A commercial real estate investment fund must report its quarterly investment performance to investors. A summary of its $(1)$ beginning and end$-$of$-$quarter assets and equity and $(2)$ cash inflows and outflows during the quarter are as follows:

Beginning of Quarter During Quarter

$$62$ million Cash $$10$ million NOI from operations

$$512$ million Market value of props $$2$ million Paid management fees

$$32$ million Other Investments $$25$ million Distributions to investors

$$324$ million Fund debt $$212$ million Investor contributions

$$187$ million Property acquisitions

$$37$ Property dispositions

Other investments will earn $4\%$ interest $(1\%$ per quarter$)$ and property debt will be at a $6\%$ rate $(1\mathrm{.}5\%$ per quarter$).$

The properties were appraised at the end of the quarter for $$667$ million.

Assume any interest on short$-$term investments is offset by interest paid on short$-$term debt.

Required

a$.$ What would be the beginning equity value?

b$.$ What would be the ending equity value $($MVEE$)?$

c$.$ Assuming that all cash flows from operations, equity contributions, acquisitions, and distributions occurred at the end of the quarter, what would be the quarterly return $($IRR$)?$

d$.$ Assume that all cash distributions to investors occurred equally in $30-$day intervals during the quarter. $($Investor contributions still occur at the end of the quarter.$)$ What would be an approximation to the IRR using the Modified Dietz approach?

e$.$ Assume that all cash distributions to investors occurred equally in $30-$day intervals during the quarter. What would the return be before fees? $($Investor contributions still occur at the end of the quarter.$)$

f$.$ Assume that all cash distributions to investors occurred equally in $30-$day intervals during the quarter. What would be return at the property level? $($Investor contributions still occur at the end of the quarter.$)$