An apartment property is expected to generate a rental income of $$255,000$ in year $1$ that will grow at an annual rate of $2\mathrm{.}5\%$ over the following years. The property will be sold at the end of year $10$ for $$4\mathrm{.}5$ million.

$1.$ What is the PV of the property$$s $10-$year rental income and sale price at the end if the annual discount rate is $8\mathrm{.}5\%?$

$2.$ What is the NPV of the project if it costs $$4$ million to develop and the discount rate is $8\mathrm{.}5\%?$

$3.$ What would be the NPV of the project if the discount rate were $7\mathrm{.}5\%?$

$4.$ What is the project$$s IRR? Does your answer match the figure the rate suggested by questions $2$ and $3?$

$5.$ By how much should the developer cut development costs of $$4$ million if she wants to earn an annual return of $9\%$ over the $10$ years