Fundamentals of Engineering Economics, ©2008 Time Value of Money Lecture No.2 Chapter 2 Fundamentals of Engineering Economics Copyright © 2008

Fundamentals of Engineering Economics, ©2008

Time Value of Money

Lecture No.2Chapter 2Fundamentals of Engineering EconomicsCopyright © 2008

Fundamentals of Engineering Economics, 2nd edition © 2008

Take a Lump Sum or Annual Installments Mr. Robert Harris and his

wife Tonya won a lottery worth $276 million on February 25, 2008.

The couple weighted a difficult question: whether to take $167 million now or $275 million over 26 years (0r $10.57 million a year).

What basis should the couple compare these two options?


Year Option A

(Lump Sum)

Option B

(Installment Plan)

0

1

2

3

25

$167M $10.57M

$10.57M

$10.57M

$10.57M

$10.57M


What Do We Need to Know? To make such comparisons (the lottery

decision problem), we must be able to compare the value of money at different point in time.

To do this, we need to develop a method for reducing a sequence of benefits and costs to a single point in time. Then, we will make our comparisons on that basis.


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).

Time value of money is measured in terms of interest rate.


The Interest Rate Interest is the cost of money—a cost to the borrower and an earning to the lender


Cash Flow Transactions for a Loan Repayment SeriesEnd of Year Receipts Payments

Year 0 $30,000.00 $300.00

Year 1 7,712.77

Year 2 7,712.77

Year 3 7,712.77

Year 4 7,712.77

Year 5 7,712.77The amount of loan = $30,000, origination fee = $300, interest rate = 9% APR (annual percentage rate)


Cash Flow Diagram for Plan 1


Simple interest: the practice of charging an interest rate only to an initial sum (principal amount).

Compound interest: the practice of charging an interest rate to an initial sum and to any previously accumulated interest that has not been withdrawn.

Methods of Calculating Interest


P = Principal amount i = Interest rate N = Number of

interest periods Example:

P = $1,000 i = 8% N = 3 years

End of Year

Beginning Balance

Interest earned

Ending Balance

0 $1,000

1 $1,000 $80 $1,080

2 $1,080 $80 $1,160

3 $1,160 $80 $1,240

Simple Interest


Simple Interest Formula

( )

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

F N

$1,000 (0.08)($1,000)(3)

$1,240

F


P = Principal amount i = Interest rate N = Number of

interest periods Example:

P = $1,000 i = 8% N = 3 years

End of Year

Beginning Balance

Interest earned

Ending Balance

0 $1,000

1 $1,000 $80.00 $1,080.00

2 $1,080 $86.40 $1,166.40

3 $1,166.40 $93.31 $1,259.71

Compound Interest


Compounding Process

$1,000

$1,080

$1,080

$1,116.40

$1,116.40

$1,259.710

1

2

3


0

$1,000

$1,259.71

1 2

3

3$1,000(1 0.08)

$1,259.71

F

Cash Flow Diagram


Compound Interest Formula

1

22 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


The Fundamental Law of Engineering Economy

(1 )NF P i

Fundamentals of Engineering Economics, ©2008

Compound Interest

“The greatest mathematical discovery of all time,”

Albert Einstein


Practice Problem: Warren Buffett’s Berkshire Hathaway (BRK.A) Went public in 1965: $18

per share Worth today (January 9,

2009): $94,750 Annual compound growth:

21.50% Current market value:

$104.721 Billion If his company continues to

grow at the current pace, what will be his company’s total market value when he reaches 100? (78 years old as of 2009)


Estimated Market Value in 2031

Assume that the company’s stock will continue to appreciate at an annual rate of 21.50% for the next 22 years.

22$104.721 (1 0.2150)

$7.598 trillions

F B


With EXCEL In 1626 the Indians sold Manhattan Island to Peter Minuit of the Dutch West Company for $24.

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

• As of Year 2009, the total US population would be close to 300 millions. If the total sum would be distributed equally among the population, how much would each person receive?


Excel Solution

383

$1

8%

383 years

$1(1 0.08) $6,328,464,547,578

P

i

N

F

=FV(8%,383,0,1)= $6,328,464,547,578

$6,328,464,547,578Amount per person

300,000,000

$21,095


Practice Problem

Problem Statement

If you deposit $100 now (n = 0) and $200 two years from now (n = 2) in a savings account that pays 10% interest, how much would you have at the end of year 10?


Solution

0 1 2 3 4 5 6 7 8 9 10

$100$200

F

10

8

$100(1 0.10) $100(2.59) $259

$200(1 0.10) $200(2.14) $429

$259 $429 $688F


Practice Problem

Problem Statement

Consider the following sequence of deposits and withdrawals over a period of 4 years. If you earn a 10% interest, what would be the balance at the end of 4 years?

$1,000 $1,500

$1,210

0 1

2 3

4

?

$1,000


$1,000$1,500

$1,210

0 1

2

3

4

?

$1,000

$1,100

$2,100 $2,310

-$1,210

$1,100

$1,210

+ $1,500

$2,710

$2,981

$1,000

Solution: Graphical Approach


$1,000$1,500

$1,210

0 1

2

3

4

?

$1,000

$2,981

Solution: Analytical Approach

4 3 1$1,000(1 0.10) $1,000(1 0.10) $1,500(1 0.10) $4,445.10

2$1,210(1 0.10) $1,464.10


Solution: Tabular ApproachEnd of Period

Beginning

balance

Deposit made

Withdraw Ending

balance

n = 0 0 $1,000 0 $1,000

n = 1 $1,000(1 + 0.10) =$1,100

$1,000 0 $2,100

n = 2 $2,100(1 + 0.10) =$2,310

0 $1,210 $1,100

n = 3 $1,100(1 + 0.10) =$1,210

$1,500 0 $2,710

n = 4 $2,710(1 + 0.10) =$2,981

0 0 $2,981

Documents

Fundamentals of Engineering Economics, ©2008 Time Value of Money Lecture No.2 Chapter 2 Fundamentals of Engineering Economics Copyright © 2008