Two projects have the following cash flows: Time 0 1 2 Project A 100 -275 300 Project B -100 300 -200 The internal rate of return (IRR) problem most likely to emerge with each project’s cash flow is: a. Both projects have a multiple IRR problem. b. Project A has a multiple IRR problem, Project B has no IRR. c. Project B has a multiple IRR problem, Project A has no IRR. How do you identify which project has a multiple IRR or no IRR? I’ll post answer shortly. Thanks!
With every change in the number being positive or negative, that’s how many IRRs you will have. So, project A goes from 100 (positive) to -275 (negative) and back to 300 (positive). So it has two IRRs Same idea for project B. Hope that helps.
c Project B has multiple neg CFs - so pot. multiple IRRs Project A has none…as initial CF is a +ve one
I think it’s A. I think it is when the sign of the cash flow changes more than once, can someone elaborate?
I agree with locoman83. I checked the manual for my BA II and it states that the number of possible IRR values is equal to the number of changes in the sign of values. Projects A and B both have two sign changes in the cash flows. Therefore both projects have two IRR values. Cheers
Then when will a project have no IRR?
Project A has multiple. B has one IRR = 0 Can’t you check this by putting CF’s into your calc? If it errors you have multiple IRR’s.
And the answers is, C. This was in Stalla’s practice exam #3 with the following explanation - “Two values of IRR satisfy the cash flow pattern in Project B (0% and 100%), giving rise to the multilpe IRR problem. No values of IRR (“no IRR” problem create a zero NPV for the cash flow pattern in Project A.” Looks as though this would fit with ov25’s description. Anyone want to elaborate?
jblamb - I took your approach and got this wrong.
Project B -100+300/(1+r) - 200/(1+r)^2 = 0 -100(1+r)^2 + 300(1+r) - 200 = 0 100+200r+100r^2 - 300 - 300r + 200 = 0 100r^2 - 100r = 0 r = 0 or 1 2 positive roots you would face a multiple IRR
Can we have a consensus here? I was also taught in college that 1 change in sign = 1 IRR
A
I think that the consensus is that generally with a more than one sign change in the cash flows, multiple IRRs exist. I am sure on the exam, it will be more straight forward than this question, as it is a bit complex when compared to the principle the CFAI is trying to teach: multiple sign changes = multiple IRRS. Everyone agree?
The answer is C. Earlier in this thread “cpl123” did some maths and showed that B has IRR values of 0% and 100% and so has multiple(2) real values. For the solution for A, he left the formulation as a quadratic equation which has 2 roots but both roots are imaginary so no real roots.