The Calculation of IRR

If calculating IRR manually, it can be estimated as follows:

Step 1   Calculate the NPV of the project at any (reasonable) rate (eg the cost of capital)

Step 2   Calculate the project NPV at any other (reasonable) rate

Step 3   Calculate the internal rate of return using the formula

Net present value working at 12%=+1,152

This analysis has been re-performed using a 20% required return as shown below:

NPV at 20%=+138

Required

Using the above information, calculate the IRR Avanti’s proposed investment.

Solution

The Drawbacks of IRR

?     IRR ignores the size of a project, and may result in a small project with a belter IRR being chosen over a bigger project even though the larger project is estimated to generate more wealth for shareholders.

?     For projects with non-normal cash flows, Cash flows where the present value each year changes from positive to negative or negative to positive more than once, there may be more than one IRR.

?     IRR assumes that the cash flows after the investment phase are reinvested at the project's IRR; this may not be realistic.

The Calculation of MIRR

IRR assumes that the cash flows after the investment phase (here time O) are reinvested at the project's IRR. A better assumption is that the funds are reinvested at the investors' minimum required return(WACC),，If we use this re-investment assumption we can calculate an alternative, modified version of IRR.

Formula provided

re=cost of capital

n=number of time periods

Net present value working at 12%=+1,152

This analysis has been re-performed using a 20% required return as shown below:

NPV at 20=+138

Required

Calculate the modified IRR of Avanti's proposed investment.

The investment phase is assumed to be time 0 only.

The returns phase is therefore time 1-5 and the sum of these present values is 4,722.

The Advantages of MIRR

?     MIRR is quicker to calculate than IRR

?     The assumption of MIRR is better that the funds are reinvested at the investors' minimum required return(WACC)

?     MIRR does not give the multiple answers that can sometimes arise with the conventional IRR.