# Internal Rate of Return

The internal rate of return (lRR) is an alternative technique for use in making capital investment decisions that also takes into account the time value of money, The internal rate of return represents the true interest rate earned on an investment over the course of its economic life This measure is sometimes referred to as the discounted rate of return.
The internal rate of return is the interest rate K that when used to discount all cash flows resulting from an investment, will equate the present value of the cash receipts to the present value of the cash outlays.

In other words, it is the discount rate that will cause the net present value of an investment to be zero. Alternatively, the internal rate of return can be described as the maximum cost of capital that can be applied to finance a project
without causing harm to the shareholders. The internal rate of return is found by solving for the value of K from the following formula:

Formula of internal rate of return

It is easier, however, to use the discount tables. Let us now calculate the internal rate of return (using discount factors based on four decimal places)for Project A in Example 6.1. The IRR can be found by trial and error by using a number of discount factors until the NPV equals zero. For example, if we use a 25 per cent discount factor, we get a positive NPV of lB4 800. We must therefore try a higher figure. Applying 35 per cent gives a negative NPV of 166 530. We know then that the NPV will be zero somewhere between 25 per cent and 35 per cent, In fact, the IRR is between 30 per cent and 31 per cent but closest to 30 per cent, as
indicated by the following calculation:

Example of IRR calculation

The decision rule is that if the IRR is greater than the opportunity cost of capital, the investment is profitable and will yield a positive NPV Alternatively, if the IRR is less than the cost of capital the investment is unprofitable and will result in a negative NPV. The calculation of the IRR is illustrated in below photo:

Interpretation of IRR

The dots in the graph represent the NPV at different discount rates. The point where the line joining the dots cuts the horizontal axis indicates the IRR (the point at which the NPV is zero). Figure 6 2 indicates that the IRR is approximately 30 per cent, and you can see from this diagram that the interpolation method can be used to calculate the IRR without carrying out trial and error calculations When we use interpolation, we infer the missing term (in this case the discount rate at which NPV is zero) from a known series of numbers. For example, at a discount rate of 25 per cent the NPV is =\$84800 and for a discount rate of 35 per cent the NPV is -166 530. The total distance between these points is \$151330 (+\$84800 and – \$66530). The calculation for the approximate IRR is therefore:

Calculation for the IRR