Welcome to our Value Investing 101 series. In Part 1, I explained what the “intrinsic value” of a stock is. Now, I’ll explain the math we’re going to need to calculate intrinsic value. Be sure to also check out Part 3.
First, a Quick Review of Intrinsic Value
Two weeks ago I explained what the intrinsic value of a stock is. So pop quiz… what is intrinsic value?
As Warren Buffett describes it, intrinsic value is simply the discounted value of a business’s future cash flows.
In other words: A business generates cash every year, every month, every day. This cash ultimately belongs to the owners of the business. Now if you could add up all of the cash that a business will ever generate – while giving less weight to cash received in the future compared to cash received today (i.e. discounting) – then you could determine the intrinsic value of a business.
This is the same way that bonds are valued. Except there are many more variables that affect a stock’s cash flows, which are of course not guaranteed. This is why stock valuation is often referred to as an art as well as a science.
Now for the math.
In Part 1 I went over the Dividend Discount Model (also called the Gordon Growth Model):
The Dividend Discount Model is a great concept, but it’s just too simple to be of any practical use. We need some real math for that. So get out your calculators and load up your Excel.
It’s valuation time.
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 divided 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 11%. How much is that future $25 worth to us today? Answer: $25.52.
Now what if we receive the $25 in two years instead of next year? Answer: $20.29.
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 next year and $25 in two years (and let’s keep the same 11% discount rate). What is the total value to us today? Answer: $42.81.
You can calculate Present Value in excel with this function:
For the second example above, this would be =PV(.11,2,0,-25). *Note that PV and FV must have opposite signs (one must be a cash inflow and one must be a cash outflow).
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 (I realize that you might be wondering, “Mr. Vintage Value, what the heck is a cash flow anyways, let alone how do I project it?” I will cover that exact topic – FCF and Owner Earnings – in Part 3. For now I just want to cover the math so you have a good basis for Part 3).
A common projection period is 10 years.
Let’s say the company’s cash flow (FCF or Owner Earnings – again…stay tuned for Part 3) for this year was $25 and we believe the company will be able to increase its cash flow by 10% a year for the next 5 years and 5% a year for the following 5 years. Let’s use the same 11% discount rate.
This is easiest to do in excel and would look something like this:
We’re not finished yet though! Did you notice what we’re missing?
This projection only provides for 10 years, but companies last into perpetuity (one assumes), cash flowing all the while.
Instead of extending our projection period out for n = eternity, we can instead calculate what’s called the terminal value.
Remember the Dividend Discount Model a.k.a. the Gordon Growth Model from earlier? Let’s put it to some practical use now.
After Year 10, let’s now assume that the company’s cash flows will continue to grow at a constant rate of 2% per year (approximately the rate of inflation in the U.S.) forever thereafter. The equation to calculate the terminal value for a 10-year projection would look this, where g is that constant rate of growth into perpetuity.
This gives us the terminal value in Year 10, which we’d then have to discount back to the present value for today.
So now, our complete Discounted Cash Flow analysis in excel looks like this:
As you can see, 52% of this company’s present value is derived from the cash flows we’ve projected through the first 10 years, and 48% is derived from the terminal value. Consequently, it’s important to be very careful when you determine the terminal growth rate, because a small change can have a great effect on the ultimate intrinsic value. Be conservative!
In this example, the intrinsic value of this company is $428.20.
Your next step would be to divide the intrinsic value of the company by the total number of shares outstanding to find the intrinsic value of one share of stock.
So if there are 100 shares outstanding, the intrinsic value of the stock would be $4.28.
We could then apply a 25% margin of safety to our calculations and decide that if the stock was trading for $3.21 a share or less ($4.28 x 75%) then we would buy it.
There you have it! Now you know how to run a Discounted Cash Flow analysis to determine the intrinsic value of a stock.
But we’re stilling missing some key points like:
- What exactly is a company’s “cash flow”?
- How do I determine the discount rate?
- How can I accurately project a company’s cash flow?
- What are the disadvantages of calculating intrinsic value using a DCF analysis?
Well don’t worry, because I have you covered! Next up in Part 3, I cover what “cash flow” actually is and how to accurately project it to calculate intrinsic value.
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