David M. Harrison, Ph.D. Real Estate Finance Texas Tech University “In general, the value of a parcel of real estate is the present value of the expected.

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David M. Harrison, Ph.D. Real Estate Finance Texas Tech University “In general, the value of a parcel of real estate is the present value of the expected future benefits associated with ownership of the property right.” What is Value?

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Market Value vs. Investment Value Market Value – Investment Value –

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Basic Valuation Concepts Sources of Return from RE Investing Valuation Concerns

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Time-Value of Money Operations Future Value Future Value of an Annuity Sinking Fund Factor Present Value Present Value of an Annuity Mortgage Constant

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

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Future Value Ex. Suppose you buy a tract of undeveloped land in rural Texas for $200,000. If the parcel appreciates at an annual rate of 4%, how much will you be able to sell the land for in twelve years?

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

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Future Value of an Annuity Ex. If you received $25,000 per year from operating an income producing property, how much would you have after 10 years assuming the opportunity cost of capital (i.e., discount rate) is 9%?

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

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Future Value of an Annuity Due Ex. If you received $25,000 per year, in advance, from operating an income producing property, how much would you have after 10 years assuming the opportunity cost of capital (i.e., discount rate) is 9%?

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Sinking Fund Payment Definition: Ex. Suppose you plan on buying a house in 5 years at an expected purchase price of $250,000. You plan on financing the house via a mortgage which requires a 20% ($50,000) down payment. If you currently have no savings, and the discount rate is 7%, how much should you set aside each year in equal installments to satisfy your down payment requirement?

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

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Present Value Ex. How much would you be willing to pay for a tract of land that you expect to be able to sell in five years, for $50,000, if the discount rate is 8%?

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

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Present Value of an Annuity Example: How much should you be willing to pay for an income producing (rental) property that provides expected after-tax cashflows of $10,000 per year for the next 10 years, if the discount rate is 8.5%?

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Present Value of an Annuity Due Example: How much should you be willing to pay for an income producing (rental) property that provides expected after-tax cashflows of $10,000 per year for the next 10 years, with payments made at the beginning of the year, if the discount rate is 8.5%?

David M. Harrison, Ph.D. Real Estate Finance 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!

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Mortgage Constant Definition: Ex. Suppose you borrow $200,000 to purchase a home. The 15-year loan requires monthly payments, and has a stated nominal interest rate (APR) of 6%. What is the mortgage constant (R m ) on this loan, and what is the required monthly payment?

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Amortization Loan Amortization Schedules Ex. Consider a $200,000, 15-year, fixed-rate monthly payment mortgage with a contract interest rate of 6%.  What is required monthly payment of this loan?  After 5 years, what is the remaining mortgage balance?  During the first year, what is the fraction of the total payments that go toward satisfying accrued interest obligations?  What is the total amount of interest paid over the life of this loan?

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University YearTurtle Beach TownhousesVermont Vacation Villas 0($3,500,000)($5,000,000) 1$250,000$400,000 2$250,000$450,000 3$250,000$500,000 4$250,000$550,000 5$4,500,000$8,100,000 Alternative Investment Projects

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Net Present Value (NPV) Definition – NPV for Turtle Beach Townhouses NPV for Vermont Vacation Villas  Decision Rules:  Independent Projects –  Mutually Exclusive Projects –

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Internal Rate of Return (IRR) Definition – IRR for Turtle Beach Townhouses IRR for Vermont Vacation Villas  Decision Rules:  Independent Projects –  Mutually Exclusive Projects –

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Capitalization Rate (R) Definition – Capitalization Rate (R) for Turtle Beach Townhouses Capitalization Rate (R) for Vermont Vacation Villas  Problems:  Independent Projects –  Mutually Exclusive Projects –  Conclusion:

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Point of Indifference? Cross-over Rate Yr.Turtle BeachVT Vacation VillasDifference 0($3,500,000)($5,000,000) 1$250,000$400,000 2$250,000$450,000 3$250,000$500,000 4$250,000$550,000 5$4,500,000$8,100,000

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Pricing Floating-Rate Securities Floaters – Pricing Determinants: » Implications of Pricing Determinants:

David M. Harrison, Ph.D. Real Estate Finance Texas Tech University Pricing Inverse-Floating Rate Securities Inverse Floaters – Pricing Determinants: Example: