In my opinion, this case is very poor, if not borderline bad. Yes, you do all kinds of profit, sales, etc. calculations. But you said: “The main goal of the client is to enhance their brand image as a sustainable retailer (…)” So the main objective WHY he wants to do this is BRAND IMAGE. However, you completely fail to clarify this case logically. What is “brand image” exactly and how is it concretely measured (as a KPI), which factors are used to calculate the brand image. This is what the client's objective is, not your profit calculations! So I would advise you to rework this case significantly. In a real-world consulting project, you would most likely fail to tell the CEO in the end (by hard facts) how much his brand image has improved.
With all the respect to you, I think you did not get the point of my question,.. let's assume you sit in an interview at McKinsey, potentially last round with a partner, and the objective of the client was clearly stated what I said above: improve brand image!... what exactly would be your answer to the interviewer (partner in this case) once you are done with all the analysis you mentioned if he asks you: "Okay fine, but please tell me exactly by how much our brand image improved in terms of hard facts, as this is what our client has asked us to do!" would you really then say, "we did our analysis, and revenue should improve by amount X"? The case stated a client objective/goal and then did something completely different, what does have revenue to do with brand image? And making an (implicit!) assumption that with a raise in revenue also brand image improves is too dangerous in my opinion. This is what I meant with my question. To my understanding, if you do what you described, you are not solving the case differently, but just straight up wrong. But of course it's just my opinion, and I wanted to know why the case was structured this way. Maybe I miss something.