The rate of return technique is one of the methods used in selecting an alternative for a project. In this method, the interest rate per interest period is determined, which equates the equivalent worth (either present worth, future worth or annual worth) of cash outflows (i.e. costs or expenditures) to that of cash inflows (i.e. incomes or revenues) of an alternative. The rate of return is also known by other names namely internal rate of return (IRR), profitability index etc. It is basically the interest rate on the unrecovered balance of an investment which becomes zero at the end of the useful life or the study period. In the following lectures, the rate of return is denoted by “i_r”.

Using present worth, the equation for rate of return can be written as follows;

PW_c = PW₁ ……………………………… (2.1)

PW_c = Present worth of cash outflows (cost or expenditure)
PW_i = Present worth of cash inflows (income or revenue)
As already stated in earlier lectures, cost or expenditures are considered as negative cash flows whereas income or revenues are considered as positive cash flows.

Equation (2.1) can be rewritten as;

0 = − PW_c + PW₁  ………………………….. (2.2)

In the above equation the net present worth is zero.
Now putting the expressions for present worth of cash outflows and that of cash inflows in equation (2.1) results in the following expression;

(2.3)

On left hand side of the above equation, P_o is the initial cost at time zero and F_C (single amount) and A_C (uniform amount series) are the expenditures occurring at future period of time. Similarly on the right hand side of the equation, F_I (single amount) and A_I (uniform amount series) are the incomes or revenues occurring at future period of time. The value of interest period ‘n’ will vary depending upon the occurrence of the future amounts (either expenditure or income).

Equation (2.3) can be rewritten as follows;

The value of rate of return ‘i_r’ can be calculated by solving the above equation. The equation (2.4) can be solved either manually through trial and error process or using Microsoft Excel spreadsheet. The first method i.e. trial and error process for determination of the rate of return consumes more time whereas the second method is faster. However the trial and error method gives a clear understanding of the analysis of calculation for the rate of return. Similar to equivalent present worth, the rate of return can also be determined by finding out the interest rate at which the net future worth or net annual worth is zero.

After determination of the rate of return for a given alternative, it is compared with minimum attractive rate of return (MARR) to find out the acceptability of this alternative for the project. If the rate of return i.e. i_r is greater than or equal to MARR, then the alternative will be selected or else it will not be selected. The MARR is the minimum rate of return from the investment, which is acceptable. In other words it is the minimum rate of return below which the investment alternatives are economically not acceptable. The minimum attractive rate of return (MARR) serves as an important criteria while selecting a single alternative or comparing mutually exclusive alternatives whenever the investments are made. For an organization, it is governed by various parameters namely availability of financially viable projects, amount of fund available for investment along with the associated risk, and type of organization (i.e. government, public sector, private sector etc.).