Weighted Average Cost of Capital (WACC): Formula, Calculation & Example

Definition of Weighted Average Cost of Capital - WACC

A company has different sources of finance, namely common stock, retained earnings, preferred stock and debt. Weighted average cost of capital (WACC) is the average after tax cost of all the sources. It is calculated by multiplying the cost of each source of finance by the relevant weight and summing the products up. A calculation of a firm's cost of capital in which each category of capital is proportionately weighted. All capital sources - common stock, preferred stock, bonds and any other long-term debt - are included in a WACC calculation. All else equal, the WACC of a firm increases as the beta and rate of return on equity increases, as an increase in WACC notes a decrease in valuation and a higher risk. The WACC equation is the cost of each capital component multiplied by its proportional weight and then summing:

Where:

• Re = cost of equity, 
• Rd = cost of debt, 
• E = market value of the firm's equity, 
• D = market value of the firm's debt, 
• V = E + D,
• E/V = percentage of financing that is equity, 
• D/V = percentage of financing that is debt, T
• c = corporate tax rate

Businesses often discount cash flows at WACC to determine the Net Present Value (NPV) of a project, using the formula: NPV = Present Value (PV) of the Cash Flows discounted at WACC.

Considerations in Calculating WACC 

The following are important considerations when calculating WACC:

1. WACC must comprise a weighted-average of the marginal costs of all sources of capital (debt, equity, etc.) since UFCF represents cash available to all providers of capital.
2. WACC must be computed after corporate taxes, since UFCFs are computed after-tax.
3. WACC must use nominal rates of return built up from real rates and expected inflation, because the expected UFCFs are expressed in nominal terms.
4. WACC must be adjusted for the systematic risk borne by each provider of capital, since each expects a return that compensates for the risk assumed.
5. While calculating the weighted-average of the returns expected by various providers of capital, market value weights for each financing element (equity, debt, etc.) must be used, because market values reflect the true economic claim of each type of financing outstanding whereas book values may not.
6. Long-term WACCs should incorporate assumptions regarding long-term debt rates, not just current debt rates.

Calculation of WACC

Where:

• E = Market value of equity
• D = Market value of debt
• P = Market value of preferred stock
• re = Cost of equity
• rd = Cost of debt
• rp = Cost of preferred stock
• t = Marginal tax rate

The market values of equity, debt, and preferred should reflect the targeted capital structure, which may be different from the current capital structure. Even though the WACC calculation calls for the market value of debt, the book value of debt may be used as a proxy so long as the company is not in financial distress, in which case the market and book values of debt could differ substantially. Multiplying the debt term in the WACC equation by (1−t) captures the benefit of the tax shield arising from interest expense.

Calculating the Cost of Equity 

The cost of equity is usually calculated using the capital asset pricing model (CAPM), which defines the cost of equity as follows:

      re= rf+ β× (rm − rf)

Where:

• rf = Risk-free rate (represented by 10-yr U.S. Treasury bond rate)
• β = Predicted equity beta (levered)
• (rm − rf) = Market risk premium

This graph shows the relationship between Market Return (%) and Stock Return (%) in portfolio management and CAPM analysis.

Interpretation of β = 1.61

• Beta (β) measures the sensitivity of a stock compared to the overall market. 
• Here, β = 1.61 means: 
• If the market rises by 1%, the stock is expected to rise by approximately 1.61%. 
• If the market falls by 1%, the stock may fall by approximately 1.61%. 

Meaning

• The stock is more volatile than the market. 
• Since beta is greater than 1: 
• It is considered an aggressive stock. 
• It carries higher risk and potentially higher return. 

Graph Explanation

• X-axis: Market Return (%) 
• Y-axis: Stock Return (%) 
• Black dots represent observed return combinations. 
• The blue regression line indicates the trend/sensitivity of stock returns relative to market returns. 

Interpretation: A beta of 1.61 indicates that the stock reacts strongly to market movements and is suitable for investors willing to take higher risk for higher expected returns.

The market risk premium has historically averaged around 7% and the risk-free rate around 4%. Beta is a measure of the volatility of a stock's returns relative to the equity returns of the overall market. It is determined by plotting the stock' and market's returns at discrete intervals over a period of time and fitting (regressing) a line through the resulting data points. The slope of that line is the levered equity beta. When the slope of the line is 1.00, the returns of the stock are no more or less volatile than returns on the market. When the slope exceeds 1.00, the stock's returns are more volatile than the market's returns.

Predicted Beta 

Equity betas can be obtained from the Barra Book. These betas will be levered and either historical or predicted. The historical beta is based on actual trading data for the period examined (often 2 years), while the predicted beta statistically adjusts the historical beta to reflect an expectation that an individual company's beta will revert toward the mean over time. For example, if a company's historical beta is less than 1.00, then the predicted beta will be greater than the historical beta but less than 1.00. Similarly, if the historical beta is greater than 1.00, the predicted beta will be less than the historical beta but greater than 1.00. It is generally advisable to use predicted beta. Betas of comparable companies are used to estimate re of private companies, or where the shares of the company being valued do not have a long enough trading history to provide a good estimate of the beta.

Predicted Beta Calculation Methods

1. Using the Company’s Beta

De-lever the beta using the following formula:

Where:

• E = Market value of existing equity 
• D = Market value of existing debt 
• P = Market value of existing preferred stock 

Re-lever the unlevered beta with the targeted capital structure using the formula:

Where:

• Levered β = β used in CAPM formula for re
• E = Market value of targeted equity 
• D = Market value of targeted debt 
• P = Market value of targeted preferred stock 

2. Using Betas of Comparable Companies

• De-lever the comparable companies’ betas using the formula stated above. 
• Calculate the average unlevered beta of the comparable companies. 
• Re-lever the average unlevered beta using the company’s targeted capital structure. 

How to Determine Your WACC

WACC is an acronym for “Weighted Average Cost of Capital” and it describes what, on average, a corporation must pay out to all its security holders. This is the average cost of the financing on a corporation’s assets. WACC is also the minimum amount of return a corporation must earn in order to satisfy all the creditors within its capital structure. WACC is of great importance when determining whether or not an investment has the potential for positive returns.

Determining a corporation’s WACC becomes more complex as the number of capital components involved in the financing increases. By taking a weighted average of a corporation’s total interest, we are able to determine how much return is required on an on-going basis to satisfy all investors providing funds.

Question 

Company λ has 1 million shares of common stock currently trading at $30 per share. Current risk free rate is 4%, market risk premium is 8% and the company has a beta of 1.2. It also has 50,000 bonds with of $1,000 par paying 10% coupon annually maturing in 20 years currently trading at $950. The tax rate is 30%. Calculate the weighted average cost of capital.

Solution:

• First we need to calculate the weights of debt and equity.
• Market Value of Equity = 1,000,000 × $30 = $30,000,000
• Market Value of Debt = 50,000 × $950 = $47,500,000
• Total Market Value of Debt and Equity = $77,500,000
• Weight of Equity = $30,000,000 / $77,500,000 = 38.71%
• Weight of Debt = $47,500,000 / $77,500,000 = 61.29%
• Weight of Debt can be calculated as 100% minus cost of equity = 100% − 38.71% = 61.29%
• Second step in our solution is to calculate the cost of equity. With the given data we can use capital asset pricing model (CAPM) to calculate cost of equity as follows:
• Cost of Equity = Risk Free Rate + Beta × Market Risk Premium = 4% + 1.2 × 8% = 13.6%

We also, need to find the cost of debt. Cost of debt is equal to the yield to maturity of the bonds. With the given data, we can find that yield to maturity is 10.61%.

• After tax cost of debt is hence 10.61% × ( 1 − 30% ) = 7.427%
• And finally, WACC = 38.71% × 13.6% + 61.29% × 7.427% = 9.8166%

Uses of WACC 

Weighted average cost of capital is used in discounting cash flows for calculation of NPV and other valuations for investment analysis.