Hello could someone explain this to me, if possible with understandable intermediate steps

A company must raise new capital externally to invest in a new project. The investment cost of the project is 100 and the project generates a certain cash flow of 140. This information is known to the potential new external investors. The company has no internal financial resources to finance the project, and it can only raise new equity externally. However, the potential new investors do not know whether the current asset value of the company (i.e., before investing in the new project) is 100 or 20 and estimate both possible values as equally likely. The manager of the company knows the true current asset value, but cannot make this information public for competitive reasons. All participants are risk-neutral, the manager acts in the interest of the existing shareholders and the risk-free rate is zero. Assume that potential new investors believe that the manager will raise new equity and invest in the new project, regardless of the true value of the existing assets.

a. What share of the company value after investing in the project does the manager have to offer to the new external investors so that they finance the investment cost of 100?

b. Assume that the current asset value of the company is 100. Does the manager raise new equity?

c. Assume that the current asset value of the company is 20. Does the manager raise new equity? Now assume that potential new investors believe that the manager will raise new equity and invest in the new project, only if the true value of the existing assets is 20.

d. What share of the company value after investing in the project does the manager have to offer to the new external investors so that they finance the investment cost of 100?

e. Assume that the current asset value of the company is 100. Does the manager raise new equity?

f. Assume that the current asset value of the company is 20. Does the manager raise new equity?