The post is continuation of earlier article NPV, IRR and their variants. For capital budgeting Internal Rate of Return (IRR) is popular measure, however, Net Present Value (NPV) method is preferred by academics since the rankings of mutually exclusive projects by IRR may not always select the project which will maximize the value of the firm, due to an implied reinvestment rate assumption by IRR. This weakness was removed by the Modified Internal Rate of Return (MIRR), the results are usually consistent with NPV.
Sometime back, I was solving capital budgeting problem and MIRR results were not consistent with NPV. After some research I found MIRR may also lead to erroneous rankings when projects have different initial outflows to start the project i.e. the scale problem, or the projects have different lives i.e. the time span problem. So here is the solution.
Scale Difference :
Imagine two projects with cashflow as shown.
As you can see the initial outlays are very wide and hence the MIRR results are inconsistent. The logic behind this is the acceptance of the smaller project also implies the acceptance of a shadow investment, equal to the difference in size between the smaller and larger projects, which earns the cost of capital. Therefore we make the shadow project with initial outlay of difference between big project and small project, with NPV of 0. Use Goal seek function of excel to make shadow project NPV 0.
After we add the shadow project and small project cashflow, and MIRR the results are consistent with NPV.
For the project with the different timelines, use the life of the longest project.
Scale and Timeline Difference:
Imagine two projects with varying initial outflow and different timeline. The adjusted MIRR can be calculated by using the largest initial outflow and the largest number of periods.
This will give rankings that are consistent with NPV for mutually exclusive projects, even if the projects are of different sizes and in some cases, different lives.