You have 2 projects. Both are independent. Company’s discount rate is same for both. NPV of project 1 > NPV of project 2 Comment on the following statements a) IRR of project 1 > IRR of Project 2 b) IRR of project 1 < IRR of project 2 c) There exists a crossover rate d) NPV of both projects can be made equal by adjusting the discount rate for which project and in which direction.

c a/b does not have enough information to make that judgement.

The question was to comment on the statements. Not to pick one. I don’t know what you are suggesting by saying c.

(a)+(b) depends on longevity of projects, timeline of payments and initial investment © the projects have the same discount rate (d) increase discout rate of project 1 edit: (a)+(b) have nothing to do with discount rate

Ok map, 2 things, first your answer to part c is inccorect I think. Second let me post a follow up question to this. If NPV of a project is x (assume positive). And I do something to increase it to Y. If IRR of project before the adjustment is t, what will be the IRR of the Project after adjustment. a) increase b) decrease c) stay the same d) can’t determine

IRR is the rate used to discount the future cash flow of a project so that when deducting the initial investment, all equals zero. Increased NPV is a signed of increased flows of cash from the investment or decreased cost, in any case an increased PV of future cash flows. To bring this PV of future cash flows to a value that equals your initial investment you would need a higher IRR if the cash flows increased, or the same IRR if the discount rate decreased.

I guess, to your second question, the answer is (d) can’t determine with the information available. To your first one, the NPV profile is a line (or a curvature/convex curve) crossing the discount rate on horizontal at IRR and NPV on the vertical ax. At the point of intersection between the 2 NPV profiles, that’s the crossover rate, and that’s the rate at which the 2 projects have the same NPV. So I was wrong.

Regarding q 1. can it be very well possible that two NPV profiles are parallel. Remember the projects are independent. Its possile that the project with greater NPV has higher IRR than the project with less NPV. let’s say Project1: NVP 10mln. IRR 15% let’s say project2: NVP 20, IRR 5% and say discount rate is 3%. Can you not create those two projects?

sure you can, they do cross, but not at 3%. IRR is the money or dollar weighted rate of return and takes into consideration both timing of cash flows and amount of cash flows.

Dollar weighted rate of return doesn’t take timing of cash flows into consideration. But that is a separate problem, lets not get into that. The question here is, that why do you think the projects 1 and projects 2 cross. I am claiming there can exist 2 projects that are parallel NVP profiles. Now this is a claim, and you could easily prove me wrong because I am uncertain about my claim. But I want you to give me a valid reason for proving me wrong.

If one has a greater NPV than the other, and a higher IRR than the other, they don’t cross.

Dollar weighted is the IRR, time weighted is the geometric and has no consideration for cash flow timing or value.

My theoram that 2 independent projects can exists such that project 1’s NPV and IRR is ALWAYS higher than Project 2 is false. here’s my proof by contradiction. Assume npv1 > npv2 IRR1 > IRR2 Now, I could arbitarily desrease irr2, and arbitarily increase irr1, such that their nvp cross over.but at the same time ensure IRR1 > IRR2 if they cross over, then that means the nvp profiles are no longer parallel. hence proven.

I am no longer following you!:)) I AM TIRED! Draw your profiles, decreasing IRR2 and increasing IRR1 with NPV1>NPV2 makes them go apart even more. I don’t see your point anyway:) Better let’s get back to those concepts, eh? or sleep, or sheep counting…

<> ALL YOU NEED TO KNOW: ID THEY ARE MUTTUALLY EXCLUSIVE, PICK THE ONE WITH THE HIGHER NPV, EVEN IF IT HAS A LOWER IRR. and know the other 4 cap budgeting equations, people forget them