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How to Calculate Cagr When One Number Is Negative

Reviewed by Calculator Editorial Team

Compound Annual Growth Rate (CAGR) is a valuable metric for measuring investment performance over time. However, when one of the values in your calculation is negative, the standard formula requires special handling. This guide explains how to calculate CAGR with negative values, including formulas, examples, and a calculator.

What is CAGR?

Compound Annual Growth Rate (CAGR) measures the mean annual growth rate of an investment over a specified period. It accounts for the compounding effect of reinvested earnings, providing a more accurate picture of long-term growth than simple annual percentage growth.

CAGR is calculated using the formula:

CAGR = [(Ending Value / Beginning Value)^(1/n)] - 1

Where:

  • Ending Value = the value of the investment at the end of the period
  • Beginning Value = the value of the investment at the start of the period
  • n = number of years in the period

Calculating CAGR

The standard CAGR formula works when both the beginning and ending values are positive. However, when one of these values is negative, the calculation requires special attention to ensure the result is mathematically valid and meaningful.

When the beginning value is negative and the ending value is positive, the investment has gone from a loss to a profit. This is a common scenario in financial analysis.

When both values are negative, the investment has continued to decline. In this case, the CAGR will be negative, indicating ongoing losses.

Handling Negative Values

To calculate CAGR with negative values:

  1. Identify the beginning and ending values
  2. Calculate the ratio of ending to beginning value
  3. Take the nth root of this ratio (where n is the number of years)
  4. Subtract 1 to get the growth rate

Important: The CAGR formula assumes that the investment is compounded annually. If your investment is compounded more frequently, you'll need to adjust the formula accordingly.

When dealing with negative values, it's important to consider the context. A negative CAGR indicates declining value, while a positive CAGR indicates growth. The magnitude of the CAGR shows how quickly the value is changing.

Worked Example

Let's calculate CAGR for an investment that starts at -$10,000 and grows to $15,000 over 5 years.

CAGR = [($15,000 / -$10,000)^(1/5)] - 1

Step 1: Calculate the ratio

$15,000 / -$10,000 = -1.5

Step 2: Take the 5th root

(-1.5)^(1/5) ≈ -1.088

Step 3: Subtract 1

CAGR ≈ -1.088 - 1 = -2.088 or -208.8%

This result shows the investment is declining at an annual rate of approximately 208.8%.

FAQ

Can CAGR be negative?

Yes, CAGR can be negative when the investment's value declines over time. This indicates ongoing losses rather than growth.

What does a negative CAGR mean?

A negative CAGR means the investment is declining at the calculated annual rate. For example, a -20% CAGR means the investment loses 20% of its value each year.

How does compounding affect CAGR with negative values?

Compounding with negative values means the losses compound each year, making the decline more severe than simple annual percentage declines.