Jules Ventures, a Boston-based VC, is planning to invest $20 million in the Series A of a startup operating in the clean-tech sector. Prior to the Series A, the startup founders own 10 million common shares and there are no other shareholders. VC investors (including Jules Ventures) expect that, if the startup is successful in developing a new high-efficiency battery it is developing, it will generate $50 million in EBITDA in four years; at that time, the startup will be able to go public via an IPO at an enterprise valuation (EV) multiple of 12x its EBITDA. In order to go public, the startup will need to raise an additional $60 million in equity from another VC firm in a Series B round in two years (i.e., two years before the IPO). The startup has no debt and does not expect to have to raise any debt in the future. Jules Ventures has a target IRR of 50%, and it anticipates that the Series B VC will have a target IRR of 40%. Please calculate the following:

a) Valuation of the startup at the time of its IPO.

] b) The pre- and post-money valuations at the Series B that will ensure that the Series B VC meets its target IRR in expectation.

c) The pre- and post-money valuations at the Series A that will ensure that Jules Ventures meets its target IRR in expectation.

d) The number of shares that Jules Ventures needs to own to ensure that it will meet its target IRR in expectation, and the corresponding ownership stakes of Jules Ventures and the Series B VC right after the Series B round.