Now that we have covered the workings of discounted cash-flow (DCF) models in general and a bit about how we treat them at Morningstar, we'll dig a little deeper into how to determine fair values for stocks. In this lesson, we'll walk you through a step-by-step sample DCF model that uses the "free cash flow to equity" method. Here are the main steps to generating a per share fair value estimate with this method:

• Step 1. Project free cash flow for the forecast period.
• Step 2. Determine a discount rate.
• Step 3. Discount the projected free cash flows to the present, and sum.
• Step 4. Calculate the perpetuity value and discount it to the present.
• Step 5. Add the values from Steps 3 and 4, and divide the sum by shares outstanding.

Step 1--Project Free Cash Flow

The first step in projecting future cash flow is to understand the past. This means looking at historical data from the company's income statements, balance sheets, and cash-flow statements for at least the past four or five years.

Once you've examined the historical data and perhaps entered it into a spreadsheet program, it's time to project the company's free cash flow in detail for the next couple of years. These projections are the meat of any DCF model. They will rely on your knowledge of the company and its competitive position, and how you expect things will change in the future. If you think profit margins will expand, or sales growth will slow dramatically, or the company needs to increase its capital expenditure to maintain its facilities, your projections should reflect those predictions.

Next, we need to estimate the company's "perpetuity year." This is the year at which we feel we can no longer adequately project future free cash flow. We also need to make a projection concerning what the company's free cash flow will be in that year.

To begin, let's suppose that the fictitious firm Charlie's Bicycles generated $500 million in free cash flow last year. Let's also assume that Charlie's current lineup of bikes are very hot sellers, and the company is expected to grow free cash flow 15% per year over the next five years. After five years, we assume competitors will have started copying Charlie's designs, eating into Charlie's growth. So after five years, free cash flow growth will slow down to 5% a year. Our free cash flow projection would look like this:

Last Year: $500.00
Year 1: 575.00
Year 2: 661.25
Year 3: 760.44
Year 4: 874.50
Year 5: 1005.68
Year 6: 1055.96
Year 7: 1108.76
Year 8: 1164.20
Year 9: 1222.41
Year 10: 1283.53

Step 2--Determine a Discount Rate

Because we're using the "free cash flow to equity" method of DCF, we can ignore Charlie's cost of debt and WACC in coming up with a discount rate. Instead, we'll focus on coming up with an assumed cost of equity, using the principles highlighted in the previous lesson.

Charlie's has been in business for more than 60 years, and it has not had an unprofitable year in decades. Its brand is well-known and respected, and this translates into very respectable returns on its invested capital. Given this and the relatively stable outlook for Charlie's profits, settling for a 9% cost of equity (lower than average) seems appropriate given the modest risks Charlie's faces.

Step 3--Discount Projected Free Cash Flows to Present

The next step is to discount each of the individual year's cash flows to express them in terms of today's dollars. Remember we are using the following formula, and the "discount factor" just represents the denominator in the equation. We can then multiply each year's cash flow by the discount factor to get the present value of each cash flow.

Present Value of Cash Flow in Year N =
CF at Year N / (1 + R)^N

CF = Cash Flow
R = Required Return (Discount Rate), in this case 9%
N = Number of Years in the Future

Last Year: $500.00
Year 1: 575.00 x (1 / 1.09^1) = 528
Year 2: 661.25 x (1 / 1.09^2) = 557
Year 3: 760.44 x (1 / 1.09^3) = 587
Year 4: 874.50 x (1 / 1.09^4) = 620
Year 5: 1005.68 x (1 / 1.09^5) = 654
Year 6: 1055.96 x (1 / 1.09^6) = 630
Year 7: 1108.76 x (1 / 1.09^7) = 607
Year 8: 1164.20 x (1 / 1.09^8) = 584
Year 9: 1222.41 x (1 / 1.09^9) = 563
Year 10: 1283.53 x (1 / 1.09^10) = 542

We then add up all the discounted cash flows from Years 1 through 10, and come up with a value of $5,870 million ($5.87 billion).

Step 4--Calculate Discounted Perpetuity Value

In this step, we use another formula from the last lesson:

Perpetuity Value =
( CFn x (1+ g) ) / (R - g)

CFn = Cash Flow in the Last Individual Year Estimated, in this case Year 10 cash flow
g = Long-Term Growth Rate
R = Discount Rate, or Cost of Capital, in this case cost of equity

For example, we'll use use 3% as the perpetuity growth rate, which is close to the historical average growth rate of the U.S. economy. So, we'll assume that after 10 years, Charlie's Bicycles will also grow at this 3% rate. Plugging the numbers into the formula:

( $1,284 x (1 + .03) ) / (.09 - .03) = $22,042 million

Notice that for the cash flow figure we used the undiscounted Year 10 cash flow, not the discounted $542 million. But because we used the undiscounted amount, we still need to express the perpetuity value in present-value terms using this trusty formula:

Present Value of Cash Flow in Year N =
CF at Year N / (1 + R)^N

Present Value of Perpetuity Value =
$22,042 million / (1 + .09)^10 = $9,311 million

Step 5--Add It All Up

Now that we have the value of all the cash flows from Year 1 through 10 as well as those from Year 11 on, we add up these two values:

Discounted Free Cash Flow, Years 1-10: $5,870 million
+ Discounted Free Cash Flow, Years 11 on: $9,311 million

which equals $15,181 million.

So there we have it! We have estimated Charlie's Bicycles to be worth $15.2 billion. The final, simple step is to divide this $15.2 billion value by the number of shares Charlie's Bicycles has outstanding. If Charlie's has 100 million shares outstanding, then our estimate of Charlie's intrinsic value is $152 per share.

If Charlie's stock is trading at $100 per share, you should start to get interested in buying the shares. We can forget about what Charlie's P/E ratio is relative to its peers as well as what Wall Street analysts have recently said about the stock. The bottom line is the stock is trading below its estimated intrinsic value. If you have confidence in your free cash flow projections, you can have an equal amount of confidence in buying the stock.

The Bottom Line

As you may tell, this is merely a simple example of how to use a DCF model, but it's still not exactly "simple." Not many people put this much work into their investments. But if you're willing to go through the effort of creating a DCF model for a company you are interested in, you will be much more informed and confident than the vast majority of other investors.

There are numerous small twists that the other type of DCF model (cash flow to the firm) uses, but the output should be approximately the same no matter which DCF method you use for a given firm. Also keep in mind that a model does not need to be super-complex to get you most of the way there and help you clarify your thinking. Remember, using a similar DCF model can take you a long way in finding superior companies trading at a discount to their intrinsic value--the key to a profitable long-term investing strategy.