what is a rate of return ror 
a rate of return ror is the net gain or loss of an investment over a specified time period expressed as a percentage of the investment s initial cost when calculating the rate of return you are determining the percentage change from the beginning of the period until the end investopedia ellen lindnerunderstanding a rate of return ror a rate of return ror can be applied to any investment vehicle from real estate to bonds stocks and 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 required rate of return before making an investment choice the formula for rorthe formula to calculate the rate of return ror is rate of return current value initial value initial value 100 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 100this simple rate of return is sometimes called the basic growth rate or alternatively 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 discounted cash flows dcf received on an investment after adjusting for inflation the average annual rate of return for the total stock market between 2013 and 2023 as measured by the growth of the s p 500 index note that actual returns vary widely from year to year and from stock to stock 1ror on stocks and bondsthe rate of return calculations 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 dividends if the investor 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 that pays 1 000 for a 1 000 par value 5 coupon bond the investment earns 50 in interest 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 returnthe simple rate of return is considered a nominal rate of return since it does not account for the effect of inflation over time inflation reduces the purchasing power of money and so 335 000 six years from now is not the same as 335 000 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 real rate of return or the inflation adjusted rate of return real rate of return vs compound annual growth rate cagr a closely related concept to the simple rate of return is the compound annual growth rate cagr the cagr is the mean annual rate of return of an investment over a specified period of time longer than one year which means the calculation must factor in growth over multiple periods to calculate 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 rorthe 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 to move into a larger place you are able to sell the house for 335 000 after deducting any realtor s fees and taxes the simple rate of return on the purchase and sale of the house is as follows 3 3 5 0 0 0 2 5 0 0 0 0 2 5 0 0 0 0 1 0 0 3 4 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 1 8 7 5 0 0 2 5 0 0 0 0 2 5 0 0 0 0 1 0 0 2 5 frac 187 500 250 000 250 000 times 100 25 250 000 187 500 250 000 100 25 internal rate of return irr and discounted cash flow dcf the next step in understanding ror over time is to account for the 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 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 discounted cash flows 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 increases 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 at 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 the rate of return is higher than the 5 discount rate the rate of return using discounted cash flows is also known as the internal rate of return irr the internal rate of return is a discount rate that makes the net present value npv of all cash flows from a particular project or investment equal to zero irr calculations rely on the same formula as npv does and utilizes the time value of money using interest rates the formula for irr is as follows i r r n p v t 1 t c t 1 r t c 0 0 where t total number of time periods t time period c t net cash inflow outflows during a single period t c 0 baseline cash inflow outflows r discount rate 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 during a single period tc0 baseline cash inflow outflowsr discount rate 