The Definitive Guide to the Cost of Equity

Cost of Equity. Probably one of the most crucial concepts in Finance. Here’s everything you need to know about it, including what it is, why it matters, and how to calculate it.

You might want to grab a tea though – this is the most extensive guide on the Cost of Equity on “the internet”.

If you’re after specific aspects of the cost of equity, feel free to explore individual sections. Each section is designed to stand on its own for the most part. Where sections depend on one another, you’ll be pointed to the appropriate section when it’s relevant.

Table of Contents hide

1 What is Cost of Equity? How is it used?

1.1 Cost of Equity Financing

1.2 Appropriate Discount Rate

1.3 Appropriate Rate of Return

2 Why Does The Cost of Equity Matter?

2.1 Importance for Companies

2.2 Importance for Investors

3 How to Calculate Cost of Equity?

3.1 How to Calculate Cost of Equity using the Capital Asset Pricing Model

3.2 How to Calculate Cost of Equity using the Dividend Discount Model (DDM)

3.3 How to Calculate Cost of Equity using Dividend Growth Model / Gordon Growth Model

3.4 How to Calculate Cost of Equity using Modigliani & Miller II

4 Do All Calculations of Cost of Equity Provide The Same Result?

5 What is the Difference Between Cost of Equity and Cost of Capital?

6 Cost of Equity Calculation Example

6.1 Calculate Cost of Equity using the CAPM

6.2 Calculate Cost of Equity using DDM

6.2.1 Solving for the Stock Price

6.3 Calculate Cost of Equity using GGM

6.4 Calculate Cost of Equity using Modigliani & Miller II

6.5 Comparing Estimates Using Different Approaches

7 Wrapping Up

What is Cost of Equity? How is it used?

Firstly, what is Cost of Equity?

As with most things in Finance, the clue is in the name.

The Cost of Equity is the cost… of equity.

More specifically, it’s the cost of raising equity capital.

It has three main interpretations or use-cases, including:

cost of raising equity finance,
appropriate discount rate, and
appropriate rate of return

Let’s consider each of these three interpretations / use-cases individually.

Cost of Equity Financing

The cost of equity is expressed in percentage terms. And it represents the amount of money a business would have to pay its shareholders for every $1 of equity capital it raises from them.

So, if the cost of equity for a company is say, 8%, then it means that the company would essentially pay its shareholders $0.08 for every $1 of equity capital it raises from them.

The payments would typically be made in the form of dividends and share buybacks. But they would also (indirectly) be made from capital appreciation.

As a result of representing the cost of raising equity finance, the Cost of Equity is also an appropriate “discount rate”.

Appropriate Discount Rate

A discount rate is a rate at which future cash flows of a business are discounted at.

The process of discounting future cash flows is a focal theme/concept within Finance.

The idea is to put a price on future cash flows as of today. That price is referred to as the Present Value of Future Cash Flows.

Now, the process of discounting is beyond the scope of this particular article. But we have linked to related/sister articles, so if you’re interested, do give those a read.

At this stage, it’s suffice for you to know that the Cost of Equity is one of a few appropriate discount rates that one can use to discount future cash flows back to the present.

And the discounting of future cash flows itself, is broadly used for two main purposes, including:

valuation (e.g., valuing a stock)
capital budgeting decisions

As far as valuation goes, the cost of equity is the appropriate discount rate if you’re using equity cash flows. This is usually either dividends or Free Cash Flow to Equity (aka “Flow to Equity”).

Appropriate Rate of Return

Recall that we said that the cost of equity is the cost of raising equity capital.

As a result of this, it also represents the return an equity investor requires in order to invest.

Intuitively, companies raise money from investors. Thus, “costs” that the company pays to raise finance is the return that investors earn!

Many people often end up getting confused between the Cost of Equity and the Expected Return on Equity or the Required Rate of Return. They’re essentially identical, excluding effects of taxation and transaction costs.

Note, importantly, that the Expected Return on Equity is not the same as Return on Equity (ROE).

ROE is simply the ratio of net income to total equity. It uses book values (i.e. accounting values) instead of market values.

The Expected Return on Equity or the Required Rate of Return is based on the Cost of Equity.

Why Does The Cost of Equity Matter?

The Cost of Equity matters a great deal for many reasons. We can broadly think of its importance to two main user-groups, including:

companies, and
investors

Importance for Companies

For companies, knowing their cost of equity can help with everything from raising money to deciding how to use their funds (e.g., in capital budgeting decisions).

Private companies can benefit from obtaining a valuation of their business by using their cost of equity to discount expected future cash flows.

Importance for Investors

Investors – at least professional ones – use the cost of equity to:

value private businesses
value stocks (to identify undervalued stocks in the stock market)
gain an idea of the expected return on a stock or investment
understand the riskiness of a business
see if an investment is worth their while

How to Calculate Cost of Equity?

There are four main ways to calculate the Cost of Equity, including:

the CAPM,
Dividend Discount Model (DDM),
Dividend Growth Model (DGM, aka “Gordon Growth Model”), and
Modigliani & Miller II

We’re going to use the mathematical notation $k_e$ going forward, to refer to the Cost of Equity.

Note that some people refer to use $r_e$ to refer to the cost of equity instead of $k_e$ . Either is okay/acceptable.

People who use $r_e$ tend to see it as the required rate of return on equity (aka return on equity). We’re choosing to use $k_e$ because $k$ is typically used to reflect costs in financial economics.

How to Calculate Cost of Equity using the Capital Asset Pricing Model

$k_e$ can be estimated by using the CAPM (i.e. the Capital Asset Pricing Model) as:

$k_e = r_f + \beta (E[r_m] - r_f)$

In this particular formula for Cost of Equity:

$k_e$ refers to the Cost of Equity
$r_f$ represents the risk free rate of return
$\beta$ reflects the Systematic Risk of a stock,
$E[r_m]$ represents the expected return on the market portfolio (e.g., the return on the S&P500 market index), and
$E[r_m] - r_f$ displays the market risk premium

This is one of the most common ways of calculating $k_e$ , but it’s certainly not the least controversial.

We talk a great deal about the limitations of the CAPM in our article (linked above). Do give that a read, especially if you’re thinking of using the CAPM to calculate $k_e$

If you’re happy to use it however, feel free to use our Cost of Equity Calculator. It uses the CAPM as the framework (despite our reservations!)

How to Calculate Cost of Equity using the Dividend Discount Model (DDM)

Another way to calculate $k_e$ is to use the Dividend Discount Model (DDM), which says that the value of a stock can be estimated as:

$P = \frac{Div_{t+1}}{k_e}$

Where $P$ refers to the price of a stock, $k_e$ represents the Cost of Equity, and $Div_{t+1}$ reflects the dividend at time 1.

We can rearrange the equation above to obtain an expression for $k_e$ as:

$k_e = \frac{Div_{t+1}}{P}$

This approach is also quite common, although you can’t use it for stocks or companies that don’t pay dividends.

Remember, companies don’t have to pay investors dividends. It’s not a legal obligation.

And many “growth companies” (those with high growth rates) tend not to pay any dividends.

How to Calculate Cost of Equity using Dividend Growth Model / Gordon Growth Model

Extending on the DDM is the DGM or “GGM”, which incorporates the aspect of growth into the cost of equity formula.

According to the DGM/GGM, the price of a stock is estimated as:

$P = \frac{Div_{t+1}}{k_e - g}$

The only new variable here is $g$ , which represents the growth rate at which a firm’s dividends grow (aka dividend growth rate).

As with the DDM case, we can rearrange the equation above to obtain an expression for $k_e$ as…

$k_e = \frac{Div_{t+1}}{P} + g$

Put another way, you can estimate $k_e$ using the GGM/DDM by simply adding the growth rate to your estimate of $k_e$ obtained via using the DDM!

How to Calculate Cost of Equity using Modigliani & Miller II

The fourth – and final – formal way of calculating $k_e$ involves using a model created by Modigliani and Miller as part of their second proposition on firm value / capital structure.

Using M&M II, the formula for cost of equity is expressed as:

$k_e = k_a + \frac{D}{E} \left(k_a - k_d \right)$

Here:

$k_e$ refers to the Cost of Equity,
$k_a$ reflects the Cost of Assets (aka Cost of Capital, or “WACC” – don’t worry about it if you don’t know what this is),
$k_d$ represents the Cost of Debt,
$D$ represents the Market Value of Debt, and
$E$ refers to the Market Value of Equity
The fraction of $D/E$ represents the firm’s capital structure, but can also be seen as a representation of its financial gearing

NOTE: If you’re familiar with M&M II, then you might well be looking at this equation and thinking “That doesn’t look right!”

Honestly, it’s right.

We’re just using slightly different notations. We’re using the notation $k_a$ instead of $WACC$ or $r_0$ or $r_u$ because this helps avoid unnecessary complications for beginner learners.

Learners who are just starting out with the Cost of Equity may not have seen/heard of the WACC, or know the difference between levered and unlevered cost of capital.

The use of M&M II is relatively less common in practice/industry. This is partly to do with its complexity, but predominantly to do with access to data.

Obtaining a value for the Market Value of Debt ( $D$ ) can be considerably difficult. Oftentimes, one would need to make “guesstimates” since debt values tend to be reported in book value terms.

These “guesstimates” can create concerns about the reliability of the estimate for $k_e$ , which is why practitioners tend to prefer other methods.

Do All Calculations of Cost of Equity Provide The Same Result?

People often wonder – indeed, strongly believe – that the estimate for $k_e$ should be identical, regardless of which approach you use to calculate it.

Sadly, this is simply almost never true.

Estimates for $k_e$ will almost certainly be different if you estimate is using the CAPM vs. the DDM vs. M&MII.

This is because of a variety of reasons, including (but not limited to):

differences in assumptions across models
differences in variables used to calculate $k_e$
variations in the use of market values exclusively vs. combining them with book values
working with different sample timeframes
reliability of the raw data used in the estimate

Anecdotal evidence suggests that many practitioners tend to take a simple average of different estimates.

This, in our opinion, is far from prudent – mainly because of the reasons of differences highlighted above.

Taking simple average of different estimates is akin to taking the average of apples and oranges and concluding it’s the average values for apples alone!

What is the Difference Between Cost of Equity and Cost of Capital?

The Cost of Equity is the cost of raising equity capital. Cost of Capital on the other hand, is the cost of raising capital (both debt as well as equity).

Generally speaking, a reference to the “Cost of Capital” will typically imply that we’re talking about the Weighted Average Cost of Capital (WACC).

It’s important to note that it is possible for the Cost of Capital to be equal to the Cost of Equity.

This will hold for a company that has no debt (0 debt financing).

Fundamentally, this is because of the Accounting Equation which says:

Assets = Liabilities + Equity

Liabilities is just another term for Debt, so we could essentially write the accounting equation as:

Assets = Debt + Equity

Now, if a company has no debt (or debt financing), then the equation becomes:

Assets = 0 + Equity

Thus, for a company with 0 debt:

Assets = Equity

And since the Cost of Capital represents the cost of raising debt and equity capital, if there’s no debt involved, then the Cost of Capital is equivalent to the Cost of Equity.

Cost of Equity Calculation Example

Okay, how that you know what the Cost of Equity is and how to calculate it, let’s apply the different formulas with an example.

Consider Starmont Inc., which recently announced its intention to pay dividends of $2.50 per share every year for the foreseeable future, for each of its 100m shares. Some analysts believe that the company may increase its dividends by up to 5% each year. They base this on the firm’s high amount of available capital, including $800m of debt (based on recent market valuations) and total assets of $3.5bn in current market value terms.

The firm’s positive exposure to the market, given its beta of 1.25, means it’s poised for strong performance ahead. Analysts expect the overall market return to be 12% per year over the coming years. Yields on risk-free securities are reported at 1.5%.

Analysts from EveningStar Inc. estimate the firm’s cost of capital to be 10% and its cost of debt to be 4%.

What is Starmont Inc.’s Cost of Equity?

The question provides sufficient information for you to calculate $k_e$ using all four approaches highlighted above.

So go on! Give it a go and try estimating Starmont Inc.’s $k_e$ on your own.

Hint: we’ve bolded items in the question for a very good reason! 😉

We’re going to assume you did that, so let’s go ahead now and solve it together.

Calculate Cost of Equity using the CAPM

Recall that $k_e$ can be estimated by using the CAPM as:

$k_e = r_f + \beta (E[r_m] - r_f)$

From the question, we know that:

$r_f$ is equal to 1.5% (since that’s the yield on risk-free securities)
$\beta$ is 1.25 (as stated in the question)
$E[r_m]$ is equal to 12% since that’s what the question suggests analysts expect

Plugging in the numbers from the question into the CAPM-based formula for cost of equity, we have…

$k_e = 0.015 + 1.25(0.12 - 0.015)$

Solving for that yields…

$k_e = 0.14625 \equiv 14.625\%$

Calculate Cost of Equity using DDM

If we use the DDM, then we can estimate $k_e$ as…

$k_e = \frac{Div_{t+1}}{P}$

We’re told that the firm expects to pay dividends of $2.50 per share for the foreseeable future. Thus, $Div_{t+1}$ is equal to $2.50

If you’re wondering why we’re just using a single instance of the dividend ($2.50) instead of multiple instances of the dividends, we’d strongly recommend reading our sister article on the Present Value of a Perpetuity.

The DDM essentially relies on the PV of a Perpetuity. The formula does use multiple instances of dividends (even though it “looks” like there’s just the one instance).

Plugging in the number into the DDM-based cost of equity formula from above, we have…

$k_e = \frac{\$2.50}{P}$

Now, we don’t explicitly have a value for the stock price $P$ from the question. But we can work it out pretty easily.

Solving for the Stock Price $P$

The question gives us values for the Market Values of Debt and Total Assets.

Recall that the Accounting Equation says:

Assets = Liabilities + Equity

Further recall that “Liabilities” is just another term for Debt. So we can write the accounting equation as…

Assets = Debt + Equity

Rearranging for Equity, we have…

Equity = Assets – Debt

Plugging in the numbers from the question, working in billions, we have…

Equity = $3.5bn – $0.8bn = $2.7bn

We know that there are 100 million shares outstanding (again, provided in the question!)

If the market value of equity (aka market capitalization) is equal to $2.7bn and there are 100 million shares outstanding, the share price must be equal to…

$P = \frac{MarketCap}{NumShares}$

Plugging in the numbers, we have…

$P = \frac{\$2.7bn}{100m} = \$27$

We now have a value for $P$ and can therefore calculate the Cost of Equity as…

$k_e = \frac{\$2.50}{\$27}$

Solving for that yields…

$k_e \approx 0.0926 = 9.26\%$

Does that make sense?

This particular calculation did have a fair bit of “tricks”/challenges in it. So do take the time to make sure you’ve fully understood it.

It’s crucial that you do in fact understand it, because we’re going to assume you understand this for the remaining calculations.

Calculate Cost of Equity using GGM

If we use the GGM, then we can estimate $k_e$ as…

$k_e = \frac{Div_{t+1}}{P} + g$

Recall that the value for $k_e$ estimated using the GGM is equal to the value of $ke_$ estimated using the DDM plus growth.

From the estimation using DDM above, we know that $k_e$ is equal to 9.26%

Thus, $k_e$ estimated using the GGM must be equal to 9.26% + 5% (being the dividend growth rate per the question) = 14.26%

Alternatively, plug in the numbers into the cost of equity formula as above:

$k_e = \frac{\$2.50}{\$27} + 5\%$

Solve for that to get…

$k_e \approx 0.1426 = 14.26\%$

And that’s it!

Calculate Cost of Equity using Modigliani & Miller II

Finally, if we were to use Modigliani & Miller II (M&MII), we can estimate $k_e$ as…

$k_e = k_a + \frac{D}{E} \left(k_a - k_d \right)$

In this case, $k_a$ is essentially the firm’s cost of capital. We’re told that this is equal to 10%.

We’re also told – again, from the question – that the firm’s cost of debt ( $k_d$ ) is equal to 4%.

We have values for $D$ and $E$ which we’ve discussed when we calculated $k_e$ using the DDM (see above).

Plugging in all our numbers into the formula for cost of equity (using M&M II), we have…

$k_e = 0.1 + \frac{\$0.8bn}{\$2.7bn} \left(0.1 - 0.04 \right)$

Solving for this by applying “BODMAS” yields…

$k_e = 0.1 + 0.2962962963 \times 0.06$

Finally, solving further, we get…

$k_e \approx 0.1178= 11.78\%$

Comparing Estimates Using Different Approaches

From our ‘simple’ example alone, we’ve obtained four different estimates for $k_e$ using four different approaches, including:

14.625% when we use the CAPM,
9.26% when we use the DDM,
14.26% when use the GGM, and
11.78% when we use M&M II

This is consistent with the point we made earlier on in the section on “Do All Calculations of Cost of Equity Provide The Same Result?|

But which one is the “correct” $k_e$ you ask?

Truthful answer – no one knows.

Seriously.

In the real world, one would likely choose the estimate the “best fits” with the story trying to be sold.

This is especially true if the purpose of calculating $k_e$ is to value a stock.

Remember, stock valuation is a story. There’s no such thing as a “true” value, despite what anyone might tell you.

Purely from a financial math standpoint however, the estimate using the DDM may be incorrect (if and only if the “analyst estimates” for cost of capital and cost of debt are correct).

If the analyst estimates for cost of capital and cost of debt are correct, then $k_e$ estimated using the DDM cannot be correct.

That’s because $k_e$ must be greater than the cost of capital.

In other words, $k_e > k_a$ by construction.

Given a cost of capital of 10%, it would be impossible for $k_e$ to be 9.26%.

Thus, one of two things is correct.

Either the analyst estimates are wrong (and the DDM estimate may be “right”).

Or, the analyst estimates are correct, in which case, the DDM estimate must be incorrect.

It’s purely a coincidence that the estimates from the CAPM and GGM are so close to one another. This doesn’t necessarily have to be the case.

Wrapping Up

Alright, hopefully, all of this makes sense, and you now have a strong understanding of the Cost of Equity including what is is, why it matters, and how to calculate it.

In summary, you learned that the Cost of Equity represents the cost of raising equity capital.

Since equity is raised by companies from investors, the Cost of Equity is also equivalent to the rate of return for an equity investor, excluding the effects of transaction costs and taxes.

Furthermore, you learned that there are 4 main ways of calculating Cost of Equity, including by using:

CAPM,
Dividend Discount Model (DDM),
Dividend Growth Model (DGM) / Gordon Growth Model (GGM), and
Modigliani and Miller II (M&M II)

Importantly, remember that the 4 approaches are unique and independent. They will NOT necessarily give you the same result for $k_e$ .

This is because each model has its own set of assumptions, and relies on its own set of variables and data.

It’s not prudent nor constructive to simply take an average across all estimates, because – again – each mode has its own set of assumptions, and relies on its own set of variables and data.

Taking a simple average of all 4 estimates is akin to taking an average of the number of apples and oranges, and describing it as the average number of apples.

If any part of this extensive guide / article on the Cost of Equity is not quite clear, please do give it another read.

If you’d like to go further and learn to invest like the pros, do check out our investing courses that are designed to help you master complex concepts in finance and investing.

That’s a wrap from us for now.

Keep learning, keep growing!

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What is Cost of Equity? How is it used?

Cost of Equity Financing

Appropriate Discount Rate

Appropriate Rate of Return

Why Does The Cost of Equity Matter?

Importance for Companies

Importance for Investors

How to Calculate Cost of Equity?

How to Calculate Cost of Equity using the Capital Asset Pricing Model

How to Calculate Cost of Equity using the Dividend Discount Model (DDM)

How to Calculate Cost of Equity using Dividend Growth Model / Gordon Growth Model

How to Calculate Cost of Equity using Modigliani & Miller II

Do All Calculations of Cost of Equity Provide The Same Result?

What is the Difference Between Cost of Equity and Cost of Capital?

Cost of Equity Calculation Example

Calculate Cost of Equity using the CAPM

Calculate Cost of Equity using DDM

Solving for the Stock Price $P$

Calculate Cost of Equity using GGM

Calculate Cost of Equity using Modigliani & Miller II

Comparing Estimates Using Different Approaches

Wrapping Up

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What is Cost of Equity? How is it used?

Cost of Equity Financing

Appropriate Discount Rate

Appropriate Rate of Return

Why Does The Cost of Equity Matter?

Importance for Companies

Importance for Investors

How to Calculate Cost of Equity?

How to Calculate Cost of Equity using the Capital Asset Pricing Model

How to Calculate Cost of Equity using the Dividend Discount Model (DDM)

How to Calculate Cost of Equity using Dividend Growth Model / Gordon Growth Model

How to Calculate Cost of Equity using Modigliani & Miller II

Do All Calculations of Cost of Equity Provide The Same Result?

What is the Difference Between Cost of Equity and Cost of Capital?

Cost of Equity Calculation Example

Calculate Cost of Equity using the CAPM

Calculate Cost of Equity using DDM

Calculate Cost of Equity using GGM

Calculate Cost of Equity using Modigliani & Miller II

Comparing Estimates Using Different Approaches

Wrapping Up

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