Table of Contents

How to calculate rate of return

How to calculate total rate of return for different types of investments

Variations on rate of return

How to calculate variations on rate of return

The bottom line

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Aug 31, 2022

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7 min read

Rate of return allows us to make clear comparisons among investments, which is essential. It puts them on a common scale.

Every investor wants to know how their holdings are performing. Measuring performance enables investors—from individuals to corporations—to decide whether to buy, sell, or do nothing.

There are any number of ways to gauge investment performance, but one of the most critical is rate of return. This article will show you how to calculate the rate of return on an investment.

The most basic way to calculate rate of return is to measure the percentage change in an investment’s value for a time period. The equation to derive this can be expressed as the ending value for the period minus the starting value, divided by the starting value.

Rate of return allows us to make clear comparisons among investments, which is essential. It puts them on a common scale.

Here is a simple example of a rate of return formula and comparison: you buy a share of ABC Corp. for $100, you sell it later for $140, a $40 gain. Your rate of return is

*$140 - $100/$100 = 0.40 or 40%*

You also buy a house for $500,000 and sell it for $600,000. Your profit is $100,000, but your rate of return is half that of ABC Corp.’s return:

$600,000 - $500,000/$500,000 = 0.20 or 20%

To calculate rate of return in an Excel spreadsheet, you can easily enter a formula:

- Enter current value of the investment in one row.
- Enter original value (cost) of investment in row below current value.
In a row above these two, enter the formula for rate of return:

*Current value - Original value)/Original value*

For example:

Current value: Cell B6

Original value: Cell B7

Rate of Return: Cell B5 (format, percent), enter: =(B6-B7)/B7

The most important rate of return calculation is total return, which adds any periodic income from the investment. For stocks, this includes dividends and capital gains. For bonds, this means interest payments. For real estate, this is rent.

Widget Inc.’s stock price rose from $60 on Jan. 1 to $75 on Dec. 31, for a $15 gain. During the year Widget made four quarterly dividend payments of 75 cents per share, for a total annual dividend of $3.

An investor’s total return from a Widget share is:

*($15 + $3)/$60 = 0.30 or 30%*

Telecable in 2020 sold $500 million of bonds that reach maturity in 2030, paying 6% annual interest. You bought one of the bonds for $1,000, the full principal value. Now you sell the bond for $1,010, for a $10 gain, after receiving the annual interest of $60 (6% of $1,000).

Your total return for the past year is:

*$60 + $10/$1,000 = 0.07 or 7%*

The XYZ Real Estate Trust a year ago acquired the Fleetwood Towers apartment building for $70 million. During the past year XYZ received total rent of $250,000. Now it is selling the building for $80 million, a gain of $10 million. XYZ’s total return is:

*$10,000,000 + $250,000/$70,000,000 = 0.1464 or 14.6%*

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Retirement AnalyzerSimple rate of return is generally not a sufficient calculation. Investors need to account for other factors:

- Any income received from the investment
- The length of time for the investment
- The investor’s goal or expectation when the investment was made
- Rates of return for other potential investments

These factors are used in the following variations on a simple return:

**Compound annual growth rate (CAGR),**or annualized return, breaks down a multiyear return into a one-year rate that grows to the multiyear rate through compounding (reinvestment of returns).

**Internal rate of return (IRR),**which calculates an estimated future rate of return on an investment; the investor then decides if the expected rate justifies the investment.

**Marginal rate of return,**which is linked to the economic concept of diminishing returns; investors use this to estimate when they can expect less return on any additional (marginal) money spent on an investment.

How does an investor determine an annual equivalent for a rate of return, when the investment is held for more than a year — say, three years? For example, if his total return for three years was 30%, does he simply divide it by three, for 10% annually?

No, because simple division ignores the effect of compounding growth. The annualized rate, or compound annual growth rate, is about 9.1%.

Let’s go back to the Widget stock example and pretend the 30% return was for three years, not one year.

Calculating a compound annual growth rate is a process of reducing the multiyear return by fractions of an exponent, based on the number of years of the investment.

So the 30% Widget return is reduced by the power of one divided by three, or 0.333.

(On a financial calculator, the operational symbol for a power or exponent is a caret (^). Per the Widget example, calculating something to the one-third power is the same as calculating the cube root.)

For annualizing Widget’s return, you decimalize 30% as 0.3, add 1 as a constant, and calculate the cube root of 1.3. Any financial calculator or online tool can do this instantly.

The annualized rate then, going out to three decimal places, is 9.139%. You can verify that by reversing the process and raising 9.139% to the power of 3:*1.09139 ^3= 1.29999, rounded to 1.3, minus 1 = 0.3 or 30%*

Or, manually,*1.09139 X 1.09139 X 1.09139 = 1.29999*

Total rate of return is an historical calculation—it looks at past performance. Investors and business managers perform another calculation that looks forward: internal rate of return, or IRR. It tries to gauge future performance of an investment by assuming how much money the investment might generate in the years ahead. IRR helps an investor decide whether to proceed with an investment.

Let’s look at a hypothetical example. Silicon Chip Corp. is considering a $100 million investment in a new semiconductor fabrication plant. Silicon Chip decides that building the plant would only be justifiable if it produces a minimum 15% rate of return. The chief financial officer (CFO) does a study to estimate the annual cash to be generated by the new plant, for five years, with the following results:

- Year 1: $20 million
- Year 2: $30 million
- Year 3: $35 million
- Year 4: $40 million
- Year 5: $50 million

Many IRR calculator tools are available on the Internet to do these computations.

In our case above, we plug in the $100 million investment and the estimated annual cash flows, and the online calculator gives us 18.868%. This exceeds the threshold of 15% set by Silicon Chip, so the company may proceed with the project.

Besides the internal rate of return, investors will also estimate the marginal rate of return. This answers the question of how much return is generated for every additional dollar spent on an investment.

In the Silicon Chip example, let’s say that in the fifth year after building the new plant, the company considers investing another $25 million in the plant. The CFO estimates this would generate an additional $28 million of cash flow. That’s a 12% marginal rate of return—below the 18.868% on the original $100 million and below the company’s 15% minimum. It’s a diminishing return, so any further investment in the plant is less likely.

Calculating rate of return can range from the rudimentary to the complex. Knowing why it matters is something with which every investor should have a passing familiarity.

At Titan, we are value investors: we aim to manage our portfolios with a steady focus on fundamentals and an eye on massive long-term growth potential. Investing with Titan is easy, transparent, and effective.

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