CAGR Calculator

What is CAGR?

CAGR, or Compound Annual Growth Rate, is a metric used to measure the annual growth rate of an investment, a company's sales, or any value that changes over time. It represents the steady percentage rate at which something would need to grow each year to go from its initial value to its final value over a specific period, assuming the growth compounds annually.

In simpler terms, CAGR smooths out the growth over multiple years into a single average annual rate. It's widely used in finance and business to compare the performance of investments or to assess how quickly a company is growing.

How Does CAGR Work?

Imagine you invest some money, and over a few years, it increases in value. CAGR tells you the consistent yearly growth rate that would take you from your starting amount (the beginning value) to your final amount (the ending value) over that time period. The key idea is compounding, meaning the growth builds on itself each year - like earning interest on interest.

For example:
• You invest $100, and after 3 years, it's worth $133.10.
• CAGR calculates the annual growth rate that turns $100 into $133.10 over those 3 years.

The CAGR Formula

The formula for CAGR is:

CAGR = ( Ending Value / Beginning Value ) ^ (1 / Number of Years) - 1

Here's what each part means:
• Ending Value: The value at the end of the period (e.g., $133.10).
• Beginning Value: The value at the start (e.g., $100).
• Number of Years: The time period in years (e.g., 3).

Example Calculation

Apply the formula to the example above:
1. Divide the ending value by the beginning value:
133.10 / 100 = 1.331

2. Raise that result to the power of 1 divided by the number of years (in this case, 1/3):
(1.331) ^ (1/3) ˜ 1.1
(Because 1.1 x 1.1 x 1.1 = 1.331, approximately.)

3. Subtract 1 to get the growth rate:
1.1 - 1 = 0.1 = 10%

So, the CAGR is 10%. This means your investment grew at an average rate of 10% per year, compounded annually.

Verifying the Calculation

Let's check if 10% annual growth makes sense:
Year 0: Start with $100.
Year 1: $100 x 1.10 = $110.
Year 2: $110 x 1.10 = $121.
Year 3: $121 x 1.10 = $133.10.

The result matches the ending value, confirming that a 10% CAGR is correct.

Why is CAGR Useful?

CAGR is a powerful tool because it:
Simplifies Growth: It condenses multi-year growth into one easy-to-understand number.
Enables Comparisons: You can compare the growth rates of different investments or businesses, even if they span different time periods or start with different amounts.

For example:
Investment A: Grows from $100 to $200 in 5 years.
CAGR = (200 / 100) ^ (1/5) - 1 = 2 ^ 0.2 - 1 ˜ 14.87%

Investment B: Grows from $50 to $150 in 3 years.
CAGR = (150 / 50) ^ (1/3) - 1 = 3 ^ (1/3) - 1 ˜ 44.22%

Investment B has a higher CAGR (44.22% vs. 14.87%), meaning it grew faster annually, despite the shorter time period and different starting value.

Limitations of CAGR

While CAGR is helpful, it has some caveats:

1. Assumes Steady Growth: CAGR smooths out growth into a constant rate, but in reality, growth can be uneven (e.g., up one year, down the next).
2. Ignores Risk: Two investments might have the same CAGR, but one could be much riskier or more volatile.
3. Best for Longer Periods: CAGR is most meaningful over multiple years, as compounding matters more over time.

For instance, if an investment grows from £100 to £132 over 2 years:
Year 1: +10% ? £110.
Year 2: +20% ? £132.

CAGR = (132 / 100) ^ (1/2) - 1 ˜ 14.89%

The CAGR (14.89%) is less than the arithmetic average of 10% and 20% (15%), because it reflects compounding, not simple averaging.

Summary

CAGR is the Compound Annual Growth Rate, a way to measure how much something grows annually, assuming steady, compounded growth. It's calculated using:

CAGR = ( Ending Value / Beginning Value ) ^ (1 / Number of Years) - 1

It's a handy tool for understanding and comparing growth over time, but it simplifies reality by assuming consistency and doesn't account for volatility. Whether you're evaluating an investment or a company's performance, CAGR gives you a clear, annualized snapshot of growth.