Buying a Start-up: You are a (risk neutral) private equity investor and want to buy a start-up, that is currently owned by its (risk neutral) founders. The start-up will succeed with probability q, which is independent of the sale, but the value of the start-up in case of success is $160m if you buy it (because of the additional funds and your expertise), and $140m if the founders keep it. If the start-up does not succeed it is worth 0. (a) Assume first that both you and the founders know that q = 50%. At which prices p is trade profitable for both parties? (b) Now assume that q can be either 50% or 25%, but that only the founders know the actual value of q, while you think q is equally likely to be 50% or 25%. You are wondering which price to offer for the stake, and are considering three options. $70m since this is the lowest price to induce the founder to sell if Offer p = q = 50%. Offer = Offer p = q= = 25%. $60m since this is your expected value of the start-up. $35m since this is the lowest price to induce the founders to sell if Which of these three options is most profitable to you (the private equity in- vestor)? At which prices p are you facing adverse selection, i.e. the founders would only sell the stake if q = 25%, but not if q = 50%? Is there any price p at which you profitably purchase the stake if q = 50%?