom by studying corporate practice, disappointment awaits.

Practice combines the worst of all worlds. Managers overwhelmingly apply a caricature of traditional theory to a world of self-made unreality.

Company-wide, even index-wide, discount rates are extensively used with no adjustment for specific risk. Estimates of WACC and CAPM are based on long-term historic averages, which include levels of achieved returns that are unlikely to be repeated.

The conclusion has to be that a useful definition and measure of cost of capital eludes us. Our guesstimates are basically arbitrary. Management should end their doomed, misleading and expensive quest until new insights become available.

Roger Lister is a chartered accountant and a visiting professor at Salford University

WACC = kb (1 - tc) (B/V) + kp (P/V) + ks (S/V) kb = pre-tax expected yield to maturity on non-callable, non-convertible debt.

tc = marginal tax rate allowing for allowances, double tax relief etc.

B = market value of interest bearing debt.

V = market value of the enterprise being valued, B + P + S.

kp = pre-tax expected yield to maturity on preference capital.

P = market value of preference capital.

ks = market determined opportunity cost of equity capital.

S = market value of equity shares.

TACC = kb (1 - tc)(B/TV) + kp (P/TV) + ks (S/TV) + kI (I/TV)

kb = pre-tax expected yield to maturity on non-callable, non-convertible debt.

tc = marginal tax rate allowing for allowances, double tax relief etc.

B = market value of interest bearing debt.

TV = market value of capital, B + P + S + I.

kp = pre-tax expected yield to maturity on preference capital.

P = market value of preference capital.

ks = market determined opportunity cost of equity capital.

S = market value of equity shares.

kI = cost of insurance capital.

I = value of insurance capital.