Hi I have a question in corporate finance regarding Mergers and Acquisitions:

Mergers and Acquisitions During a general meeting, shareholders in company XYZ are debating about the degree of protection to give to minority shareholders in case of a successful takeover. In partic- ular, they are considering whether the raider should he allowed to dilute nontendering shareholders up to a fraction 5 of the posttakeover value of their shares. A potential raider (he) with no initial shareholding in the corporation is considering whether to invest an amount K to search for improvemclts in XYZ management. The extra prots that can be generated with such improved management is a an exponential random variable 15' whose densit)r H19} is linked to K as follows 1 t? t? = __ _ ) VII{ml Jr The realization of 15' occurs, and is observed by the potential raider, only after the initial investment K has been realized. After observing :9, the pot-Itial raider decides whether to attempt a takeover of XYZ. The potential raider can make unrestricted offers conditional on acquiring at least 50% of outstanding shares. Initial shareholders in XYZ are not able to observe 15' and consider themselves as nonpivotal for the success of the takeover. Assume for simplicity that everyone is risk neutral and that the riskfree interest rate is zero. Furthermore, both the prot generated by XYZ under current management and the administrative cost of the takeover are zero. Assume also that initial shareholders play syrrmletric pure strategg,r in their tendering decision. Eve-ts unfold as follows: 1:] Initial shareholders x 6 E [0,1]; 2} The potential raider invest K \"3 D; 3) The potential raider observes 15' and decides whether to malre an unrestricted tender offer 5 \"3 [I to gain control of XYZ; 4) Initial shareholders observe b, but not 19 and K, and decide whether to tender or not their shares; 5} Payoffs are realized. (a) For xed :5, K and 15', determine the minimum bid if necessary,r for a successful takeover. Is it optimal for the raider to bid 5"? (b) For xed :5, determine the investment K " that maximizes the potential raider expected takeover prots (net of the investment). (c) Determine the value 5"\" that maximizes the initial value of XYZ shares of stock