# Rate of Return: Formula, Calculation & Examples

## What Is Rate of Return

Rate of return is the measure of an investment’s performance over a period of time, expressed as a percentage of its initial cost. A positive return reflects a gain in the investment’s value, while a negative return reflects a loss in value. A rate of return calculates the percentage change in value for any investment, regardless of whether it continues to be held, or was sold.

## How Rate of Return Works

Rate of return can be used to measure the monetary appreciation of any asset, including stocks, bonds, mutual funds, real estate, collectibles etc. Calculating a rate of return requires two inputs: i) the investment purchase amount, and ii) the current or ending value of the investment for the period being measured. The income received from holding of the asset like interest and dividends, if applicable, is also incorporated into the calculation.

Rate of return can be measured over any time period as well as sub-periods. For example, it can be calculated for a one-year period, and it could be calculated for each month or quarter within that period. When tracking the rate of return for shorter periods, such as months, these rates of return can be compounded to reach an annualized return.

Investors use rate of return to measure the performance of their investments. The realized rate of return can be assessed against their own return expectations, or compared to the performance of other investments, indices, or portfolios. Companies can use rates of return to measure the performance of various business segments or assets which can assist them in making future decisions about how to best invest their capital.

## Rate of Return Formula

A simple rate of return is calculated by subtracting the initial value of the investment from its current value, and then dividing it by the initial value. To report it as a %, the result is multiplied by 100.

Rate of return % = [(Current Value – Initial Value) / Initial Value] x 100

## Rate of Return Example

For example, if a share price was initially \$100 and then increased to a current value of \$130, the rate of return would be 30%.

[(\$130 – \$100) / \$100] x 100 = 30%

Rate of returns can certainly be negative as well, if the asset has lost value. For the above example, if the share price had declined to \$70, it would reflect a -30% rate of return.

Important: A simple rate of return can be calculated over any holding period, be it 1 day, 3 days, 1 month, 4 months, 18 months, 3 years etc. It is not necessarily an annualized return.

## Rate of Return (RoR) on Investments That Yield Income

Rates of return normally incorporate the income received from the underlying asset, such as interest from bonds, or dividends from stocks. For example, consider the purchase of a bond at par value for \$1,000, with a 3% coupon rate. The interest paid on this bond would be \$30 per year. If the investor sells the bond after one years at a value of \$1,100, it will result in a \$100 gain. For the year, the bond would have distributed \$30 in interest payments. The overall rate of return would be:

[((\$1,100 – \$1,000) + \$30)) / \$1,000] x 100 = 13%

## Annual Rate of Return

The annual rate of return is a measure of an investment’s gain or loss over the period of one year. Most investors measure returns on an annualized basis, which facilitates the comparison of how different investments are performing. To calculate a 1-year annual return, take the end-of-year investment value, deduct the value from the beginning of the year, and then divide it also by the beginning-of-year value.

Annual Rate of Return % = [(End of year price – Beginning of year price) / Beginning of year price] x 100

For example, if an investment is worth \$70 at the end of the year and was purchased for \$60 at the beginning of the year, the annual rate of return would be 16.66%.

Important: Calculating an annualized rate of return isn’t as straightforward as multiplying or dividing a simple rate of return to bring the holding period to 1 year. For example, a 24% two-year return doesn’t equate to a 12% annualized return. The reason is due to compounding.

## Compound Annual Growth Rate (CAGR) vs. Rate of Return

The compound annual growth rate (CAGR), also called the annualized rate of return, differs from the simple rate of return in that it considers the compounding effect of returns over multiple periods of time. The CAGR presents the total return over a holding period as an effective annualized rate.

CAGR % = {[(End of period price / Beginning of period price)^1/t] – 1} x 100

where t = the amount of time in terms of years

Example 1:

For example, consider an investment that rose from \$100 to \$105, or 5%, over a quarterly period. The holding period of 3 months represents 25% (or 0.25x) of a year. We can calculate the CAGR of this investment as:

CAGR = {[(\$105 / \$100) ^(1/0.25)] -1} x 100

={[1.05^(1/0.25)] -1} x 100

={[1.05^4] -1} x 100

={1.2155 -1} x 100

=21.55%

Key Takeaway: For holding periods of less than 1 year, the CAGR will be higher than the % found by multiplying the simple % rate of return by the number of periods needed to reach one year.

Example 2:

Consider an investment that rose from \$100 to \$125, or 25%, over a 2-year period. The holding period of 2 years represents 200% (or 2.00x) of a year. We can calculate the CAGR of this investment as:

CAGR = {[(\$125 / \$100) ^(1/2)] -1} x 100

={[1.25^(1/2)] -1} x 100

={[1.25^0.5] -1} x 100

={1.1180 -1} x 100

=11.80%

Key Takeaway: For holding periods of more than 1 year, the CAGR will be lower than the % found by dividing the simple % rate of return by the number of years in the period.

## Real Rate of Return vs. Nominal Rate of Return

All the above examples apply a simple rate of return, also referred to as a nominal rate of return, which doesn’t account for the impact of inflation on investment returns over time. Inflation can have the effect of reducing the purchasing power of money. For example, if a piece of land increases in value by 3% per year, but inflation is running at 4% per year, the value of the land isn’t keeping up with inflation, so is delivering a real return of -1% per year.

Key Takeaway: The real rate of return accounts for the effect of inflation on returns over time.

## Discounted Cash Flow (DCF) vs. Internal Rate of Return (IRR)

The Internal Rate of Return (IRR) is the annual rate of growth that an investment or project generates over time. IRR follows the same principle as CAGR, but makes an allowance for withdrawals or deposits throughout the holding period. For example, consider a bond that is purchased for \$1000, pays a 3% coupon, and is sold for \$1050 after 5 years.

This investor would have realized a \$50 capital gain and \$150 (5 x \$30) in interest payments, for total profits of \$200. Against a \$1000 purchase price, the investor has earned 20%.

However, the interest payments represent a return of capital each year. The IRR calculation would take these interim cashflows into consideration.

The discounted cash flow (DCF) formula takes projected future cash flows and reduces them for each year by applying a discount rate. The values ​​are discounted all the way back to the present. The % discount rate represents the time value of money of capital that is tied up in a project, and reflects the minimum rate of return needed to produce an acceptable investment result for a given level of risk. The remaining value of the discounted cash flows is called net present value.

## Bottom Line

Rate of return is the percentage change in the value of any investment over time. Investors often use annualized rates of return (the CAGR) to assess the financial performance of an asset relative to benchmarks or other investments. The real rate of return measures investment performance adjusted for inflation.

A discounted cash flow analysis returns all forecasted future cash flows back to the present value using a discount rate to help investors or companies assess whether the investment is creating value on a risk-adjusted basis.