What is the rate of return?
The rate of return (RoR), also called the return on investment (ROI), is the amount gained or lost from a trade over a period of time, calculated by comparing the current worth of your position with its initial cost. The rate of return is a simple way to check your current investment status.
A positive rate of return means you have gained money from your position, and a negative rate of return means you’ve currently lost money. Calculating the rate of return is more common for investors seeking to understand whether their initial outlay will be worth it in the long term, but it can also be used by traders to evaluate the outcome of their trades.
Understanding the rate of return
The rate of return can be applied to any trade or investment, but the calculation works best when the asset has a clearly defined value throughout the period of investment, such as a stock or bond.
For example, the rate of return can be calculated for any position such as a forex trade, the purchase of a house, or investment in fine art. However, the forex trade will have the most concrete rate of return of the three because the exchange rate is always clearly defined by central banks and brokerages. Something like a house purchase or art investment may be worth different amounts depending on who performs the appraisal.
Investments like these with more indeterminable cash flows are judged by the rate of return on similar assets.
Most investors prefer to determine a minimum rate of return before committing to an opportunity.
Simple rate of return formula
The simple rate of return is calculated with an easy formula:
Rate of return = ((ending value – purchase price) / purchase price) x 100
Rate of return calculation example
Say you buy a house for $685,000. Five years later you sell the same house for $710,000. The rate of return would be:
((710,000 – 685,000)/685,000) x 100 = 3.65%
Rate of return for stocks and bonds
Calculating the rate of return for stocks and bonds becomes slightly more complicated because you must include the earnings from dividends and interest.
Rate of return for stocks
When calculating the rate of return for stocks, you will add any dividends earned to the end value of your investment. Say you bought 20 shares of Microsoft stock at $107 a share in early 2017 and sold your holdings when Microsoft reached $336 a share in early 2022. During that time Microsoft also paid a dividend of $0.58 per share every quarter.
You would have received a total dividend payment of $11.6 per share, totaling $232 altogether. Let’s add those dividend earnings to the end value of your investment and calculate the rate of return.
The end value of your investment = ($336 x 20) + $232 = $6,952
The initial value = $107 x 20 = $2,140
Your rate of return = ((6,952 – 2,140) ÷ 2,140) x 100 = 225%
Rate of return for bonds
The rate of return for a standard bond is known as the coupon rate. Bonds pay a fixed amount of annual interest, known as the coupon. Some people may refer to a bond’s rate of return as the coupon rate because the rate of return is determined by dividing the coupon by the initial cost of the bond.
So, a bond that cost $1,000 with a coupon of $75 would have a rate of return, or coupon rate, of 7.5%.
Often, bonds are traded on bond markets after they are first purchased. The bonds are then resold for a different value, sometimes more than the initial cost, sometimes less. This is dependent on the bond’s level of risk and interest rate.
When bonds are resold, the rate of return changes. In these instances, the rate of return is calculated by dividing the coupon cost by the new cost of the bond.
Say you purchased a bond for $1,100 with a coupon of $75. After four years the bond reaches maturity and is paid out for the original price – $1,000.
To determine the rate of return, you would subtract the price you paid for the bond from the total amount gained: $1,300 - $1,100 = $200. You can then divide your net earnings by the $1,100 you paid and express the amount as a percentage.
200 ÷ 1100 × 100 = 18% RoR
Additional rates of return
There are many different variations to the rate of return. We’ve covered the most common form and uses. The following versions are ways you can modify the formula for specific amounts of time or more complex investments.
Annual rate of return
The annual rate of return measures the amount gained or lost from an investment over one year. The formula for the annual rate of return is similar to the formula for the standard rate of return, but it uses the beginning of year (BYP) and end of year (EYP) prices instead of the purchase price and ending value.
Annual rate of return = [(EYP – BYP) / BYP] × 100
Internal rate of return (IRR)
The internal rate of return is a more complicated method of calculating the profitability of potential investments and includes the monetary growth generated by an investment or project. This growth is based on the time value of money, which refers to money’s earnings potential both now and in the future.
The internal rate of return considers the time value of money to measure the annual rate of growth of an investment. So, while the simple rate of return measures the total growth of an investment, the IRR identifies the rate at which that investment grows each year. The two figures are likely to be exact the first year but will differ the longer the investment is active.
Accounting rate of return (ARR)
The accounting rate of return calculates the percentage rate of an asset or investment’s revenue compared to its initial cost. While the rate of return considers the eventual sale price of an investment, the accounting rate of return looks only at the income derived during the life of the asset.
To calculate the accounting rate of return, you must first determine your net profit including annual revenue along with costs or depreciation if applicable. Then, divide this net profit by the initial cost of the asset or investment and multiply by 100 to express the figure as a percentage.
Accounting rate of return = (average annual revenue)/(initial investment) X 100
The ARR is helpful in determining a project’s annual percentage rate of return before proceeding with the investment. It looks at the default profitability of an investment or asset without considering the time frame and payment schedule.
Compound annual growth rate (CAGR)
The compound annual growth rate is another variation of the rate of return that measures the mean annual rate of return over a holding period, typically longer than one year. This means the CAGR must factor in compound growth over multiple years wherein the profits are reinvested at the end of each year.
The compound annual growth rate is calculated by dividing the ending value (EV) by the beginning value (BV), raising the sum to a value of 1 over the number of years (n), subtracting 1, and multiplying by 100 to express the figure as a percentage.
CAGR = (EV/BV)(1/n) – 1 × 100
The CAGR isn’t a true return rate, as it depends on the rate of return staying consistent each year, an unlikely occurrence. However, the CAGR helps you determine a simplified projection of returns.
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