Understanding and Calculating CAGR Using Different Methods

Introduction

The Compound Annual Growth Rate (CAGR) is a useful measure to determine the mean annual growth rate of an investment over a specified period, assuming the profits were reinvested at the end of each year. It provides a clear picture of an investment’s performance over time. Various methods can be used to calculate CAGR, including Excel's IRR, XIRR, TVM functions, and a standard mathematical formula.

Simple CAGR Calculation Example

Let’s assume you invested $10,000 in a portfolio on January 1, 2005. Over time, the investment grew as follows:

• $13,000 by January 1, 2006

• $14,000 by January 1, 2007

• $19,500 by January 1, 2008

If you liquidate your investment on January 1, 2008, the CAGR can be calculated using the following methods:

1) Excel IRR Method

• Define the cash flows, with negative values for outflows (initial investment) and positive values for inflows (returns).

• Ignore intermediate portfolio growth that does not contribute to cash flow; zeros should be explicitly stated where applicable.

• Use the IRR function for the selected range: =IRR(B4:B7).

2) Excel XIRR Method

• Define the cash flows, with the same convention of negative for outflows and positive for inflows.

• Assign transaction dates to each cash flow.

• Use the XIRR function to calculate the internal rate of return based on specific transaction dates: =XIRR(B12:B13,A12:A13).

3) Excel TVM (Time Value of Money) Method

• Use the RATE function with the formula:

  =RATE(n, pmt, PV, FV, mode)

  Where:

  • n = number of years

  • pmt = periodic payment (if applicable)

  • PV = present value (initial investment)

  • FV = future value (final value of investment)

  • mode = 0 or 1 (payment timing)

4) Mathematical Formula Method

• The CAGR formula:

  CAGR = (FV / PV)^(1/n) - 1

  Where:

  • FV = final value

  • PV = initial investment

  • n = number of years

Real-Life CAGR Calculation

In reality, investments involve multiple transactions, such as:

• Initial investment

• Additional top-up investments

• Dividend payouts

• Bonus issues

• Partial or full liquidation

Since these transactions occur at different times, the XIRR function in Excel is the most versatile method for computing CAGR. It considers the timing of cash flows, making it more precise for real-world applications.

Conclusion

Understanding CAGR is crucial for evaluating investment performance over time. While the mathematical formula provides a quick approximation, Excel’s IRR, XIRR, and TVM functions offer more flexibility for various scenarios. For real-life investment tracking, XIRR is the most reliable method as it accounts for irregular cash flows.