The owner of firm F wants to get financed by VC funds, but wants to keep control over

her firm and therefore wants to be sure to always keep a share in the firm that is larger

than 50%.

Firm F has no debt, and needs to raise $500,000 at the beginning of year 0 (1st round).

With probability 0.7, F will fail in the rst development stage (phase 1) and firm value

will then be 0.

If F successfully completes phase 1, it will then need an additional $1 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.

The expected return for F is 9%.

1. If phase 1 is successful, what share of F's equity will a year-2 investor require (in

exchange for a $1 million investment)? (4 points)

2. What share of F's equity will a year-0 investor require (in exchange for a $500,000

investment)? (6 points)

3. Show that the owner will accept the deal on both financing rounds. Taking the year

0 costs as given, what is the maximum value for the year 2 costs such that the owner

of the firm accepts the deal on the second financing round? (5 points)

4. Investors realize 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 rm at the beginning of year 6, in case of success (i.e. if F

successfully completes the three phases). Find V such that year-0 investors would

not change the share of equity they require, that is, such that they would accept the

same equity stake as in the previous question. N.B. you do not need the answers to

the previous questions for this question (5 points)