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Calculating a firm's cost of capital: three different methods of determining the weighted average cost of capital for Microsoft and general electric produce different results for each firm. Thus, careful judgment and sensitivity analysis are important components for developing reliable cost of capital estimates

Management Accounting Quarterly, Spring, 2004 by Michael S. Pagano, David E. Stout

The idea of the "cost of capital" is fundamental to what managerial finance and accounting professionals do, directly or indirectly, as part of their participation on cross-functional decision teams. They need to understand and apply techniques for estimating the cost of capital for long-term capital budgeting; merger and acquisition analysis; use of Economic Value Added (EVA[R]) as a firm-wide financial performance indicator; incentive systems for financial control, using residual income for evaluating financial performance; equity valuation analyses; and accounting for purchased goodwill. (1)

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Here we offer readers an overview of theoretical and empirical issues involved in estimating a firm's weighted average cost of capital (WACC), and we review and apply several methods for estimating WACC for two widely held U.S. firms: General Electric (GE) and Microsoft. The most difficult to estimate component of a firm's WACC relates to the cost of equity capital ([K.sub.s]), a process complicated in practice by the need to make various assumptions and practical choices. Conventional methods for estimating WACC, therefore, can yield substantially different approximations depending on the assumptions used in estimating [K.sub.s], so good judgment and sensitivity analysis are required when attempting to estimate a firm's cost of capital for applications in accounting and finance.

THEORETICAL FRAMEWORK

Conceptually, a firm's cost of capital is an investor's opportunity cost of investing his or her capital in that firm. An estimate of the firm's WACC is an attempt to quantify the average return expected by all investors in the firm: creditors of short-term and long-term interest-bearing debt, preferred stockholders, and common stockholders. (2) The firm's cost of capital is a weighted average where the weights are determined by the value of the various sources of capital. (3)

In Equation 1 we show the conventional formula for estimating a firm's WACC.

EQUATION 1

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where,

[w.sub.i] = the weight of the i-th source of capital (i = 1, ..., N) based on that source's aggregate market value in relation to the firm's total value,

[[summation of].sub.i][w.sub.i] = 1, and

[K.sub.i] = the expected return on the i-th security.

The portion to the right of the equal sign in Equation 1 can be rewritten in a simplified equation when there are only two sources of capital: long-term interest-bearing debt and (common) equity, as shown in Equation 2.

EQUATION 2

WACC = [w.sub.d][K.sub.d](1 - T) = [w.sub.s][K.sub.s]

where,

[K.sub.d] is the expected cost of long-term debt,

T is the firm's marginal income tax rate (combined federal and state),

[K.sub.s] is the expected cost of common stock, and

[w.sub.d] and [w.sub.s] are the weights of long-term debt and common stock in the firm's capital structure. (4) Note that this could be either its target or self-professed optimal capital structure. (5)

When determining the weights of debt and equity, we use their market values rather than book values because market values are more reflective of the true worth of the company.

There are two models that can be used to estimate [K.sub.s]: (1) a single-factor model called the Capital Asset Pricing Model (CAPM) and (2) a multiple-factor model called the Arbitrage Pricing Model (APM). (6) Next, we briefly outline these models below and a third model, the "bond yield plus risk premium model," that financial analysts frequently use.

ESTIMATING THE COST OF EQUITY WITH CAPM

To calculate Equation 2, we need a means of estimating the required returns ([K.sub.i]) for each component of the firm's capital structure. An asset-pricing model such as the CAPM can provide a convenient and theoretically consistent set of return estimates. The standard CAPM method says the required return on a risky asset such as common stock is related linearly to a nondiversifiable risk, otherwise known as "systematic" risk. Systematic risk is the riskiness of the "market portfolio" of all risky marketable assets. This relationship can be summarized concisely, as shown in Equation 3.

EQUATION 3

[K.sub.i] = [K.sub.rf] + [[beta].sub.i] ([K.sub.m] - [K.sub.rf])

where,

[K.sub.rf] = the expected return on a riskless security;

[K.sub.m] = the expected return on the systematic risk factor, i.e., the market portfolio's return, which is represented by the return on a large equity portfolio such as the S&P 500; and

[[beta].sub.i] = beta = a measure of the i-th security's sensitivity to the systematic risk factor.

A firm's beta can be estimated from a regression using historical data for the returns on the stock ([K.sub.s]) and a market portfolio proxy ([K.sub.m]). Typically, monthly returns data are used when estimating this regression. This CAPM beta will be biased when estimating a forward-looking cost of equity capital. A forward-looking estimate for [K.sub.s] is important for our analysis because the CAPM (as well as the APM) assumes that investors base their investment decisions on expected returns on all marketable securities. In deriving their published estimates of corporate betas, brokerage and analytical firms such as Merrill Lynch, Bloomberg, and Value Line have used Marshall Blume's idea to reduce the bias in the estimated beta and, in theory, improve one's ability to develop forward-looking return estimates. (7) Value Line's adjustment technique is relatively simple, as shown in Equation 4.

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Management Accounting Quarterly, Spring, 2004 by Michael S. Pagano, David E. Stout

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