$7.$ You are considering the purchase of an apartment complex. The following assumptions are made:

$$ The purchase price is $$1,000,000.$

$$ Potential gross income $($PGI$)$ for the first year is projected to be $$171,000.$

$$ PGI is expected to increase at $4\mathrm{.}00\%$ per year.

$$ No vacancies are expected.

$$ Operating expenses are estimated at $35\%$ of effective gross income.

$$ The market value of the investment is expected to increase $4\mathrm{.}00\%$ per year.

$$ Selling expenses will be $4\mathrm{.}00\%.$

$$ The holding period is $4$ years.

$$ The appropriate unlevered rate of return is $12\mathrm{.}00\%.$

$$ The required levered rate of return is $14\mathrm{.}00\%.$

$70$ percent of the acquisition price can be borrowed with a $30-$year mortgage.

$$ The annual interest rate on the mortgage will be $8\mathrm{.}00\%.$

$$ Financing costs will equal $2\mathrm{.}00\%$ of the loan amount.

$$ There are no prepayment penalties.

a$.$ Calculate net operating income $($NOI$)$ for each of the four years.

b$.$ Calculate the net sale proceeds from the sale of the property.

c$.$ Calculate the unlevered NPV of this investment. Should you purchase?

d$.$ Calculate the unlevered IRR of this investment. Should you purchase?

e$.$ Calculate the monthly mortgage payment. What is the annual debt service?

f$.$ Calculate the remaining principal balance at the end of year $4.$