"TRADE4U", a B2B commerce startup intends to rise $10M in order to develop its first prototype and patent the new algorithm. In previous rounds one single "Incumbent Investor" invested $50M. As result the II holds 50% of company's stock.The Firm has a contract with a large concern to be acquired for $100M pending on proof that the prototype actually works and the patent is granted. The entrepreneur received also an offer from a local TV producer to act in a reality show series by allowing the producer to film her daily activities at the firm in secret (without the agreement of employees, investors, etc.). The compensation for this job is $1M. If the entrepreneur concentrates all her efforts working on the project the probability of success is 80% but in case she has to split the effort between the project and the TV show the probability of success drops to 25%. Please answer the following questions:

1. Shall a rational investor without budget constraints invest in "TRADE4U"? Please explain.

2. I the answer to question one is yes, what share in the company shall the investor receive?

Please explain.

3. The entrepreneur receives a $0.5M gift from a rich aunt and considers investing it in the startup and reduces the investors share. Would you advise her to invest the gift in "TRADE4U"? Please explain.

4. BONUS (5 points): Shall a New Investor and the II have different strategies?