Zenith Investment Company is considering the purchase of an office property. It has done an extensive market analysis and has estimated that based on current market supply$/$demand relationships, rents, and its estimate of operating expenses, annual NOI will be as follows:

Year NOI

$1$ $ $1,000,000$

$21,000,000$

$31,000,000$

$41,200,000$

$51,250,000$

$61,300,000$

$71,339,000$

$81,379,170$

A market that is currently oversupplied is expected to result in cash flows remaining flat for the next three years at $$1,000,000.$ During years $4,5,$ and $6,$ market rents are expected to be higher. It is further expected that beginning in year $7$ and every year thereafter, NOI will tend to reflect a stable, balanced market and should grow at $3$ percent per year indefinitely. Zenith believes that investors should earn a $12$ percent return $($r$)$ on an investment of this kind.

Required:

a$.$ Assuming that the investment is expected to produce NOI in years $1$ to $8$ and is expected to be owned for seven years and then sold, what would be the value for this property today? $($Hint: Begin by estimating the reversion value at the end of year $7.$ Recall that the expected IRP $=12\%$ and the growth rate $($g$)$ in year $8$ and beyond is estimated to remain level at $3\%.)$

b$.$ What would the terminal capitalization rate $($RT$)$ be at the end of year $7?$

c$.$ What would the going$-$in capitalization rate $($R$)$ be based on year $1$ NOI?