# Rate of Return - Definition

### Rate of Return Definition

Rate of Return (RoR) refers to the net profit or loss of an investment over a period expressed as a proportion of the original cost of an investment. Profits are the income realized from the sale of an investment plus the capital gains. A loss is described as negative returns when the amount invested is greater than zero. Rate of return is usually expressed as a percentage.The Rate of return can be calculated on any investment or asset like vehicle, real estate, shares, stocks among others as long as the asset was bought at one point and sold in future. A Little More on What is the Rate of Return

### Calculating Rate of Return

The simple rate of return is also called growth rate of return on investment (ROI). Taking into consideration the time, value of money and inflation effects, the rate of returns can also be expressed as the net amount of discounted cash flow realized from an investment once the adjustment of inflation is done. Rate of return can be considered for over a single period of time. This can be for any length of time. However, the period can instead be divided into sub-periods. In this case, there is more than one period. The end of one sub-period marks the beginning of another sub-period. Where we have multiple connecting sub groups, the rate of return of the whole period can be calculated by adding the returns of each sub-period. The formula below is used to calculate the rate of return:

### Formula for Rate of Return

Rate of return (RoR) = (Current value Initial Value) 100 Initial value Example: By taking an example of buying a home so as to understand how rate of return can be calculated. Lets say you purchase a house for \$365,000 in cash. Years later, you plan to sell your house and you are able to sell the house at \$492,750 after deducting the real estate agents fee and commission plus any tax. The rate of return will be: Current price - \$492,750 Initial Price - \$365,000 (492,750-365,000)/365,000 x 100 = 35% Now lets say for instance you sold the house at a less price than the amount you used to purchase it, for instance at a cost of \$292,000, the same formula is used to calculate the rate of return which in this case will be a loss or negative return. RoR = (292,000 365,000)/365,000 X 100= -20%

### Rate of Returns for stocks and Bonds

When calculating the rate of returns for stocks and bonds are a little different. Assuming an investor purchases a stock for \$75 per share, stays with the stock for five years and receives a total dividend of \$10. Later, the investor sells the stock for \$95 per share, this means that the gain earned per share is \$95 - \$75=\$20. He has also earned \$10 the dividend income making the gain to be \$20+\$10= \$30. The rate of return for the stock is therefore \$30 per share. This is divided by \$75 which is the initial cost. This makes 0.4, multiplied by 100 to make 40%. In case 2, consider an investor who pays \$2,500 for 5% bond. The investment makes \$100 interest income yearly. Lets say the investor sells the bond after two years for \$3,000 premium value earning \$500 plus \$200 total interest. The rate of return in this case will be \$500 gin plus \$200 interest income, divided by the initial cost of \$2,500, resulting into 28%. (\$3,000 - \$2,500) + \$200 X 100 = 28% \$2,500

### Real versus Nominal Rate of Return

The simple rate of return discussed above of buying a house is known as nominal rate of return. This is because it does not put into account the inflation effect over time. Inflation lowers the buying power of money. The value we talked about of \$492,750 will never be the same 6 years later. This is due to inflation effect. In cases where the effect of inflation is considered, the rate of return is known as real rate of return.

### Rate of return versus Compound annual growth rate (CAGR)

CAGR factors in the growth over several periods unlike simple rate of return. CAGR is the average rate of return of an investment over a stated period of time which is longer than one year. Compound annual growth rate is also known as Annualized Rate of Return. While rate of return expresses the loss or profit of an investment over a random period of time, annualized RoR or CAGR describes the return of an investment over every year. To calculate compound annual growth rate, its the value of an investment at the end of the period, divided by the value at the start of that period, raise result to the power of one, divided by the number of years and minus one from the result. This is also written as CAGR = (Value of an investment at the end) 1/no.of years 1 Beginning value of an investment Lets use an example to fully understand the difference. We will use the above case of a simple rate of return where an investor purchased a house at \$365,000 and sold it \$492,750. To calculate the CAGR, it will be: [(492,750/365,000)1/6 -1] x 100 = 5% per year Someone would just calculate the simple rate of return, which was 35% and divide it by six years. This would be = 5.83%. There is a difference because CAGR level returns such that they are the same each year then compounds them.

### Discounted cash flow

It is a method used to value an investment based its cash flow in future. It takes the proceeds from an investment and discounts each of the cash flow according to the discount rate. Discount rate represents the lowest rate of return an investor can accept.

### Internal Rate of Return (IRR)

IRR is the interest that makes the net present value of all the cash flows from a particular investment equals to zero. It is used to assess how attractive a project or an investment is in terms of profitability. If the IRR of a new project goes below the desired rate of return, the project is rejected.However,if it exceeds the required rate, the new project is embraced. IRR is an important tool in a company that plans to take multiple new development projects. The management is able to know the projected return of each project.

### Uses of Rate of Return

• Rate of returns can be used to make investment decisions.
• Financial analysts use rate of return to compare the performance of a company over a specified period of time.
• Used to compare the performance between companies.
• Companies use it compare internal rate of returns of different projects and decide which project to pursue and which one will bring more returns in the company.

### Research articles for Rate of Return

The extreme value method for estimating the variance of the rate of return, Parkinson, M. (1980). Journal of business, 61-65.[PDF]The rate of obsolescence of patents, research gestation lags, and the private rate of return to research resources, Pakes, A., & Schankerman, M. (1984). In R&D, patents, and productivity (pp. 73-88). University of Chicago Press.PE ratios, PEG ratios, and estimating the implied expected rate of return on equity capital, Easton, P. D. (2004). The accounting review79(1), 73-95. The rate of return to the HighScope Perry Preschool Program, Heckman, J. J., Moon, S. H., Pinto, R., Savelyev, P. A., & Yavitz, A. (2010). Journal of public Economics94(1-2), 114-128.On patents, R & D, and the stock market rate of return, Pakes, A. (1985). Journal of political economy93(2), 390-409.Market share and rate of return, Gale, B. T. (1972). The Review of Economics and Statistics, 412-423.R & D capital, rate of return on R & D investment and spillover of R & D in Japanese manufacturing industries, Goto, A., & Suzuki, K. (1989). The Review of Economics and Statistics, 555-564.Input choices and rate-of-return regulation: An overview of the discussion, Baumol, W. J., & Klevorick, A. K. (1970). The Bell Journal of Economics and Management Science, 162-190.An evaluation of accounting rate-of-return, Penman, S. H. (1991). Journal of Accounting, Auditing & Finance6(2), 233-255.The rate of interest, Fisher's rate of return over costs and Keynes' internal rate of return, Alchian, A. A. (1955). The American Economic Review, 938-943.