An institutional investor is comparing management fees for two competing real estate investment funds. Both funds expect to begin operations and are accepting capital commitments. When the funds begin acquiring properties, capital calls will be made for capital contributions during the investment period. Fund A will charge a fee of $45$ BP on capital committed and $60$ BP on capital invested after the investment period ends. Fund B will charge a fee of $50$ BP on capital committed and $55$ BP on capital invested after the investment period ends. Both funds expect to have $$507,500,000$ in capital commitments when the fund commences operations and both project a five$-$year cycle for startup and acquisitions. Capital flows are expected as follows:

Fund A

Contributed Capital Capital Returned Invested Capital

Year $1$ $ $203,000,000$ $ $0$ $ $203,000,000$

Year $2304,500,0000507,500,000$

Year $30507,500,000$

Year $4101,500,000406,000,000$

Year $550,750,000355,250,000$

Fund B

Contributed Capital Capital Returned Invested Capital

Year $1$ $ $304,500,000$ $ $0$ $ $304,500,000$

Year $2203,000,0000507,500,000$

Year $30507,500,000$

Year $450,750,000456,750,000$

Year $5101,500,000355,250,000$

Required:

a$.$ What will total fees be for Fund $($A$)?$ For Fund $($B$)?$

b$.$ Would one of the fee structures cause the manager to want to hold the properties longer before selling than the other fee structure? if so$,$ which one?