Problem $23-3$

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:

$\backslash$table$[[,$Beginning of Quarter,,$],[$$$61$ million,Cash,$$10$ million,NOI from operations$],[$$$511$ million,Market value of props,$$2$ million,Paid management fees$],[$$$31$ million,Other Investments,$$25$ million,Distributions to investors$],[$$$322$ million,Fund debt,$$211$ million,Investor contributions$],[,,$$$186$ million,Property acquisitions$],[,,$$$36,$Property dispositions$]]$

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 $$666$ 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.$)$