**Weighted Average Cost of Capital**

**Introduction**

The weighted average cost of capital (“WACC”) is the rate of return that investors expect from investing in a given company instead of other companies with similar risk^{125}. The WACC can be calculated by determining its three components: the after-tax cost of debt, the cost of equity and the company’s target capital structure^{126}. Thus, the formula for WACC is^{127}:

Where D/V = Target level of debt to enterprise value using market values

E/V = Target level of equity to enterprise value using market values

R debt= cost of debt

R equity= cost of equity

Tc= company’s income tax rate

The following sections analyze the determination of the after-tax cost of debt and the cost of equity in the WACC formula.

**Cost of Debt**

**Pre Tax Cost of Debt**

The cost of debt is the rate that a company pays to borrow money^{128}. Borrowers of the firm bear the risk of not getting their expected payments (interest and principal). To compensate for this risk, the lenders add a credit spread to the risk free rate^{129}. A credit spread is the difference between the risk free rate and the interest rate that a company pays to borrow money.

**After Tax Cost of Debt**

The last part for determining the cost of debt is the tax rate. Interest payments on debt are subtracted from income before tax is determined, thus debt can act as a tax shield^{131}. The advantages of debt besides the tax shield include committing managers to operate efficiently in order to fulfill principal and interest payments and encouraging lenders to monitor the firm^{132}. However, due to the disadvantages of extreme borrowing such as financial distress, companies do not borrow to the maximum level. The formula for the after tax cost of debt is^{27}:

After tax cost of debt = (Pre Tax Cost of Debt) * (1- income tax rate)

**Cost of Equity Derivation**

**Risk Free Rate**

The risk free rate can be determined by looking at the long-term government default-free bonds. Government bonds have different maturities ranging from for example one month to 20 years. As a result, a firm‘s cash inflows / outflows must be discounted with a yield to maturity from a bond with a similar maturity. For European firms, the 10 year Germany Eurobond can be used, because it is believed to have a higher liquidity and lower credit risk compared to bonds of other European countries. Additionally, the cash inflows / outflows and the discount rate have to be expressed in the same currency for inflation consistency reasons^{134}.

**Beta**

A stock‘s expected return depends on its beta, which is a measure of how much the stock price fluctuates in relation to the market (the stock‘s volatility)^{136}. Companies with a beta higher than 1 are considered aggressive in that their stock price fluctuates more than the market, while companies with a beta lower than 1 are considered defensive as their stock price fluctuates less than the market^{137}. The beta can be calculated through regression analysis and by applying the market model. In other words the returns on the firm’s stock price (dependent variable) are regressed on the market’s percentage return for a certain period of time (usually either 2 years weekly data or 5 years monthly data). The market model can be stated as^{138}:

**Ri = α + β * Rm + ε **

Where: Ri is the return on the stock and Rm is the return on the Stock Exchange general index and beta (ß) is the slope of the regression, α is the excess return of the stock and ε is the error term.

**Equity Risk Premium**

The equity risk premium (“ERP”) cannot be directly observed in the market as it is the difference between the market index return and the risk free rate. Therefore, a universally accepted model for estimating the ERP does not exist. It is common practice to determine the market risk premiums by using past risk premiums, this refers to premiums that investors have earned over long periods. An alternative option for determining the ERP involves calculating a forward looking premium from current stock price levels and expected future cash flows^{139}. Since forecasting stock price levels and future cash flows is a challenging exercise that would deviate from our scope of work, we will use historical estimates as described below.

In order to quantify the Equity Risk Premium we will use historical estimates calculated as the average difference between stocks and treasury bonds for the period 1928 to 2011 which yields 5.8%.

**Cost of Equity**

The cost of equity can be estimated by using an asset pricing model which is used to determine the expected rate of return on a company‘s stock. The most widely used asset pricing models are: the capital asset pricing model (CAPM), Fama and French three factor model and the arbitrage pricing theory (APT).

**The Capital Asset Pricing Model **

The capital asset pricing model (“CAPM”) is a set of assumptions based on which the expected returns of risky assets (mainly traded equity securities) are predicted. The main contributors to the CAPM are Harry Markowitz in 1952^{141} regarding the efficient frontier of risky assets through diversification, William Sharpe^{142}, John Lintner^{143}^{,} and Jan Mossin^{144}.

The main simplifying assumptions that represent the foundation of the CAPM are summarized below:

There exists a perfect competition between investors which means that all investors are price takers and cannot affect through their trades the security prices.

The investors allocate their investments for only one holding period which is also identical for all investors.

The availability of securities is limited to bonds, stocks and unlimited lending or borrowing at the risk free rate. Therefore all other assets are excluded from the analysis.

Neither taxes nor transaction costs exist on trades in stocks or bonds.

All investors use the Markowitz portfolio selection model, which means that they seek the maximum return possible for a certain level of risk, or alternatively the minimum risk for a certain level of return.

All investors have homogeneous expectations and beliefs.

Based on the above assumptions when the model equilibrium is reached the following implications result:

All investors will choose a portfolio that replicates the market portfolio that is a portfolio that includes all risky assets.

All investors hold the market portfolio as their optimal risky portfolio. The only difference between investors is the proportion invested between the risk free asset and the market portfolio.

The equity risk premium of the market portfolio is a proportion of the degree of risk aversion of the representative investor and the risk of the market portfolio.

The equity risk premium of individual assets will be a proportion of the equity risk premium of the market portfolio. That proportion is called the beta which measures the extent to which returns on the stock and returns of the market are correlated.^{145}

To summarize the above the basic version of the CAPM is represented by the following equation:

Where:

Equity Risk Premium of the Market Portfolio (“ERP”): E(Rm) – Rf.

Equity Risk Premium of Individuals Assets: E(Ri) – Rf

Beta: βi

The above equation can be restated as a function of the return of the individual asset as:

**Reasons to include a Country Risk Premium **

The question that is central to the inclusion or exclusion of a country risk premiums in the cost of equity is whether an investor should demand higher equity risk premiums in some emerging or distresses markets as compared to mature markets.

The arguments against a country risk premium can be separated into the following main points, which are presented below together with counter arguments that favor a country risk premium^{146}:

__The country risk is diversifiable__

Conventional portfolio theory such as the CAPM as presented in the previous paragraphs states that the only risk that should be used for estimating the cost of equity is the risk that cannot be diversified away. If the risk can be diversified away then no country risk should be used, however if it cannot be diversified away then a country risk should be used. To this point we have to add the home bias that is existent in most investor’s portfolios (high percentage of securities or assets from their home countries).

Additionally even if the investor is diversified in a global context, there should also be a low correlation across markets in order to benefit from the diversification. If returns across countries have significant positive correlations, then the risk cannot be diversified away and one should use a country risk premium. Studies during 1970 - 1980 indicated that the correlation between markets and countries was low which supported international diversification^{147}. However recent studies indicate that the correlation across markets has increased over time due to the world globalization and that the correlation across equity markets increases during periods of crisis and high volatility^{148}^{,}^{149} (Lehman Brothers crisis, Greek Debt Crisis etc…).

__The Global Asset Pricing Model__

Another argument considers that all assets independently of where they are traded should have the same global equity risk premium, and any differences among assets should be captured by their betas. However this argument fails in that the average beta in a specific market should average to one and as such does not capture the effect of the increased risk.

__Country Risk is Embedded in the Cash Flows __

The last argument ascertains that by adjusting cash flows for the country risk we eliminate the need for a country risk premium. However this is true for a risk neutral investor that would be indifferent between two outcomes with the same average return. In contrast, for a risk averse investor the increased risk should be compensated by an extra return, the country risk premium.

The evidence that supports the inclusion of a country risk premium is presented below:

__Historical Equity Risk Premiums __

Donadelli and Prosperi conclude that emerging market companies (from a pool of 12 developed and 19 emerging markets) had both higher equity risk premiums and more volatility during the period 1988 to 1990 than developed market companies^{150}.

__Survey on Equity Risk Premiums__

Surveys conducted by Fernandez et al on academics, analysts and companies, on the equity risk premiums in 56 countries concluded that average premiums fluctuate across markets and are higher for emerging markets than for developed markets^{151}.

In order to decide whether to include or not a country risk premium we should take into account mostly empirical findings on the matters described above (correlation between markets, home bias, contagion effects across markets etc) instead of a theoretical approach with very simplifying assumptions. As of today the evidence as presented above pinpoints the importance of the inclusion of a country risk premium in the discount rates used^{152}.

__Estimation of the Country Risk Premium__

The country risk premium reflects the extra default risk in a specific market such as the stability of a country’s currency, its budget and trade balances, political uncertainty etc. One of the simplest and most accessible measures of country risk is the rating assigned to a country’s debt by a ratings agency.

In order to calculate the country risk premium, we estimate the default spread for the local currency sovereign rating (from Moody's) based upon traded country bonds over a default free government bond rate^{153}.

An adjusted country risk premium can be estimated by multiplying the default spread by the relative equity market volatility for that market (standard deviation in country’s equity market/ standard deviation in country’s bond).

The capital asset pricing model based on Markowitz‘s portfolio theory adjusted with the country risk component as proposed by Damodaran for firms operating in emerging markets is defined as^{155}^{,}^{156}:

Where: E(Ri) = expected return on security i

Rf= risk free rate

βi= sensitivity of the stock‘s return to the return on the market portfolio

E(Rm)= expected return of the market

CRP=country risk premium

**Weighted Average Cost of Capital**

**Company Target Capital Structure**

In order to estimate the most appropriate capital structure in the WACC, we have to use target weights instead of the company‘s current capital structure. A company‘s capital structure may change and using today‘s structure may lead to an overestimation (or underestimation) of the value of tax shields for a firm whose debt level may increase (or decrease)^{157}. A company‘s target capital structure should be determined by first examining its current capital structure and then forming some expectations about the future^{158}.

**Weighted Average Cost of Capital**

In order to calculate the WACC, the after tax cost of debt, the cost of equity, and target value weights as calculated in the previous sections are inserted in the WACC formula. Thus, by replacing the terms in the WACC formula we get the following result:

**Conclusion**

More precisely when using the dividend discount model, the free cash flows to equity and the economic profit model we will use the cost of equity as the discount rate since these flows determine the cash flows remaining to the equity holders. However when using the free cash flows to the firm, and the economic value added model we will use the weighted average cost of capital as these flows determine the cash flows remaining to the company stakeholders, that is debt holders and equity holders.

*References:*

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