I understand that this topic has been discussed in the past a few times but I found the threads to be pretty confusing…anyway, I was looking through my notes and came upon a CFAI question from either the first or second sample test. Basically it stated the following: If the cost of capital is less than the cross-over rate, than the IRR and NPV will have conflicting results. Could someone fully explain this? Thanks!

from what i know when evaluating 2 projects of different sizes and ages they have different profiles- look at it as 2 lines with different slopes The only rate at which they would give same npv ( npv1-npv2=o ) is at the crossover rate basically that tells you that 2 project with different life span and/or different sizes will have same npv at the crossover rate

If you have the Schweser notes - go to Page 20 on Book 4. That has the NPV profile listed there… and you can take it from there.

For a cost of capital smaller than crossover rate, NPV and IRR would give conflicting rankings for 2 mutually exclusive projects.

would it help to say… for 2 projects with different discounter rates, the project with the higher discount rate produces a smaller Net Present Value before the crossover rate because the cash flow is heavier towards maturity.

After looking over the material and drawing a chart or two, I would agree. When comparing two projects that are somewhat similar in NPV but vary greatly in regard to CF timing, the project wth a greater IRR receives most of its cash flow earlier. Therefore, if the discount rate fell below the crossover rate, then this would most certainly benefit the project that receives a large part of its CF at a later point in time (the one with the lower IRR.