Get a cup of coffee.

(Or, as the wise @JohnLegere says, get many cups of coffee!)

In this thread, I'll show you how to do CAGR calculations.

For those unfamiliar, CAGR = Compounded Annual Growth Rate. It's also called IRR (Internal Rate of Return).

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Well, your initial investment was $75,888 (100 shares times $758.88 per share).

That $75,888 has now grown to $151,555 (100 shares times $1,515.55 per share).

This growth has happened between 2015-Dec-31 and 2020-Jul-17 -- a period of 1,660 days.

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Essentially, what this 16.43% CAGR means is:

Suppose you found a bank that paid 16.43% interest annually.

And suppose you deposited $75,888 into that bank on 2015-Dec-31.

Then, your money would have grown to $151,555 by 2020-Jul-17 -- same as your $GOOG investment.

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But you don't usually just buy a stock once and hold on forever.

You add to your position over time. Sometimes, you trim your position.

How do you calculate your CAGR in such cases?

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Going back to the bank analogy: every cash *outflow* is like a *deposit* you make into a hypothetical bank account that's compounding your money.

And similarly, every cash *inflow* is like a withdrawal you make from the same bank account.

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Imagine what would happen if you actually made these deposits and withdrawals.

Each deposit will give you a "benefit" that compounds over time, and each withdrawal will negate some of the benefit created by the deposits.

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For example, buying 100 shares of $GOOG on 2015-Dec-31 gives you the benefit of $75,888 compounding for 1,660 days.

And selling 70 shares on 2018-Jul-27 erases the benefit of $86,695 compounding for 721 days.

This all follows from the "cash flow timeline" above.

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All that remains is to solve this equation to find R (our CAGR).

But this equation is *not* like the earlier equation we solved.

In the earlier equation, we could just rearrange the terms to solve for R.

But here, that's not possible. We need more powerful techniques.

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There's also another way to solve the CAGR equation.

You start with a "guess" for R.

Say, R = 10%.

If R was really 10%, what would your end balance (on 2020-Jul-17) be after the compounding effect of all the deposits and withdrawals?

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Easy. This is just your LHS evaluated at R = 10%. In this case, it works out to $32,808.

This is *lower* than your real end balance: $121,244 (the RHS).

So your CAGR has got to be better than 10%.

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OK. Let's try 20% then.

Now, the LHS works out to $128,209.67.

This is *higher* than your end balance of $121,244.

So your CAGR can't possibly be as high as 20%.

That means your CAGR lies somewhere between 10% and 20%.

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OK. What about 15%?

Turns out the LHS for R = 15% is only about $97,534 -- also *lower* than your end balance.

So your CAGR has to be higher than 15% but lower than 20%.

Carrying on this way, you can narrow down your CAGR into a very tight range.

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This is called "the bisection method" of solving the CAGR equation.

You start with a CAGR guess. At the beginning, this guess may be wide off the mark. But you keep iterating and improving upon it. Pretty soon, you're really close to the right answer.

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Dividends can complicate the picture a little. But don't worry: the principle is the same.

Just treat each dividend as a cash inflow on its pay date. Add these inflows to the cash flow timeline. Then use the same procedure (graphical or bisection) to calculate CAGR.

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CAGR is a key metric we investors use to judge the performance of individual investments, portfolios, funds, and even fellow investors.

It's super important to know how to calculate CAGRs correctly. I hope this thread helps.

Thanks for reading. Enjoy your weekend!

/End

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