Transcript Slide 1
What is Value?
“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.”
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 -
FVn = PV(1 + i)n
1
0
PV=x
»
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
2
N
FV = ?
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 -
(1 i ) n 1
FVAn
i
0
»
1
2
N
A
A
A
FVA = ?
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
0
1
2
N
A
A
A
1
2
N
A
A
i%
Annuity Due
0
i%
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:
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
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 -
PV = P0 = FV / (1 + i)n
1
0
PV= ?
»
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
2
N
FV = x
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 1
1 (1 i ) n
PVA
i
0
PVA = ?
»
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
1
2
N
A
A
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%?
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
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!
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Mortgage Constant
Definition:
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
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?
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Alternative Investment Projects
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
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 Beach
VT 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
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Difference
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:
David M. Harrison, Ph.D.
Real Estate Finance
Texas Tech University
Example: