Fervent | Finance Courses, Investing Courses

Rigorous Courses, Backed by Research, Taught with Simplicity.

Formula for Stock Valuation – Full Walkthrough

Formula for Stock Valuation – Full Walkthrough

By Leave a Comment

In this article, we’re going to explore the formula for stock valuation, including what it is and how it works. Let’s get into it.

The Formula for Stock Valuation

Firstly, what’s the formula for stock valuation? While there are many, a generalized equation would look like this…

    \[P = \sum_{t=1}^{n=\infty} \frac{CF_t}{(1 + k_e)^t}\]

If the equation above is freaking you out, please don’t let it freak you out.

It’s actually a lot simpler than it looks.

Let’s first understand what each variable in the generalized formula for stock valuation actually means.

  • P here denotes the price of a stock (aka “stock price” or “share price”)
  • CF reflects a generic cash flow on a per-share basis
  • k_e reflects the cost of equity which is the amount it costs a company to raise money through equity (expressed in percentage terms)

The equation as a whole is equivalent to the Present Value of Future Cash Flows.

And now let’s consider each of these 3 core variables in more detail

Core Variable #1: Stock Price

The stock price or P strictly relates to what’s called the “intrinsic stock price” or the “intrinsic value”.

And “intrinsic value” refers to the fair value of the stock. It’s what the stock should be trading at in the market. But the stock price won’t always trade at the intrinsic value.

It’s deviations from the intrinsic value that pave the way for investments. For example, if the current market price is greater than the intrinsic value, then we say the stock is overvalued.

If, on the other hand, the current market price is lower than the intrinsic value, then the stock is undervalued.

Finally, if the current stock price is equal to the intrinsic value, then we say the stock is fairly priced.

The use of the letter P to denote stock price is fairly consistent, but some people in Finance do tend to use the letter S, while trying to imply they’re referring to the Stock price.

Related Course: Stock Valuation (using Multiples)

Want to learn how to value stocks using real world data? Explore our course on Stock Valuation (using Multiples).

Detailed walkthroughs, templates built from scratch, quizzes, assignments, and more. Check out the course.

Core Variable #2: Cash flow

While the cash flow (CF) is a generic one, we typically tend to use one of the following:

  • future dividend payments per share (aka “DPS” or “Div”)
  • future free cash flow to equity (aka FCFE or “Flow to Equity”, “FTE”)

You can use the future free cash flow, which is perhaps the most widely used cash flow in stock valuation, but you’ll need to make some adjustments to the formula for stock valuation above.

Regardless of which specific cash flow you end up using though, the key takeaway is that it’s a cash flow that occurs in the future.

It’s a “future cash flow” if you like.

Core Variable #3: Cost of Equity

The Cost of Equity is the amount it costs a company to raise money/finance through equity. That is, the cost of them raising money by, say:

  • issuing new shares to the public for the first time (e.g., in an IPO)
  • issuing new shares to existing shareholders (e.g., in a “rights issue”), or
  • conducting an “SEO” (seasoned equity offering)

The cost of equity is expressed in percentage terms, for example, 10%.

And if a company’s cost of equity is 10%, then it means the company will pay $0.10 for every $1 of capital it raises via equity finance.

The cost of equity can also be seen as a proxy for risk in that it will typically incorporate the two main kinds of risk, including:

In addition to showing the cost of financing, the cost of equity is also an appropriate discount rate.

Okay, now you know what the 3 main variables in the formula for stock valuation are and what they mean.

Some of you may well be getting a tad bit freaked out by some of the other mathematical symbols in the stock valuation formula so let’s just go over those, too.

Math Operators and Notations

If you’re freaked out by the funky symbol that looks like an “E” (this one: \sum), then again, please don’t let it freak you out.

This “funky symbol” (\sum) is the sigma summation operator. And all it’s doing… is it’s adding everything that’s in front of it.

You’ll actually see this work in action further down when we expand the stock valuation formula. For now, just remember – all it’s doing, is adding everything that’s in front of it!

The only other notations in the equation above are \infty and the letter t.

The letter t is simply referring to a specific point in time “t”. It could be time period 1, time period 2, 3, 4, …, \infty – it’s whichever time period you want it to be.

\infty means infinity. Think of the biggest number you possibly can. Now double that, or maybe even treble it. Or raise it to the power of itself. And now, you may have a number that’s close to infinity!

Infinity is just a really, really massive number. In the context of the stock valuation formula, by using \infty we’re essentially saying we’re looking at all of the firm’s future cash flows, for every year, forever.

Want to go beyond the stock valuation formula?

Get the Stock Valuation (using Multiples) Study Pack (for FREE!).

Stock Valuation (using Multiples) Study Pack Feature

While this sounds crazy, it actually makes intuitive sense. Companies can last and exist forever, thanks to the separation of ownership and management.

Put simply, companies can outlive humans. And that is why it makes sense to look at their cash flows over an infinite time period.

Okay, now that you know what each and every variable inside the stock valuation formula means, let’s go ahead and expand the equation.

Expanding the Formula for Stock Valuation

If you were to open up (or “expand”) the generalised formula for stock valuation above, you’d have…

    \[P =\frac{CF_1}{(1 + k_e)^1} + \frac{CF_2}{(1 + k_e)^2} + \cdots + \frac{CF_{\infty}}{(1 + k_e)^{\infty}}\]

In English, we’d read the equation is follows…

The stock price is equal to the sum of all discounted future cash flows, starting from time period 1, and going all the way up to and including the infinith time period.

Discounted future cash flow

Now, what’s a “discounted future cash flow” (aka discounted cash flow)? It’s each one of the fractions in the equation above.

It’s called “discounted” because we’re discounting the cash flows from the future, back to the present. We do this by essentially calculating the Present Value (PV).

Geometric series

Now, the equation above (after expansion) actually displays what’s called a “geometric progression”.

Put differently, we’re looking at a “geometric series”.

And while there is a formal proof of the result we’re showing below, it’s way outside the scope of this particular article.

But essentially, if 3 conditions hold, then the equation above simplifies to this…

    \[P = \frac{CF_t}{k_e}\]

The formula for stock valuation transforms into the equation for the Present Value of a Perpetuity.

Importantly, all three of the following conditions must hold:

  1. cash flows remain constant (i.e., CF_1 = CF_2 = \cdots = CF_{\infty})
  2. discount rate remains unchanged (i.e., k_e_1 = k_e_2 = \cdots = k_e_{\infty})
  3. the time period is infinite (i.e., t \rightarrow \infty)

If and only if those 3 conditions hold, then this holds…

    \[P = \sum_{t=1}^{n=\infty} \frac{CF_t}{(1 + k_e)^t} \equiv \frac{CF_t}{k_e}\]

Incidentally, the equation above is in fact the Dividend Discount Model (or DDM valuation model), which in turn is essentially based on the PV of a Perpetuity.

Stock Valuation Example

Let’s now apply the formula for stock valuation in an example. Consider the following information.

Question

McNeil Inc. recently reported a dividend payment of $2.50 per share. Analysts estimate its cost of equity to be 8.5% and do not expect the company to ever change its dividend payout policy. What is McNeil Inc.’s stock price? Please round off your answer to 2 decimal places.

Solution

McNeil Inc.’s stock price is approximately equal to $29.41.

Can you figure out how we got this?

Do give it a go before reading any further.

We’re going to assume you gave it a shot, so let’s now solve it together.

Recall that the generalised formula for stock valuation is…

    \[P = \sum_{t=1}^{n=\infty} \frac{CF_t}{(1 + k_e)^t}\]

In this example, instead of a generic cash flow, we’re given information about a dividend payment. Thus, we can rewrite the stock valuation formula like this…

    \[P = \sum_{t=1}^{n=\infty} \frac{Div_t}{(1 + k_e)^t}\]

Now, since analysts don’t expect the company to ever change its dividend payout policy, we can (somewhat unreasonably) assume the dividends remain constant.

In other words, we assume 0% dividend growth (or no dividend growth).

The lack of information about changes to the discount rate means we can also assume the cost of equity remains unchanged.

And since this is a company we’re dealing with, we can assume has the potential to exist forever. In other words, we can assume we’re dealing with an infinite time period.

The 3 conditions stated above, therefore, hold; meaning the formula for stock valuation above can simplify to this…

    \[P = \frac{Div_t}{k_e}\]

Recall that this is essentially equivalent to the Dividend Discount Model (or DDM valuation model).

And now it’s just a simple case of plugging in our numbers! That looks like this…

    \[P = \frac{\$2.50}{0.085} \approx \$29.41\]

The stock value is therefore $29.41

Alternative Formulas and Approaches for Stock Valuation

But the story doesn’t quite end there. Because this is just one formula for stock valuation.

This particular equation is based on discounted cash flows (DCF) valuation method. And it uses it without the presence of growth. Or put differently, it assumes (implicitly) that the growth rate is equal to 0%.

Incorporating growth into a valuation model is fairly straightforward, but there are considerations that one would need to make.

This is especially true if the growth rate is greater than the cost of capital.

Further, this formula only uses one valuation method (discounted cash flows).

You can also use Multiples for stock valuation, which is often also known as relative valuation. But in fairness, we think you’ve probably had enough for 1 article though, no?

If you’d like to learn about another stock valuation method or learn about other ways of estimating the stock price, we recommend reading our article on How to Calculate Stock Price.

Wrapping Up

So there you have it! You now know:

  • what the formula for stock valuation is,
  • exactly how it works, and
  • why it works the way it does

If you would like to explore other stock valuation formulas and approaches for valuation, do check out the linked articles above, and explore the course below.

Our Stock Valuation (using Multiples) course really is one of a kind, designed to help you build a robust stock valuation system using Multiples.

As always, keep learning and keep loving Finance!

That’s a wrap from us for now, thanks very much.

Related Course: Stock Valuation (using Multiples)

Do you want to build your own robust stock valuation system?

Explore the Course

Reader Interactions

Leave a Reply