Which of the following statements about the internal rate of return (IRR) for a project with the following cash flow pattern is CORRECT? Year 0: -$ 2,000 Year 1: 10,000 Year 2: - 10,000 A) It has two IRRs of approximately 38% and 260%. B) No IRRs can be calculated. C) It has a single IRR of approximately 38%. ----------------------------------------------------------------------- The number of IRRs equals the number of changes in the sign of the cash flow. In this case, from negative to positive and then back to negative. Although 38% seems appropriate, one should not automatically discount the value of 260%. Check answers by calculation: 10,000 ÷ 1.38 - 10,000 ÷ 1.382 = 1995.38 And: 10,000 ÷ 3.6 - 10,000 ÷ 3.62 = 2006.17 Both discount rates give NPVs of approximately zero and thus, are IRRs. -------------------------------------------------------------- I don’t think I’m understanding this question correctly… I understand there are multiple NPVs because of the change in signs… but is there any way to calculate this on my calculator? I’m not understanding their formulas. Thanks!

hi, i don’t really understand why you’re having a problem here since you say: "Both discount rates give NPVs of approximately zero and thus, are IRRs. " and thus have solved the question already. there are no several NPVs but IRRs in this case. you are right, for each change of the sign of the CFs there may be one possible IRR, but thus must not be the case all the time… meaning you can have a non-normal CF pattern with only one IRR. answer c is a “trick answer”. inuputting the values in your calculator CF sheet will yield IRR of 38%. BUT, because of the change of signs, you should check for the other IRR that is given (260%) as well. a quick way to check this: -2000 + 10000/3.6 -10000/3.6^2 = 6.1728 for this question this is close enough to zero (note that the question asks for the approximate IRRs). the second “real” IRR will be above 260%. alternatively, after typing in the values in the CF sheet of your calculator (TI BA II+ in my case), you could just hit the npv button instead of the irr button, enter i=260%, and compute IRR. this will yield the same result.

P.S.: if there is a question that implies several possible IRRs, you “could” compute those without your calculator (since it itself cannot) using the formula to solve quadrastic equations (http://en.wikipedia.org/wiki/Quadratic_equation#Quadratic_formula). but only if it is a 2-period problem. for periods > 2 you might iterate for possible solutions. BUT, this takes way too much time. CFAI will not pose such questions on the exam.

I’m going to disagree with chefe_ here because I think this is a typical type of exam question. Yes, it would take you a while to figure it out on your calculator. However, if you understand the concept it takes all of a split second to answer. Basically, if you have unconventional cash flows (ie. not an outflow followed by an inflow) you will have multiple IRR’s. Once you understand this, you can automatically discount C & B. The only way you could ever have no IRR would be if you had an outflow only. Then your return would be zero percent. That’s B gone. Unconventional cash flows have multiple IRR’s. That’s C gone. Answer A.

I am not sure of any direct method on the calculator unless you want use for IRR=38%–> N=1,FV=10000, i/y=38, PV=-7246.3768 N=2,FV=10000,i/y=38, PV=5250.9977 When you add them, it comes to 1995.38 which is approximately equal to the outflow=2000 at the beginning. Similarly, for I/Y= 260, t=1, PV=2777.78 & for t=2, PV=-771.604 When you add both the PVs you still get 2006.176 approx. 2000. So, in both the cases of IRR i.e., 38% & 260% we get a NPV=0 hence, the option a) is correct based on the fact that IRR is the rate which makes a project’s NPV=0. Hope this helps!

I agree with Soddy1979 - you don’t even need a calculator for this one. If there are unconventional cash flows, i.e. more than one cash OUT flow, there will be more than 1 IRR. There may be a question related to the “problems of IRR” related to this also.

soddy1979 Wrote: ------------------------------------------------------- > […] > > Basically, if you have unconventional cash flows > (ie. not an outflow followed by an inflow) you > will have multiple IRR’s. > > Once you understand this, you can automatically > discount C & B. no, not automatically. if there is an unconventional CF pattern, there MIGHT be several IRRs (possibly one for each change in signs) but this is not a MUST. > The only way you could ever have no IRR would be > if you had an outflow only. Then your return would > be zero percent. That’s B gone. don’t you think that your return would be -100%? about the relevance of finding a possibly additional IRR: ok, let me rephrase: it is possible with your calc to find it, sure… but what is the benefit? to show that you can calculate NPVs with a range of different rates and see which one brings NPV closest to zero? the concept is important, but i rather think, that if a question related to several IRRs is posed, than - either you’ll have some direction on in what range to start iterating (like in the description of the question above), - it is obvious for some reason what the IRR must be, or - it will be a conceptual question without calcs

chefe_ Wrote: ------------------------------------------------------- > soddy1979 Wrote: > -------------------------------------------------- > > The only way you could ever have no IRR would > be > > if you had an outflow only. Then your return > would > > be zero percent. That’s B gone. > > don’t you think that your return would be -100%? Sorry I should have said this is indeterminate (ie it’s not -100% or 0%). It still means there is no IRR though. However, as the question has multiple cash flows it still rules out B. I stand corrected on this, but I thought the number of IRRs was the same as the number of changes in cash flow direction. I didn’t think this was ambiguous. This is definitely a conceptual question though.

thank you for all the input everyone! definitely helped a lot!