## DCF: Discounted Cash Flow Analysis

While there are many ways to determine the intrinsic value of a company, I don’t believe any are more popular than the DCF — or Discounted Cash Flow method of analysis. It’s widely regarded to be the most accurate means of determining what a company is really worth, and is commonly used by professional analysts and individual investors alike.

Essentially DCF is nothing more than looking at projections of what the company will earn in the future, and translating that into a dollar amount today. How we get from point A to point B in all of this takes a bit of work and lots of assumptions, but after running through it a few times it is fairly straightforward. Determining the true worth of a company is important, since price is not the same thing as value, and allows us an opportunity to profit from temporary irrationality in the market.

In the next few sections, we’ll look at how to properly conduct a Discounted Cash Flow analysis for a company. Since it’s better to use real numbers, let’s look at a company I recently determined a value for using another method: Chipotle Mexican Grill (CMG). Using the EPS Growth Capitalization method, I determined the true value of CMG to be \$292.26. Let’s see what we come up with using DCF.

## The Basic Idea of DCF

DCF works on the principle that money in your pocket today is worth more than it is tomorrow — or ten years from now for that matter. For example, what if I were to give you the choice of taking \$1 million today, or that same million dollars in exactly one year. Which would you choose? This one is hopefully a no-brainer – you would take it today of course! But let’s think about this a little bit and try to figure out why this is such an obvious choice.

Let’s also assume that you are looking at the million bucks purely as an investment (ie. you aren’t going to go out right away and buy a new house and car). The reason money today is worth more than it is next year is then quite straightforward: You can invest the money today and it will be worth more in the future. If you were to invest that money very conservatively, you might make 3% interest over the course of a year. That means the million dollars you have today will be worth \$1,030,000 in a year, or an extra \$30,000.

The key to DCF is to look at this process in reverse. In other words we know that we have \$1,030,000 in the future, and the question then becomes how much that money is worth today. More generally in the context of stock investment: How do we calculate the present value of a company that has sales & earnings every year for the foreseeable future?

## What is Free Cash Flow?

There are several methods of conducting a discounted cash flow analysis, but we’re specifically going to use the most common which starts with annual revenue and makes adjustments line by line to arrive at free cash flow. By taking a line by line approach it is possible to forecast smaller pieces of the puzzle rather than attempting to forecast FCF directly. Specifically, we need to work the numbers into a form by which we can use the following equation:

FCF = NOPAT + Depreciation & Amortization – Change in Net Working Capital – Capital Expenditure

This may look fairly complex at first, but in laymen’s terms FCF is the cash left over after the company has taken what it needs to continue operations and to grow. This is why the Net Working Capital and the Capital Expenditure are deducted in the equation above. FCF is the true representation of the money that a company generates.

## Determining Free Cash Flow (FCF)

The first step is to decide how far into the future to forecast cash flows to be used in the analysis. This is quite a subjective number, but there are some rules of thumb to go by:

• If the company is in its infancy stages and is experiencing high levels of growth, the typical forecast period used is 10 years
• If the company is growing, but there are competitors in the market and growth is slowing, the forecast period is usually 5 years
• Large, mature, established companies with low margins and slow growth typically use a forecast period of just one year

Those are some good rules of thumb, but what we’re really doing is estimating what’s called the excess return period, which is defined as the number of years the company is expected to outpace the growth of the economy as a whole. Small, fast growing companies will likely outpace the economy for years to come, while large established companies with lots of competition are more likely to just keep pace.

If we look at CMG, we see that it is experiencing extreme levels of growth on both the top and bottom lines. The company is opening hundreds of new restaurants per year, and is planning to expand internationally. This is definitely a company we will want to forecast out for 10 years at least.

Our next task is to estimate the amount of free cash flow that CMG will generate over the next 10 years. We start by looking at revenue growth.

The table above shows the phenomenal growth CMG has achieved over the past number of years. This works out to a compound annual growth rate (CAGR) of 23% over the past five years. This is a good starting point for forecasting future growth, however most companies are not able to sustain that level of growth over the long term. It’s even evident in the table above as CMG grew revenues at 31% in 2006/2007 but now is only achieving growth in the 20% range.

Therefore it’s typical to forecast revenue growth to be somewhat lower than past history for DCF analysis. In this example I am going to predict that CMG will be able to sustain 20% growth for the next 3 years, but then decline by 1% every year for the next 7. Using a simple excel spreadsheet, we can now easily forecast revenue for the next 10 years. I’ve summarized below:

With a revenue forecast in hand, we must now work line by line to arrive at an annual projected free cash flow. In other words, we know how much the company is bringing in, but how much is actually free. As discussed above, free cash flow is the amount of money left over after all cash expenses are removed. It’s a true picture of what’s left over to increase shareholder value.

We can determine free cash flow from revenue by taking the following steps:

1. Deduct Cost of Goods Sold (COGS) to arrive at Gross Profit
2. Deduct operating expenses (OPEX) to arrive at EBIT (operating income)
3. Deduct taxes to determine Net Operating Profit After Tax (NOPAT)
4. Add D&A expenses back in
5. Deduct capital expenditures (CAPEX)
6. Deduct the YoY change in working capital
7. The end result is Free Cash Flow (FCF)!

As with revenue, it’s not the current values we’re interested in, but future values, forecast for each year. Let’s look at each one individually.

### Operating Costs

Operating costs are the costs associated with such things as salaries, research and development, the cost of raw materials, marketing, etc. – you get the idea. Starting with revenue, and applying steps 1 & 2 above will give us EBIT. While we can simply look up EBIT directly using any number of websites (or the company financials directly, it’s useful to look at the individual contributions to OPEX directly so that they can be forecast forward. For example, on GuruFocus I can see that CMG’s revenue in 2011 was \$2,270 million, and its EBIT (earnings before interest & taxes) was \$351 million. However we’re going to break it down into separate components of COGS, D&A, and other expenses.

First let’s subtract COGS from revenue to arrive at Gross Profit every year for the past five years. Let’s also calculate COGS as a percentage of revenue so that we can identify the trend. COGS has been averaging about 73.5% of total revenue. We can use that as the basis going forward. Now we know revenue, COGS, and gross profit for the next 10 years, as shown in the following table (click to enlarge).

Step 2 is to determine Depreciation & Amortization costs, as well as other expenses and subtract these from gross profit to determine the operating profit (EBIT). There are usually several types of expenses that make up the other category, but all we’re really interested in is separating out the D&A portion, since we need to add that back in later to determine FCF. We do so, and since we’re looking at this line by line, can see that D&A is in a slight downtrend, which we project going forward as a decline from 3.3% of revenue to 3.0% of revenue over the next 10 years. We also see that total OPEX is holding steady at around 11.1% so we hold that ratio going forward as well. We subtract OPEX from gross profit to determine EBIT as shown in the following table (click to enlarge).

### Taxes

Step 3 is to deduct taxes from EBIT, which gives us the net operating profit after tax (NOPAT). Total tax paid for each year can be found as a line item on the income statement. It’s useful to calculate the tax rate as a percentage of EBIT, and in this way we can look at the trend and project taxes going forward. In doing so it appears that CMG is paying roughly 37.4% tax, which I will project forward for the next 10 years. The results are shown in the following table (click to enlarge).

### Capital Expenditure (CAPEX)

Capital expenditures refers to the money a company expends to foster growth, and is calculated by taking the company’s Capital Expenditure found on the cash flow statement. Since this money has been consumed, we will subtract it from NOPAT as part of the FCF calculation. We will also add back in the D&A expenses that had been removed previously since although depreciation is booked as an expense, it’s a paper expense and that cash is still available.

CMG spent \$151 million on capital expenditures in 2011 and 74.9 million in depreciation. We can now tabulate these for the past five years and look at the trend in CAPEX spending. CMG has been steadily decreasing its expenditures as a percent of revenue to its current level of approximately 6.7%. We will use this as the basis for future CAPEX spending. Chipotle has a very aggressive strategy for growth which primarily consists of the opening of new restaurants, but it appears that revenue will increase at the same pace as CAPEX.

### Working Capital

Working capital is the short term cash that a company needs to cover its day to day operations such as replenishing inventory. In balance sheet lingo, it’s the cash required to maintain the current assets on the company’s balance sheet and is calculated by subtracting current liabilities from current assets. From CMG’s latest annual report, we see total current assets of \$501 million and total current liabilities of \$157 million, resulting in \$344 million of working capital for 2011. We can do this for the past five years:

What we really need for the FCF calculation however is not the working capital itself, but the change in working capital from one year to the next. It’s counted as a deduction/addition against FCF. To determine the change in working capital YoY, we simply subtract the prior year’s working capital. We can also project working capital into the future. Looking at the previous trend, I am going to assume that CMG maintains 12% of its revenue as working capital going forward.

### Calculating FCF

We now have all of the inputs required to calculate free cash flow for every year of our 10 year forecast period. It’s usually easiest to summarize everything in an excel worksheet as I’ve done below (click to enlarge):

Starting with NOPAT, we follow steps 4 through 7 to add D&A expenses back in, deduct capex, and deduct change in working capital to arrive at free cash flow. We now have a projection of Chipotle’s cash flow over the next 10 years. Now it’s up to us to discount these cash flows to a present day value.

## Determining the Discount Rate

Remember back at the beginning when we were looking at how much that \$1 million was worth a year from now? To arrive at the answer we applied an interest rate. Now the question we’re trying to answer is how to convert all of those future cash flows back to a present value, and you guessed it – we’re going to use an interest rate to find it. Since we’re actually reducing a future value back to the present, this interest rate is called the discount rate.

Many investors will calculate the Weighted Average Cost of Capital (WACC) for the company and use that number as the discount rate. I’ve written a detailed article on how to calculate WACC if you want to go that route. WACC represents the rate of return that a company must pay on average to finance its assets. From that point of view it kind of makes sense why we would consider using it for the DCF analysis. But what we’re really after is OUR desired rate of return, which may be wildly different than the 8 or 9% that the company pays for its capital.

Let’s think about this a bit more and fully understand this concept. To do so, let’s go back to our example of that \$1 million that we’re going to get paid next year. How much are we willing to pay today to get that million a year from now? The answer depends completely on the rate of return we require. Maybe we’re satisfied with a 5% rate of return. If that’s the case then we would be willing to pay \$952,381 today. What if we consider this to be a risky investment however and decide we don’t want to buy it for any less than a 15% rate of return. By increasing our required rate of return to 15% our buying price today actually drops quite significantly to \$869,565. That’s the basic concept – a higher discount rate means a lower present value. The future value stays exactly the same, but the present value is defined completely by the rate of return we require.

When setting a fixed rate of return as the discount rate, I usually refer to it as the Minimum Acceptable Rate of Return, or MARR. For investments that I deem to be risky, I typically use a MARR of 15%, and for lower risk investments as low as 9%. Note that on average the market as a whole over history has returned around 8% per year.

I am going to set my minimum acceptable rate of return for this investment to 12% – in other words 12% will be the discount rate used to convert future cash flows to a present day value.

## Terminal Value

So far we’ve only looked at forecasting CMG’s cash flow over the next 10 years, but the company won’t cease to exist at that point — in fact it better not or we’re in trouble! To account for the fact that the company is still worth something after the forecast period, we’re simply going to calculate what’s called the Terminal Value. It’s going to be a single number that represents the sum of all future cash flows from year 11 onwards. But why not simply increase our forecast period to a longer timeframe to account for this? Why not forecast 30 years into the future? The reason is that it’s impossible to forecast with any accuracy at this long a period. 10 years is pushing it already. Therefore we simplify things and use the terminal value as an approximation.

Benjamin Graham is a big proponent of the Gordon Growth Model, which is defined as follows:

TV = Final yr cash flow x (1 + LT growth rate) / (Discount rate – LT growth rate)

The only unknown in the above equation right now is what to use for the long term cash flow growth rate. Typically a growth rate in the range of 3 – 4% is used. For this example, I am going to assume a LT growth rate of 3.5%. We use the final year of our projection as the basis for calculating terminal value. Based on this rate, a final cash flow in year 10 of \$564 million, and a discount rate of 12%, we determine that the present value of the terminal value for CMG is \$2,478 million.

## Enterprise Value

We can now calculate the present value of all future cash flows, add it to the present value of the terminal value calculated above, and arrive at what’s called the company’s enterprise value. Following are the results (click to enlarge):

The present value for each year is summed to arrive at an enterprise value of \$3,733 million today. Enterprise value is a measure of the company’s total value — including debt.

## Equity Value

We’re only interested in the value of the equity within the company, not the debt. We therefore need to remove debt from the enterprise value. We also want to account for any cash that the company has on hand, so we’ll add that back in as well:

Equity Value = Enterprise Value – Debt + Cash

Chipotle has zero debt so that term of the equation gets eliminated. CMG does have a total of \$456 million in cash, cash equivalents, and short term investments on its balance sheet, so we can add that back in. This results in an equity value of \$4,189 million. It’s more useful to look at this on a per share basis. CMG currently has 31.22 million shares outstanding. We divide and arrive at an intrinsic value of \$134.17 / share.

## Comparisons to other methods

The DCF method of valuation is much more complex than the EPS Growth Capitalization Method, and infinitely more complex than simple methods such as Peter Lynch Fair Value. It’s interesting then to see how the final numbers compare. I recently completed a very detailed evaluation of CMG using EPSGC. Let’s see how the numbers look:

1. Discounted Cash Flow Method: \$134.17
2. EPS Growth Capitalization Method: \$292.26
3. Peter Lynch Fair Value: \$172.25 (with growth capped at 25%)

As expected there’s a range of values calculated depending on the method used. This is because there are assumptions and estimates that play a part in any estimate of future value. It’s therefore important to use as realistic and accurate numbers as possible in an attempt to drive accuracy in the final result. This also emphasizes the importance of putting an adequate margin of safety on any entry targets derived from a calculated value which will hopefully act as a suitable buffer for errors that result in an artificially high value.

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## 8 thoughts on “DCF: Discounted Cash Flow Analysis”

1. This is my FAVORITE type of analysis to do and it is the easiest for me. I love finding the free cash flow of a company. It’s such a strong indicator of a businesses strength and dominance in their industry!

Great detailed explanation Dustin!

• Dustin Small says:

Hi Marvin,

I’ve got a great spreadsheet I’m putting together to simplify DCF even more and hope to be able to share it soon.

• Fathima Hoosen says:

Hi Dustin and Marvin

I am currently serving my internship for my accoutancy qualification, We are planning an interactive debate for this friday and your above explanation really helped. Any luck with the spreadsheet you are putting together? Id like to beef up my presentation with a trusted example to keep the debate interactive.

2. […] had several requests to make my discounted cash flow (DCF) spreadsheet publicly available. As a refresher, DCF analysis is a method of forecasting the […]

3. Derek says:

Hi Dustin,

Great article! I’m pretty new to investing and I’ve learned a lot from your website! I was wondering why your numbers for FCF differ from the numbers for FCF on the GuruFocus website, if you seem to be using the same data. If they use a more comprehensive method, wouldn’t it be easier to just use their FCF and work from there?

Thanks so much!

4. Dan says:

Dustin-

I am a novice investor and really appreciate you taking the time to share your knowledge. Reading about discounted cash flow investing got me quite interested in it but I thought I would probably not be able to learn much about it. Then I discovered your website. Thanks again.

5. Jun says:

Dear Dustin,

This is one of the best explanations of DCF that I have read. Thumbs up for your efforts!

There’s only one thing that’s not fully clear to me: I notice that in the above example you calculate the terminal value from year 10, that is, you sum the PV’s of year 1 up to year 9. But year 10 assumes a growth of 13%. Shouldn’t the PVs be summed from year 1 to year 10 instead, and, then calculate the terminal value into perpetuity starting from year 11?

Thanks,

Jun