 # Corp Finance Question

In the CFAi text, Page 35/36 Q 13,14 they ask you to determine what discount rate would result in the same npv for both projects and then in the next question, how many discount rates produce a zero NPV, subsequently asking what those rates were…how does one find the answers to these? I see it nowhere in the text… Is there any easy way to do this on the BAII?

Both questions use the concept that the IRR is the rate that results in a zero NPV. For the rate that equates the NPVs of the projects, first realize that "the NPV of the difference equals the difference of the NPVs). Tirst create a new project where the cash flows are equal to the difference in the cash flows of the two projects. In other words, for each year, subtract the cash flow of project A from the CF of project B. Then calculate the IRR of this project. The IRR is the discount rate that results in an NPV of zero. So, the NPV of the “difference project” is zero at this rate. Now (don’t take my word for it), just verify that this rate results in identical NPVs for the two projects. As for the second question, if the project is a “normal” one (i.e. either all outflows (or zeros) followed by all inflows (or vice-versa), it will have one rate that results in a zero NPV (i.e. one IRR). If cash flows change direction more than once, you could pick up one potential IRR for each CF directional change. To find the discount rate that result in a zero NPV, just calculate the IRR of the project.

For problem 13 check this out: http://www.analystforum.com/phorums/read.php?11,823860,823860#msg-823860 For problem 14, since the sign of the cash flows changes more than once, (-50 initial outflow, then 100, then 0 then -50) it has more than one IRR. The first os indeed 0, for the second IRR try out the options in the problem. CF0=-50 CF1=100, F1=1 CF2=0, F2=1 CF3=-50, F3=1 Hit IRR, that will give the 0 discount rate. Hit NPV and try out the 32, 62 and 92 rates. At 62 gets you a bit under 0.