What Is a Rate of Return (RoR)?

An investment’s rate of return (RoR) is a measurement of how much it has gained or decreased in value when it's purchased at one point and produces cash flow in the future. You’re determining the percentage change from the beginning of the period until the end. It can be applied to any asset from stocks and bonds to fine art.

Understanding a Rate of Return (RoR)

A rate of return (RoR) can be applied to any investment vehicle, from real estate to bonds to stocks to fine art. The RoR works with any asset, provided the asset is purchased at one point in time and produces cash flow at some point in the future. Investments are assessed based, in part, on past rates of return, which can be compared against assets of the same type to determine which investments are the most attractive. Many investors like to pick a 澳洲幸运5开奖号码历史查询:required rate of return before making an investment choice.

The Formula for RoR

The formula to calculate the rate of return (R🍸oR) is:

$\text{Rate of return} = [\frac{(\text{Current value} - \text{Initial value})}{\text{Initial value}}]\times 100$Rate of return=[Initial value(Current value−Initial value)​]×100

This simple rate of return is sometimes called the basic 澳洲幸运5开奖号码历史查询:growth rate or 澳洲幸运5开奖号码历史查询:return on investment (ROI). If you also consider the effect of the time value of money and inflation, the real rate of return can also be defined as the net amount of 澳洲幸运5开奖号码历史查询:discounted cash flows (DCF) received on an investment after adjusting for inflation🌜.

RoR on Stocks and Bonds

The rat𓂃e of return calculation for stocks 💎and bonds is slightly different. Assume an investor buys a stock for $60 a share, owns the stock for five years, and earns a total amount of $10 in 澳洲幸运5开奖号码历史查询:dividends. If the in♕vestor sells the stock for $80, their per-share gain is $80 - $60 = $20. In addition, they have earned $10 in dividend income for a total gain of $20 + $10 = $30. The rate of return for the stock is thus a $30 gain per share, divided by the $60 cost per share, or 50%.

On the other hand, consider an investor who pays $1,000 for a $1,000 par value 5% 澳洲幸运5开奖号码历史查询:coupon bond. The investment earns $50 in intere꧟st income per year. If the investor sells the bond for $1,100 in premium value and earns $100 in total interest, the investor’s rate of return is the $100 gain on the sale, plus $100 interest income divided by the ♊$1,000 initial cost, or 20%.

Real Rate of Return vs. Nominal Rate of Return

The simple rate of return is considered a 澳洲幸运5开奖号码历史查询:nominal rate of return since it does not account for the effect of inflation over time. 澳洲幸运5开奖号码历史查询:Inflation reduces the purch🃏asing power of▨ money so $1,000 six years from now is not the same as $1,000 today.

Discounting is one way to account for the time value of money. Once the effect of inflation is taken into account, we call that the 澳洲幸运5开奖号码历史查询:real rate of return (or the inflation-adjusted rate of retꩵurn).

Real Rate of Return vs. Compound Annual Grow💟th Rate (CAGR)

A closely related concept to the simple rate of return is the 澳洲幸运5开奖号码历史查询:compound annual growth rate (CAGR). The CAGR i♛s the mean annual rate of return of an investment over 𝐆a specified period longer than one year, which means the calculation must factor in growth over multiple periods.

To calculate the compound annual growth rate, we divide the value of an investment at the end of the period in question by its value at the beginning of✱ that period; raise the result to the power of one divided by the number of holding periods, such as years; and subtract one from the subsequent result.

Example of RoR

The rate of return can be calculated for any investment, dealing with any kind of asset. Let's take the example of purchasing a home as a basic example for understanding how to calculate the RoR. Say that you buy a house for🥂 $250,000 (for simplicity, let's assume♕ you pay 100% cash).

Six years later, you decide to sell the house—maybe your family is growing and you need ꧑to move into a larger place. You're able to sell the house for $335,000, after deducting any realtor's fees andꦉ taxes. The simple rate of return on the purchase and sale of the house is as follows:

$\frac{(335,000-250,000)}{250,000} \times 100 = 34\%$250,000(335,000−250,000)​×100=34%

Now, what if, instead, you sold the house for less than you paid for it—say, for $187,500? The same equation can be used to calculate your loss, or the negative rate of return, on the transaction:&n൲bsp;

$\frac{(187,500 - 250,000)}{250,000} \times 100 = -25\%$250,000(187,500−250,000)​×100=−25%

Internal Rate of Returnꦡ 𝓰(IRR) and Discounted Cash Flow (DCF)

The next step in understanding RoR over time is to account for the 澳洲幸运5开奖号码历史查询:time value of money (TVM), which the CAGR ignores. Discounted cash flows take the earnings of an investment and discount each of the cash flows based on a 澳洲幸运5开奖号码历史查询:discount rate. The discount rate represents a minimum rate of return acceptable to the investor, or an assumed rate of inflation. In addition to investors, businesses use dis๊counted cash flowsꦓ to assess the profitability of their investments.

Assume, for example, a company is considering the purchase of a new piece of equipment for $10,000, and the firm uses a discount rate of 5%. After a $10,000 cash outflow, the equipment is used in the operations of the business and ꦕincreases cash inflows by $2,000 a year for five years. The business applies present value table factors to the $10,000 outflow and to the $2,000 inflow each year for five years.

The $2,000 inflow in year five would be discounted using the discount rate of 5% for five years. If the sum of all the adjusted cash inflows and outflows is greater than zero, the investment is profitable. A positive net cash inflow also means that t▨he rate of return is higher than the 5% discount🐈 rate.

The rate of return using discounted cash flows is also known as the 澳洲幸运5开奖号码历史查询:internal rate of return (IRR). The 澳洲幸运5开奖号码历史查询:internal rate of return is a discount rate that makes the 澳洲幸运5开奖号码历史查询:net present value (NPV) of all cash flows from a particular p🅺roject or investment equal to zero. IRR calculations rely on the same formula as NPV does and utilize the time value of money (using interes๊t rates). The formula for IRR is as follows:

$\begin{aligned} &IRR = NPV = \sum_{t = 1}^T \frac{C_t}{(1+ r)^t} - C_0 = 0 \\ &\textbf{where:}\\ &T=\text{total number of time periods}\\ &t = \text{time period}\\ &C_t = \text{net cash inflow-outflows during a single period }t \\ &C_0 = \text{baseline cash inflow-outflows}\\ &r = \text{discount rate}\\ \end{aligned}$​IRR=NPV=t=1∑T​(1+r)tCt​​−C0​=0where:T=total number of time periodst=time periodCt​=net cash inflow-outflows&nbs🍰p;during a singl꧃e period tC0​=baseline cash inflow-outflowsr=discount rate​

The Bottom Line

The rate of return (ROR) is a simple metric that shows the net ꦫgain or loss of an investment or project over a set period. The RoR is expressed as a percentage of ♍the initial value.

The internal rate of return (IRR) also measures the performance of investments or projects, but while ROR shows the total growth since the start of the project, ꧋IRR shows the annual gr🐽owth rate. The Compound Annual Growth Rate (CAGR) is another metric that shows the annual growth rate of an investment, but this time taking into account the effect of compound interest.