Companies are financed by either debt, equity or both. This capital isn’t free and there is a cost associated with it. The weighted average cost of capital or WACC is the minimum return that providers of capital expect for investing their money in a particular company.

The value of a company can be calculated by discounting its future cash flows to the present value terms using WACC. Valuation is very sensitive to cost of capital and even a small change can have a major impact on valuation.

WACC is calculated by taking into account the respective weight and associated cost of each component of finance in the overall capital structure. In order to get WACC, multiply the cost of equity by the weight of equity in the capital structure. This weight is simply the equity component divided by the sum of total debt and equity. To this, add the multiplication of cost of debt, the associated tax shield and the weight of debt in the overall capital structure.

WACC = Cost of equity * ( Equity / (Debt + Equity) ) + Cost of debt * (1-tax rate) * ( Debt /( Debt + Equity ) )

Some companies may have preference shares in their capital structure as well. Preference shares represent a special type or a more senior ownership interest in the firm. They are entitled to receive fixed dividend payments and a company can only pay dividends to its ordinary shareholders after preference dividends have been paid out. The cost of preferred shares can be simply obtained by dividing dividends with preference share capital.

Cost of equity * (Equity /(Debt + Equity +Preferred Stock)) + Cost of debt * (1-tax rate) * ( Debt / Debt + Equity +Preferred Stock ) + Cost of preferred stock * ( Preferred Stock / ( Debt + Equity +Preferred Stock ) )

Determining the cost of debt is quite straight forward. But cost of equity needs various variables and can be quite challenging.

**COST OF EQUITY**

Unlike the cost of debt which is an explicit return, cost of equity is an implicit return and not directly observable in the market. Cost of equity is the minimum return that shareholders’ expect for parting with their capital and investing in a company.

Though there are a number of ways of calculating cost of equity such as the arbitrage pricing theory or APT, the Fama French model, the most favored and widely used is the Capital Asset Pricing Model or CAPM. Using the CAPM, Ke or cost of equity can be calculated as Rf which is the risk free rate, plus the security’s beta multiplied by the equity risk premium, which is the expected return on the market portfolio (Rm) minus the risk free rate (Rf).

K_{e} = R_{f} + β ( R_{m} - R_{f} )

( R_{f} = Risk Free Rate , β = Beta , ( R_{m} - R_{f} ) = Equity risk premium
)

**RISK FREE RATE**

In the CAPM, the security that is used as a proxy for Rf or the risk free rate should ideally have no volatility and a beta of zero. In other words, there is no default risk associated with this security. In reality, it is difficult to find a security that has no volatility, a beta of zero and no default risk. Barring some exceptions, sovereign bonds are considered to be risk free by and large.

Which country bond to choose? There can be multiple opinions on this, but typically sovereign bonds are chosen based on where a company is headquartered and/or the currency of underlying cash flows. For a US company, use the yield on Treasuries . For the UK, use the yield on Gilts. If the company is in continental Europe, then use the yield on German bunds. For Japan, take the yield on JGBs and so on and so forth.

**BETA **

There are two main types of risks inherent in making investment decisions. The first is stock specific or unsystematic risk. This type of risk can be addressed easily by holding a diversified portfolio of securities.

But there is another type of risk that cannot be diversified away and impacts the market as a whole. This is known as systematic risk and arises due to factors such as war, acts of god, interest rate fluctuations, currency risk, political risk, macro economic risk and a range of other factors. Beta is a measure of this systematic risk or volatility of a security in comparison to the market as a whole.

If volatility of the stock as measured by beta is higher, that stock is considered to be risky. Beta for the market is 1.

- A stock with a beta of 1 will move in line with the market. So if the market increases by 10%, this stock will increase by 10% as well
- A stock with a beta of 2, implies that its share price increases 20% when the market moves by 10%. In other words, this stock is twice as volatile as the overall market
- Similarly, a beta of 0.5 implies that if the market rises by 10%, the stock will increase by 5%

There are 2 common approaches to calculate beta. Under the first method, it can be calculated as the covariance of the stock with the market and dividing this with the variance of the market. But how is return on the market or Rm measured?

- This is a contentious issue and a source of great debate between different academics and practitioners
- The return on the market theoretically reflects a weighted index of all possible investments available to an investor including common stocks, preferred stocks, bonds, commodities, real estate, etc, both domestically and internationally
- The most widely used index is the S&P 500 as it is highly liquid, diversified and has been frequently used to calculate market return or Rm
- Bankers may use a benchmark index as well depending on where a company is headquartered

Covariance (stock versus market returns) / Variance of the stock market

Beta can also be calculated by running regression analysis using appropriate software. If not, simply use the slope function in excel and divide change in stock with change in the market. Beta is the slope of the line of best fit.

**EQUITY RISK PREMIUM**

Equity risk premium represents the return that equity investors expect that is over and above the risk free rate. In other words, this is the return that investors expect for investing in equities as an asset class.

In order to calculate the equity risk premium, a longer horizon is usually preferred. The time frame over which to calculate equity risk premium is also a matter of considerable debate and judgment. Ibbotson Associates calculates equity risk premiums over many times periods, the longest being from 1926 till date.

- By using long term returns, practitioners can avoid the seemingly random forecasts that short term observations often produce
- Equity risk premium can be calculated by using either a geometric or arithmetic mean of historical returns. The arithmetic average represents a simple average of annual returns over a given period. The geometric average represents the compounded return achieved over the same period, assuming reinvestment ie, it reflects the return achieved, had the investor held on to the stock over the given time period

Ibbotson Associates, Duff & Phelps and Damodaran are the most commonly used sources for equity risk premiums. Risk premiums vary across markets depending on the riskiness and stage of development of each market. Consensus is difficult to reach on this, so avoid lengthy debates! Equity risk premiums can range anything between 5 to 8 percent, with developed markets being at the lower end of this range and emerging markets at the higher end.

**COST OF DEBT**

Unlike cost of equity, cost of debt is an explicit cost that is readily observable. Free cash flows to the firm or FCFF represent cash flows to both equity and debt investors. FCFF does not reflect any interest component. But companies are financed by debt as well and debt has a cost associated with it which must be captured. How is this achieved?

The cost and weight of debt are added to the cost and weight of equity in order to arrive at WACC. Cost of debt is captured by making adjustments to WACC directly, since FCFF is capital structure neutral.

- If debt is actively traded then use the market price of a company’s debt. The yield to maturity or YTM on long term debt is the cost of debt
- If debt isn’t traded then rely on current cost of debt obtained by dividing interest expense and total debt
- The other approach is to find peers with a similar target capital structure or credit rating. Determine the cost of debt for peers and apply to the company being valued

It is also important to keep in mind that debt has the benefit of providing a tax shield. Assume that there are 2 companies A and B. Both have EBIT of $100. Company A has an interest expense of $30. At a 30% tax rate, Company A has a lower tax burden of $21 v/s $30 for company B. So debt has a tax shield associated with it which is captured through WACC directly.