# NPV vs. EAA analysis

Hello,

I am trying to understand why (if a project is expected to be continued forever) we cannot use the NPV method (must instead use the EAA method or the least common multiple of lives method).

With the NPV method, couldn’t you simply calculate the PV on the perpetuity of the indefinite amount of operating cash flows?

This tells me you could simply employ the NPV comparison method between projects rather than the EAA or the least common multiple of lives method.

Thanks,

"Using Wiley for my CFA journey was by far the best option… I was able to pass on my first attempt.”– Moe E., Canada

Where did you get the idea that you cannot use NPV in this case?

You can, of course.

Simplify the complicated side; don't complify the simplicated side.

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In problem 15 of the capital budgeting portion of the curriculum, they if the projects have different services life (and are mutually exclusive), you must use the EAA method.

I am basically wondering why (when the projects are mutually exclusive) we have to use the EAA or least common multiple of lives method over the NPV method

Thanks,

NPV is a useful comparison for projects of the same length, but not for projects of different lengths.  When they have different lengths you need to do something to correct for that; that’s what the LCM of lives and EAA do.

Simplify the complicated side; don't complify the simplicated side.

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But doesn’t the NPV method take into account the time horizons of different project?

If two projects have different time horizons, then the NPV for each project will take into account the time horizon. So if two projects have different time horizons, then longer OCF stream on a project with a longer life would have a greater value.

That is where I get confused.

Thanks again,

what if you are comparing the longer time horizon project against the smaller horizon project and deciding which one is better for you?

how would you do that?

Does a longer smaller NPV project necessarily rule itself out because the smaller higher NPV project came up?

CP

If you compare a 2-year project with an NPV of \$10 to a 4-year project with an NPV of \$15, which is better?

Simplify the complicated side; don't complify the simplicated side.

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To CPK’ question.

Yes, that would make sense to me, especially since if two projects have the same initial investment outlay but the longer term project has a expense cash flow stream that extends farther into the future than the project with the smaller time horizon.

Thus, in this case the NPV would be higher on the smaller life project and we should pursue this over the longer term project (that essentially contains more expenses with the same initial  investment outlay as the shorter term project).

I guess I do not understand the intuition behind this.

Thanks,

The issue is that you can have a project A of 2 years with NPV of 10 and a project B of 3 years NPV of 15. You repeat the choice once the project is over. Which one would you choose? You need a way to see whether the NPV of project A makes less or more than 15 every 3 years if you are to compare it with project B. You can’t simply average or guess, discounting and cash flow distribution over time prevents this (as one can be cash inflow heavy at the start, the other at the end).

One way to do it is to check for the same period how the two projects would do, taking the least common multiple, i.e. 6 years in this case - then you calculate NPV of 3 times project A and 2 times project B and compare those.

The other way (my favorite, as it is 4-5 keystrokes on the calculator and you get your answer) is to calculate the equivalent annual annuity.

keep_running wrote:

Yes, that would make sense to me, especially since if two projects have the same initial investment outlay but the longer term project has a expense cash flow stream that extends farther into the future than the project with the smaller time horizon.

too many assumptions there.

what if none of those were true

what if there was just given a scenario that project A has these Cash flows applicable for 2 years

Project B has these cash flows for 5 years

decide which one is better.

—-

EAA takes out the need for those projects to have identical “this” or identical “that” – any of these may or may not be equal.

It is calculating how much you would outlay on a project on an annual basis.

and based on taht number you can decide which one is better to go with.

and it considers all of the cash flows on each project.

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CP