REAL ESTATE
REAL ESTATE PRINCIPLES
TIME VALUE OF MONEY
REAL ESTATE
Time Value of Money
You are going to lend $100,000 to somebody.
1 year later, how much do you expect to get back?
$100,000
Today
$100,000 ?
$110,000 ?
1 year later
REAL ESTATE
Time Value of Money
You won $100,000 in the lottery today.
1. Which do you prefer?
$100,000
Or
$100,000 ?
1 year later
Today
2. How about this option?
$100,000
Today
Or
$110,000 ?
1 year later
3
REAL ESTATE
Liquidity Preference and Return
People prefer present cash flow to future cash flow
Why?
Investment opportunity: You can increase your wealth by
investing the money today
Inflation: Purchasing power may decrease
Uncertainty: Future is uncertain and your future cash flow
may not be realized
Your borrower may disappear
Lottery company may go out of business in six months after you
won
REAL ESTATE
Liquidity Preference and Return
People demand a return for the risks involved in
future cash flows
Ex) Bank gives you a 1% return on the money you
keep in your savings account
Ex2) Bank charges you 5% interest on a loan you took
out to purchase your car
REAL ESTATE
Time Value of Money
We want compare
Present cash flows and future cash flows
Our investment options
Tools
1. Future Value(FV)
2. Present Value(PV)
3. Net Present Value(NPV)
4. Internal Rate of Return(IRR)
REAL ESTATE
Time Value of Money
You are going to lend $100,000 to somebody.
1 year later, how much do you expect to get back?
$100,000
Today
$100,000 ?
$110,000 ?
1 year later
REAL ESTATE
Time Value of Money
You won $100,000 in the lottery today.
1. Which do you prefer?
$100,000
Or
$100,000 ?
1 year later
Today
2. How about this option?
$100,000
Today
Or
$110,000 ?
1 year later
8
REAL ESTATE
Time Value of Money
You placed $1,000 in a savings account at your bank.
1 year later, how much do you expect to get back?
$1,000
Today
$1,000 ?
$1,100 ?
1 year later
REAL ESTATE
Future Value
You placed $1,000 into your savings account
Interest rate is 1% per year
How much do you get one year later?
$1,010
How?
$1,000 x 1% = $10
interest
$1,000
principal
$1,010
FV(Future Value)
Or
$1,000 x (1 + 1%) = $1,000 x (1 + 0.01) = $1,010
10
REAL ESTATE
Future Value
Principal:
PV = $1,000
Interest rate: r = 1%
FV = 1,000(1+0.01)
1 year
PV = -1,000
FV = 1,000(1+0.01)(1+0.01)
=1,000(1+0.01)2
2 year
PV = -1,000
FV = 1,000(1+0.01)(1+0.01)(1+0.01)
=1,000(1+0.01)3
3 year
PV = -1,000
FV = 1,000(1+0.01)(1+0.01)(1+0.01)
=1,000(1+0.01)n
n year
n-1
PV = -1,000
11
REAL ESTATE
Future Value
= (1 + )
where
FV : Future value
PV : Input at time 0
r : interest rate
n : number of periods
12
REAL ESTATE
Future Value
= (1 + )
Example
If you save $24,000 at a 1% interest rate today, how much will
this grow to in 6 years?
Ans.)
PV = 24,000, r = 0.01, n = 6
FV = 24,000(1+0.01)6 = $25,476
13
REAL ESTATE
Present Value
You will receive $1,100 from your investment one
year later.
You are able to earn 10% per year return from
another investment
How much is $1,100 one-year-later worth, if you
convert it into todays value (present value)?
14
REAL ESTATE
Present Value
The answer is $1,000.
How can we calculate it?
If you invest PV , you will earn 10% return in a year.
And your FV is $1,100
Thus, FV = $1,100 = PV x (1+0.1)
Reverse procedure of FV(Discount)
PV
$1,100
1 + 0.1
= $1,000
Discount
15
REAL ESTATE
Present Value
Future Cash Flow:
FV = $1,000
Discount rate: r = 10%
FV = 1,000
1 year
PV = 1,000/(1+0.1)
FV = 1,000
2 year
PV = 1,000/[(1+0.1)(1+0.1)]
= 1,000/(1+0.1)2
3 year
FV = 1,000
2
PV = 1,000/[(1+0.1)(1+0.1)(1+0.1)]
= 1,000/(1+0.1)3
n year
FV = 1,000
2
n-1
PV = 1,000/[(1+0.1)(1+0.1)(1+0.1)(1+0.1)]
= 1,000/(1+0.1)n
16
REAL ESTATE
Present Value
FV
PV =
(1 + r)n
where
PV : Present Value
FV : Outcome at time n
r : discount(interest) rate
= opportunity cost
= required return
n : number of periods
17
REAL ESTATE
Present Value
FV
PV =
(1 + r)n
Example
If your investment opportunity will give you $50,000 in 6 years,
how much are you willing to pay today? You are able to earn 10%
return on other investment.
Ans.)
FV = 50,000, r = 0.1, n = 6
PV = 50,000/(1+0.1)6 = $28,224
18
REAL ESTATE
Net Present Value(NPV)
Return of an investment (project) in $ amount, today.
=
Example
If you invest $35,000 today you will receive $7,800 in year 1,
$6,500 in year 2, $11,000 in year 3, $9,988 in year 4 and
$12,000 in year 5. What is the todays value of this investment?
Your discount rate is 5%.
19
REAL ESTATE
Net Present Value(NPV)
7,800
6,500
11,000
9,998
12,000
-35,000
7,429 = 7,800/(1+0.05)
5,896 = 6,500/(1+0.05)2
9,502 = 11,000/(1+0.05)3
8,217 = 9,998/(1+0.05)4
9,402 = 12,000/(1+0.05)5
5,446 = NPV
20
REAL ESTATE
Net Present Value(NPV): Negative case
7,800
6,500
5,000
3,000
12,000
-35,000
7,429 = 7,800/(1+0.05)
5,896 = 6,500/(1+0.05)2
4,319 = 5,000/(1+0.05)3
2,468 = 3,000/(1+0.05)4
9,402 = 12,000/(1+0.05)5
-5,486 = NPV
21
REAL ESTATE
Net Present Value(NPV)
=
General Investment Decision Rules(Not exactly correct)
Only one investment
NPV > 0, then invest
Multiple investment options
Invest at max NPV project.
22
REAL ESTATE
PV of annuity
Net present value of constant cash flows
$500 payment every year for 5 years. Interest rate is 5%
500
500
500
500
500
476= 500/(1+0.05)
454= 500/(1+0.05)2
432= 500/(1+0.05)3
411= 500/(1+0.05)4
392= 500/(1+0.05)5
2,165= PV of annuity
23
REAL ESTATE
PV of annuity
Net present value of constant cash flows
PMT
PMT
PMT
PMT
1 1/(1 + )
=
1 1/(1 + )
24
REAL ESTATE
Internal Rate of Return(IRR)
Annual return of an investment (project) in %, today.
=
=0
=0
(1 + )
IRR
Discount rate which makes NPV = 0 or
At this discount rate, your investment returns you $0.
25
REAL ESTATE
Internal Rate of Return(IRR)
7,800
6,500
11,000
9,998
12,000
-35,000
NPV @ Discount Rate = 5%
NPV = $5,446
NPV @ Discount Rate = 15%
NPV = - $4,393
NPV @ Discount Rate = 10%
NPV = $0
IRR = 10%
?
This investment gives you 10% return.
26
REAL ESTATE
Internal Rate of Return(IRR)
-20,000
-15,000
10,000
15,100
20,000
-10,000
IRR = 0.09%
This investment gives you 0.09% return.
Will you invest?
27
REAL ESTATE
Internal Rate of Return(IRR)
General Investment Decision Rule
IRR > your required return, then invest
28
REAL ESTATE
Time Value of Money(TVM)
= (1 + )
FV
PV =
(1 + r)n
1 1/(1 + )
=
1 1/(1 + )
=
=0
=0
(1 + )
29
REAL ESTATE
Time Value of Money (TVM)
TVM function in Calculator
Your Mortgage
Interest rate : 5% and
N: 30 years
$250,000 = Loan Amount
Payments..
0
$16,263
$16,263
$16,263
20
$16,263
Remaining balance = $125,572
30
REAL ESTATE
Time Value of Money(TVM)
TVM function in Calculator
Interest rate : r %
PV
Payments..
0
PMT
PMT
PMT
PV = f( r, n, PMT, FV)
PMT
FV
Give calculator 4 of 5 elements of TVM and it will calculate
5th element for you.
31
REAL ESTATE
End of Lecture 6
32
