# 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.

Thanks in advance!

Method 1, calculating the incremental IRR using the IRR function gives an answer of 7.52%

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%.

Method 2, calculating the incremental IRR using the Present Value (PV) function gives an answer of 10.85%

Using the definition of IRR:
$$IRR=PW of Benefits - PW of Costs=0$$
First, I calculated the present values of everything. Then, I used goal-seek to find the rate that makes the net-present worth = 0. This results in an incremental IRR of 10.85%. This is the same answer my professor got when he solved the problem. He used a similar PW-based approach by solving for NPW=0 at various rates, and then using interpolation to find the rate where the value switched between positive and negative.

• Sorry for using images. I spend about 25 minutes trying to get the first table to format correctly, and I couldn't get it to work. I followed the advice in the link below, but even copying/pasting the suggested "correct" code from the accepted answer resulted in nothing more than a box around the code block (just like the original poster). math.meta.stackexchange.com/questions/6734/… Oct 29, 2022 at 20:23