We review the *intuition* behind the Gordon Growth Formula used to calculate Terminal Value in a Discounted Cash Flow (DCF) analysis.
By http://breakingintowallstreet.com/ "Financial Modeling Training And Career Resources For Aspiring Investment Bankers"
Lots of people, textbooks, training programs, professors, and so on present this formula, but hardly anyone takes the time to explain what it means, where it comes from, and how it works.
We'll explain here both the INTUITION behind the formula, and
then also give a mathematical derivation for it, based on the
sum of a geometric series.
If you like math, you'll really like that part!
Here's the Table of Contents for the lesson:
1:12 Gordon Growth Method Intuition
2:37 The Intuition -- No Growth in Cash Flows
7:46 The Intuition -- Growth in Cash Flows
15:23 The Algebra Behind Gordon Growth
17:40 The Common Ratio
18:41 The Algebra: Putting It All Together
22:49 Gordon Growth Method Summary
Gordon Growth Method Intuition
The basic intuition here is that we can pay:
Annual Free Cash Flow / Discount Rate
For an investment, if the cash flow stays the same
each year and we're targeting a specific yield on
our investment (known as the "discount rate" in a DCF).
Think about if you could make an investment that earned
$100 in cash flows each year.
You're targeting a 10% yield on your investment.
How much could you pay for it?
$1,000, because $1,000 * 10% = $100 in cash flows each year.
You can use the NPV function in Excel with $100 in cash flow
each year (e.g., =NPV(10%, Long series of $100 you've entered in
consecutive cells)) to verify this.
The NPV, or "net present value," IS this number - what we could
afford to pay for a series of cash flows at a given yield we're
The Intuition -- Growth in Cash Flows
This works fine if there's no growth and the cash flows stay
the same each year, but what if they're growing?
Well, in that case we can afford to pay MORE than that $1,000 and
still get the same 10% yield... because there's growth!
Specifically, we can now pay:
First Year Free Cash Flow / (Discount Rate - FCF Growth Rate)
for this investment.
In the Terminal Value calculation, that "First Year Free Cash Flow" is written
as Final Year Projected Free Cash Flow * (1 + FCF Growth Rate)...
...because we're going one year BEYOND the end of our projection period in
By *subtracting* the growth rate in the denominator, we make the
denominator smaller... which makes the amount we can pay significantly
If cash flows grow more quickly, the denominator gets even smaller and
the entire number gets even bigger.
If cash flows grow more slowly, the denominator gets bigger and the entire
number gets smaller.
Let's say the cash flows start at $100 and grow by 3% per year.
We're targeting a discount rate of 10%.
The NPV here would be $1,429, or $100 / (10% - 3%).
Why does this work?
Why can we pay $1,429 and still get that 10% yield?
Think about it like this...
The yield in Year 1 is is $100 / $1429, or 7.0%
But then by Year 5, it's $113 / $1429, or 7.9%.
And then as you keep going, the Yield gets higher and higher...
because we have growth.
By Year 20, it's $175 / $1429, or 12.3%.
So, over all those years into the future, the average comes out
to 10%... because it's LESS than 10% in the early years and greater
than 10% much later on.
So the weighted average, factoring in the time value of money, still
comes out to that 10% yield we were targeting.
The Algebra Behind Gordon Growth
Please see the video for this part - it's almost impossible to explain
in text form, and it would be too long to post in the YouTube description.
Gordon Growth Method Summary
We care about this because everyone uses this formula to calculate
Terminal Value in a DCF, but hardly anyone explains where it comes from.
The basic idea is that you can pay more for a company that's growing its
cash flows than for one that's NOT growing its cash flows.
And to represent that, you use the formula:
Final Year, Projected Period Free Cash Flow * (1 + FCF Growth Rate) / (Discount Rate - FCF Growth Rate)
To approximate the amount you could pay for the Free Cash Flows in
the Terminal Period - which is the Terminal Value in a DCF.