Time Value of Money

REAL ESTATE

REAL ESTATE PRINCIPLES

TIME VALUE OF MONEY

REAL ESTATE

Time Value of Money

2

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

3

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

4

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

5

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)

6

REAL ESTATE

Time Value of Money

7

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

9

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?

10

$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

11

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

12

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

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 today’s value (present value)?

14

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)

15

PV

$1,1001 + 0.1

= = $1,000

PV

PV

Discount

REAL ESTATE

Present Value

16

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

17

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

18

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%.

19

𝑁𝑃𝑉 = Σ 𝑃𝑉 𝑖𝑛𝑓𝑙𝑜𝑤 − Σ 𝑃𝑉 𝑜𝑢𝑡𝑓𝑙𝑜𝑤

REAL ESTATE


20

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

21

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


General Investment Decision Rules(Not exactly correct)

• Only one investmentNPV > 0, then invest

• Multiple investment optionsInvest at max NPV project.

22


REAL ESTATE

PV of annuity

Net present value of constant cash flows

23

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

24

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)

25

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


26

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


27

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


General Investment Decision Rule

• IRR > your required return, then invest

28

REAL ESTATE

Time Value of Money(TVM)

29


PV =FV

(1 + r)n


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

30

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

31

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

32

Time Value of Money

Documents

Transcript of Time Value of Money