Imagine that you are a venture capitalist at Conrad Ventures evaluating the following startup idea today (assume todays date is January 1, 2022). Your fund typically seeks a 25% IRR on its investments. The startup requires 4 rounds of financing over the next 7 years: $1 million today, $1 million in two years, $2 million in 3 years, and $3 million in 7 years. If the company has an IPO at the end of 10 years, the company will be worth $1.2 billion; the probability of an IPO is 10%. Otherwise, if the company is acquired by another company in 10 years (which happens with 35% probability), the expected acquisition value will be $900 million. If the company does not get acquired, it will be worth 0. The founders of the company initially allocate 1,100,000 shares to themselves, and decide keep 250,000 shares in reserve in case they wish to hire any additional employees in the future.

a) Please provide the share price of the startup in each round of financing and the number of shares issued to investors in each round.

b) How do your answers to part a) change if the probability of acquisition is only 15% (assume all other information in the problem stays the same)? Please provide one sentence explaining intuition for how the results change.

c) Suppose the founders wish to understand how potential changes in the investment amounts would impact the share price in each round. If the share price in round 2 were to decrease by 2.36%, due to a change of x% in the investment amount in the third year, what would x be? (Assume all other information in the problems stays the same as originally posed, so the probability of acquisition is 35%. Also assume that the number of new shares issued to investors at time 0 stays the same as what you calculated in part a). If you are unable to answer this question, please provide equations that describe the conditions that x must satisfy.