$1.$ Suppose that the following four funds$$all with committed capital of $$100$M$$ have combined to form a syndicate to invest in Newco: $($I$)$ DEF Fund, management fees of $2\mathrm{.}5$ percent per year for the first $5$ years, then decreasing by $25$ basis points per year in each year from $6$ to $10.$ All fees calculated based on committed capital. $($II$)$ UVW fund, management fees of $2$ percent per year. During the first $5$ years of the fund, these fees are charged based on committed capital. Beginning in year $6,$ the fees are charged based on net invested capital. UVW expects to be fully invested by the beginning of year $6,$ and also to have realized $25$ percent of all investment capital by this time. In each of the subsequent $5$ years, UVW expects to realize about $15$ percent of all investment capital. $($III$)$ XYZ fund, management fees of $2$ percent per year of committed capital for all $10$ years. The XYZ fund expects to make all exits very quickly and to reinvest capital back into new investments. The total amount of investments is limited to $$100$M$.($a$)$ Suppose that each fund in the syndicate invests $$5$M in Newco. What is the LP cost for each fund? $($b$)$ It is possible that all four funds could agree on all the assumptions to the VC method, but still disagree about the wisdom of making this investment $($making different investment decisions$).$ Explain the economic logic behind this possibility.