# Cost of Equity (ke)

Guide to Understanding the Cost of Equity

• From the perspective of investors, what does the cost of equity represent?
• What are the three underlying drivers that determine the cost of equity?
• Is the cost of equity typically higher or lower than the cost of debt?
• When would the cost of equity be the appropriate discount rate to use in a DCF?

## How to Calculate the Cost of Equity (ke)

One simple method to think about the cost of equity is that it signifies the opportunity cost of investing in the equity of a specific company.

In other words, the cost of equity represents the “hurdle rate” that must be surpassed for an investor to proceed further with an investment.

For instance, if a company’s shares have a cost of equity of 8.0%, an investor should anticipate an ~8.0% return post-purchase. Simultaneously, comparable investments with similar risk profiles should yield similar returns – assuming the investor made a reasonable decision.

Since the cost of equity is the rate of return that an investor necessitates prior to investing in a particular company or taking on a project, it addresses the question of whether the potential return from the investment justifies the risk.

Additionally, along with the cost of debt and the cost of preferred stock, the cost of equity is a central piece in calculating the weighted average cost of capital (WACC).

###### Cost of Equity Components

The calculation of the cost of equity has three major components, which we’ll discuss in the coming sections:

1. Risk-Free Rate (rf)
2. Beta (β)

## Risk-Free Rate (rf)

The risk-free rate (rf) typically refers to the yield on default-free, long-term government securities.

Theoretically, government-issued bonds are viewed as risk-free because if deemed necessary, the government could print more money at their discretion to avoid defaulting.

The current yield on the US 10-year note is the preferred proxy for the risk-free rate when it comes to valuing US-based companies.

The yield on government bonds can be found on various news sources – for example, the front page of the Wall Street Journal (WSJ).

In the chart posted below, we can observe the steady decline in the historical yield on the US 10-year note, especially around early 2020.

U.S. Treasury 10-Year Note 3-Year Historical Yields (Source: WSJ)

## Beta (β)

Beta is defined as the sensitivity of a specific security to the systematic risk of the market overall – or put differently, beta captures the relationship in the price movements of a particular company’s stock and the overall market (e.g. S&P 500).

The risk associated with beta can be bifurcated into two parts:

1. Unsystematic Risk: Often called company-specific risk, unsystematic risk can be reduced via diversification and is therefore ignored
2. Systematic Risk: On the other hand, systematic risk (or market risk) is referred to as “undiversifiable” risk – and as implied by the name, a company’s sensitivity to systematic risk cannot be decreased through diversification

As a general rule, the higher the beta, the higher the cost of equity (and vice versa).

Since systematic risk does not diminish even if the portfolio is further diversified, as a consequence, investors demand more compensation (i.e. higher potential returns) for assuming the extra risk.

The rationale is that greater volatility stemming from increased sensitivity to market fluctuations should result in higher potential investor returns.

The final component of the cost of equity calculation is called the equity risk premium (ERP), which is the incremental risk of investing in equities rather than risk-free securities, namely bonds.

Equity Risk Premium (ERP) = Expected Market Return – Risk-Free Rate

Historically, the equity risk premium in the U.S. has ranged from around 4.0% to 6.0%.

Since the possibility of losing invested capital is substantially greater in the stock market in comparison to risk-free government securities, there must be an economic incentive for investors to place their capital in the public markets, hence the equity risk premium.

###### Cost of Equity – Discount Rate

If you’re building an unlevered discounted cash flow (DCF) model, the weighted average cost of capital (WACC) is the appropriate cost of capital to use when discounting the unlevered free cash flows.

Similar to unlevered free cash flows (FCFs), the WACC represents the cost of capital to all capital providers (e.g. common equity, preferred stock, debt).

But in the case of a levered DCF model, the cost of equity would actually be the correct cost of capital to discount the levered FCFs, as it captures the risk and expected returns to only equity holders.

## Cost of Equity Formula

Despite the widespread criticism from academia as well as practitioners, the capital asset pricing model (CAPM) remains the most prevalent approach for estimating the cost of equity.

The CAPM links the expected return on securities to their sensitivity to the broader market – typically with the S&P 500 serving as the proxy for market returns.

The formula to calculate the cost of equity is as follows:

###### Cost of Equity (ke) Formula
• Cost of Equity = Risk-Free Rate + (β * Equity Risk Premium)

## Cost of Equity vs. Cost of Debt – Higher or Lower?

In general, the cost of equity is going to be higher than the cost of debt.

The cost of equity is higher than the cost of debt because the cost associated with borrowing debt financing (i.e. interest expense) is tax-deductible, creating a tax shield – whereas, dividends to common and preferred shareholders are NOT tax-deductible.

Further, unlike lenders, equity holders have the lowest priority claim under a liquidation scenario because of their placement at the very bottom of the capital structure.

Note that the two concepts are closely interrelated, and raising more debt will impact not only the cost of debt but the cost of equity as the credit risk of the entire company is affected negatively. If more debt is incrementally added to the capital structure, the risk to all company stakeholders rises.

If a company carries no debt on its balance sheet, its WACC will be equivalent to its cost of equity.

While early-stage, high-risk companies often do not have any debt, the vast majority of companies will eventually raise a moderate amount of debt financing once their operating performance stabilizes.

If a potential borrower has a track record showing historical profitability, banks and other lending institutions are far more willing to work with them (and provide more favorable lending terms).

###### Optimal Capital Structure

Regarding the topic of the “optimal” capital structure, the vast majority of companies should be financed using a mixture of both debt and equity.

1. Initially, as the proportion of debt in the capital structure increases, WACC gradually decreases due to the tax-deductibility of interest expense (i.e., the “tax shield” benefits).
2. WACC continues to decrease until the “optimal” capital structure is reached.
3. However, past this threshold, the cost of potential financial distress offsets the tax benefits of leverage, and the WACC reverses course – before starting an upward trajectory in which the risk to all debt and equity holders increases at a rapid rate.

## Cost of Equity Calculator – Excel Template

We’ll now move to a modeling exercise, which you can access by filling out the form below.

Submitting ...

## Cost of Equity Example Calculation

In our modeling exercise, we’ll be looking at three companies, each consisting of distinct values for the risk-free rate, beta, and equity risk premium.

###### Model Assumptions

Base Scenario

• Risk-Free Rate (rf): 2.5%
• Beta (β): 1.00
• Expected Market Return: 6.0%

Upside Scenario

• Risk-Free Rate (rf): 2.0%
• Beta (β): 1.20
• Expected Market Return: 7.0%

Downside Scenario

• Risk-Free Rate (rf): 3.0%
• Beta (β): 0.80
• Expected Market Return: 5.0%

For each scenario, if we subtract the risk-free rate from the corresponding expected market return, we get the equity risk premium (ERP).

• ERP – Base: 6.0% – 2.5% = 3.5%
• ERP – Upside: 7.0% – 2.0% = 5.0%
• ERP – Downside: 5.0% – 3.0% = 2.0%

The only remaining step is to input our assumptions into our cost of equity formula, as shown below.

The cost of equity under each scenario comes out to:

• Cost of Equity – Base: 6.0%
• Cost of Equity – Upside: 8.0%
• Cost of Equity – Downside: 4.6%

The reason we titled each case as “Base”, “Upside”, and “Downside” is that we deliberately adjusted each of the assumptions in a direction that would either increase or decrease the cost of equity.

In conclusion, the drivers of the cost of equity can be found in the image above, while a screenshot of the completed output sheet has been posted right below.

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