# Compound Annual Growth Rate (CAGR) Formula and Calculation

Contents

## What Is the Compound Annual Progress Charge (CAGR)?

The compound annual progress charge (CAGR) is the speed of return (RoR) that might be required for an funding to develop from its starting steadiness to its ending steadiness, assuming the income have been reinvested on the finish of every interval of the funding’s life span.

### Key Takeaways

- The compounded annual progress charge (CAGR) is likely one of the most correct methods to calculate and decide returns for something that may rise or fall in worth over time.
- It measures a smoothed charge of return.
- Buyers can evaluate the CAGR of two or extra alternate options to judge how properly one inventory carried out in opposition to different shares in a peer group or a market index.
- CAGR is thus a great way to judge how completely different investments have carried out over time, or in opposition to a benchmark.
- The CAGR doesn’t, nevertheless, replicate funding threat.

## The best way to Calculate Compound Annual Progress Charge (CAGR)

$$

C

A

G

R

=

(

(

E

V

B

V

)

1

n

−

1

)

×

100

the place:

E

V

=

Ending worth

B

V

=

Starting worth

n

=

Quantity of years

beginaligned&CAGR=left(left(fracEVBVright)^frac1n-1right)times100&textbfwhere:&EV=textEnding worth&BV=textBeginning worth&n=textNumber of yearsendaligned

CAGR=((BVEV)n1−1)×100the place:EV=Ending worthBV=Starting worthn=Quantity of years

To calculate the CAGR of an funding:

- Divide the worth of an funding on the finish of the interval by its worth firstly of that interval.
- Elevate the consequence to an exponent of 1 divided by the variety of years.
- Subtract one from the following consequence.
- Multiply by 100 to transform the reply right into a proportion.

## What the CAGR Can Inform You

The compound annual progress charge isn’t a real return charge, however moderately a representational determine. It’s primarily a quantity that describes the speed at which an funding would have grown if it had grown on the identical charge yearly and the income have been reinvested on the finish of every yr.

In actuality, this type of efficiency is unlikely. Nevertheless, the CAGR can be utilized to clean returns in order that they might be extra simply understood in comparison with different strategies.

## Instance of The best way to Use CAGR

Think about you invested $10,000 in a portfolio with the returns outlined under:

- From Jan. 1, 2018, to Jan. 1, 2019, your portfolio grew to $13,000 (or 30% in yr one).
- On Jan. 1, 2020, the portfolio was $14,000 (or 7.69% from January 2019 to January 2020).
- On Jan. 1, 2021, the portfolio ended with $19,000 (or 35.71% from January 2020 to January 2021).

We are able to see that on an annual foundation, the year-to-year progress charges of the funding portfolio have been fairly completely different as proven within the parentheses.

Alternatively, the compound annual progress charge smooths the funding’s efficiency and ignores the truth that 2018 and 2020 have been vastly completely different from 2019. The CAGR over that interval was 23.86% and will be calculated as follows:

$$

C

A

G

R

=

(

$

19

,

000

$

10

,

000

)

1

3

−

1

×

100

=

23.86

%

CAGR=left(frac$19,000$10,000right )^frac13-1times100=23.86%

CAGR=($10,000$19,000)31−1×100=23.86%

The CAGR of 23.86% over the three-year funding interval may help an investor evaluate alternate options for his or her capital or make forecasts of future values. For instance, think about an investor is evaluating the efficiency of two uncorrelated investments.

In any given yr throughout the interval, one funding could also be rising whereas the opposite falls. This might be the case when evaluating high-yield bonds to shares, or an actual property funding to rising markets. Utilizing CAGR would clean the annual return over the interval so the 2 alternate options can be simpler to match.

As one other instance, let’s say an investor purchased 55 shares of Amazon.com (AMZN) inventory in December 2017 at $1,180 per share, for a complete funding of $64,900. After three years, in December 2020, the inventory has risen to $3,200 per share, and the investor’s funding is now value $176,000. What’s the CAGR?

Utilizing the CAGR method, we all know that we want the:

- Ending Stability: $176,000
- Starting Stability: $64,900
- Variety of Years: 3

So to calculate the CAGR for this straightforward instance, we’d enter that knowledge into the method as follows: [($176,000 / $64,900) ^ (1/3)] – 1 = 39.5%.

## Extra CAGR Makes use of

The CAGR can be utilized to calculate the common progress of a single funding. As we noticed in our instance above, attributable to market volatility, the year-to-year progress of an funding will seemingly seem erratic and uneven.

For instance, an funding could improve in worth by 8% in a single yr, lower in worth by -2% the next yr, and improve in worth by 5% within the subsequent. CAGR helps clean returns when progress charges are anticipated to be risky and inconsistent.

### Evaluating Investments

The CAGR can be utilized to match completely different funding sorts with each other. For instance, suppose that in 2015, an investor positioned $10,000 into an account for 5 years with a set annual rate of interest of 1% and one other $10,000 right into a inventory mutual fund. The speed of return within the inventory fund can be uneven over the following few years, so a comparability between the 2 investments can be troublesome.

Assume that on the finish of the five-year interval, the financial savings account’s steadiness is $10,510.10 and, though the opposite funding has grown erratically, the ending steadiness within the inventory fund was $15,348.52. Utilizing the CAGR to match the 2 investments may help an investor perceive the distinction in returns:

$$

Financial savings Account CAGR

=

(

$

10

,

510.10

$

10

,

000

)

1

5

−

1

×

100

=

1.00

%

textSavings Account CAGR =, left ( frac$ 10,510.10$ 10,000 proper )^frac15-1 instances 100= 1.00%

Financial savings Account CAGR=($1,$1,51.1)51−1×1=1.%

And:

$$

Inventory fund CAGR

=

(

$

15

,

348.52

$

10

,

000

)

1

5

−

1

×

100

=

8.95

%

textStock fund CAGR =, left ( frac$ 15,348.52$ 10,000 proper )^frac15-1 instances 100= 8.95%

Inventory fund CAGR=($1,$15,348.52)51−1×1=8.95%

On the floor, the inventory fund could seem like a greater funding, with almost 9 instances the return of the financial savings account. Alternatively, one of many drawbacks of the CAGR is that by smoothing the returns, The CAGR can not inform an investor how risky or dangerous the inventory fund was.

### Observe Efficiency

The CAGR may also be used to trace the efficiency of assorted enterprise measures of 1 or a number of firms alongside each other. For instance, over a five-year interval, Huge-Sale Shops’ market share CAGR was 1.82%, however its buyer satisfaction CAGR over the identical interval was -0.58%. On this method, evaluating the CAGRs of measures inside an organization reveals strengths and weaknesses.

### Detect Weaknesses and Strengths

Evaluating the CAGRs of enterprise actions throughout related firms will assist consider aggressive weaknesses and strengths. For instance, Huge-Sale’s buyer satisfaction CAGR may not appear so low in contrast with SuperFast Cable’s buyer satisfaction CAGR of -6.31% throughout the identical interval.

## How Buyers Use the CAGR

Understanding the method used to calculate CAGR is an introduction to many different ways in which buyers consider previous returns or estimate future income. The method will be manipulated algebraically right into a method to search out the current worth or future worth of cash, or to calculate a hurdle charge of return.

For instance, think about that an investor is aware of that they want $50,000 for a kid’s school schooling in 18 years and so they have $15,000 to speculate in the present day. How a lot does the common charge of return have to be to achieve that goal? The CAGR calculation can be utilized to search out the reply to this query as follows:

$$

Required Return

=

(

$

50

,

000

$

15

,

000

)

1

18

−

1

×

100

=

6.90

%

textRequired Return =, left ( frac$ 50,000$ 15,000 proper )^frac118-1 instances 100= 6.90%

Required Return=($15,$5,)181−1×1=6.9%

This model of the CAGR method is only a rearranged current worth and future worth equation. For instance, if an investor knew that they wanted $50,000 and so they felt it was affordable to anticipate an 8% annual return on their funding, they may use this method to learn the way a lot they wanted to speculate to satisfy their objective.

## Modifying the CAGR Formulation

An funding is never made on the primary day of the yr after which offered on the final day of the yr. Think about an investor who desires to judge the CAGR of a $10,000 funding that was entered on June 1, 2013, and offered for $16,897.14 on Sept. 9, 2018.

Earlier than the CAGR calculation will be carried out, the investor might want to know the fractional the rest of the holding interval. They held the place for 213 days in 2013, a full yr in 2014, 2015, 2016, and 2017, and 251 days in 2018. This funding was held for five.271 years, which is calculated by the next:

- 2013 = 213 days
- 2014 = 365
- 2015 = 365
- 2016 = 365
- 2017 = 365
- 2018 = 251

The full variety of days that the funding was held was 1,924 days. To calculate the variety of years, divide the full variety of days by 365 (1,924/365), which equals 5.271 years.

The full variety of years that the funding was held will be positioned within the denominator of the exponent inside CAGR’s method as follows:

$$

Funding CAGR

=

(

$

16

,

897.14

$

10

,

000

)

1

5.271

−

1

×

100

=

10.46

%

textInvestment CAGR =, left ( frac$ 16,897.14$ 10,000 proper )^frac15.271-1 instances 100= 10.46%

Funding CAGR=($1,$16,897.14)5.2711−1×1=1.46%

## Clean Charge of Progress Limitation

A very powerful limitation of the CAGR is that as a result of it calculates a smoothed charge of progress over a interval, it ignores volatility and implies that the expansion throughout that point was regular. Returns on investments are uneven over time, apart from bonds which might be held to maturity, deposits, and related investments.

Additionally, the CAGR doesn’t account for when an investor provides funds to a portfolio or withdraws funds from the portfolio over the interval being measured.

For instance, if an investor had a portfolio for 5 years and injected funds into the portfolio throughout the five-year interval, then the CAGR can be inflated. The CAGR would calculate the speed of return primarily based on the start and ending balances over the 5 years, and would primarily rely the deposited funds as a part of the annual progress charge, which might be inaccurate.

## Different CAGR Limitations

Apart from the smoothed charge of progress, the CAGR has different limitations. A second limitation when assessing investments is that regardless of how regular the expansion of an organization or funding has been prior to now, buyers can not assume that the speed will stay the identical sooner or later. The shorter the time-frame used within the evaluation, the much less seemingly it will likely be for the realized CAGR to satisfy the anticipated CAGR when counting on historic outcomes.

A 3rd limitation of the CAGR is a limitation of illustration. Say that an funding fund was value $100,000 in 2016, $71,000 in 2017, $44,000 in 2018, $81,000 in 2019, and $126,000 in 2020. If the fund managers represented in 2021 that their CAGR was a whopping 42.01% over the previous three years, they’d be technically appropriate. They’d, nevertheless, be omitting some crucial details about the fund’s historical past, together with the truth that the fund’s CAGR over the previous 5 years was a modest 4.73%.

## CAGR vs. IRR

The CAGR measures the return on an funding over a sure time period. The inner charge of return (IRR) additionally measures funding efficiency however is extra versatile than the CAGR.

A very powerful distinction is that the CAGR is easy sufficient that it may be calculated by hand. In distinction, extra difficult investments and tasks, or those who have many alternative money inflows and outflows, are greatest evaluated utilizing IRR. To again into the IRR, a monetary calculator, Excel, or portfolio accounting system is good.

These fascinated by studying extra about CAGR and different monetary matters could wish to take into account enrolling in among the finest investing programs at the moment out there.

## What Is an Instance of Compound Annual Progress Charge (CAGR)?

The CAGR is a measurement utilized by buyers to calculate the speed at which a amount grew over time. The phrase “compound” denotes the truth that the CAGR takes under consideration the results of compounding, or reinvestment, over time. For instance, suppose you will have an organization with income that grew from $3 million to $30 million over a span of 10 years. In that situation, the CAGR can be roughly 25.89%.

## What Is Thought of a Good CAGR?

What counts as a very good CAGR will rely on the context. However usually talking, buyers will consider this by enthusiastic about their alternative value in addition to the riskiness of the funding. For instance, if an organization grew by 25% in an {industry} with a mean CAGR nearer to 30%, then its outcomes might sound lackluster by comparability. But when the industry-wide progress charges have been decrease, corresponding to 10% or 15%, then its CAGR is likely to be very spectacular.

Usually, a better CAGR is best.

## What Is the Distinction Between the CAGR and a Progress Charge?

The primary distinction between the CAGR and a progress charge is that the CAGR assumes the expansion charge was repeated, or “compounded,” annually, whereas a standard progress charge doesn’t. Many buyers favor the CAGR as a result of it smooths out the risky nature of year-by-year progress charges. As an illustration, even a extremely worthwhile and profitable firm will seemingly have a number of years of poor efficiency throughout its life. These dangerous years might have a big impact on particular person years’ progress charges however would have a comparatively small impression on the corporate’s CAGR.

## Can the CAGR Be Adverse?

Sure. A detrimental CAGR would point out losses over time moderately than positive aspects.

## What Is Danger-Adjusted CAGR?

To check the efficiency and threat traits amongst numerous funding alternate options, buyers can use a risk-adjusted CAGR. A easy technique for calculating a risk-adjusted CAGR is to multiply the CAGR by one minus the funding’s customary deviation. If the usual deviation (i.e., its threat) is zero, then the risk-adjusted CAGR is unaffected. The bigger the usual deviation, the decrease the risk-adjusted CAGR can be.