Lecture no04 time value of money

Time Value of Money

Lecture No. 4
Chapter 3
Contemporary Engineering Economics
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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 recommend?

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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

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Time Value of Money

 Money has a time value because it can earn
more money over time (earning power).

 Money has a time value because its
purchasing power changes over time
(inflation).

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The Market Interest Rate

o
o

Interest is the cost of money, a cost to
the borrower and a profit to the
lender.
Time value of money is measured in
terms of market interest rate, which
reflects both earning and purchasing
power in the financial market.

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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
o
o

n = 0: $20,000
n = 0: $200
n = 1 ~ 5: $5,141.85

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End-of-Period Convention

 Convention: Any cash flows occurring

during the interest period are summed to a
single amount and placed at the end of the
interest period.
Logic: This convention allows financial
institutions to make interest calculations
easier.



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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accumulated interest that has not been withdrawn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.

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Simple Interest

Formula

•

P = $1,000, i = 10%, N = 3 years

End of Year

Beginning

Interest Earned

Ending Balance

Balance

0
1

•

Park

$1,000

F = $1,000 + (0.10)($1,000)3
2
$1,100
= $1,300
3

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$1,000

$1,200

$100

$1,100

$100

$1,200

$100

$1,300

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Compound Interest

 Formula

•

P = $1,000, i = 10%, N = 3 years

End of

Beginning Balance

Year

Interest
Earned

0

1

•

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Ending Balance

$1,000

$1,000

$100

$1,100

2
$1,100
$110
F = $1,000(1 + 0.10)3 = $1,331

$1,210

3

$1,331

$1,210

$121

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Compounding Process

$1,100

$1,210

0

$1,331
1

$1,000
2
3
$1,100
$1,210
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The Fundamental Law of Engineering Economy

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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

 Assume that the company’s stock

of 2015.)

will continue to appreciate at an annual rate
of 20.65% for the next 15 years. The stock price per share at his 100
birthday would be

F = 214,800(1 + 0.2065)

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15

= $3,588,758

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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.

 Given: If they saved just $1 from the proceeds in a bank account that paid 8% interest, how much would
their descendents have in 2010?

 Find: As of 2015, the total U.S. population would be close to 308 million. If the total sum would be
distributed equally among the population, how much would each person receive?

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Solution

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