BetaGo is a paper mill, which is considering to build a new factory at date t0 beside a river. The new factory costs BetaGo 800 at t0, and can generate cash flows 330 at t1 and 726 at t2. Because the new factory will pollute the river for sure, at date t0, BetaGo can invest in a new technique, which can completely eliminate any potential pollutions. (Hence, by investing in the new technique, BetaGo is sure that it will NOT pollute the river.) However, if BetaGo does not invest in the new technique at t0, it cannot invest in the new technique later. The new technique costs BetaGo 550. By law, BetaGo is fined 363 whenever it pollutes the river.

The rate of return used in this question is 10%.

(a) What is BetaGo's optimal project choice at date t0? [Hint: how many choices does BetaGo have at t0?]

Suppose that at t0, for some reasons, BetaGo has to build the new factory. BetaGo knows that if it does not invest in the new technique, it may potentially acquire GammaGo at t1, which is a pollution-removing specialist. [Hint: obviously, if BetaGo invests in the new technique, it will not acquire GammaGo.] At t0, BetaGo knows that if not acquired, GammaGo's cash flow at t2 depends on the weather at t1: if t1 is sunny (with probability 0:3), GammaGo itself generates a cash flow 605 at t2; if t1 is rainy (with probability 0:7), GammaGo itself will generate a cash flow 121. BetaGo negotiates with the GammaGo about the Merger and Acquisition deal after knowing the weather at t1.

(b) If BetaGo does not invest in the new technique at t0, and it is sunny at t1, is there a price such that BetaGo can successfully acquire GammaGo? Why? [Hint: even if BetaGo acquires GammaGo successfully at t1, it is still fined at t1.]

(c) Suppose that at t0, BetaGo knows that the price of acquiring GammaGo will be exactly GammaGo's present value at t1. Should BetaGo invest in the new technique at t0?

Why?