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

David M. Harrison, Ph.D.Real Estate FinanceTexas 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?


Market Value vs. Investment Value

Market Value –

Investment Value –


Basic Valuation Concepts

Sources of Return from RE Investing

Valuation Concerns


Time-Value of Money Operations

Future Value Future Value of an Annuity Sinking Fund Factor Present Value Present Value of an Annuity Mortgage Constant


Future Value (FV)

Definition -

»

FV = ?

0 1 2 N

PV=x

FVn = PV(1 + i)n


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?


Future Value of an Annuity (FVA)

Definition -

»

FVA = ?

0 1 2 N

i

iFVA

n

n

1)1(

AA A


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%?


Ordinary Annuity vs. Annuity Due

Ordinary Annuity

A AA

0 1 2 Ni%

A A

0 1 2 Ni%

Annuity Due

A


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%?


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?


Present Value (PV)

Definition -

»

FV = x

0 1 2 N

PV= ?

PV = P0 = FV / (1 + i)n


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%?


Present Value of an Annuity (PVA)

Definition -

» PVA = ?

0 1 2 N

ii

PVAn)1(

11

AA A


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%?


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%?


TVM Properties Future Values

An increase in the discount rate

An increase in the length of time until the CF is received, given a set interest rate,

Present Values An increase in the discount rate

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!


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 (Rm) on this loan, and what is the required monthly payment?


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?


Year Turtle Beach Townhouses Vermont 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


Net Present Value (NPV)

Definition –

NPV for Turtle Beach Townhouses

NPV for Vermont Vacation Villas

Decision Rules: Independent Projects – Mutually Exclusive Projects –


Internal Rate of Return (IRR)

Definition –

IRR for Turtle Beach Townhouses

IRR for Vermont Vacation Villas

Decision Rules: Independent Projects – Mutually Exclusive Projects –


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:


Point of Indifference?

Cross-over Rate

Yr. Turtle Beach VT Vacation Villas Difference

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


Pricing Floating-Rate Securities

Floaters – Pricing Determinants:

» »

Implications of Pricing Determinants:


Pricing Inverse-Floating Rate Securities

Inverse Floaters – Pricing Determinants:

Example:

Documents

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