Many people have a hard time understanding Discounted Cash Flow (DCF).

In the following we will in an easy-to-understand language describe the concept so that you understand the DCF after reading this.


Premise of DCF

numbers-money-calculating-calculationDiscounted Cash Flow (”DCF”) is a valuation method used to estimate the value of a company or an investment.

The core idea in DCF is to estimate future cash flows (the CF in DCF) of a company and discount these (the D in DCF) to get the value of the company today.

This makes intuitive sense as it says that the value of a company is equal to the sum of all future cash flows it produces.

In the following, we will use examples to guide you through a DCF to give you a thorough understanding of discounted cash flow valuation.

We will show how to set up your own DCF model as well as the main pitfalls to avoid. So without further ado let’s get on with it.


Step-by-step guide to discounted cash flow valuation

In the guide below we will provide a complete guide with a check list and after reading this you should be well equipped to value a company through the use of discounted cacsh flow valuation.

Step 1. Estimate free cash flow in forecast period

WACCThe first part in doing a DCF is to forecast the free cash flow in the forecast period. The most common way to forecasting free cash flow is to make a financial statement analysis for a period covering at least the last three years. This will give an indication of the EBIT margin as well as level of capital expenditures and net working capital.

Based on this financial statement analysis and the expectation for the future, one can forecast free cash flow for the forecast period. If the company is expected to perform at the same level going forward without any major strategic initiatives historical performance will serve as a good indicator of future performance.

On the other hand, if there are major developments expected, the levels relative to revenue going forward should potentially be adjusted. An example could be if investing in a new production facility. This would result in higher capital expenditures, however, it would usually also lead to a higher EBIT margin.

In this example, there would be a negative impact on free cash flow from capital expenditures and a positive impact from a higher EBIT.

Step 2. Estimate terminal value

In estimating the terminal value we’ve already “come a long way” as we already have cash flow for the last period. We now need to estimate the growth rate of the company, which is usually based on the growth level seen in the historical period as well as the forecast period.

With that said, a word of caution should be issued. If you forecast a growth level above the long-term inflation level of 2% for the terminal value, you should have very solid arguments for doing so. The reason for this is, that it is rare for companies to outperform the growth rate of the economy in the long term.

Step 3. Estimate discount rate

P/E ratioWe will not do a deep dive into estimating the discount rate, as this is still a large subject for discussion in the academical world and can get extremely technical. Suffice to say here is, that the rule of thumb is:

Discount rate rule: The larger the risk in the company, the higher the discount rate

If you want a sound estimate of the discount rate to apply in a given industry, we suggest visiting Aswath Damodoran’s “Cost of Capital by Sector”. The page has discount rates for virtually all industries. When using Aswath Damodoran’s estimates, one thing to remember is, that there is usually a size premium in the discount rate for smaller companies (i.e. it is higher).

Step 4. Use discount rate to calculate terminal value and discount all cash flows to get present value

Having estimated the free cash flow, terminal value and the discount rate we now have all the building blocks needed for a DCF. Step four is to discount all the cash flows to get the present value of these.

Step 5: Sum all cash flows to get the valuation

black-calculator-near-ballpoint-pen-on-white-printed-paperHaving discounted all cash flows to a present value, the final step is to sum these to get the value of the company. And that’s it. Congratulations! Having followed these steps, you have just made a valuation of a company through the most academically correct way – discounted cash flow valuation.

In the ideal world, however, you are not done yet. First off, you should run sensitivity analysis on your valuation and compare value you arrived at with the value derived from other valuation. These other methods could include relative multiple valuation and net asset valuation. However, these steps are not a mandatory part of doing a discounted cash flow valuation.

Below are more detailed and advanced topics in regards to doing a DCF. However, it is strictly speaking not necessary to read further although we of course recommend it.


DCF formula

The formula used to calculate the value of a company can be daunting at first glance, but is relatively simple once you understand the concept, which we will explain below. DCF formula:

01. DCF - Formula

where d=discount rate and CF=Cash flow

Looks rather complex, doesn’t it? Let’s take the first part:

02. DCF - First part

In the nominator we have the estimated cash flow for the first period. Simply enough, right? In the denominator we have the discount factor which enables us to get the present value of this cash flow. So let us assume that in one year, we have an estimated cash flow of 1,000 (=CF1) and our discount rate is 10% (=d). As this is in one year we also have n=1. The discounted value of year 1 cash flow is thus:

03. DCF - first year

Going forward with the same logic for year 2, let’s assume cash flow in the second year is 1,000 (=CF2). The discount rate was already defined
as d=10% and now we have n=2.

04. DCF - second year

This logic continues for each successive year.

When valuing a company or an investment, it is reasonable sane to estimate cash flows for the first period. It is also relatively safe to do this for the second year, however, it is not as “safe” as the first year. When you get five or ten years out it becomes significantly harder to estimate these cash flows. Estimates of these cash flows moves from very educated guesses to pure guesses.

To avoid making guesses in our model we introduce the concept of terminal value.


Terminal value (Gordon’s growth model)

Terminal value covers the concepts of “all cash flows beyond a certain date bundled into “one large cash flow”.

The method most widely used is named Gordon’s Growth Model. Again, let’s start with the formula and below, we will explain it in terms that are easier to understand.

05. DCF - terminal value

Where g = long term cash flow growth rate

In the nominator we have the free cash flow in the final period which is multiplied by the expected growth rate of this cash flow. The logic is, that growing companies naturally should be valued higher compared to companies with no growth.

In the denominator we have our discount rate (our required rate of return) minus the growth rate of the company (required return covered by growth in free cash flow).

Following on with our example from above let us assume our final cash flow is in year 5 and that it is still 1,000. As our cash flow has been stable in these five years it will be safe to say there is no growth in this company, so g=0. Our discount rate is still 10%.

Putting these variables into Gordon’s Growth Rate model yields:

06. DCF - terminal value calc

In other words, in year five we have a terminal value of 10,000. As this is a “year five value” it will have to be discounted just like the cash flow in year 5. The value then becomes:

07. DCF - PV TV

Note: Mathematical properties in Gordon’s Growth Model…

… will not be covered here. However, it should be noted that this growth model is based on solid, hard math. If you want to read more about the mathematics in Gordon’s Growth Model you can take a look at Aswath Damodoran’s valuation slides.


Value of a company with DCF and Gordon’s growth model

In the examples given above, we have shown the cash flows of a company in year 1, year 2, year 5 and by extension of year 5 cash flows, the terminal value of the company.

Putting all of these together and expanding the model to also include year 3 and 4 gives the following cash flows with associated present values.

08. DCF - company valuation

Valuing in an investment

AssetIn the example above we have valued a company, but DCF can also be used to value investments. The mechanics to do so are exactly the same. In the example, it could just as well have been a new machine, plant or a building we were valuing.

Let’s assume the valuation above was a new machine instead. We know this machine will be worth 10,000 to the company.

If it costs 5,000 it would thus be a good decision to acquire this. One could ask whether it is a good decision if it costs 9,500? Our estimates show it will have a positive value of 500, however, there is little margin for error now.

This touches upon principles of capital budgeting, which is another chapter for itself.


Caution: DCF is highly sensitive to its input

Another thing to consider when doing a discounted cash flow valuation is that the valuation is highly sensitive to input. By DCF practitioners there is high awareness that DCF can easily become a “garbage-in, garbage-out” model. One should thus be fairly certain of the input parameters, and the more articulated the model is, the better.

Sensitivity to growth rates

Previously, our company was in a steady state with a growth of 0% and was valued at 10,000 by the DCF and Gordon’s Growth Model.

In the following table, we have calculated the value of the same company, at different growth levels. It can be seen, that at a growth rate of 2%, the company is worth 27.5% more – quite a difference for a company growing at the level of inflation. This highlights the sensitivity of the model to different growth rates.

The sensitivity to growth rates is why tech companies trade at very high trading multiples, whereas established, blue-chip companies in mature industries trade at lower multiples. This expected growth is “priced in to the stock price”.

Sensitivity to discount rates

Another way to see the sensitivity to input is to look at discount rates. In the following table, we have kept the growth rate of the company “locked” at 0% as in the original example, and varied the discount rate.

It can be seen that at the (very low) discount rate of 5% the value of the company doubles! Further, an increase or decrease of just 1% in the discount rate gives a value effect of 10%.

Again, this highlights the sensitivity to the input parameters in the DCF. There are no easy solutions to “fix” this issue. Instead, one should make sure to include sensitivity analysis to the key parameters in the model.

After all, we are dealing with estimates and it is important to see what small changes to the parameters do to the value of the company.

This is also important in strategic plans, as it can help managers answer questions about their company. An example could be, that the DCF can help answer whether it is most beneficial to grow the company by growing revenue or cutting costs.

The sensitivity to discount rates is the reason why stock plunge at events such as Brexit. This event lead to marketwide uncertainty which is basically equivalent to the discount rate for the company above to go from 10% to 11% corresponding to a decrease in value of 9%. This is what is meant when the adage “the stock market doesn’t like uncertainty” is uttered.


Free Cash Flow formula

In our example, we have “taken free cash flow for granted”. However, there is no line items in the annual report of a company named “free cash flow”. Instead, we have to derive the free cash flow of the company. The formula is:

EBIT
+ Depreciation & amortization
– Capital expenditures
+/- Changes in net working capital
= Free cash flow (pre-tax)
– Tax on EBIT
= Free cash flow (post-tax)

The intuition is, that we value cash flow, not profits. Depreciation & amortization has no cash effect so these should be added to our EBIT.

Further, capital expenditures have no direct income statements effect, but has a very real effect on our cash flow. Finally, if more (or less) money has been tied up in net working capital (i.e. trade receivables, inventory), this will also lessen the cash flow to the owners.

To make a full DCF, we thus have to estimate EBIT in the company as well as depreciation & amortization, capital expenditures and changes in net working capital.


Further considerations

Although we have covered the DCF entirely in this article, there are still other factors to consider.

Estimating the discount rate

In this article, we have advocated using Aswath Damodoran’s industry analysis as the discount rate basis. However, in an academic setting one would have to estimate this through the use of CAPM and WACC. We will not cover this method here. In an academic sense it is worthwhile to know, however, in the practitioner’s handbook, using Aswath Damodoran’s industry discount rates is the preferred way to go.

 Tax on EBIT

In the derivation of free cash flow the last line item needing to be estimated is “tax on EBIT”. In other words, the tax rate in deriving free cash flow post-tax is not the actual taxes paid by the company, but tax on EBIT.

Tax rate on EBIT * EBIT = taxes paid in deriving free cash flow

The tax rate paid varies from country to country. If you are in the US the tax rate is 40%.

Discounted cash flow valuation (DCF)