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

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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

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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?

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

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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

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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?

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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

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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?

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

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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?

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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!

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

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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: »

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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:

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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:

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

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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?

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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?

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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 % =

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

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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?

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