Consider a $200,000$ SF office building complex, with NOI of $$25/$SF$/$year with rents and operating expenses paid in arrears $($at the end of the year$)$ annually, and no capital expenditures. The rent will increase by $3\%$ per year. The discount rate is $10\%/$year$.$

a$.$ What is the value of this office building, assuming that the building is sold at the end of year $10$ and the cap rate at that time is expected to be $10\%?$What is the cap rate at time $0?$

b$.$ What is the value of this office building, assuming that the building will be held and rented indefinitely $($perpetually$)?$What is the implied cap rate at time $0?$

$$c$.$ What is the value if the rents are paid in advance $($at the beginning of the year$)$ and the building is rented perpetually?