I just went through the case as to be able to provide an answer.
From what I understand, you are looking for a metric to express the profit (22M) vs investment (110M) without having to use NPV.
For this particular case, I would say you could rely on basic "common sense", which is a key skill as consultant. Often you won't have the time to go for the nitty gritty analysis and will have to use some "common sense".
The client expects a payback period of 3 years. Let's just ignore the discounting for this:
- Given the profit of 22M, the payback period without discounting would be 110M/22M = 5 years
- Given discounting will make the future profits lower today (dividing by (1+WACC)^years), the real payback period will be even longer
- Therefore, the client should not progress with this project
I truly hope this is of any help to you!