# mutually exclusive projects

If you have mutually exclusive projects with different lives, and they are NOT expected to be replaced indefinitely how do you select ? do you simply take the one with higher NPV ?

you have to find the equivalent annual annuity (EAA) formula to basically get them on the same playing field (same life), then take the one w/ bigger EAA

andrew are you sure ? i know of the EEA and least common lives approach… but are not those for only when you expect them to be replaced indeinitely ? and if you can tell me the logic so that i would understand, that would be great

I thought EAA assumes infinite replacement? Which makes using an annuity possible?

sdanalyst Wrote: ------------------------------------------------------- > I thought EAA assumes infinite replacement? Which > makes using an annuity possible? me 2… the other question i have is if your a firm and you have \$100, wacc=10% you have only two mutaly exclusive investments invest 1, get 5 in a year invest 100, get 110 in a year do you invest 1, and return 99 to your investors since that creates a higher NPV ? ugh my silly brain, i come up with questions that keep me busy for hours, and they will never be tested !

ahmadmadoff Wrote: ------------------------------------------------------- > sdanalyst Wrote: > -------------------------------------------------- > ----- > > I thought EAA assumes infinite replacement? > Which > > makes using an annuity possible? > > me 2… > > the other question i have is > if your a firm and you have \$100, wacc=10% > > you have only two mutaly exclusive investments > invest 1, get 5 in a year > invest 100, get 110 in a year > > do you invest 1, and return 99 to your investors > since that creates a higher NPV ? > > ugh my silly brain, i come up with questions that > keep me busy for hours, and they will never be > tested ! I think if the projects cannot be repeated, you just take the one with the higher NPV. I don’t think you can do EAA with non-repeating projects. Concerning the 2nd question, I think it depends on what the circustances are. On a purely corporate finance NPV basis, your answer could be different than the “right” answer. The invest 1, get 5 back has a higher NPV than the invest 100 get 110, and since the WACC is 10%, the invest 100 get 110 back doesnt really make sense. Most likely the company can find something else to put the 99 towards other than a project (buy back stock, invest, etc).

i dont think it matters wheather or not project is gonna be replaced indefinitely. i think it is just an assumption that we make so that it helps us pick which project is more “efficient” in earning positive NPVs.

For those who suggest using EAA even if the projects do not repeat indefinitely consider the following two NOT repeating projects: R=10% Project Short: -100 60 90 Project Long -140 80 70 60 Since project Short is one year shorter, let’s add 1 cent to it in year 4, what diff 1 cent is going to make, you can neglect its effect. So it becomes -100 60 90 0.01 So now they have equal lives, we can simply use NPV, Long has a higher NPV of 35.66 vs. 28.93 for short so Long wins. If you use EAA with original cash flows (not add the negligible 1 cent), you have an EAA of 16.66 for Short and 14.34 for long so Short wins. I hope you can see that applying EAA for no repeating projects yields results that are inconsistent with the intuitive NPV rule. And thus EAA is only for repeating projects…. Also to support my concept, page 40 in corp book: “the analysis of a one-shot investment differs from that of an investment chain.” So clearly they do not want us applying EAA for one shot investments.

Also to answer my own other question, since I owe it to those who I might have consfused, here is what I reached. Since you investors have a 10% required return (say all equity for simplicity) Giving them back 99 as div today, and 5 in 1 year has an npv of 103.54 giving them 100 in 1 year, had an npv of 100 so your investors would prefer the first option they can simply take the 99 you paid out as diff and invest it in another firm with equal risk to your firm and get their required return, thus they would have gotten more than they demand on 1 investment, and equal to what they demand on the other 99, which is better than getting what they demand on 100 but for this to be valid, there must be no transaction costs, if they are going to pay part of the 99 to buy another stock, you are going to need a very impressive return on that 1 invested to make up for that fact also markets must be efficient, else they will oncur costs to find a correctly priced stock with the same risk…. Someone else before suggested using money to buyback stocks…that’s basiclly returning it, so same thing as I am talking about here… Now remmber this is a scenario from hell where a firm has only two investments to chose from and nothing else possible… If after reading it once you don’t get it, move on, you will never see it again in your life. Sucks for me I keep coming up with these scenarios and spending hours on them.

sorry, i didn’t realize this one-shot, non-repeating project thing was that common…the only EAA problems I have seen they just give you the projects w/ different lives and you have to find the EAA, then NPV and make a choice. Can you find a problem in schweser or CFAI text with this one-shot problem?

AndrewUNH Wrote: ------------------------------------------------------- > sorry, i didn’t realize this one-shot, > non-repeating project thing was that common…the > only EAA problems I have seen they just give you > the projects w/ different lives and you have to > find the EAA, then NPV and make a choice. Can you > find a problem in schweser or CFAI text with this > one-shot problem? well you would think in the real world it is more common than repeating… how many investments do you think of that a firm will be making forever ? markets change etc…nothing will go on for ever… as far as finding one in cfa or schweser, you wont, cause the LOS is trying to teach you about how to handle the repeating the non repeating is a simple npv thing you would have seen in level 1… good luck on exam.

you are right, but that’s good we won’t see it here…good luck to you too