1. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University  TVM - Compounding $ TodayFuture $ Discounting Time Value of Money

2. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Future Value (FV)  Definition - » FV = ? 0 12 N PV=x FV n = PV(1 + i) n

3. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Future Value Calculations  Suppose you have $10 million and decide to invest it in a security offering an interest rate of 9.2% per annum for six years. At the end of the six years, what is the value of your investment?  What if the (interest) payments were made semi-annually?  Why does semi-annual compounding lead to higher returns?

4. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Future Value of an Annuity (FVA)  Definition - » FVA = ? 012N AAA

5. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Ordinary Annuity vs. Annuity Due Ordinary Annuity AAA 012N i% A A 012N Annuity Due A

6. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Future Value of an Annuity Examples  Suppose you were to invest $5,000 per year each year for 10 years, at an annual interest rate of 8.5%. After 10 years, how much money would you have?  What if this were an annuity due?  What if you made payments of $2,500 every six-months instead?

7. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Present Value (PV)  Definition - » FV = x 0 12 N PV= ? PV = P 0 = FV / (1 + i) n

8. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Present Value Calculations  How much would you pay today for an investment that returns $5 million, seven years from today, with no interim cashflows, assuming the yield on the highest yielding alternative project is 10% per annum?  What if the opportunity cost was 10% compounded semi-annually?  Why does semi-annual compounding lead to lower present values?

9. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Present Value of an Annuity (PVA)  Definition - » PVA = ? 012N AAA

10. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Present Value of an Annuity Examples  How much would you spend for an 8 year, $1,000, annual annuity, assuming the discount rate is 9%?  What if this were an annuity due?  What if you were to receive payments of $500 every six-months instead?

11. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University TVM Properties  Future Values F An increase in the discount rate F An increase in the length of time until the CF is received, given a set interest rate,  Present Values F An increase in the discount rate F An increase in the length of time until the CF is received, given a set interest rate,  Note: For this class, assume nominal interest rates can’t be negative!

12. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University  Definition - Perpetuities PV perpetuity = ? 012 $$$ 

13. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Perpetuity Examples  What is the value of a $100 annual perpetuity if the interest rate is 7%?  What if the interest rate rises to 9%? F Principles of Perpetuities: »

14. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Uneven Cash Flow Streams F Description -  Ex. Given a discount rate of 8%, how much would you be willing to pay today for an investment which provided the following cash flows:

15. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Uneven Cash Flow Streams  Ex. Given a discount rate of 8%, what is the future value of the following cash flows stream:

16. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Nominal vs. Effective Rates  Nominal Rate -  Effective Rate -  What’s the difference?

17. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Nom. vs. Eff. Rate Examples  Ex. #1: A bond pays 7% interest semi-annually, what is the effective yield on the bond?  A credit card charges 1.65% per month (APR=19.8%), what rate of interest are they effectively charging?  What nominal rate would produce an effective rate of 9.25% if the security pays interest quarterly?

18. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Amortization  Amortized Loan -  Ex. Suppose you borrow $10,000 to start up a small business. The loan offers a contract interest rate of 8.5%, and must be repaid in equal, annual installments over the next 4 years. How much is your annual payment?  What percentage of your payments go toward the repayment of principal in each year?

19. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Amortization Schedules Year #1, Principal % = Year #2, Principal % = Year #3, Principal % = Year #4, Principal % =

20. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University Continuous Compounding  Definition/Description -

21. Real Estate Investments David M. Harrison, Ph.D. Texas Tech University  What is the present value of $200 to be received 2 years from today, if the discount rate is 9% compounded continuously?  How much more would the cash flow be worth if the discount rate were 9% compounded annually?  What is the future value, in 10 years, of a $5,000 investment today, if the interest rate is 8.75% compounded continuously?  How much lower would the future value be if the interest rate were 8.75% compounded annually? Does Compounding Matter?