Consider the two projects below. Rate of return = 10 Year 0 1 2 3 4 NPV IRR Project 1: -100 36 36 36 36 14.12 16.37% Project 2: -100 0 0 0 0 19.53 15.02% What discount rate would result in the same NPV for both projects? A) a rate between 0 and 10 B a rate between 10 and 15.02 C) a rate between 15.02 and 16.37 D) a rate above 16.37 This is number 13 in CFAI text. Is the answer always going to be between the cost of capital (10) and the IRR that corresponds with the higher NPV project? How do you figure it out if this isn’t the case? Thanks

To find the discount rate that equalizes the two projects, first create a new project whos cash flows are the differences between the two projects. Then calculate the IRR of the “difference” project. However, I think you have an error in project numbers (the cash flows for project 2 are all zeros). Get the correct ones and I’ll work it out for you (if someone else doesn’t beat me to it first.)

for project 2, year 4 is 175. My bad.

The cash flows on the “Difference” project are as follows (I subtracted #2 from #1, but it works just as well the other way): CF0: 100-100=0 CF1: 36-0=36 CF2: 36-0=36 CF3: 36-0=36 CF4: 36-175 = -139 The IRR = 13.16 (Verify for yourself that the NPV for both priojects at this rate is $6.72) The concept behind this approach is that the IRR is the rate that forces the NPV to zero. Since we’re doing it in “differences”, this is the rate that makes the difference in the NPVs zero.

Wow thanks a lot. That helps tremendously.