Cost of Capital

INTRODUCTION

Cost of capital is the expected rate of return that the market participants require in order to attract funds to a particular investment. In economic terms, the cost of capital for a particular investment is an opportunity cost—the cost of forgoing the next best alternative investment. In this sense, it relates to the economic principle of substitution—that is, an investor will not invest in a particular asset if there is a more attractive substitute.

The term market refers to the universe of investors who are reasonable candidates to provide funds for a particular investment. Capital or funds are usually provided in the form of cash, although in some instances capital may be provided in the form of other assets. The cost of capital usually is expressed in percentage terms, that is, the annual amount of dollars that the investor requires or expects to realize, expressed as a percentage of the dollar amount invested.

Put another way:

Since the cost of anything can be defined as the price one must pay to get it, the cost of capital is the return a company must promise in order to get capital from the market, either debt or equity. A company does not set its own cost of capital; it must go into the market to discover it. Yet meeting this cost is the financial market’s one basic yardstick for determining whether a company’s performance is adequate.

As the quote suggests, most of the information for estimating the cost of capital for any company, security, or project comes from the investment markets. The cost of capital is always an expected (or forward-looking) return. Thus, analysts and would-be investors never actually observe it. We analyze many types of market data to estimate the cost of capital for a company, security, or project in which we are interested.

As Roger Ibbotson put it, “The Opportunity Cost of Capital is equal to the return that could have been earned on alternative investments at a specific level of risk.” In other words, it is the competitive return available in the market on a comparable investment, with risk being the most important component of comparability.

Components of a Company’s Capital Structure

The term capital in this context means the components of an entity’s capital structure. The primary components of a capital structure include:

• Debt capital
• Preferred equity (stock or partnership interests with preference features, such as seniority in receipt of dividends or liquidation proceeds)
• Common equity (stock or partnership interests at the lowest or residual level of the capital structure)

There may be more than one subcategory in any or all of the listed categories of capital. Also, there may be related forms of capital, such as warrants or options. Each component of an entity’s capital structure has its unique cost, depending primarily on its respective risk.

The next explanation shows how the cost of capital can be viewed from three different perspectives:

On the asset side of a firm’s balance sheet, it is the rate that should be used to discount to a present value the future expected cash flows. On the liability side, it is the economic cost to the firm of attracting and retaining capital in a competitive environment, in which

investors (capital providers) carefully analyze and compare all return-generating opportunities. On the investor’s side, it is the return one expects and requires from an investment in a firm’s debt or equity. While each of these perspectives might view the cost of capital differently, they are all dealing with the same number.

When we talk about the cost of ownership capital (for example, the expected return to a stock or partnership investor), we usually use the phrase cost of equity capital. When we talk about the cost of capital to the firm overall (for example, the average cost of capital for both equity ownership interests and debt), we commonly use the phrases weighted average cost of capital (WACC) or blended cost of capital or overall cost of capital.

Simply stated, the cost of equity is the rate of return investors require on an equity investment in a firm.

Recognizing that the cost of capital applies to both debt and equity investments, the following concept explains the role of WACC:

Since free cash flow is the cash flow available to all financial investors (debt, equity, and hybrid securities), the company’s Weighted Average Cost of Capital (WACC) must include the required return for each investor.

COST OF CAPITAL IS A FUNCTION OF THE INVESTMENT

As Ibbotson puts it, “The cost of capital is a function of the investment, not the investor.” The cost of capital comes from the marketplace. The marketplace is the universe of investors “pricing” the risk of a particular asset.

Allen, Brealey, and Myers state the same concept: “The true cost of capital depends on the use to which the capital is put.” They make the point that it would be an error to evaluate a potential investment on the basis of a company’s overall cost of capital if that investment were more or less risky than the company’s existing business. Each project should in principle be evaluated at its own opportunity cost of capital.

When a company uses a given cost of capital to evaluate a commitment of capital to an investment or project, it often refers to that cost of capital as the hurdle rate. The hurdle rate is the minimum expected rate of return that the company would be willing to accept to justify making the investment. As noted, the hurdle rate for any given prospective investment may be at, above, or below the company’s overall cost of capital, depending on the degree of risk of the prospective investment compared to the company’s overall risk.

The most popular focus of contemporary corporate finance is that companies should be making investments, either capital investments or acquisitions, from which the returns will exceed the cost of capital for that investment. Doing so creates economic value added, economic profit, or shareholder value added.

COST OF CAPITAL IS FORWARD LOOKING

The cost of capital represents investors’ expectations. There are two elements to these expectations:

1. The risk-free rate, which includes:

The “real” rate of return — the amount (excluding inflation) investors expect to obtain in exchange for letting someone else use their money on a risk-free basis.

Expected inflation — the expected depreciation in purchasing power while the money is in use.

2. Risk — the uncertainty as to when and how much cash flow or other economic income will be received.

It is the combination of the first two items that is sometimes referred to as the time value of money. While these expectations, including assessment of risk, may be different for different investors, the market tends to form a consensus with respect to a particular investment or category of investments. That consensus determines the cost of capital for investments of varying levels of risk.

The cost of capital, derived from investors’ expectations and the market’s consensus of those expectations, is applied to expected economic income, usually measured in terms of cash flows, in order to estimate present values or to compare investment alternatives of similar or differing levels of risk.

Present value, in this context, refers to the dollar amount that a rational and well-informed investor would be willing to pay today for expected future economic benefits.Would be willing to pay today for the stream of expected economic income. In mathematical terms, the cost of capital is the percentage rate of return that equates the stream of expected income with its present cash value.

COST OF CAPITAL IS BASED ON MARKET VALUE, NOT BOOK VALUE

The cost of capital is the expected rate of return on some base value. That base value is measured as the market value of an asset, not its book value. For example, the yield to maturity shown in the bond quotations in the financial press is based on the closing market price of a bond, not on its face value.

Similarly, the implied cost of equity for a company’s stock is based on the market price per share at which it trades, not on the company’s book value per share of stock. It was noted earlier that the cost of capital is estimated from market data. This data refers to expected returns relative to market prices.

By applying the cost of capital derived from market expectations to the expected cash flows (or other measure of economic income) from the investment or project under consideration, the market value can be estimated.

COST OF CAPITAL IS USUALLY STATED IN NOMINAL TERMS

Keep in mind that we have talked about expectations, including inflation. The return an investor requires includes compensation for reduced purchasing power of the dollar over the life of the investment. Therefore, when the analyst or investor applies the cost of capital to expected returns in order to estimate value, he or she must also include expected inflation in those expected returns.

This obviously assumes that investors have reasonable consensus expectations regarding inflation. For countries subject to unpredictable hyperinflation, it is sometimes more practical to estimate cost of capital in real terms rather than in nominal terms.

COST OF CAPITAL EQUALS THE DISCOUNT RATE

The essence of the cost of capital is that it is the percentage return that equates expected economic income with present value. The expected rate of return in this context is called a discount rate.

By discount rate, the financial community means an annually compounded rate at which each increment of expected economic income (for example, net cash flow, net income, or some other measure of economic benefits) is discounted back to its present value. A discount rate reflects both time value of money and risk and therefore represents the cost of capital.

The sum of the discounted present values of each future period’s incremental cash flow or other measure of return equals the present value of the investment, reflecting the expected amounts of return over the life of the investment.

The terms discount rate, cost of capital, and required rate of return are often used interchangeably.

The economic income referenced here represents total expected benefits. In other words, this economic income includes increments of cash flow realized by the investor while holding the investment as well as proceeds to the investor upon liquidation of the investment.

The rate at which these expected future total returns are reduced to present value is the discount rate, which is the cost of capital (required rate of return) for a particular investment.

DISCOUNT RATE IS NOT THE SAME AS CAPITALIZATION RATE

Because some practitioners confuse the terms, we point out here that discount rate and capitalization rate are two distinctly different concepts.

As noted in the previous section, discount rate equates to cost of capital. It is a rate applied to all expected incremental returns to convert the expected return stream to a present value.

A capitalization rate, however, is merely a divisor applied to one single element of return to estimate a present value.

The only instance in which the discount rate is equal to the capitalization rate is when each future cash flow is equal (that is, no growth), and the expected returns are in perpetuity. One of the few examples would be a preferred stock paying a fixed amount of dividend per share in perpetuity.

SUMMARY

As stated in the introduction, “The cost of capital estimate is the essential link that enables us to convert a stream of expected income into an estimate of present value.”

Cost of capital has several key characteristics:

It is market driven. It is the expected rate of return that the market requires to commit capital to an investment.

It is a function of the investment, not a particular investor; to make the discount rate a function of the particular investor would imply changing the standard of value to what is commonly termed investment value rather than fair market value.

It is forward looking, based on expected returns. Past returns are, at best, to provide guidance as to what to expect in the future.

The base against which cost of capital is measured is market value, not book value.

It is usually measured in nominal terms, that is, including expected inflation.

It is the link, called a discount rate, that equates expected future returns for the life of the investment with the present value of the investment at a given date.

Note: 

COST OF CAPITAL AND RATE OF RETURN VARIABLES

k = Discount rate (generalized)

kc = Country cost of equity

ke = Discount rate for common equity capital (cost of common equity capital)

ke500 = Cost of equity for the S&P 500

keu = Cost of equity capital, unlevered (cost of equity capital assuming firm financed

with all equity)

kni = Discount rate for equity capital when net income rather than net cash flow

is the measure of economic income being discounted

k(pt) = Discount rate applicable to pretax cash flows

ke(pt) = Cost of equity prior to tax affect

kp = Discount rate for preferred equity capital

kd = Discount rate for debt (net of tax affect, if any)

(Note: For complex capital structures, there could be more than one class of

capital in any of the preceding categories, requiring expanded subscripts.)

kd = kd(pt) × (1 – tax rate)

kd(pt) = Cost of debt prior to tax effect

kTS = Rate of return used to present value tax savings due to deducting interest expense

on debt capital financing

kNWC(pt) = Rate of return for net working capital financed with debt capital

(measured pretax) and equity capital

kFA(pt) = Rate of return for fixed assets financed with debt capital (measured pretax)

and equity capital

kdRU = After-tax rate of return on debt capital of the reporting unit

kdRU = kd(pt)RU × (1 – tax rate)

kd(pt)RU = Rate of return on debt capital of the reporting unit without taking into account

the tax deduction on interest expense (pretax cost of debt capital)

keRU = After-tax rate of return on equity capital of the reporting unit

kNWC = Rate of return for net working capital

kNWCRU = Rate of return for net working capital of the reporting unit financed with debt

capital (return measured after-tax) and equity capital

kNWC(pt)RU = Rate of return for net working capital of the reporting unit financed with

debt capital (measured pretax) and equity capital

kFA = Rate of return for fixed assets

kFARU = Rate of return for fixed assets financed with debt capital (return measured

after tax) and equity capital

kFA(pt)RU = Rate of return for fixed assets of the reporting unit financed with debt

capital (measured pretax) and equity capital

kIA = Rate of return for intangible assets

kIARU = Rate of return for identified and individually valued intangible assets financed

with debt capital (return measured after tax) and equity capital

kUIV = Rate of return for unidentified intangibles value

kUIVRU = Rate of return for unidentified intangibles value of the reporting unit financed

with debt capital (return measured after tax) and equity capital

kIA+UIV = After-tax rate of return on all intangible assets, identified and individually

valued, plus the unidentified intangible value

kIA+UIV(pt) = Pretax rate of return on all intangible assets, identified and individually

valued, plus the unidentified intangible value financed with debt capital

(measured pretax) and equity capital

kIA+UIVRU = After-tax rate of return on all intangible assets, identified and individually

valued, of the reporting unit plus the unidentified intangible value of the reporting unit

kIA+UIV(pt)RU = Pretax rate of return on all intangible assets, identified and individually

valued, plus the unidentified intangible value of the reporting unit financed with

debt capital (measured pretax) and equity capital

kTSRU = Rate of return used to present value tax savings due to deducting interest expense on debt capital financing of the reporting unit

c = Capitalization rate

ce = Capitalization rate for common equity capital. Unless otherwise stated, it

generally is assumed that this capitalization rate is applicable to net cash flow

available to common equity.

Cni = Capitalization rate for net income

c(pt) = Capitalization rate on pretax cash flows

cp = Capitalization rate for preferred equity capital

cd = Capitalization rate for debt

(Note: For complex capital structures, there could be more than one class of

capital in any of the preceding categories, requiring expanded subscripts.)

D/P = Dividend yield on stock

DRj = Downside risk in the local market (U.S. dollars)

DRw = Downside risk in global ("world") market (U.S. dollars)

Pn = Stock price in period n

P0 = Stock price at valuation period

R = Rate of return

Rf = Rate of return on a risk-free security

Rf,n = Risk-free rate in current month

Rf local = Return on the local country government’s (default-risk-free) paper

Rf u.s. = U.S. risk-free rate

Rn = Return on individual security subject stock in current month

Rm = Historical rate of return on the "market"

RP = Risk premium

RPm = Risk premium for the "market" (usually used in the context of a market

for equity securities, such as the NYSE or S&P 500)

RPs = Risk premium for "small" stocks (usually average size of lowest quintile

or decile of NYSE as measured by market value of common equity)

over and above RPm

RPm+s = Risk premium for the market plus risk premium for size

(Duff & Phelps Risk Premium Report data for use in build-up method)

RPu = Risk premium for company specific or unsystematic risk attributable

to the specific company

RPw = The equity risk premium on a "world" diversified portfolio

RPi = Risk premium for the ith security 

RPlocal = Equity risk premium in local country’s stock market

RIi = Risk index (full-information beta) for industry i

RIiL = Full-information levered beta estimate of the subject company

E(R) = Expected rate of return

E(Rm) = Expected rate of return on the "market" (usually used in the context

of a market for equity securities, such as the NYSE or S&P 500)

E(Ri) = Expected rate of return on security i

E(Rdiv) = Expected rate of return on dividend

E(Rcap-gains) = Expected rate of return on capital gains

B = Beta (a coefficient, usually used to modify a rate of return variable)

BL = Levered beta for (equity) capital

BU = Unlevered beta for (equity) capital

BLS = Levered segment beta

Bd = Beta for debt capital

BUi = Beta unlevered for industry (or guideline companies) equity capital

BLi = Beta levered for industry (or guideline companies) equity capital

Be = Beta (equity) expanded

Bop = Operating beta (beta with effects of fixed operating expense removed)

Bi = Beta of company i (F-F Beta)

Bn = Estimated market coefficient based on sensitivity to excess returns on

market portfolio in current month

Bn-1 = Estimated lagged market coefficient based on sensitivity to excess

returns on market portfolio last month

Blocal = Market risk of the subject company measured with respect to the

local securities market

Bw = Market or systematic risk measured with respect to a "world" portfolio

of stocks

bcw = Country covariance with world

bcr = Country covariance with region

K1…Kn = Risk premium associated with risk factor 1 through n for the average

asset in the market (used in conjunction with arbitrage pricing theory)

si = Small-minus-big coefficient in the Fama-French regression

SMBP = Expected small-minus-big risk premium, estimated as the difference

between the historical average annual returns on the small-cap and

large-cap portfolios

hi = High-minus-low coefficient in the Fama-French regression

HMLP = Expected high-minus-low risk premium, estimated as the difference

between the historical average annual returns on the high book-to-market

and low book-to-market portfolios

Fd = Face value of outstanding debt

WACC(pt) = Weighted average cost of capital (pretax)

WACCBE = Overall rate of return for the business enterprise

WACC(pt)BE = Pretax WACC of the business enterprise

WACCRU = Overall rate of return for the reporting unit

= Weighted average cost of capital for the reporting unit

WACC(pt)RU = Pretax WACC of the reporting unit

Me = Market value of equity capital (stock)

Md = Market value of debt capital

Mp = Market value of preferred equity

σ² = Variance of returns for subject company stock

σ²M = Variance of the returns on the market portfolio (e.g., S&P 500)

σ²e = Variance of error terms

σ = Standard deviation

σB = Standard deviation of operating cash flows of business before cost of financing

σrev = Standard deviation of revenues of output

σlocal = Volatility of subject (local) stock market

σu.s. = Volatility of U.S. stock market

σstock = Volatility of local country’s stock market

σbond = Volatility of local country’s bond market

dr = Regional risk not included in RPw

CCRc = Country credit rating of country

λ = Company’s exposure to the local country risk

t = Tax rate (expressed as a percentage of pretax income)

ti = Federal and state income tax rate for industry (or guideline companies)

r = Property tax rate (expressed as a percentage of total fair market value)

C = Proportion of the entity that is assessed property tax

h = Holding period