(Valuation of real estate) You are considering buying a 500-unit apartment complex in suburban Springfield. The current owner of the apartment complex is asking $25 million. Assume the following:

• The apartment complex can be fully depreciated over 40 years.

• On average, each unit produces $15,000 of pre-tax income per year.

• The vacancy rate in Springfield averages 8%.

• Operating expenses per unit are $2,000 annually. These expenses are incurred whether or not the units are occupied.

• Income and expenses occur at year-end.

• Your tax rate is 40% on pre-tax income and 20% on capital gains.

• Your discount rate is 18%.

• Real estate prices in the Springfield area have been increasing at 6% per year, and you anticipate that this rate will continue for the foreseeable future. You anticipate selling the apartment complex at the end of 10 years.

a. Use the data above to value the apartment complex.

b. Suppose that the cash flows from rentals (including expenses and depreciation) occur in mid-year. Suppose that the resale cash flow of the complex occurs at the end of 10 years. Recalculate the value of the apartment complex.