A VC firm is considering two different structures for its $$250$M fund. Both structures would have management fees of $2\%$ per year of committed capital for all $10$ years. Under Structure $1,$ the fund would receive an X$\%$ carry with a basis of all committed capital. Under Structure $2,$ the fund would recieve a Y$\%$ carry with a basis of all investment capital. For a given amount of total exit proceeds $=$ $Z$,$ sole for the amount of carried interest under both structures.$$

Carried Interest Under Structure $1=$

X$\%*($z $+250)$

$$

$$

Carried Interest Under Structure $2=$

Y$\%*($z $+250-(250*10\%)$

Carried Interest Under Structure $2=$

Y$\%*($z $+200)$

Carried Interest Under Structure $1=$

X$\%*($z $-250)$

$$

$$

Carried Interest Under Structure $2=$

Y$\%*($z $-250-(250*2\%*10)$

Carried Interest Under Structure $2=$

Y$\%*($z $-200)$

Carried Interest Under Structure $1=$

X$\%*($z $-200)$

$$

$$

Carried Interest Under Structure $2=$

Y$\%*($z $-200-(200*2\%*10)$

Carried Interest Under Structure $2=$

Y$\%*($z $-250)$