Discounted Cash Flow Calculator (DCF)

Q: Which is a good value for the perpetual growth rate in the discounted cash flow model?

Theoretically, the discounted cash flow model can use any perpetual growth rate . However, a company cannot grow faster than the gross world product (GWP), as, otherwise, the company would be more significant than the world one day. Consequently, investment analysts use perpetual growth rates that oscillate between the company's home country's GDP and inflation rate. It is very common to use 2-3%.

Created by Arturo Barrantes and Bogna Szyk

Reviewed by Małgorzata Koperska, MD and Adena Benn

Based on research by

Pignataro, P. Financial Modeling and Valuation: A Practical Guide to Investment Banking and Private Equity; 2013See 1 more source

Cipra, T. Financial and Insurance Formulas; 2010

Last updated: Jan 18, 2024

Table of contents:

The discounted cash flow calculator is a fantastic tool that investment analysts use to determine the fair value of an investment. By adding the company's free cash flow to firm (see our FCFF calculator) or the earnings per share to the discount rate (WACC), we can find out if the current price of a security or business is cheap or expensive.

By reading this article, you will understand what the discounted cash flow (DCF) model is and how to calculate the discounted cash flow using either the free cash flow to the firm (FCFF) or the earnings per share (EPS). We will also help you understand how to determine if a share price is undervalued or overvalued.

To illustrate all these concepts, we will go together through examples of discounted cash flow valuation (see pre and post-money valuation). However, before we dive into more complex topics, let's talk about the definition of the DCF.

What is the discounted cash flow model?

The discounted cash flow model is an income valuation method that determines the fair value of a company or stock by analyzing the future expected cash flows and defining how much they value in the present.

Let's think about it for a second: what is the value of a company to its owners? As mentioned in the free cash flow calculator, owners expect to receive cash flows from the company. Such cash flows can be in the form of dividends, for example.

So, cash flows are valuable and represent the return on the investment shareholders/owners made when they started the company. The same approach can be used when new investors want to buy shares of the business or, on a bigger scale, when a company wants to acquire another one:

We have to value the business's future cash flows, which represent the return, and see if what we are going to pay for the company in the present makes it a sound investment.

And that's the strategy of the discounted cash flow approach. The expected future cash flows are projected up to the company's life. Then these future cash flows have to be valued in the present. To facilitate that, we use the concept of the net present value, which considers a discount rate.

Some analysts prefer to use earnings per share to project future cash flows because they are the net earnings to the shareholders. In this DCF calculator, we will show you both methods.

Discounted cash flow formula using FCFF

We now know what the discounted cash flow method is all about, so let's discuss the math behind it. The main discounted cash flow formula is:

\footnotesize {\rm DCF} = \sum{\cfrac{{\rm FCFF}_t}{\left(1+r\right)^t}}

where:

$\rm FCFF$ – Free cash flow to the firm and represents the future expected cash flows of the company;
$t$ – Time associated with the future expected cash flows we are going to consider in our analysis; and
$r$ – Discount rate needed to value such future cash flows in the present.

Note that the DCF result, the sum, can be infinite; however, that's not realistic because no company will exist forever; thus, we have to choose an appropriate $t$ according to certain guidelines explained below.

The FCFF considers all the money available to the owners and creditors. Consequently, we obtain the firm's present value when we apply the DCF formula.

Note that this formula is the sum of all the FCFF in the future but brought to the present by the net present value (NPV). The NPV uses a discount rate, as mentioned above.

Since we are using free cash flow to the firm, the discount rate has to be the weighted average cost of capital (WACC) because this discount rate includes the effect of both sources of funding for a company: equity + creditors. Remember that if we were to use free cash flow to equity (FCFE) (FCFE calculator), we would need to discount the FCFE by the cost of equity.

Consequently, we have:

\footnotesize {\begin{split}\rm value\ of\\ \rm the\ firm\end{split}} = \sum{\cfrac{{\rm FCFF}_t}{ \left(1 + {\rm WACC}\right)^t}}

However, this formula can be used for as long as the company exists (there is no upper limit to $t$ ), meaning you would have to project FCFF for a long distant future, which includes many uncertainties.

In order to avoid this, the discounted cash flow method approach separates the future lifetime of the company into two: one is the projectable future that usually includes 5 to 7 periods in the future and the terminal value that represents all the future cash flows after the projectable periods.

Terminal value is, in other words, the business value after the period for which cash flows are forecasted. We calculate it using the perpetual growth rate method.

If we define $n$ as the period until when the projectable free cash flow to the firm is forecasted and $g$ as the chosen perpetual growth (%), then we have the terminal value formula:

\footnotesize {\rm TV}_n = {\rm FCFF}_n \times \left(\cfrac{1+g}{{\rm WACC} - g}\right)

Then, the discounted cash flow formula becomes:

\footnotesize \begin{split} {\begin{split}\rm value\ of\\ \rm the\ firm\end{split}} = &\sum{ \left( \cfrac{{\rm FCFF}_t}{\left(1 + {\rm WACC}\right)^t} \right)} \\[1em] &+\cfrac{{\rm TV}_n}{\left(1 + {\rm WACC}\right)^n} \end{split}

where $t$ goes up to $n$ . Note that the terminal value must also be discounted to its present value by using WACC.

Now, we need to adjust the value of the firm to be the value of the equity so that we can find the business price per share:

value of the equity = value of the firm - net outstanding debt,

where:

net outstanding debt = outstanding debt - cash

Finally, we obtain the fair value per share calculated by the discounted cash flow method if we divide the value of the equity by the outstanding shares:

fair value per share = value of the equity / outstanding shares

In our discounted cash flow calculator, we have included a feature where you can find out if the market stock price is overvalued or undervalued relative to the company's DCF so that you can make wiser investment decisions.

As a side note, the terminal value can be calculated with the EBITDA multiple method.

Discounted cash flow approach using EPS

Now that you understand the principle of DCF valuation, it's time to introduce the DCF formula based on net earnings.

Similarly, as above, the total intrinsic value consists of two parts:

intrinsic value = growth value + terminal value

The growth value describes how your company's value will increase during the growth stage. You can calculate it with the following equation:

\footnotesize \mathrm{growth \ value} = {\rm EPS} \times A \times \cfrac{(1 - A^n)}{1-A}

where:

$\rm EPS$ – Earnings per share;
$A$ – A coefficient equal to $A = (1 + g) / (1 + r)$ ;
$g$ – Growth rate;
$r$ – Discount rate (equal to WACC); and
$n$ – Number of years when your startup is growing at a growth rate $g$ .

The other part of the intrinsic value called the terminal value, can be found with the following formula:

\footnotesize \begin{split} {\begin{split}\rm terminal\\ \rm value\end{split}} = \cfrac{{\rm EPS} \times A^n \times B \times (1 - B^i)}{(1 - B)} \end{split}

where:

$EPS$ – Earnings per share;
$A$ – A coefficient equal to $A = (1 + g) / (1 + r)$ ;
$g$ – Growth rate;
$r$ – Discount rate (equal to WACC);
$n$ – Number of years when your startup is growing at the growth rate $g$ ;
$B$ – A coefficient equal to $B = (1 + t) / (1 + r)$ ;
$t$ – Terminal growth rate; and
$i$ – Number of years in terminal growth.

As you can see, the DCF method involves a lot of computations. Thankfully, Omni's discounted cash flow calculator can take care of them for you and help you get to break even very quickly.

Discounted cash flow example using FCFF

In this section, we will perform an analysis of a company using the discounted cash flow valuation method. Let's assume Company Alpha which has the following expected free cash flow to the firm:

FCFF₁ = 90,000 USD

FCFF₂ = 100,000 USD

FCFF₃ = 108,000 USD

FCFF₄ = 116,200 USD

FCFF₅= 123,490 USD

WACC = 9.94%

g = 4.48%

Then,

terminal value = 2,363,046.74 USD

After we bring all the cash flows back to the present, we get

value of the firm = 1,873,573.51 USD

As mentioned above, we need to discount the net outstanding debt. For that, Company Alpha has reported:

cash = 100,000 USD

outstanding debt = 900,000 USD

Resulting in:

net outstanding debt = 800,000 USD, then:

value of the equity = 1,873,570 USD - 800,000 USD= 1,073,573.51 USD

The next step needs information about the outstanding shares and the current market price of the security; let's say:

outstanding shares = 100,000 USD.

Finally,

fair value per share = 10.74 USD.

Assume the current share value of the Alpha company is 5 USD / share. We find out that the stock is undervalued by 114.71%, meaning if we invest in this company at its current stock price, we can more than double our investments.

Do not hesitate to repeat all these calculations with the help of our discounted cash flow calculator to get a better grasp of the discounted cash flow model!

Discounted cash flow example using EPS

You are an investor and want to buy shares in a startup, paying $300 per share. During the last 12 months, the startup's earnings per share were $50. Will your investment pay off?

Ask the management of the startup about their projected growth. The CEO is confident that they will be able to achieve a stable growth of 8% annually for the next five years.
The next step is the evaluation of terminal growth. After some research, you assume that a terminal growth rate of 3% over the following five years seems realistic.
Last but not least, you check the average values of WACC and decide to choose 11% as the discount rate.
Once you know all of these values, all you need to do is plug them into the discounted cash flow formulas:

\footnotesize \begin{split} A &= \cfrac{(1 + g)}{(1 + r)} = \cfrac{(1 + 0.08)}{(1 + 0.11)} = 0.973 \\ B &= \cfrac{(1 + t)}{(1 + r)} = \cfrac{(1 + 0.03)}{(1 + 0.11)} = 0.928 \\ \end{split}

\footnotesize \begin{split} {\begin{split}\rm growth\\ \rm value\end{split}} &= EPS \times A \times \cfrac{(1 - A^n)}{(1 - A)} \\ &= \$ 50 × 0.973 × \cfrac{(1 - 0.973^5)}{(1 - 0.973)} \\ &= \$ 230.45 \end{split}

\footnotesize \begin{split} {\begin{split}\rm terminal\\ \rm value\end{split}} &= {\rm EPS} \times A^n \times B \times \cfrac{(1 - B^i)}{(1 - B)} \\[1.3em] = \$ 50 &\times 0.973^5 \times 0.928 \cfrac{(1 - 0.928^5)}{(1 - 0.928)} \\ &= \$ 175.15 \end{split}

Finally, sum up the growth value and terminal value:

\quad \footnotesize \begin{split} \text{intrinsic value} &= \text{growth value} \\ &\quad + \text{terminal value} \\ &= \$ 230.45 + \$ 175.15 \\ &= \$ 405.60 \end{split}

The intrinsic value, equal to $405.60, is higher than the amount you wanted to invest ($300). Theoretically, it means that the investment will pay off in the end. If you look more closely, though, you will notice that the growth value is lower than $300! It means that after five years, the investment will still not bring a profit. If you don't mind such a long-term investment, then it's not a problem. If you do – well, maybe other options will bring profit much faster.

As before, experimenting with our discounted cash flow calculator can help you develop a better intuition of the DCF method.

Discounted cash flow analysis – How to interpret?

It is important to recall that we are trying to forecast the future. Because there are many uncertainties, our results can vary significantly from what ends up happening. Regarding interpretation, there are two main insights:

The investor always wants to buy the company's shares below the fair value of the equity.

This might be tricky to do due to stock price fluctuation. Still, in case you find yourself with a stock cost basis over the current market share price, you can either sell the position (and take the loss) or increase your asset allocation percentage to reduce your stock average cost per share.
The value you choose as WACC, and perpetual growth rate does matter.

Because we assume the company will operate forever, even a change of 1% can make the discounted cash flow valuation vary greatly. Thus, it is of utmost importance to remember that the valuation is a mere mathematical result, and investing risk must be considered.

When not to use DCF?

There are a few conditions that need to be met for the discounted cash flow to work:

The company must not pay dividends. This is because dividends are cash flows that go out of the company directly to shareholders; meanwhile, free cash flows to the firm are cash flows to the creditors and shareholders.

In case you want to value a company based on its dividends that are expected to be paid, it is better to consider the dividend discount model (see the dividend discount model calculator).
If the company pays dividends, the dividends shall be a small part of the company's net income. This relation can be evaluated using the dividend payout ratio. The lower this ratio, the better and more accurate the discounted cash flow model; however, some analysts recommend a dividend pay-out ratio under 20%.
When projecting free cash flows, the future growth rate used has to be aligned with the growth rate seen in the past. Because free cash flows are derived from the operating cash flows, it is essential to understand the capital expenditures over the years that the company conducts to create a reliable forecast.

FAQ

Can I use negative free cash flow in the discounted cash flow analysis?

Yes, you can use negative free cash flow in the discounted cash flow analysis. But at a certain point, you have to project positive free cash flows. This is even more important in the perpetual growth phase. If not, the discounted free cash flow method will negatively value the firm, which is basically nonsense.

How to discount cash flows to the firm?

Follow these steps when you need to discount cash flows to the firm (and have no access to a dedicated discounted cash flow calculator):

Calculate the last five free cash flows to the firm and find out the growth rate.
By using that growth rate or a lower one, project the following 5-7 periods of free cash flows to the firm.
Consider the last projected cash flow and calculate the terminal value using a reasonable perpetual growth rate (2-3%).
Bring all that cash flows to the present using the net present value and WACC as the discount rate. Now you have the present value of the firm.

How to discount cash flows?

There are two methods in the discounted free cash flow method:

The first one is to consider free cash flow to the firm and discount it to the present through the net present value by using WACC.
The second one is using the free cash flow to equity and discounting it using the cost of equity(Ke).

Which is a good value for the perpetual growth rate in the discounted cash flow model?

Theoretically, the discounted cash flow model can use any perpetual growth rate. However, a company cannot grow faster than the gross world product (GWP), as, otherwise, the company would be more significant than the world one day. Consequently, investment analysts use perpetual growth rates that oscillate between the company's home country's GDP and inflation rate. It is very common to use 2-3%.

Can WACC be equal to the perpetual growth rate in the discounted cash flow method?

The discounted cash flow valuation method does not allow WACC to be equal to the perpetual growth rate because you would have a division by zero. Besides, it is improbable for a company to have such an enormous perpetual growth rate. Likewise, a WACC value that low matches a proper perpetual growth rate would attract all the investors in the world because it would be cheap to invest in.

Arturo Barrantes and Bogna Szyk

DCF method

DCF using FCFF

First FCFF

Second FCFF

Net debt

Cash

Outstanding debt

Growth and discount rate

Perpetual growth

WACC

Shares and its market value

Outstanding shares

Share price

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Discounted Cash Flow Calculator (DCF)

What is the discounted cash flow model?

Discounted cash flow formula using FCFF

Discounted cash flow approach using EPS

Discounted cash flow example using FCFF

Discounted cash flow example using EPS

Discounted cash flow analysis – How to interpret?

When not to use DCF?

FAQ

Can I use negative free cash flow in the discounted cash flow analysis?

How to discount cash flows to the firm?

How to discount cash flows?

Which is a good value for the perpetual growth rate in the discounted cash flow model?

Can WACC be equal to the perpetual growth rate in the discounted cash flow method?

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