Understanding Weighted Average Cost of Capital (WACC): A Comprehensive Guide

 Weighted Average Cost of Capital (WACC)

A company typically has multiple sources of finance, including common stock, retained earnings, preferred stock, and debt. The Weighted Average Cost of Capital (WACC) represents the average after-tax cost of all these sources, weighted according to their proportion in the company’s capital structure.

WACC is calculated by multiplying the cost of each source of finance by its respective weight and summing the results. It effectively measures the overall cost of financing for a firm and is used as a discount rate in evaluating investment projects.

All capital sources common stock, preferred stock, bonds, and other long-term debt are included in a WACC calculation. Generally, a higher WACC indicates increased risk, as it reflects a higher required rate of return by investors, which in turn lowers the valuation of the firm.

The WACC formula is:

Where:

• Re= Cost of equity
• Rd= Cost of debt
• E= Market value of equity
• D= Market value of debt
• V= E+D= Total market value of the firm’s financing
• E/V= Proportion of financing that is equity
• D/V= Proportion of financing that is debt
• Tc= Corporate tax rate

Businesses often use WACC to discount expected cash flows and calculate the Net Present Value (NPV) of a project:

Considerations in Calculating WACC

When calculating the Weighted Average Cost of Capital (WACC), the following factors are important:

1. Use of Marginal Costs: WACC should reflect the weighted average of the marginal costs of all sources of capital (debt, equity, etc.), since unlevered free cash flows (UFCFs) are available to all providers of capital.
2. After-Tax Computation: WACC must be calculated after corporate taxes, as UFCFs are expressed on an after-tax basis.
3. Nominal Rates: WACC should be based on nominal rates of return, which are derived from real rates adjusted for expected inflation, because UFCFs are typically projected in nominal terms.
4. Adjustment for Risk: WACC must account for the systematic risk borne by each capital provider, as each expects a return that compensates for the risk assumed.
5. Market Value Weights: The weighted average should use market value weights for each source of financing (equity, debt, etc.), since market values reflect the true economic claims, unlike book values which may not.
6. Long-Term Assumptions: When estimating long-term WACC, incorporate assumptions regarding long-term debt rates, rather than relying solely on current debt rates.

Calculation of WACC (including preferred stock)

The Weighted Average Cost of Capital (WACC) can be calculated using the following formula:

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 corporate tax rate

Explanation:

1. Each source of capital (equity, debt, preferred stock) is weighted according to its proportion in the company’s total financing (E+D+P).
2. Debt is adjusted for taxes because interest is tax-deductible (rd⋅(1-t)).
3. The sum of these weighted costs gives the firm’s overall cost of capital, which can be used to discount future cash flows when evaluating investments.

Market Values and Capital Structure in WACC Calculation

When calculating WACC, the market values of equity, debt, and preferred stock should ideally reflect the targeted capital structure, which may differ from the current structure.

1. Although the formula calls for the market value of debt, the book value may be used as a reasonable proxy if the company is not in financial distress. In such cases, the market and book values of debt generally do not differ significantly.
2. The debt component in the WACC formula is multiplied by (1 -t)to account for the tax shield provided by interest expenses.

Calculating the Cost of Equity

The cost of equity is typically estimated using the Capital Asset Pricing Model (CAPM):

Where:

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

This model reflects the return required by equity investors to compensate for the systematic risk associated with holding the company’s stock.

Historically, the market risk premium has averaged approximately 7%, while the risk-free rate has been around 4%. Beta measures the volatility of a stock’s returns relative to the returns of the overall equity market. It is calculated by plotting the stock’s returns against the market’s returns at discrete intervals over a given period and fitting a regression line through the resulting data points. The slope of this line represents the stock’s levered equity beta.

A beta of 1.00 indicates that the stock’s returns are as volatile as the market’s returns. A beta greater than 1.00 signifies that the stock’s returns are more volatile than the market, while a beta less than 1.00 indicates lower volatility relative to the market.

Predicted Beta

Equity betas can be obtained from sources such as the Barra Book. These betas are levered and may be either historical or predicted. A historical beta is calculated using actual trading data over a specified period (commonly two years). A predicted beta, on the other hand, statistically adjusts the historical beta to reflect the tendency of a company’s beta to revert toward the market mean over time.

For example, if a company’s historical beta is less than 1.00, the predicted beta will be higher than the historical beta but still below 1.00. Conversely, if the historical beta exceeds 1.00, the predicted beta will be lower than the historical beta but remain above 1.00. In practice, it is generally advisable to use the predicted beta.

Betas of comparable companies are often used to estimate the cost of equity (rₑ) for private companies or for firms whose shares do not have a sufficiently long trading history to produce a reliable beta estimate.

Methods for Calculating Predicted Beta

Predicted beta may be estimated using one of the following two approaches:

1. Using the Company’s Own Beta

Step 1: De-lever the beta

Where:

• E = Market value of existing equity
• D = Market value of existing debt
• P = Market value of existing preferred stock
• t = Corporate tax rate

Step 2: Re-lever the unlevered beta

The unlevered beta is then re-levered using the company’s target capital structure typically based on the industry average rather than the firm’s current structure:

Where:

• Levered β = Beta used in the CAPM formula to estimate rₑ
• D = Market value of targeted debt
• P = Market value of targeted preferred stock

2. Using Betas of Comparable Companies

• De-lever the betas of each comparable company using the formula above, based on each company’s existing capital structure.
• Calculate the average unlevered beta across the comparable companies.
• Re-lever the average unlevered beta using the target capital structure of the company being valued.

How to Determine WACC

WACC is an acronym for Weighted Average Cost of Capital. It represents the average rate of return a corporation must pay to all its security holders both debt and equity investors for the use of their capital. In other words, WACC reflects the average cost of financing a company’s assets.

WACC also represents the minimum required return a company must earn on its investments to satisfy all providers of capital within its capital structure. It plays a critical role in evaluating whether a proposed investment is expected to generate positive value for the firm.

As the number of financing sources increases, the calculation of WACC becomes more complex. By computing a weighted average of the costs of all capital components, WACC captures the ongoing return required to compensate all investors supplying funds to the company.

Question

Company λ has the following capital structure:

• Common equity: 1 million shares trading at $30 per share
• Risk-free rate: 4%
• Market risk premium: 8%
• Equity beta: 1.2
• Debt: 50,000 bonds with $1,000 par value, 10% annual coupon, 20 years to maturity, currently trading at $950
• Corporate tax rate: 30%

Required: Calculate the weighted average cost of capital (WACC).

Solution

Step 1: Determine the Capital Structure Weights

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 Capital $30,000,000+$47,500,000=$77,500,000

Weight of Equity (Wₑ) $30,000,000/$77,500,000=38.71%

Weight of Debt (Wd) $47,500,000/$77,500,000=61.29%

Step 2: Calculate the Cost of Equity

The cost of equity is calculated using the Capital Asset Pricing Model (CAPM):

• re=Rf+β×Market Risk Premium
• re=4%+(1.2×8%)=13.6%

Step 3: Calculate the Cost of Debt

The cost of debt is equal to the bond’s yield to maturity (YTM).

• YTM: 10.61%
• After-tax cost of debt: rd (1-t)=10.61%×(1-0.30)=7.427%

Step 4: Calculate WACC

• WACC = (We×re)+(Wd×rd (1-t))
• WACC =(38.71%×13.6%)+(61.29%×7.427%)
• WACC =9.82%  (approximately)

Uses of WACC

1. WACC is used as the discount rate in capital budgeting techniques such as Net Present Value (NPV) and firm valuation models.
2. It represents the average risk level of the firm’s existing operations.
3. When evaluating projects:
• Projects riskier than the firm’s average require an upward adjustment to WACC.
• Projects less risky than the firm’s average require a downward adjustment.

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