Firm F has no debt, and needs to raise $600,000 at the beginning of year 0 (1st round). With probability 0.7, F will fail in the first development stage (phase 1) and firm value will then be 0.

If F successfully completes phase 1, it will then need an additional $1.5 million at the beginning of year 2 (2nd round).

If that second cash injection is made, the firm will have a 0.5 probability of completing the second phase, in which case F can be sold at an expected equity value of $15 million at the beginning of year 4. If F fails in the second phase, firm value is 0.

Unlevered expected return on equity for F is 10%


2.1 If phase 1 is successful, what share of F's equity will a year-2 investor require (in exchange for a $1.5 million investment)?

2.2 What share of F's equity will a year-0 investor require (in exchange for a $600,000 investment)?

2.3 Investors realize before the first round of financing that the project will actually need a third round of financing: if phases 1 and 2 are successful, F will not be sold right away, but will instead need to raise another $1 million at the beginning of year 4 to fund a third development phase that lasts 2 years and has a probability of success of 0.8. Let V denote the expected value of the firm at the beginning of year 6, in case of success (i.e. if F successfully completes the three phases). For what values of V would year-0 investors be willing to finance the first phase of the investment.