**Welcome to our**Value Investing 101**series. In**Part 1**, I explained what the “intrinsic value” of a stock is and in**Part 2**, I explained how to determine Free Cash Flow. In Part 3, I am running through an example with a real company.****Discounted Cash Flow Analysis**

**The Present Value Equation**

Do you remember the Present Value formula? If not, here it is again:

In the PV equation we take a future cash flow and divide it by 1 plus the discount rate, taken to the power of n (where n is the number of periods).

For example, let’s say we are going to receive $25 next year and our discount rate is 15%. How much is that future $25 worth to us today? Answer: $22.75.

Now what if we receive the $25 in *two years* instead of next year? Answer: $18.90.

As you can see, the $25 received in two years is worth less to us today than the $25 received next year.

Now let’s say we’re going to receive $25 for the next 10 years (and let’s keep the same 15% discount rate). What is the total value to us today? Answer: $125.47.

So, in order to get a 15% return on a cash flow of $25 per year, you would need to pay $125.47 today.

**Discounted Cash Flow**

Now that you’re an expert on calculating present values, we can easily run a DCF analysis to value a stock.

First we must project the company’s future cash flows. If you need a refresher on Free Cash Flow and Owner’s earnings, then please check back at Part 2.

These are the inputs you need to calculate the intrinsic value of a stock:

**Free Cash Flow**(found in the cash flow statement)**Shares Outstanding**(found in the income statement)**Terminal Value**(multiplier determined by the investor)**Discount Rate**(rate of return)**Margin of Safety**(a percentage subtracted from the calculated value)**Growth Rate**(value determined by the investor)

**Example: AAPL**

Now, lets use Apple (AAPL) as an example. All you need to do is fill in the appropriate fields. You can find most of this information for free at sites like Quick FS.

So, according to our research, AAPL currently has $73,365 million in Free Cash Flow and has 17,257 million in shares outstanding (we’ll get to terminal value later).

The Discount Rate is essentially your rate of return, since you are discounting the cash flows to the return you desire. This input is up to the investor of course, but I normally default to 15%.

The Margin of Safety is simply a percentage off of the intrinsic value calculation. You can set this to whatever you desire, but a greater margin of safety lowers your risk. This input is also up to the investor, but I generally go with 10% to 15%. We will discuss this later on as well.

Lastly, we have the Growth Rates. This is simply the calculation that you think the Free Cash Flow will compound per year. Since companies rarely grow at an exact rate year after year, it is best to break it down into years 1-5 and 6-10 with different rates for each period.

But how do you determine a growth rate? This is a very subjective number, as each investor will probably come up with different growth rates depending on their individual analysis. To keep things simple for this example, let’s assume that AAPL will continue to grow its cash flow at a rate of 10% per year for the next five years, then slow down to 6% per year for the following five years.

After we come up with all the numbers, we plug them into our calculation. Here’s the result:

As you can see, the calculator discounted the present values of all the future cash flows. You’ll notice that with each passing year the values get smaller and smaller. This is due to the time value of money. I have written an entire article about it, so go check it out if you are not familiar with this concept. In a nutshell, money is more valuable today than it is tomorrow. Therefore, an investor can pay a lesser amount today to receive more tomorrow.

Now, all we have to do is add up all of our present values and divide them by the number of shares outstanding.

According to our calculations, our intrinsic value of AAPL is $32.06 per share. If you were to look up the share price today, you would see that AAPL is currently trading at $120.89! What’s wrong with our calculation? Did we mess up?

**Terminal Value**

Here’s where we can get into Terminal Value, and why it is so important. Projecting the cash flows of a business for 10 years is hard enough, but most businesses last much longer than that. So how do we account for those years?

Think of terminal value as the entire rest of the business’s future cash flows. There are multiple ways to calculate this, but I find the terminal multiple to be the easiest method. Basically, we are multiplying the year 10’s cash flows and discounting by our discount rate. My default multiplier is usually 10x.

Another way to think of the terminal value is if the business was sold at year 10 for a multiple of its cash flows. To do this, you could determine the multiplier based on the company’s historical Price to Free Cash Flow. This number is easy to calculate on your own, but in order to quickly view a historical perspective, a platform like Stock Rover makes it really easy to do. Here is AAPL’s historical P/FCF ratio:

AAPL’s current P/FCF is currently over 28, which is a 10-year high. This is a relatively high multiple for any company, not just AAPL. However, when the company was trading at more reasonable valuations, the P/FCF ratio hovered between 10 – 15. For our example, let’s split the difference and go with a terminal multiple of 12. Plug it into our DCF calculation, and let’s see what AAPL’s intrinsic value is now:

By plugging in the terminal value, we can now see that the sum of the present values ballooned, as did the intrinsic value price, which is now $59.24 per share. That was almost double the intrinsic value of our previous calculation!

This is why terminal value is so important. Too large of a number can really inflate the intrinsic value of your calculations. The same goes for growth rates as well. In order to combat over calculating and inflating your intrinsic values, be sure to use conservative growth rates and terminal multiples.

**Margin of Safety**

Lastly, we come to the Margin of Safety. I also have written more about this topic, but to summarize, in order for an investor to reduce their risk, they should buy a stock at a price that trades below its intrinsic value. That means we should still look to buy AAPL at an even lower price than we have calculated.

So what should that amount be? Again, this is another personal decision by each investor. Sometimes a margin of safety for a stock may not be price, but the strength in its business operations. In this example, AAPL is the largest company in the world by market capitalization and therefore is highly unlikely to go bankrupt anytime soon.

Taking this into account, let’s assume a modest margin of safety discount of 10%. This 10% is simply a percentage knocked off of the intrinsic value calculator that we already made. Think of this as a sale at a store that has reduced the price of your favorite T-shirt by 10%. Now here is our final buy price:

And there you have it, we have finally calculated our buy price for AAPL for a total of $53.31! Now, AAPL is currently trading far above this value and would therefore be considered to be quite overvalued. However, now you know what this business is really worth to you as an investor. You can simply set this value on your watch list and wait for a buying opportunity.

**Summary**

There you have it! Now you know how to run a Discounted Cash Flow analysis to determine the intrinsic value of a stock. There are many other ways that investors use to calculate intrinsic value, but this is the most basic method. Just because it may be the most basic, does not mean that is not valid. Quite the contrary; I am a firm believer that in investing, simpler methods are better that over complicated ones.

The DCF valuation method is a great way to help an investor establish a baseline intrinsic value for a stock. By using this method, you can know whether or not you a stock is overvalued or undervalued.

Thanks for putting in the time to write these articles and adding your knowledge to the collective interwebs!

Reading through the Letters to Shareholders now and your definition of intrinsic value was incredibly insightful.

All the best

great articles! where is part 4?

great articles! where is part 4?

Thanks Vin! Part 4 has been on my to-do list for a while – I’ve just never gotten around to it. But I’ll try to have it done soon!