Numerator–denominator play (the quest's thesis)

The whole quest in one picture

This lesson is the heart of the whole quest. If you only remember one thing from this entire syllabus, remember what's in this lesson.

Here is the picture: a fraction.

Some quantity P equals A over B. Two quantities. One on top (the numerator). One on bottom (the denominator). That's it.

Now the question. How many ways are there to make P bigger?

Stop. Think.

Answer: exactly two. Either A goes up, or B goes down. Or both at once. There's no third path.

To make P smaller? Same two paths in reverse. A goes down, or B goes up. Or both.

That is finance.

The Gordon Growth Model — same picture, longer names

One of the most important valuation equations in finance looks like this:

Where:

• P — price of the company (or stock)
• FCF — free cash flow (the cash the business actually generates)
• r — discount rate (basically the prevailing interest rate environment)
• g — growth rate (how fast the cash flow is growing)

Don't worry about exactly what each one is yet — Tracks 4–6 cover them. Just look at the shape. It's A / B. Numerator is FCF. Denominator is r - g. That's the entire equation.

So how many ways can the price P go up?

1. FCF goes up — the company makes more cash. (Numerator up.)
2. r goes down — interest rates fall. (Denominator down.)
3. g goes up — growth expectations rise. (Denominator down.)

Three drivers. Three. That's it. Every news headline you've ever read about a stock going up — any stock — is one of these three things, or some combination.

Real cases — the same equation, two different stocks

NVDA pulling back even after a great quarter. Earnings beat expectations. FCF went up. Numerator: ✓. So why did the stock drop on the news? Because the market's expected g was so high that even a big beat didn't keep up. Denominator (r - g) got slightly bigger because g came down a touch. Numerator went up, but the denominator got bigger by more. Net: P down.

Adobe falling 30% in 2024. The fundamentals weren't catastrophic. Earnings were okay. So why the carnage? Because the market started believing AI tools would eat Adobe's lunch — that g wasn't slowing, it was going to zero or negative. The denominator (r - g) shot up (because g is being subtracted, smaller g means bigger denominator). The numerator barely changed. Bigger denominator, same numerator → smaller P. The crash had a math reason.

Two stocks, two stories, same equation, same picture. Numerator–denominator play.

Why most people miss this

Most finance education starts with the equation and tries to teach you what r is, what g is, where FCF comes from. By the time you've waded through that, the simple picture (A / B, two ways up, two ways down) is buried under jargon. You learn the trees, never see the forest.

The thing that took me a while to land on is this: the trees are easier to learn once you've already seen the forest. So we're doing it backwards. Forest first. Trees later.

Whatever investing philosophy you decide to follow eventually — value, growth, indexing, contrarian, anything — every one of them is making a bet on the numerator, the denominator, or both. This is the floor everyone shares, even if no one talks about it that way.

The takeaway

Finance is numerator–denominator play. One picture, three drivers. The rest of this quest is filling in what those drivers actually are and how they move. But the shape — A / B — never changes.