1. Real Estate Investment Chapter 13 Discount Analysis © 2011 Cengage Learning

2. Key Terms Annuity Compound interest Future value Go dark Internal rate of return Inverse Net present value Perpetuity Present value Reversion Simple interest

3. © 2011 Cengage Learning Risk, Return, and the Time Value of Money Risk Changing Discount Rates and Risk Aversion Over Time Return Time Value of Money Future Values

4. © 2011 Cengage Learning Future Value Calculation FV = PV(1 + i) ^ t, where “(1 + i) ^ t” is the future value factor FV = the future value PV = the present value “i” is the interest rate and “t” is the number of periods ^ indicates an exponent

5. © 2011 Cengage Learning Present Value Calculation PV = FV÷(1 + i)^t, where “(1 + i)^t” is the future value factor FV = the future value PV = the present value “i” is the interest rate and “t” is the number of periods ^ indicates an exponent

6. © 2011 Cengage Learning Valuing an Annuity Stream, or Present Value of a Set of Monthly Mortgage Payments −1,199.10 PMT 30 x 12 = N 6 ÷ 12 = I/Y CPT PV ¼ 199,999.83 (or approximately $200,000)

7. © 2011 Cengage Learning Cash Flow Considerations Present and Future Values of Equally- Sized Cash Flows The Present Value of a Perpetuity The Time Value of Money and Unequal Cash Flows A Net Present Value Approach An Internal Rate of Return Approach

8. © 2011 Cengage Learning The Net Present Value or NPV Approach to Real Estate Analysis Condo Purchase Price $40,000 Annual Cash Flows: Potential Gross Income (12 $650) = $ 7,800 Vacancy Allowance (.08 $7,800) = (624) Effective Gross Income (EGI) $ 7,176 Operating Expenses (30.28% of EGI) (2,173) Annual Net Operating Income (Cash Flow): $ 5,003 Assumed sale in 3 years for a net sales price of: $45,000 Net Present Value = Present Value of income and net sale − purchase price

9. © 2011 Cengage Learning Concluding Remarks Present and future value calculations, NPV analyses, and IRR discoveries are used by the real estate analyst in an attempt to discern the best risk-adjusted choices. Given what is known about a property and the economy as a whole, do the purchase terms and cash flows make sense for the investor?