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Explaination of IRR, MIIR, NPV

Below are notes poted by my instructor. I need help understanding what he is telling me, can you help?

Let's take a look at tools we can use to analyze capital investments by firms. These sorts of projects most commonly are for things such as equipment, machinery, buildings, etc. The same ideas apply to decisions on how to price acquisitions and divestitures.


When we analyze projects we often do not distinguish among the various types of risks we've discussed in prior weeks. Indeed, many firms seem to focus their risk analyses on the systemic risks. That does make some sense because those factors are beyond the control of the firm ... what management group would admit it could not fully control what happens within the firm. Yet, it is the internal factors that most influence the success or failure of the majority of projects.

The text indicates project risk as being the risk that a project performs below expectations. That may appear to conflict with the definition of risk I gave earlier in the course, but it is subsumed into the broader definition. The technical term for what the text describes is "one-tailed risk." We call it that because it represents one-tail of a normal distribution of outcomes (a true normal distribution has two-tails ... one above and one below the expected value). Looking at one-tailed risk is convenient because in most situations we can easily deal with projects that exceed expectations. It is the ones that do not meet our expectations that often are problematical ... in any event, failing to meet expectations means that shareholder wealth is not increased by as much as we expected.


We can classify projects into several types:

Independent: Acceptance or rejection has no effect on other projects

Mutually Exclusive: Acceptance of one automatically rejects the others

Contingent: Acceptance is dependent upon the selection of another

If all projects are independent, the limitation on which projects we accept is based on our cost of capital and the amount of capital we have to invest. All companies have constrained resources ... that is, there is a finite limit to how much we have available for investment.

When funds are not constrained, our investment strategy generally follows the following strategy:

1. Expand output until marginal revenue equals marginal cost

2. Invest in the most profitable projects first

3. Continue accepting projects as long as the rate of return exceeds the MCC

None of us really can tell the future. That creates a quandary when we need to develop our capital budget.

1. All projects may not be known at one time

2. Changing markets, technology, and corporate strategies can make current projects obsolete and make new ones profitable

3. Difficulty in determining the behavior of the MCC

4. Estimates of cash flows have varying degrees of uncertainty

The last one is quite significant. My own experience is that in most projects the positive cash flows are over estimated and cash outflows are under-estimated. That means that projects rarely turn out as favorable as they were estimated to be when they are approved.

None-the-less, we do need to estimate them to the best of our ability. A good CFO will challenge the numbers ... trying to force a bit of reality into them. If you do a good job estimating the cash flows over a number of projects, you will be more likely to get your projects approved.

Early in my career, I was Corporate Manager of Financial Analysis for a Fortune 500 firm. We had one subsidiary that was particularly inaccurate in its project cash flow estimates (we did post implementation reviews of all major projects). We certainly did not have the time to completely investigate every one of their projects at the depth needed to figure out which new projects were badly projected and which were not. Our solution, heavy handed and crude as it may be, was to add an additional premium in calculating the required return for its projects. They complained, of course. Our CFO was quite firm and blunt ... until they could demonstrate accurate cash flow estimating, they had no credibility in the capital budgeting process and the premium stayed.


A couple of comments on "incremental cash flow." Only those cash flows that would change if the project were done should be included in the project analysis. Past cash flows are "sunk" and are not relevant. Cash flows that would be the same whether or not the project is done are not relevant. Be honest about these issues ... you'll have greater credibility for your projects if you scrupulously use only those cash flows that are truly incremental. One common gray area is working capital investment ... often it is difficult to be sure about what the effect of a project will be on inventory and/or accounts receivable. In those cases, be conservative and lean towards the high side of additions and the low side of reductions.


Companies have used a variety of techniques to analyze projects. Only those that include time value of money have any theoretical validity. None-the-less, you may still see some companies that use payback period. Payback period is a very dangerous technique and can lead to poor project choices. It does not look at any cash flows past the payback period. Avoid payback period ...

The two most common methods using time value of money are Net Present Value (NPV) and Internal Rate of Return (IRR). Only NPV is correct in theory because only NPV properly states the affect on shareholder wealth. Having said that, I'm aware that in many folks' minds the concept of return on an investment means a percent. For those folks, IRR is a way to express a percent while being quite close to theory. IRR is really just a special case of NPV. The IRR is the discount rate that sets the NPV for a series of cash flows to zero.

NPV and IRR make certain assumptions about discount rates and the return on future cash flows. In NPV, all cash flows are handled at the discount rate used to calculate the NPV. In IRR, all cash flows are mathematically assumed to be affected by the IRR. That can introduce a distortion in the analysis because it assumes that the future positive cash flows can be reinvested at the IRR. IRR also has one other difficulty ... for each sign change in the cash flows, there is an IRR solution. For "normal projects" that's not a problem because there is only one sign change (from outflow to inflow).

T-0 T-1 T-2 T-3 T-4 T-5 Number IRR solutions

- + + + + + 1 ("normal project")

- + + + + - 2

- + + - + + 3

- + + - + - 4

And so on. See the problem?

To resolve both deficiencies, we adjust IRR to create "Modified Internal Rate of Return" (MIRR). I prefer the original name for this "Net Terminal Value Discounted to Present" because that's a good description of what we actually do. To calculate the MIRR, take each positive cash flow (cash inflow) and calculate its future value at the end of the project using the risk-adjusted cost of capital as the interest rate. Take each negative cash flow (cash outflow) and discount it to present value using the risk-adjusted cost of capital as the discount rate. Add all the future values together and add all the present values together. The MIRR is the discount rate that equates the future value sum to the present value sum using the life of the project as the number of years. So ... if you absolutely, positively must report the project return as a percent, use MIRR ... it has the same theoretical accuracy as NPV for the most part. NPV is still preferred though ... it tells us by how much the value of the organization will be changed by doing the project.

Solution Summary

Breakdown of instructors notes to simplify understanding