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Â Last time we looked at drawbacks of using payback period and

Â some possible ways of addressing those drawbacks.

Â In this video, we will continue looking at drawbacks of other decision tools.

Â In this context,

Â we will also look at ways of addressing al least some of these drawbacks.

Â The couple of things we will talk about are the modified IRR and

Â the profitability index.

Â We will also talk about a couple of other ways of addressing these drawbacks

Â in greater detail later in the course.

Â First, we discuss the drawbacks of IRR.

Â One of the main assumptions with IRR is the idea of compounding.

Â It assumes that all cash flows generated over the project's life are reinvested in

Â the project.

Â And these cash flows also earn the same IRR over the remaining life of

Â the project.

Â How are this may not always be possible for two reasons.

Â One investment in a project maybe made only at fixed points in time over

Â its life.

Â We can reinvestment cash flows on an annual basis.

Â Reinvestment of the project means the project scale is constantly increasing

Â over time, which may not be feasible or also may make the project unattractive.

Â Even if one were able to reinvest the cash flows in the project,

Â there is no guaranteed that those cash flows would continue to generate the same

Â internal rate of return.

Â So the IRR may actually always state the return a project generates.

Â One lead to address the problem is to use the modified IRR, MIRR in short.

Â For this, we are to calculate the future value of all cash inflows

Â at the end of the projects useful life using its cost of capital.

Â The initial investment is already in present value terms, and

Â nothing needs to be done to it.

Â For a project with a useful life of n years,

Â then the MIRR is calculated as the future value of cash flows

Â divided by the present value of the initial investment.

Â The whole thing raised to the power of 1 over n minus 1.

Â Let's go back to our original example with an initial investment of $1 million

Â followed by annual cash flows of $200,000 for 9 years.

Â The project had a cost of capital of 15% and an IRR of 13.7%.

Â The future value of the annual cash flows can be calculated using the FV function

Â in Excel.

Â For us to input that the function is the cost of capital which is 0.15.

Â The number of cash flows is 9 which is the second input.

Â The third input is the annual cash flow of $200,000.

Â This gives us a future value of $3,357,168.

Â Now the MIRR is 3,357,168 divided by the initial investment of $1

Â million the whole thing raised to the power of 1 over 9 minus 1.

Â The MIRR of the project comes out to 14.4%,

Â which is higher that the IRR of 13.7%.

Â The MIRR still has to be compared to the hurdle rate of 15%.

Â Since, it is lower than the hurdle rate, we will still reject the project.

Â A second problem with IRR is there are times of project may have multiple IRR.

Â This is especially true when cash flows change sign more than once during

Â the project's life.

Â Let's look at a very simple example.

Â A two year project requires an initial investment of $6 million at year 0.

Â Generates cash flows of $15.5 million in year 1 and

Â has a net outflow of $10 million in year 2.

Â This project has two valid IRRs, 25% and 33.3%.

Â See the graph to understand what is happening.

Â The graph has NPV on the vertical axis and the discount rate on the horizontal axis.

Â The curve cuts the horizontal axis at two points,

Â which means that the project has two IRRs.

Â For projects where the cash flows change sign more than once,

Â it is better to use NPV as a decision tool.

Â Alternatively, we could use the MIRR and compare it to the hurdle rate.

Â A third drawback of IRR is that times an IRR may not even exist.

Â This happens when all project cash flows are of the same sign.

Â These are however rare instances, in such cases too,

Â it is better to use NPV as a decision tool.

Â A fourth drawback is something we saw earlier.

Â IRR and NPV may give us contradictory decisions when trying to select one

Â projects from among many, in which case, it is again better to use NPV.

Â Finally, when we look at the drawback of NPV,

Â remember NPV depends on future cash flows, most of which are unknown.

Â This requires us to estimate what these future cash flows are likely to be.

Â Regardless of how well we estimate these cash flows,

Â there's always uncertainty in the cash flows.

Â This uncertainty in the cash flow forecast leads to uncertainty in NPV.

Â This requires further analysis on identifying our assumptions that

Â critically impact our NPV calculations.

Â This is what sensitivity analysis is all about which we will discuss in

Â a later video.

Â Another drawback of NPV analysis is that it assumes the decision to accept or

Â reject a project cannot be revisted.

Â A project may have a positive NPV today, and

Â the company decides to go ahead with the project.

Â After a year or two, the company realizes that the project isn't doing as well as

Â they expected it to do, because sales revenues did not pick up,

Â our costs were higher than anticipated.

Â At this point, the company may be better off abandoning the project rather than

Â continuing with it.

Â Traditional NPV analysis assumes that such outcomes are not possible.

Â This is the idea of real options, which we will also cover in a later video.

Â A third drawback of NPV is that it ignores the scale of the project,

Â which project should one select?

Â One with an initial investment of $1 million and NPV of $10 million or

Â another that requires initial investment of $100 million and NPV of $12 million.

Â NPV analysis says that we should accept the second project.

Â But clearly the first project allows us to earn more bang for the buck.

Â Further because of limitations and the amount of capital a firm has.

Â It may not even have $100 million to invest.

Â A fix for this is to use a profitability index.

Â It is defined as the NPV of the project divided by it's initial investment.

Â It measures how much NPV is generated for each dollar invested.

Â The two projects have profitability indexes of $10 million divided by 1

Â million which is 10, and 12 million divided by 100 million which is 0.12.

Â Clearly, the first project gives the bigger bang for the buck, and

Â should be selected over the second one.

Â Next time,

Â we will look at free cash flows which are necessary to calculate MPV and IRR.

Â We will discuss how we go about calculating free cash flows and

Â their relation to net income.

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