# Calculate Total Return and Compound Annual Growth Rate or CAGR

## Evaluate Your Investment Performance by Calculating Total Return and CAGR

Calculating an investment's total return and an investment's compound annual growth rate (CAGR) can help you evaluate your investment performance more easily. You'll be able to gauge how much richer or poorer you've become from your investments in various asset classes such as stocks, bonds, mutual funds, gold, real estate, or small businesses.

## The Concept of Total Return

The total return on an investment is straightforward, and it's a highly accurate measure. It tells an investor the percentage gain or loss on an asset based on its purchase price.

Divide the selling value of the position plus any dividends received by its total cost to calculate the total return. This essentially works out to capital gains plus dividends as a percentage of the money you laid out to buy the investment.﻿﻿

A capital gain—or capital loss—is the difference between your basis in an asset and the sale price when you eventually dispose of the asset. Your basis is basically what you paid for it, plus certain allowable costs of maintaining it.﻿﻿

## The Concept of CAGR

An investor needs a metric that can compare the return generated by different investments over different time periods when accounting for the length of time it takes to produce a given total return. This is where CAGR comes in. It doesn't represent economic reality, but it's a valuable academic concept.

A stock position might be up 40% in one year and down 5% the next. CAGR provides the annual return for such an investment as if it had grown at a steady, even pace. It tells you how much you would have to earn each year, compounded on your principal, to arrive at the final selling value.

## How to Calculate Total Return

Let's say that an investor had a cost basis of \$15,100 in PepsiCo stock. They purchased \$15,000 worth of PepsiCo and paid \$100 total commissions on the buy and sell orders. They received \$300 cash dividends during the time they held the stock, and they later sold the position for \$35,000.

Plug the variables into the total return formula to find the total return:

• Divide this by the cost basis of \$15,100

The result is 2.3377%, or 133.77% total return on invested principal. Remember that 1.0% of the total return is the principal, so you must subtract it out to express the gain or loss as a percentage: 2.3377 - 1.0 = 1.3377, or 133.77%.

Total return can't answer that question of whether this is a good rate of return on the investment because it doesn't take into account the length of time that the investment was held. It's cause for celebration if the investor earned 133.77% in five years, but it would have been a terrible investment if it had taken the investor 29 years to produce it.﻿﻿

The real-world journey could be—and often is—far more volatile. Practically all the best stock investments in history have experienced declines of 50% or even more, peak-to-trough, all while making their owners fabulously wealthy.

## Calculating Annual Return

You can't just take the simple return and divide it by the number of years the investment was held, Let's go back to PepsiCo and assume that the investor had held their position for 10 years.

Dividing the total return of 133.77% by 10 years, you would calculate that their annual return was 13.38%. Try to check the math using the future value of a single amount formula. You'll discover that had the investment of roughly \$15,000 grown by 13.38% annually, it would have been worth an ending value of \$52,657.﻿﻿

That's a far cry from the \$35,000 for which the investment was sold because this method doesn't take compounding into account. The result is a gross misstatement of the actual return the investor enjoyed each year.

## How to Calculate CAGR

You must begin with the total return and the number of years in which the investment was held to calculate CAGR. In the example we've been using, the total return was 2.3377 or 133.77%. You also know that the investment was held for 10 years.

You can find the CAGR for this scenario by plugging the information into the following formula:

CAGR = Ending value / Starting value)^(1 / # years) -1

Multiply the total return of 2.3377 by the X root—the number of years the investment was held. This can be simplified by taking the inverse of the root and using it as an exponent as shown in the above formula.

In this example, it's 1/10, or .10. Had the number of years been two, you could have taken 1/2 or .5 as the exponent. Three years would be 1/3 or .33 as the exponent, and four years would be 1/4, or .25.

In the above example, CAGR would be calculated as follows:

CAGR = 2.377(.10) = 1.09

This answer equates to a 9% compound annual growth rate. Again, the 1.0 represents the principal value which must be subtracted: 1.09 - 1.0 = .09, or 9% CAGR expressed as a percentage.

The investment grew at 9% compounded annually if the gains on the PepsiCo investment were smoothed out. Use the future value of a single amount to check the result. The investor would have ended up with the same balance of \$35,300 at the end of the period if they had taken the roughly \$15,000 to a bank for 10 years and earned 9% on their money.

Michael Adams purchased \$5,000 shares of Wing Wang Industries, Inc. 30 years ago. He recently sold the stock for \$105,000. He received a total of \$16,500 in cash dividends during his holding period. Both his original and selling commissions were \$50 each.

Calculate the total return and CAGR of his investment position:

### Step 1: Calculate Total Return

Begin with \$105,000 received upon sale + \$16,500 cash dividend received = \$117,000 divided by \$5,000 investment + \$100 total commissions = \$5,100 cost basis = 22.94 total return. You would have to subtract 1 (22.94 – 1) to get 21.94, or 2,194% if you want to express total return as a percentage.

### Step 2: Calculate CAGR

Find the inverse of the X root: 1/30 years = 0.33, 22.94 (.033) = 1.1098, or 10.98% CAGR.

Again, remember that in you must subtract the result by 1 to express as a percentage: 1.1098 – 1 = .1098, or 10.98% CAGR.

All in all, this is a decent return for the time period.

## Final Thoughts on Total Return and CAGR

Investors are often duped into ignoring total return, which is ultimately the only thing that matters when you've adjusted for risk and moral considerations.

One illustration is the way most stock charts are structured. This has important real-world consequences because you can materially improve your understanding of your investment performance, and you can make better-informed decisions as a result by focusing on total return.

Consider a former blue-chip stock, the now-bankrupt Eastman Kodak. You'd think that a long-term investor did poorly with the shares getting wiped out, that they would have lost all the money put at risk, but that didn't necessarily happen.

An owner of Eastman Kodak for the 25 years prior to its wipeout would have more than quadrupled their money due to the total return components, driven by dividend payments and a tax-free spin-off. In addition, there were tax benefits to the ultimate bankruptcy that, for many investors, could shield future investment profits, further softening the blow.

The important thing is to internalize how extraordinarily powerful the CAGR can be over long stretches of time. An extra percentage point or two over 25 or 50 years, which most workers will be fortunate enough to enjoy if they begin the investing process early, can mean the difference between a mediocre retirement and ending up on top of a sizable fortune.