# NPV and IRR

Question 13 in Reading 44 gives the cash flows for 2 projects. It then asks what discount rate would result in the same NPV for both projects. Is there a precise way to calculate this? I have a BAII Plus Pro, but it seems like trial and error is the only way to do it.

I should qualify that I understand this represents the point of intersection on the NPV profile, but this still requires calculating the NPV for a large number of discount rates for both projects.

There is set the 2 equations = to each other it will simplify to 0 36 36 36 -139 punsh those in your calculator and you get the correct rate

Project 1 has several cash flows throughout the life of the project. Project 2 has one cash flow near the end. Projects with cash flows mostly near the end of the project have a steeper slope on the NPV profile (the NPV will be more volatile to changes in the discount rate – kind of like how zero coupon bonds have the highest interest rate risk). So it is known that Project 2 has a steeper slope and yet has a lower IRR. If you draw out the NPV profile, you’ll see that the slopes of the two projects cross at some point where there is a positive NPV; therefore, the discount rate that would equate the two projects’ NPV’s is somewhere between 0% and 15.02% (I don’t think it can be between 15.02% and 16.37%, since it appears to me that the slope of Project 2 would have to be negative for that to occur). And also you can see that at the discount rate shown in the problem, 10%, Project 2’s NPV is greater than Project 1’s. So the crossover point can’t be less than 10% because this would just accentuate the difference, as seen from the NPV profile. By the process of elimination and by looking at the chart, you can see that the crossover point must be between 10% and 15.02%. I know that explanation is confusing and probably not a very practical way to think come exam time when you’ve got barely any time to work each problem, but that’s how I thought about it when I worked it.

Brilliant - thanks!