Question

Determine the cumulative compound growth rate (CGR) for the design traffic.

Answer 1

Compound annual growth rate (CAGR) is the rate of return that would be required for an investment to grow from its beginning balance to its ending balance, assuming the profits were reinvested at the end of each year of the investment’s lifespan.

CORPORATE FINANCE & ACCOUNTING  FINANCIAL RATIOS

Compound Annual Growth Rate – CAGR

By CHRIS B. MURPHY

Reviewed By JULIUS MANSA

Updated Jul 23, 2020

TABLE OF CONTENTS

EXPAND

• Compound Annual Growth Rate

• Formula and Calculation of CAGR

• What CAGR Can Tell You

• Example of How to Use CAGR

• Additional CGAR Uses

• Investor Use of CAGR

• Modifying the CAGR Formula

• Smooth Rate of Growth Limitation

• Other CAGR Limitations

• CAGR vs. IRR

• Example of How to Use CAGR

What Is Compound Annual Growth Rate – CAGR?

Compound annual growth rate (CAGR) is the rate of return that would be required for an investment to grow from its beginning balance to its ending balance, assuming the profits were reinvested at the end of each year of the investment’s lifespan.

Formula and Calculation of CAGR

​​​​To calculate the CAGR of an investment:

Formula and Calculation of CAGR 1 EV n CAGR - (EV BV where: EV = Ending value BV = Beginning value Number of n = years

1. Divide the value of an investment at the end of the period by its value at the beginning of that period.
2. Raise the result to an exponent of one divided by the number of years.
3. Subtract one from the subsequent result.

Example to Use CAGR

Imagine total increment in traffic is 10,000 with the following manner:

• From Jan 1, 2014, to Jan 1, 2015, grow in traffic 13,000 (or 30% in year one).
• On Jan 1, 2016, grow in traffic14,000 (or 7.69% from Jan 2015 to Jan 2016).
• On Jan 1, 2017,grow in traffic 19,000 (or 35.71% from Jan 2016 to Jan 2017).

We can see that on an annual basis, the year-to-year growth rates are quite different as shown in the parenthesis.

On the other hand, the compound annual growth rate smooths the investment’s performance and ignores the fact that 2014 and 2016 were so different from 2015. The CAGR over that period was 23.86% and can be calculated as follows:

CAGR=(19,000/10,000)^{frac{1/3}}-1=23.86%

The compound annual growth rate of 23.86% over the three-year period can help to compare alternatives for traffic or make forecasts of future values.