1. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 Chapter 8 Present Value Mathematics for Real Estate SLIDE 1

2. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 CHAPTER OUTLINE 8.1Single-Sum Formulas 8.1.1 Single-Period Discounting and Growing 8.1.2 Single-Sums over Multiple Periods of Time 8.1.3 Simple versus Compound Interest 8.1.4 Effective versus Nominal Rates 8.1.5 Bond Equivalent and Mortgage Equivalent Rates *8.1.6 Continuously Compounded Interest Rates 8.2 Multiperiod Problems *8.2.1 Geometric Series Formula 8.2.2 Present Value of a Level Annuity in Arrears 8.2.3 Present Value of a Level Annuity in Advance 8.2.4 Present Value of a Constant-Growth Annuity in Arrears 8.2.5 Present Value of a Constant-Growth Perpetuity SLIDE 2

3. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 CHAPTER OUTLINE (continued) 8.2.6 Some Basic Economic Implications of the Perpetuity Formula *8.2.7 Introducing Long-Term Leases 8.2.8 Summarizing the Present Value of Geometric Cash Flow Streams 8.2.9 How to Convert Annuities to Future Values 8.2.10 Solving for the Cash Flows 8.2.11 Solving for the Number of Payments 8.2.12 Combining the Single Lump Sum and the Level Annuity Stream: Classical Mortgage Mathematics 8.2.13 How the Present Value Keys on a Business Calculator Work 8.2.14 IRR and Multiperiod DCF Formula 8.3 Chapter Summary SLIDE 3

4. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 LEARNING OBJECTIVES After reading this chapter, you should understand: The basic formulas and procedures for converting typical real estate future cash flow and risk patterns to present value, given the appropriate discount rates. The origin or derivation of these formulas, in such a way that you can apply them with some flexibility to new situations. How to invert the present value formulas to compute the implied return or the time until a future value is received. How a typical business or financial calculator works to make these calculations quick and easy. SLIDE 4

5. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.1 Single-Sum Formulas SLIDE 5

6. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.1.1 Single-Period Discounting and Growing SLIDE 6

7. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.1.2 Single-Sums over Multiple Periods of Time SLIDE 7

8. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.1.3 Simple versus Compound Interest SLIDE 8

9. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.1.4 Effective versus Nominal Rates SLIDE 9

10. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.1.5 Bond Equivalent and Mortgage Equivalent Rates SLIDE 10

11. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 *8.1.6 Continuously Compounded Interest Rates SLIDE 11

12. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.2 Multiperiod Problems SLIDE 12

13. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 *8.2.1 Geometric Series Formula SLIDE 13

14. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.2.2 Present Value of a Level Annuity in Arrears SLIDE 14

15. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.2.3 Present Value of a Level Annuity in Advance SLIDE 15

16. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.2.4 Present Value of a Constant-Growth Annuity in Arrears SLIDE 16

17. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.2.5 Present Value of a Constant-Growth Perpetuity SLIDE 17

18. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.2.6 Some Basic Economic Implications of the Perpetuity Formula SLIDE 18

19. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 *8.2.7 Introducing Long-Term Leases SLIDE 19

20. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.2.8 Summarizing the Present Value of Geometric Cash Flow Streams SLIDE 20

21. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.2.9 How to Convert Annuities to Future Values SLIDE 21

22. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.2.10 Solving for the Cash Flows SLIDE 22

23. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.2.11 Solving for the Number of Payments SLIDE 23

24. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.2.12 Combining the Single Lump Sum and the Level Annuity Stream: Classical Mortgage Mathematics SLIDE 24

25. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.2.13 How the Present Value Keys on a Business Calculator Work SLIDE 25

26. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.2.14 IRR and Multiperiod DCF Formula SLIDE 26

27. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 8.3 Chapter Summary SLIDE 27

28. ©2014 OnCourse Learning. All Rights Reserved. CHAPTER 8 KEY TERMS single-sum formulas present value future value discounting growing discount rate interest rate compounding growth rate compounding frequency effective annual rate (EAR) equivalent nominal annual rate (ENAR) mortgage equivalent rate bond equivalent (coupon equivalent) rate continuous compounding annuity perpetuity geometric series formula common ratio level annuity constant-growth annuity constant-growth perpetuity intralease rate interlease rate internal rate of return (IRR) calculator registers (N, I, PV, PMT, FV, NPV, IRR, CF) SLIDE 28