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 or demand relationships, rents, and its estimate of operating expenses, annual NOI will be as follows:

Year NOI

$1$ $ $1,255,000$

$21,255,000$

$31,255,000$

$41,285,000$

$51,335,000$

$61,385,000$

$71,424,000$

$81,464,170$

A market that is currently oversupplied is expected to result in cash flows remaining flat for the next three years at $$1,255,000.$ 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?