David M. Harrison, Ph.D.

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.

2
Market Value vs. Investment Value

• Market Value
• Investment Value

3
Basic Valuation Concepts

• Sources of Return from RE Investing
• Valuation Concerns

4
Time-Value of Money Operations

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

5
Future Value (FV)

• Definition -

FVn PV(1 i)n
1
2
0
N
FV ?
PVx
6
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?

7
Future Value of an Annuity (FVA)

• Definition -

0
1
2
N
A
A
A
FVA ?
8
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?

9
Ordinary Annuity vs. Annuity Due
Ordinary Annuity
0
1
2
N
i
A
A
A
Annuity Due
0
1
2
N
i
A
A
A
10
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?

11
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?

12
Present Value (PV)

• Definition -

PV P0 FV / (1 i)n
1
2
0
N
FV x
PV ?
13
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?

14
Present Value of an Annuity (PVA)

• Definition -

0
1
2
N
A
A
A
PVA ?
15
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?

16
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?

17
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 cant be negative!

18
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?

19
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?

20
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
21
Net Present Value (NPV)

• Definition
• NPV for Turtle Beach Townhouses
• NPV for Vermont Vacation Villas
• Decision Rules
• Independent Projects
• Mutually Exclusive Projects

22
Internal Rate of Return (IRR)

• Definition
• IRR for Turtle Beach Townhouses
• IRR for Vermont Vacation Villas
• Decision Rules
• Independent Projects
• Mutually Exclusive Projects

23
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

24
Point of Indifference?

• Cross-over Rate

Yr. Turtle Beach Turtle Beach VT Vacation Villas Difference
0 0 (3,500,000) (5,000,000)
1 1 250,000 400,000
2 2 250,000 450,000
3 3 250,000 500,000
4 4 250,000 550,000
5 5 4,500,000 8,100,000
25
Pricing Floating-Rate Securities

• Floaters
• Pricing Determinants
• Implications of Pricing Determinants

26
Pricing Inverse-Floating Rate Securities

• Inverse Floaters
• Pricing Determinants
• Example