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Based on your prior question on another case, you seem to be "obsessed" with sunk cost.
I'd advise you to get off this thinking. You're recruiting for a consulting role, not an economics/research assistant role.
Sunk cost is a useful concept to know in life, but they're not particularly common in cases!
All that said, the case explicity states "The total investment has to consider both, i.e. the acquisition cost of the island should not be considered as sunk." As such, you just need to take the interviewer at their word...especially given that ROI in business still needs to be calculated off all total investments (sunk cost or not)
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Hi Vasco, thanks for your comment.
It's totally reasonable wondering if consider the acquisition cost as already incurred ("sunk cost"). However, as mentioned by Ian, if the interviewer - when asked - recommends to include it in the NPV analysis, you are supposed to follow it.
Regarding your alternative option for the investment, I would mention it in the next step (i.e. compare the NPV calculated for the resort vs the other ideas). Also here the interviewer had led you into the resort idea, therefore you are supposed to follow it.