Consider a $100,000$ sqf office building with the following cash flows: The gross rent in year $1$ is $$30/$sqf$/$year and the rents are expected to grow at $2\%$ per year. The operating expenses in the first year are $$5/$sqf$/$year and are expected to increase at $3\%$ per year. There are no capital expenditures. All cash flows are in arrears. The discount rate for the property is $9\%.$

a$.$ What is the value of the building if the building will be held and rented indefinitely? $$What is the cap rate at time $0?$

b$.$ What is the value of the building if the building is sold at the end of $10$ years at a $8\%$ cap rate? $$What is the cap rate at time $0?$