time value of money
DESCRIPTION
Real estate time value of money lecture notesTRANSCRIPT
REAL ESTATE
REAL ESTATE PRINCIPLES
TIME VALUE OF MONEY
REAL ESTATE
Time Value of Money
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You are going to lend $100,000 to somebody.1 year later, how much do you expect to get back?
Today 1 year later
$100,000$100,000 ?
$110,000 ?
REAL ESTATE
Time Value of Money
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You won $100,000 in the lottery today.
Today 1 year later
$100,000 $100,000 ?
1. Which do you prefer?
Or
2. How about this option?
Today 1 year later
$100,000 $110,000 ?Or
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
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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
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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)
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REAL ESTATE
Time Value of Money
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You are going to lend $100,000 to somebody.1 year later, how much do you expect to get back?
Today 1 year later
$100,000$100,000 ?
$110,000 ?
REAL ESTATE
Time Value of Money
8
You won $100,000 in the lottery today.
Today 1 year later
$100,000 $100,000 ?
1. Which do you prefer?
Or
2. How about this option?
Today 1 year later
$100,000 $110,000 ?Or
REAL ESTATE
Time Value of Money
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You placed $1,000 in a savings account at your bank.1 year later, how much do you expect to get back?
Today 1 year later
$1,000$1,000 ?
$1,100 ?
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?
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$1,000principal
$1,000 x 1% = $10interest
$1,010FV(Future Value)
Or$1,000 x (1 + 1%) = $1,000 x (1 + 0.01) = $1,010
REAL ESTATE
Future Value
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0 1
PV = -1,000
FV = 1,000(1+0.01)
Principal: PV = $1,000Interest rate: r = 1%
1 year
0 1
PV = -1,000
FV = 1,000(1+0.01)(1+0.01)
=1,000(1+0.01)2
2 year
0 1
PV = -1,000
3 year
0 1
PV = -1,000
n year
2
2
FV = 1,000(1+0.01)(1+0.01)(1+0.01)
=1,000(1+0.01)3
3
2 3 n-1 n
FV = 1,000(1+0.01)(1+0.01)…(1+0.01)
=1,000(1+0.01)n
REAL ESTATE
where
– FV : Future value
– PV : Input at time 0
– r : interest rate
– n : number of periods
𝐹𝑉 = 𝑃𝑉(1 + 𝑟)𝑛
Future Value
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REAL ESTATE
Future Value
• 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
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𝐹𝑉 = 𝑃𝑉(1 + 𝑟)𝑛
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 today’s value (present value)?
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REAL ESTATE
Present Value
• The answer is $1,000.
• How can we calculate it?
– If you invest , you will earn 10% return in a year.
And your FV is $1,100
– Thus, FV = $1,100 = x (1+0.1)
• Reverse procedure of FV(Discount)
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PV
$1,1001 + 0.1
= = $1,000
PV
PV
Discount
REAL ESTATE
Present Value
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0 1
PV = 1,000/(1+0.1)
FV = 1,000
Future Cash Flow: FV = $1,000Discount rate: r = 10%
1 year
0 1
PV = 1,000/[(1+0.1)(1+0.1)]
= 1,000/(1+0.1)2
2 year
0 13 year
0 1n year
2
2 3
2 3 n-1 n
FV = 1,000
FV = 1,000
FV = 1,000
PV = 1,000/[(1+0.1)(1+0.1)(1+0.1)]
= 1,000/(1+0.1)3
PV = 1,000/[(1+0.1)(1+0.1)(1+0.1)……(1+0.1)]
= 1,000/(1+0.1)n
REAL ESTATE
where
– PV : Present Value
– FV : Outcome at time n
– r : discount(interest) rate= opportunity cost= required return
– n : number of periods
PV =FV
(1 + r)n
Present Value
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REAL ESTATE
Present Value
• 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
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PV =FV
(1 + r)n
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 today’s value of this investment? Your discount rate is 5%.
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𝑁𝑃𝑉 = Σ 𝑃𝑉 𝑖𝑛𝑓𝑙𝑜𝑤 − Σ 𝑃𝑉 𝑜𝑢𝑡𝑓𝑙𝑜𝑤
REAL ESTATE
Net Present Value(NPV)
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0 1 2 3 4 5
-35,000
7,800 6,500 11,000 9,998 12,000
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
REAL ESTATE
Net Present Value(NPV): Negative case
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0 1 2 3 4 5
-35,000
7,800 6,500 5,000 3,000 12,000
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
REAL ESTATE
Net Present Value(NPV)
General Investment Decision Rules(Not exactly correct)
• Only one investmentNPV > 0, then invest
• Multiple investment optionsInvest at max NPV project.
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𝑁𝑃𝑉 = Σ 𝑃𝑉 𝑖𝑛𝑓𝑙𝑜𝑤 − Σ 𝑃𝑉 𝑜𝑢𝑡𝑓𝑙𝑜𝑤
REAL ESTATE
PV of annuity
Net present value of constant cash flows
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0 1 2 3 4 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
$500 payment every year for 5 years. Interest rate is 5%
REAL ESTATE
PV of annuity
Net present value of constant cash flows
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0 1 2 3 n
PMT PMT PMT PMT
……………
𝑃𝑉 = 𝑃𝑀𝑇1 − 1/(1 + 𝑟)𝑛
𝑟
𝑃𝑀𝑇 = 𝑃𝑉1 − 1/(1 + 𝑟)𝑛
𝑟
REAL ESTATE
Internal Rate of Return(IRR)
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Annual return of an investment (project) in %, today.
IRR
• Discount rate which makes NPV = 0 or
• At this discount rate, your investment returns you $0.
𝑁𝑃𝑉 =
𝑡=0
𝑛𝐶𝐹𝑡
(1 + 𝐼𝑅𝑅)𝑡= 0
REAL ESTATE
Internal Rate of Return(IRR)
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0 1 2 3 4 5
-35,000
7,800 6,500 11,000 9,998 12,000
NPV @ Discount Rate = 5%
IRR = ?IRR = 10%
This investment gives you 10% return.
NPV = $5,446
NPV @ Discount Rate = 15% NPV = - $4,393
NPV @ Discount Rate = 10% NPV = $0
REAL ESTATE
Internal Rate of Return(IRR)
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0 1 2 3 4 5
-20,000
10,000 15,100 20,000
IRR = 0.09%
This investment gives you 0.09% return.
-15,000 -10,000
Will you invest?
REAL ESTATE
Internal Rate of Return(IRR)
General Investment Decision Rule
• IRR > your required return, then invest
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REAL ESTATE
Time Value of Money(TVM)
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𝐹𝑉 = 𝑃𝑉(1 + 𝑟)𝑛
PV =FV
(1 + r)n
𝑁𝑃𝑉 = Σ 𝑃𝑉 𝑖𝑛𝑓𝑙𝑜𝑤 − Σ 𝑃𝑉 𝑜𝑢𝑡𝑓𝑙𝑜𝑤
𝑃𝑉 = 𝑃𝑀𝑇1 − 1/(1 + 𝑟)𝑛
𝑟𝑃𝑀𝑇 = 𝑃𝑉
1 − 1/(1 + 𝑟)𝑛
𝑟
𝑁𝑃𝑉 =
𝑡=0
𝑛𝐶𝐹𝑡
(1 + 𝐼𝑅𝑅)𝑡= 0
REAL ESTATE
Time Value of Money (TVM)
• TVM function in Calculator
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0 1 2 3 20
$16,263
……………
$250,000 = Loan Amount
Interest rate : 5% and N: 30 years
Your Mortgage
$16,263 $16,263 $16,263
$125,572
Payments…..
Remaining balance =
REAL ESTATE
Time Value of Money(TVM)
• TVM function in Calculator
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0 1 2 3 n
PMT
……………
PV
Interest rate : r %
PMT PMT PMT
FV
Payments…..
PV = f( r, n, PMT, FV)
Give calculator 4 of 5 elements of TVM and it will calculate 5th element for you.
REAL ESTATE
End of Lecture 6
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