The bank determined that the net gain they would get from renovating the house and then selling it, will be lesser than $10.
Net gain from selling post renovation=Expected gain from auction-(65000+2000+taxes).
Expected gain from auction=probability of house getting sold*price at which house will be sold + probability of house not being sold*0.
So,
Net gain from selling post renovation=probability of house getting sold*price at which house will be sold + probability of house not being sold*0 - (67000+taxes)
It is given that there were many houses in the neighborhood which were not selling since years. So probability of house being sold was also very low. The bank determined that the net gain from renovating and trying to sell was going to be below $10 and hence was willing to sell the house at that price.
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