$2.$ You and your classmate from UW years are considering investing in an apartment building opportunity. You project rents to be $$8,000,000$ during the first year and grow at $4$ percent per year. Vacancies and collection losses are expected to be $10\%$ of rents. Operating expenses will be $35$ percent of effective gross income. You have been approved for a $20-$year FRM $($fixed rate mortgage$)$ loan for $65$ percent of the purchase price at $9$ percent interest rate. The asking price is $$100,000,000.$ The property is expected to appreciate in value at $3$ percent per year $($use n$=4$ years of appreciation$)$ and is expected to be owned for five years and then sold.

a$.$ Write down the cash flows statement for years $1$ through $5.$

b$.$ What is the expected before$-$tax internal rate of return? Show your work.

c$.$ Re$-$do parts a$.$ and b$.$ with no borrowing $(100\%$ cash purchase$).$

d$.$ What is the impact of leverage on the IRR?