You work at Apple and you are interested in buying a startup with some exciting virtual reality gaming technology that you hope to integrate with your new VR glasses.

Your instructions are to find a VR gaming firm to acquire.  If possible, you would like to do a deal, but your overriding goal is to maximize the expected value of the company your firm purchases.

A new VR firm ("YouWillNowQuestionReality.com") is offering to sell themselves to your firm.  They offer you a chance to make a single bid for the company in the next 24 hours.  They will say yes or no to your offer.

Your analysts believe the company could be worth 0.5 Billion, 2 Billion, 3.5 Billion, 5 Billion or 6.5 Billion with equal probabilities.  But you can't determine which value is correct.

The VR firm knows its true value.

As you already have some technology in this area and a top team of executives, you believe you will add 3 billion in value to any firm you buy.  Yes, your team is simply that amazing - being full of NYU Stern Alum of course! 

 

(a)  What price should you offer to maximize expected profit? 

 

(b)  What is your expected profit with that offer? 

 

(c)  What if the VR firm did NOT know its true value?  They are as in the dark as you are in terms of the quality of their technology.  What price would you offer then to maximize your profit?