Mark founded a company and owns 100% of the shares. The book value of the company is $100mill, but the market value is different. If the company is not good, it's market value is $70mill. If it's good, it's market value is $150mill. There is a new project opportunity, and Mark needs $50mill. The PV of the project cash inflow is $55mill, so the NPV of the project is $5mill. The company will raise the money by issuing new shares. There is asymmetric information about the quality of the company between Mark and external investors. Only Mark knows the book value of the company's assets. But there is no asymmetry in information about the new project. The external investors think the company has 55% probability of being not good, and 45% probability of being good. Everyone is risk neutral.

a. Assume the market is competitive and there are no transaction costs. What would be the equilibrium portion of shares held by external investors when the company issues the new shares?

b. Suppose the company is not good. What are Mark's gains or losses from executing the new shares and investing in the project? Compare the outcomes with and without the equity issue and investment.

c. Supposed the company is good. What are Mark's gains or losses from executing the new shares and investing in the project? Compare the outcomes with and without the equity issue and investment.

d. What signal will the issuing of the new shares give external investors?

e. What hypothesis explains the corporate financing pattern based on similar argument seen in this question?