Consider another company, Lateco, which has just received its fifth round of investment.  These rounds have been:

Series A: CP ($5M FV) or converts to 5M shares of common.

Series B: CP ($10M FV with 2X liquidation preference) or converts to 5M shares of common.

Series C: RP+CS ($15M FV) with 5M shares of common.

Series D: CP ($30M FV) or converts to 5M shares of common.

Series E: RP+CS ($15M FV) with 5M shares of common.

The FV of each series is equal to the dollars invested in that Series. You can assume that all VC investors have a lifetime fee percentage of 25% and carried interest of 20%, and that, in the event of an exit or liquidation, the Series E investors are redeemed first, followed by Series D, then Series C, Series B, Series A.

In addition to the VC investors, the founders of Lateco also have 5M shares of common. 
 
a)  Find the formula for the partial valuation of these founder shares following the Series E investment. Show all your work, including expiration diagrams and any necessary calculations of conversion conditions and carried-interest cutoffs.

b)  Compute the LP valuation for the series A investors.