$1.$ A real estate private equity fund has raised $$95$ million from outside investors and the sponsor is contributing another $$5$ million. The fund plans to borrow a $$300$ million interest$-$only mortgage at the interest rate of $5\%.$ The average going$-$in cap rate on the properties the fund looks to invest is $8\%,$ and the net operating income is expected to grow at $3\%$ per year. The fund will be liquidated after three years with an average going$-$out cap

of $8\mathrm{.}5\%.$ Please calculate the cash flow distributions and the IRRs for both the LPs and the sponsor if the cash flow is distributed as follows:

a$.$ The LPs will first get a preferred return of $10\%,$ and then $70\%$ of the remaining cash flow will be distributed to the LPS and $30\%$ of the remaining cash flows will be distributed to the sponsor.

b$.$ The fund will return the initial capital contributed by the LPS and then split the remaining cash flows by $70/30.$

c$.$ The fund will return the initial capital contributed by the LPS$,$ and then a $10\%$ preferred return to the LPs$,$ and then a $60/40$ split between the LPS and the sponsor.

d$.$ The fund will return the initial capital contributed by the LPS$,$ and then a $10\%$ preferred return to the LPs$,$ then the LPs will receive additional cash flows until their IRR is $15\%.$ The remaining cash flows will split $50/50.$