Blackstone Venture Partners is looking at the possible investment of $$1$ million in an early$-$stage

company $($BeginCo$).$ Given the stage of the investment, Blackstone requires a $40\%$ annual rate of

return. The company earned $$750,000$ in EBITDA last year, and this amount is expected to grow

at a rate of $30\%$ per year over the next five years. Companies like BeginCo are currently being

valued at five times EBITDA, and Blackstone Venture Partners thinks this is a reasonable multiple

for the valuation of the firm in five years.

a$)$ Assuming that BeginCo currently has no debt and does not plan to borrow over the next five

years, what do you estimate the enterprise value of the company will be at the end of five years?

b$)$ What fraction of BeginCo does Blackstone Venture Partners need to own at the end of five

years in order to realize the required rate of return on its investment?