Cost of capital
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The cost of capital for a firm is a weighted sum of the cost of equity and the cost of debt (see 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 are external financing), and reinvesting prior earnings (internal financing).
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[edit] Summary
Capital (money) used to fund a business should earn returns for the capital owner who risked their saved money. For an investment to be worthwhile the estimated return on capital must be greater than the cost of capital. Otherwise stated, the risk-adjusted return on capital (incorporating not just the projected returns, but the probabilities of those projections) must be higher than the cost of capital.
The cost of debt is relatively simple to calculate, as it is composed of the interest paid (interest rate), including the cost of risk (the risk of default on the debt). In practice, the interest paid by the company will include the risk-free rate plus a risk component, which itself incorporates a probable rate of default (and amount of recovery given default). For companies with similar risk or credit ratings, the interest rate is largely exogenous.
Cost of equity is more challenging to calculate as equity does not pay a set return to its investors. Similarly to the cost of debt, the cost of equity is broadly defined as the risk-weighted projected return required by investors, where the return is largely unknown. The cost of equity is therefore inferred by comparing the investment to other investments with similar risk profiles to determine the "market" cost of equity.
The cost of equity is also known as the discount rate, the rate at which projected earnings will be discounted to give a present value.
[edit] 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. This is used for large corporations only.
[edit] 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.
[edit] 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.
[edit] 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. 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:
Where:
- Es
- The expected return for a security
- Rf
- The expected risk-free return in that market (government bond yield)
- βs
- The sensitivity to market risk for the security
- RM
- The historical return of the equity market
- (RM-Rf)
- 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 (%))
- Put another way the expected rate of return (%) = the yield on the treasury note closest to the term of your project + the beta of your project or security * (the market risk premium)
- the market risk premium has historically been between 3-5%
[edit] 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 market 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]). 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 retained earnings are a component of equity, and therefore the cost of retained earnings is equal to the cost of equity. Dividends (earnings that are paid to investors and not retained) are a component of the return on capital to equity holders, and influence the cost of capital through that mechanism.
[edit] 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 should 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.
[edit] Formula
The cost of capital is then given as:
Kc= (1-δ)Ke+δKd
Where:
- Kc
- The weighted cost of capital for the firm
- δ
- The debt to capital ratio, D / (D + E)
- Ke
- The cost of equity
- Kd
- 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:
- WACC = (1 - debt to capital ratio) * cost of equity + debt to capital ratio * cost of debt
[edit] Capital structure
Because of tax advantages on debt issuance, it will be cheaper to issue debt rather than new equity (this is only true for profitable firms, tax breaks are available only to 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. By utilizing too much debt in its capital structure, this increased default risk can also drive up the costs for other sources (such as retained earnings and preferred stock) as well. 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.
[edit] Weighted average cost of capital
The Weighted Average Cost of Capital (WACC) is used in finance to measure a firm's cost of capital.
[edit] 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.)
[edit] References
- F. Modigliani and M. Miller, "The Cost of Capital, Corporation Finance and the Theory of Investment", American Economic Review (June 1958)
