# ROR/IRR Analysis of mutually exclusive alternatives

I've got this homework problem, and I get two different answers solving it two different ways. I'd like to know which is the right answer and, if it's easy to explain, what is the flaw in the method that gives the incorrect answer?

We're given the cashflow table below and asked to use Excel to find 1) the more attractive option using rate of return (ROR) analysis, and 2) the delta-ROR for B-A (answer as a percent to two decimal places). My professor doesn't see any problem with either method, however, the answers from the two methods aren't even close. I feel like Method B is probably the right answer, but then what logical mistake did I make with Method A that makes it give me the wrong answer?

This type of comparison seems like it has practical real-world value, so I'd really like to ensure I am understanding this concept correctly.

It's easy enough to create a cash-flow table in Excel and just use the IRR function. This was my first attempt at this problem. In the images below, you can see I've gone out 100 yrs on the infinite portion of the annual beneftis. I've stretched this out as far as 1000 yrs and the answer only changes out at like the 10th significant digit, so it's converging right around 7.52%.  $$IRR=PW of Benefits - PW of Costs=0$$