A start-up company is raising its Series A round at a $15M pre-money valuation and a $13 price per share. The amount raised in the Series A round is $2M. Two years before the Series A round, the company raised its seed round by issuing a convertible note with a $5M valuation cap and a 25% discount. The principal amount of the convertible note is $1M, with an annual non-cumulative interest rate of 5%.

1. Without taking the seed financing round into consideration, what is the fraction of shares that Series A investors intend to get with IA = $2M and P RE = $15M?

2. What is the fraction of shares held by Series A investors if the seed investor chooses to convert its convertible note using a valuation cap?

3. Series A investors realize that the pre-money valuation ($15 million) does not take into account the shares that are converted from the convertible note, and understand that their fraction of shares will depend on the seed investors conversion choice. They are unhappy with it and they propose to invest $1,000,000 for 8.68% of the shares at the closing of Series A round. Compute the number of shares Series A investors will get in this case.