CAGR

If Buyer 1 bought a condo unit in 2017 for Php10 Mn and sold it for Php20 Mn in 2022, he earned 100% in 5 years.

If Buyer 2 bought a condo unit in 2012 for Php10 Mn and sold it for Php20 Mn in 2022, he also doubled his money.

Both examples exhibit huge wins. But is one better than the other? How can we measure?

This is where the Compounded Annual Growth Rate (or CAGR) is applicable. It's a formula that coughs up a percentage you can use to compare investments (e.g., bonds, stocks, real estate).

Averaging the gain based on the number of years doesn't work. In the first example, it's wrong to say that Buyer 1 earned 20% per year (100% / 5 years = 20%).

CAGR's formula is:

= ( new price / old price ) ^ ( 1 / n ) -1

where

n = number of years

(or see the photo posted above). The ^ is called a "circumflex" or, more popularly, "raise to the."

Let's use Buyer 1's example.

New Price = 20 Mn

Old Price = 10 Mn

n = 5 years

So plug everything in

= ( 20,000,000 / 10,000,000 ) ^ (1/5) -1

You can try this in Excel (or on Mac Computer's spotlight search field; type it without the equals sign).

The answer should be 0.1487 or 14.87%

Simply put, he earned 14.87% on an annual basis. Try checking it:

= 10 Mn x (1+0.1487) * (1+0.1487) * (1+0.1487) * (1+0.1487) * (1+0.1487)

= 20 Mn (the answer might be a bit off because of rounding)

Now try it out for Buyer 2. The plug-ins are the same as Buyer 1 except for "n."

You should get 7.1773%. And as the numbers point out, Buyer 1 was the better investor since he has an annualized percentage return of 14.87%.

Why is this important?

With the CAGR, you'll be able to know then whether that condo you bought was a better investment than, say, the stock market. It allows investors to make more informed decisions. It's an essential metric for anyone looking to grow their money long-term.

Here are some exercises.

Answers are in the comments section.