To determine the WACC, an analyst or investment banker must first estimate the individual component costs of capital — the cost of debt and the cost of equity. The cost of debt capital is very straightforward — there is little controversy on how it's estimated and there are few alternatives.

The cost of equity, on the other hand, can be estimated using several different methods, which may produce widely different cost estimates. Again, this is where the art of investment banking deviates a bit from the science.

## Cost of debt capital

To estimate the cost of debt capital for a firm with publicly traded bonds, the investment banking analyst has to look no further than the bond market to determine at what yield to maturity the firm's bonds are selling for in the marketplace.

Companies usually have more than one outstanding bond issue, so analysts will calculate an average bond yield — using market value weights. This average yield to maturity of all the outstanding debt of the firm is that firm's before-tax cost of debt.

But there's one more step. Because the Internal Revenue Service allows companies to deduct interest costs before arriving at net income that is subject to taxation, the true after-tax cost of debt is considerably lower than the before-tax cost of debt. In fact, it's adjusted for the firm's corporate tax rate. Thus, the formula for after-tax cost of debt is as follows:

After-Tax Cost of Debt = Before-Tax Cost of Debt × (1 − Tax Rate)

If the average yield to maturity on a company's bonds is 8 percent and the company's tax rate is 30 percent, the firm's after tax cost of debt is as follows:

After-Tax Cost of Debt = 8% × (1 − 0.3) = 5.6%

## Cost of equity capital

One of the most difficult and controversial aspects of completing a discounted cash flow analysis is determining the appropriate required rate of return (or cost) on equity. The relationship between risk and required return is perhaps the most basic in investments.

Riskier assets should provide higher returns in the long run to compensate investors for assuming that risk. There is an old saying in investments: You can eat well or you can sleep well. This refers to the fact that if you take more risk, your returns are likely to be higher. However, in the short run, the volatility of those riskier investments may cause you to lose sleep at night.

In general, stocks are riskier than bonds, so stockholders should expect to earn higher returns than bondholders over the long run — and they do.

Few analysts would disagree about the methodology to estimate the cost of debt capital, but there is no one universally accepted method for estimating the cost of equity capital. So, different analysts will come up with widely different estimates of a firm's cost of equity capital.

All methods, however, start out with a fundamental premise — they start out with a risk-free rate and add a premium or series of premiums for the risk that the equity holder is bearing. And all analysts agree that the cost of equity capital is higher than the cost of debt capital.

Two of the more popular methods for determining the cost of equity capital are the build-up method and the capital asset pricing model (CAPM). The build-up method is generally used for smaller, privately held firms, while the CAPM is more appropriate for large, publicly traded firms. The CAPM occupies a prominent place in investment banking. Here, you see a focus on the build-up method.

The build-up method simply starts with the current risk-free rate and adds various premiums for different sources of risk inherent in equity securities. Both the number of premiums and the values for each of the categories will vary from analyst to analyst, but a typical build-up method will add premiums for the following categories:

• Market risk premium: This is the additional return that is required for an investor to purchase an average stock rather than simply invest and earn the risk-free rate by buying government securities. The equity risk premium is generally considered for the market as a whole and often is thought of as the premium applying to large capitalization stocks (like the Standard & Poor's 500).

The equity risk premium is most often determined by using historical data.

Some analysts chose not to use historical equity risk premiums and instead simply plug in a forward-looking forecast that they believe is more applicable to the current investing environment. To that point, many investment professionals believe that the equity risk premium is smaller today than it has been historically.

• Size premium: Small stocks are generally considered riskier than large stocks for many reasons. Over time, small stocks have earned higher returns than large stocks.

• Idiosyncratic premium: This is a catch-all category where the analyst can apply her own judgment to adjust the cost of equity for a myriad of factors. Perhaps the analyst feels that the firm will be subject to significant litigation risks in the future or is in an industry that may be negatively influenced by future government policy changes.

So, assuming that current yields on long-term government bonds (the risk free rate) was 3.2 percent, for a hypothetical small company with an idiosyncratic premium of 2 percent, using historical values for the premiums, the build-up method would estimate the cost of equity capital at: