You are an early$-$stage VC conducting due diligence on an IT start$-$up$.$ You are willing to cotribute $$1,545,000$ in the A round of financing and require a capital return $($i$.$e$.,$ capital multiplier$)$ of $12.$ You anticipate B and C rounds of financing in years $3$ and $6$ that will dilute your position by $30\%$ and $40\%,$ respectively, because your firm will not participate in either additional round. You estimate firm value at $$120,000,000$ in nine years.

Required:

What initial ownership position should you require for your investment?

What is your initial valuation of the company before your investment?

What is the expected IRR of the investment?

Suppose you stage the distribution of the capital into $$545,000$ installments disbursed immediately, at the end of the first year, and at the end of the second year. What is the IRR of the investment in this scenario?