The compound annual growth rate and the internal rate of return are both commonly used types of rates of return.

Individual investors and businesses can use these two metrics to compare different investment options. Both of these metrics offer different perspectives and can be used in different situations.

Let us discuss what are CAGR and IRR and their key differences.

## What is Compound Annual Growth Rate?

The compound annual growth rate is a rate of return that shows how an investment would grow from the beginning date to the ending date if all of its profits were reinvested at the same rate.

CAGR is not an actual rate of return as it is unlikely in practice. Most investment returns fluctuate over the years and offer fluctuating returns.

The CAGR is a single rate of return that offers a smooth (or even) rate over the total span of investment. It is a hypothetical rate that gives an idea to investors of what could have been achieved if they reinvested all profits at the same rate.

## How to Calculate CAGR?

The formula for calculating CAGR is:

**CAGR=[(EV/BV) ^{1/n} − 1]×100**

EV = Ending value of investment

BV= Beginning Value of Investment

And n = number of years for investment

The CAGR formula uses only three input values. When you know the beginning and ending investment values, you can put them into the formula for the span of investment to get the CAGR.

In some cases, the beginning and ending years of the investment are not full years. You can convert these broken years into number of days and then add the rest of the years (converted into days) as well.

Then, you can divide the result by 365 to get the total number of years to be used in the same formula.

## Example

Suppose an investor buys ABC company’s shares worth $ 10,000. The investor held this investment for 5 years and the value of the investment changed during this period.

Beginning Value at Y1 = $ 12,000

Value at Y2 = $14,000

Y3 = $15,000

Y4 = $17,000

Ending Value at Y5 = $18,000

The growth rate for the first year was 20%, 16.67% for Y2, 6.67% for Y3, 13.3% for Y4, and 5.88% for Y5.

We can use the CAGR formula to get a compound annual growth rate for this investment as well.

CAGR = [(EV/BV)1/n −1] × 100

CAGR = [($ 18,000/$ 10,000) 1/5 – 1] × 100

**CAGR = 12.47% **

## Uses of CAGR

The compound annual growth rate converts varying rates of return into a single and smooth rate of return.

It can be used to adjust the fluctuating rates where investors want to see a single compound rate of return.

As it considers only the beginning and ending values, investors can use it to analyze the historic performances of an investment over a defined period.

They can then use this analysis to predict the future performance of the investment. However, like any other historic analysis, CAGR should also be used carefully as it represents only past performances.

One of the limitations of CAGR is to ignore investment risks. You can use the risk-adjusted CAGR by using the following formula to get a better evaluation of an investment.

**Risk-Adjusted CAGR = CAGR × (1 – Standard Deviation) **** **

Investors can use CAGR to calculate the required initial investment or a required rate of return when they target a specific financial goal for the future.

For instance, an investor can estimate how much should be invested for 10 years with a CAGR of 15% to get $ 50,0000? Solving it with the CAGR formula can give you the beginning value or initial investment amount.

## What is the Internal Rate of Return (IRR)?

The internal rate of return (IRR) is a compound rate of return where the net present value of future cash flows of an investment is equal to zero.

It simply means the initial investment is equal to the net present value of all future cash flows arising from that investment.

It is a compound rate of return for the full length of the investment or project. Once you know the IRR, you can compare it with other investments to make a decision.

IRR is a percentage term and it is used the same way as the NPV is used. However, it does not offer a dollar value like the NPV formula.

Generally, a higher IRR is desirable but it should be considered in the full context of the investment requirements.

## How to Calculate IRR?

You can use the following formula to calculate the IRR of an investment or project.

**0 = NPV = ****Σ ****CF/(1+IRR) ^{n }**

Or

**0 = CF _{0} + CF_{1}/(1+IRR) + CF_{2}/(1+IRR)^{2} + CF_{3}(1+IRR)^{3} + CF_{n}/(1+IRR)^{n}**

Solving the equation where the net present value of all future cash flows equals zero is a complex task. It can only be achieved by trial-and-error method through iterations.

Alternatively, you can use the Excel spreadsheet to easily calculate the IRR or use the software.

The initial investment in this calculation will always be negative. Future cash flows can be positive (inflow) or negative (outflow).

## Example

Suppose a company ABC wants to compare two investment options by using the IRR formula. It has an initial investment of $ 600,000. The company’s calculated WACC or hurdle rate is 7%.

Option 1 gives ABC company an opportunity to invest in a fixed-income investment that yields 8% per annum for five years.

Option 2 is to invest in new machinery that costs the same and the expected cash flows for the next five years are $ 200,000 and the residual value of the machine $ 75,000.

Using the excel sheet, we can calculate the IRR for option 2 as below:

Year | Cash Flow |

0 | -600,000 |

1 | 150,000 |

3 | 150,000 |

4 | 150,000 |

5 | 225,000 |

IRR | 11% |

As we can see option 2 returns a higher IRR of 11% which is higher than option 1 and also the WACC.

## Uses of IRR

IRR is widely used in investment appraisal scenarios. It is a good starting point to compare different investments with similar choices.

However, the IRR analysis must also be used in conjunction with other metrics like the NPV. A higher IRR is considered a better investment option usually.

In other uses, companies use IRR to evaluate their project appraisals and new purchases. Again, the analysis should be considered as a starting point and the business must analyze other aspects as well.

Companies can also use IRR to evaluate their share buyback programs. In this scenario, the IRR formula will show whether reinvesting in a company’s own stock is a better option as compared to other investments.

IRR is widely used in comparing positive NPV projects as the primary goal of a company is to increase the shareholder’s wealth. If two projects have the same lifespan, the project with a higher IRR will yield more profits.

## CAGR Vs IRR – Key Differences

Let us summarize some key differences between CAGR and IRR below.

### Ease of Calculation

The compound annual growth rate is easy to calculate and understand. It only considers three input values that are readily available when comparing different investments.

On the other hand, IRR uses a complex formula to calculate the results. It is very difficult to calculate manually. However, using Excel or software can solve this issue.

### Uses

CAGR is used to find a single compound growth rate of an investment. It is widely used to analyze the historic performances of stocks and other investment options.

IRR compares investment options but it is used for forecasting rather than analyzing the historic returns.

### Advantages

CAGR has the following advantages:

- Easy to calculate and use
- Offers a single and uniform rate of return
- Compares different investments for the same periods
- Can be used to appraise the performance of business products, segments, and divisions

IRR has the following advantages:

- Can be used in capital budgeting decisions
- Investors use it to compare investment options
- It can be used in project appraisals and business valuations
- Considers the time value of money

### Disadvantages

CAGR has the following disadvantages:

- It ignores the time value of money
- It does not consider additional investments
- It does not consider the investment risks and other external factors

IRR has the following disadvantages:

- It assumes a constant rate of return throughout the investment period.
- It assumes all cash flows are reinvested at the same rate.
- It may give multiple IRRs for the same investment analysis.
- It ignores the length of the investment period.

### When to Use CAGR?

CAGR should be used for investments where only beginning and ending values matter. It is suitable where investors do not make additional investments.

It is also a better choice than using the common averaging method of aggregating the returns.

### When to Use IRR?

IRR is superior to CAGR as it considers the market volatility. It offers a forecast of future investment outcomes rather than appraising historic returns only.

However, both IRR and CAGR analysis should be adjusted for certain assumptions such as ignoring relevant investment risks, time value of money, size of the investment, and most importantly the length of the investment period.