You are a venture capitalist at Apex Capital, analyzing a potential startup investment on January 1, 2023. Your firm targets an internal rate of return (IRR) of 25% on its investments. The startup under consideration requires four rounds of funding over the next eight years, with the following investment schedule:$1 million today, $2 million in two years, $3 million in 3 years, and $2 million in 6 years.

At the end of Year 8, the startup's potential outcomes are as follows:

• Initial Public Offering (IPO): The company would be valued at $1.6 billion, with a 10% probability.
• Acquisition: The startup could be bought by another firm for $1.1 billion, occurring with a 30% probability. Failure: If no acquisition occurs, the company's value will be zero.

In terms of equity structure, the founders have initially allocated 1,000,000 shares to themselves. Additionally, an option pool of 450,000 shares has been set aside for future employees.

a) Determine the startup's share price at each financing round and calculate the number of shares issued to investors in each round.

b) If the probability of an acquisition decreases to 20%, how do the share prices and shares issued in each round change? Assume all other details remain the same. Provide a brief explanation of why these results shift.

c) If the IPO valuation increases by 10%, how does this impact the share prices and the number of shares issued in each financing round? Keep all other assumptions from the original scenario (e.g., acquisition probability remains 30%). Provide a one-sentence explanation of the reasoning behind these changes.

d) How answers to part a) change if option pool decreases by 100,000 shares (assume all other information stays the same as in the original problem). Please provide one sentence explaining intuition for how the results change.