Lecture no04 time value of money

Time Value of MoneyLecture No... What Do We Need to Know?o Be able to compare the value of money at different points in time... Time Value of Moneybecause it can earn more money over

Time Value of Money

Lecture No 4 Chapter 3 Contemporary Engineering Economics

Copyright © 2016

Chapter Opening Story Take a Lump Sum or Annual Installments

 Dearborn couple claimed

Missouri’s largest jackpot:

$293.75 million in 2012.

 They had two options.

 Option 1: Take a lump

sum cash payment of

$192.37 M.

 Option 2: Take an annuity

payment of $9.79 M a year

for 30 years.

 Which option would you

What Do We Need to Know?

o Be able to compare the value of money at

different points in time

o A method for reducing a sequence of

benefits and costs to a single point in time

Time Value of Money

because it can earn more

money over time

( earning power ).

power changes over time

(inflation).

The Market Interest Rate

o Interest is the cost of

money , a cost to the

borrower and a profit to

the lender.

o Time value of money is

measured in terms of

market interest rate ,

which reflects both

earning and purchasing

power in the financial

market

Cash Flow Diagram

( A Graphical Representation of Cash Transactions over Time)

Borrow $20,000 at 9%

interest over 5 years,

requiring $200 loan

origination fee upfront The

required annual repayment

is $5,141.85 over 5 years.

o n = 0: $20,000

o n = 0: $200

o n = 1 ~ 5: $5,141.85

End-of-Period Convention

flows occurring during the

interest period are

summed to a single

amount and placed at the

end of the interest period.

allows financial

institutions to make

interest calculations

easier.

Methods of Calculating Interest

 Simple interest : Charging an interest rate only to

an initial sum (principal amount)

 Compound interest : Charging an interest rate to

an initial sum and to any previously

accumulated interest that has not been

withdrawn

 Note: Unless otherwise mentioned, all interest rates used in engineering

economic analyses are compound interest rates .

Simple Interest

Formula • P = $1,000, i = 10%, N = 3

years

• F = $1,000 + (0.10)($1,000)3

= $1,300

End of Year Beginning Balance Interest Earned Balance Ending

1 $1,000 $100 $1,100

2 $1,100 $100 $1,200

3 $1,200 $100 $1,300

( )

where

= Principal amount

= simple interest rate

= number of interest periods

= total amount accumulated at the end of period

F P iP N

P

i

N

 ( )

where

= Principal amount

= simple interest rate

= number of interest periods

= total amount accumulated at the end of period

F P iP N

P

i

N

 

Compound Interest

1

2

2 1

0 :

1: (1 )

2: (1 ) (1 )

: (1 ) N

n P

n F P i

n F F i P i

n N F P i





1

2

2 1

0 :

1: (1 )

2: (1 ) (1 )

: (1 ) N

n P

n F P i

n F F i P i

n N F P i





• P = $1,000, i = 10%, N = 3 years

• F = $1,000(1 + 0.10) 3 = $1,331

End of Year Beginning Balance Interest Earned Balance Ending

1 $1,000 $100 $1,100

2 $1,100 $110 $1,210

3 $1,210 $121 $1,331

 Formula

Compounding Process

$1,000

$1,100

$1,100

$1,210

$1,210

$1,331 0

1

2

3

The Fundamental Law of Engineering

Economy

Warren Buffett’s Berkshire

Hathaway

 Went public in 1965: $18 per

share

 Worth today (May 29, 2015):

$214,800 per share

 Annual compound growth:

20.65%

 Current market value:

$179.5 billion

 If his company continues to

grow at the current pace,

what will be his company’s

total market value when he

reaches 100? (He is 85 years

old as of 2015.)

will continue to appreciate at an annual rate

of 20.65% for the next 15 years The stock

Example 3.2: Comparing Simple with

Compound Interest

In 1626, American Indians sold Manhattan Island to Peter

Minuit of the Dutch West Company for $24.

account that paid 8% interest, how much would their

descendents have in 2010?

308 million If the total sum would be distributed equally among the population, how much would each person

receive?

384

$1 8%

384 years

P

i

N

F







$1 8%

384 years

P

i

N

F







$164,033,801,073,200 Amount per person

308,000,000

$532,577



