Cost of capital

The cost of capital for a firm is a weighted sum of the cost of equity and the cost of debt (see corporate finance#the financing decision). Firms finance their operations by three mechanisms: issuing stock (equity), issuing debt (borrowing from a bank is equivalent for this purpose) (those two is external financing), and reinvesting prior earnings (internal financing).

Contents

1 Summary 2 Cost of debt 3 Cost of equity 3.1 Expected return 3.2 Capital asset pricing model 3.3 Comments 4 Cost of capital 4.1 Formula 5 Capital structure 6 Capital asset pricing model 7 Weighted average cost of capital 8 Modigliani-Miller theorem 9 References 10 See also 11 External links 11.1 Definition 11.2 Articles

Summary

Capital (money) fund enterprise and earn returns for the capital owner that risked his saved money. For an enterprise to function the return on capital must be greater than the cost of capital.

The easy part of the cost of capital is the cost of debt that carry a set interest, its cost of capital is the interest payments. The tougher part of it is the cost of equity or cost of retained earnings, equity doesn't pay a set definite interest, its cost has to do with risk and expectations of return elsewhere.

Cost of debt

The cost of debt is computed by taking the rate on a non-defaulting bond whose duration matches the term structure of the corporate debt, then adding a default premium. This default premium will rise as the amount of debt increases (since the risk rises as the amount of debt rises). Since in most cases debt expenses is a deductible expense, the cost of debt is computed as an after tax cost to make it comparable with the cost of equity (earnings are after-tax as well). Thus, for profitable firms, debt is discounted by the tax rate.

Cost of equity

The cost of equity is calculated as the "expected" return on equity during a past or future period (usually a year or annualized) based on interest rate levels and historical average equity market return. It can be calculated for an individual company's equity, or for a whole portfolio of companies. For a diversified portfolio, the equity risk is close to the average market risk.

Expected return

The expected return can be calculated as the "dividend capitalization model" which is (dividend per share / price per share) + growth rate of dividends. Which is the dividend yield + growth rate of dividends.

Capital asset pricing model

The expected return on equity according to the capital asset pricing model. The market risk is normally characterized by the β parameter. Thus, the investors would expect (or demand) to receive:

E_s=R_f+β_s(R_M-R_f)

Where:

E_s

The expected return for a security

R_f

The expected risk-free return in that market (government bond yield)

β_s

The sensitivity to market risk for the security

R_M

The historical return of the equity market

(R_M-R_f)

The risk premium of market assets over risk free assets.

In writing:

• The expected return (%) = risk-free return (%) + sensitivity to market risk * (historical return (%) - risk-free return (%))

Comments

The models states that investors will expect a return that is the risk-free return plus the security's sensitivity to market risk times the risk premium.

The risk free rate is taken from the lowest yielding bonds in the particular market, such as government bonds.

The risk premium varies over time and place, but in some developed countries during the twentieth century it has averaged around 5%. The equity market real capital gain return has been about the same as annual real GDP growth. The capital gains on the Dow Industrials have been 1.6% 1910-2005 ([1] (http://home.earthlink.net/~intelligentbear/com-dj-infl.htm)). The dividends have increased the total "real" return on average equity to the double, about 3.2%.

The sensitivity to market risk (β) is unique for each firm and depends on everything from management to its business and capital structure. This value cannot be known "ex ante" (beforehand), but can be estimated from "ex post" (past) returns and past experience with similar firms.

Note that the cost of retained earnings can also be estimated according to this formula, since investors expect retained earnings to produce the same return as dividends reinvested in the firm.

Cost of capital

The total capital for a firm is the value of its equity (for a firm without outstanding warrants and options, this is the same as the company's market capitalization) plus the cost of its debt (the cost of debt shold be continually updated as the cost of debt changes as a result of interest rate changes). Notice that the "equity" in the debt to equity ratio is the market value of all equity, not the shareholders' equity on the balance sheet.

Formula

The cost of capital is then given as:

K_c= (1-δ)K_e+δK_d

Where:

K_c

The weighted cost of capital for the firm

δ

The debt to capital ratio, D / (D + E)

K_e

The cost of equity

K_d

The after tax cost of debt

D

The market value of the firm's debt, including bank loans and leases

E

The market value of all equity (including warrants, options, and the equity portion of convertible securities)

In writing:

Cost of capital = (1 - debt to capital ratio) * cost of equity + debt to capital ratio *  cost of debt

Capital structure

Main article: capital structure

Because of tax advantages on debt issuance, it will be cheaper to issue debt rather than new capital (this is only true for profiatble firms, tax breaks are available only profitable firms). At some point, however, the cost of issuing new debt will be greater than the cost of issuing new equity. This is because adding debt increases the default risk - and thus the interest rate that the company must pay in order to borrow money. Management must identify the "optimal mix" of financing – the capital structure where the cost of capital is minimized so that the firms value can be maximized.

The Thomson Financial league tables show that global debt issuance exceeds equity issuance with a 90 to 10 margin.

Capital asset pricing model

Main aticle: capital asset pricing model

The capital asset pricing model (CAPM) is used in finance to determine a theoretically appropriate price of an asset such as a security.

Weighted average cost of capital

Main article: weighted average cost of capital

The Weighted Average Cost of Capital (WACC) is used in finance to measure a firm's cost of capital.

Modigliani-Miller theorem

Main article: Modigliani-Miller theorem

If there were no tax advantages for issuing debt, and equity could be freely issued, Miller and Modigliani showed that the cost of debt and the cost of equity should be the same. (Their paper is foundational in modern corporate finance.)

References

• F. Modigilani and M. Miller, "The Cost of Capital, Corporation Finance and the Theory of Investment", American Economic Review (June 1958)

See also

• Capital asset pricing model
• Modigliani-Miller theorem
• Weighted average cost of capital

External links

Definition

• Cost of Equity (http://www.investopedia.com/terms/c/costofequity.asp)

Articles

• TeachMeFinance.com - Cost of Capital (http://teachmefinance.com/costofcapital.html)