Omega Ventures, a San Deigo-based VC, is planing to invest $20 million in the Series A of a startup operating in the distance learning sector. Prior to the Series A, the startup founders own 30 million common shares and there are no other shareholders.

VC investors (including Omega Ventures) expect that, if the stratup is successful, it will generate $100 million in EBITDA in five years; at that time the startup will be able to go public via an IPO at an enterprise valuation (EV) mutiple of 10x 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., three years before the planned IPO). All VCs wil receive convertible preferred shares with a 1x liquidation preference and they all expect to convert to common and sell their shares at the IPO. The startup has no debt or excess cash, and it does not expect to have to raise any debt in the future.

Omega Ventures has a target IRR of 40%, and it anticipates that the Series B VC will have a target IRR of 20%. All VCs will receive convertible preferred shares with a 1x liquidation preference and they all expect to convert to common and sell their shares at the IPO.

Please calculate the following:

Valuation of the startup at the time of IPO.
The pre- and post-money valuation at the Series B that will ensure that the Series B VC meets its target IRR in expectation.
The pre-and post-money valuation at the Series A that will ensure that Omega Ventures meets its target IRR in expectation.
The number of shares that Omega Ventures needs to own to ensure that it will meet its target IRR in expectation, and the corresponding ownership stakes of Omega Ventures and the Series B VC right after the Series B round.