If we are looking at this issue purely from an economic point of view, Mike should buy the engine and then resell the airplane. This would give him a greater marginal benefit (relative to marginal cost) from this point forward.
Economists say a person should not let their decisions be affected by money they have paid out in the past. In other words, Mike should not pay any attention to how much he has already spent or what he had thought would happen when he bought the plane. The money that he has already spent is called a “sunk cost.” It should have no effect on what he does going forward. All he should think about is what will make him the most money (or lose him the least) starting right now.
So, we have to think about this as if Mike were starting from zero right now. He has two choices. He can sell the plane as is for $180,000 without incurring any further costs. His “profit” from here on out would therefore be $180,000. His other choice would be to buy the engine for $95,000, at which point he could sell the plane for $310,000. When you subtract $95,000 from $310,000, you get a figure of $215,000. That means that Mike’s “profit” from here on out would be $215,000 if he were to buy the new engine, fix the plane, and resell it.
From this, it is clear that Mike should buy the engine, finish restoring the plane, and sell it. He will still lose money overall, but this is the best choice given that he cannot go back and refrain from buying the plane in the first place. Mike needs to forget his sunk cost and just look forward. If he does this, he will see his marginal benefit from buying the new engine and then selling the plane will exceed the marginal benefit of just selling the plane as is.