L2: Time Value of Money

1
L2 Time Value of Money

• ECON 320 Engineering Economics
• Mahmut Ali GOKCE
• Industrial Systems Engineering
• Computer Sciences

2
Chapter 2Time Value of Money

• Interest The Cost of Money
• Economic Equivalence
• Interest Formulas Single Cash Flows
• Equal-Payment Series
• Dealing with Gradient Series
• Composite Cash Flows.

Power-Ball Lottery
3
Decision DilemmaTake a Lump Sum or Annual
Installments

• A suburban Chicago couple won the Power-ball.
• They had to choose between a single lump sum 104
  million, or 198 million paid out over 25 years
  (or 7.92 million per year).
• The winning couple opted for the lump sum.
• Did they make the right choice? What basis do we
  make such an economic comparison?

4
Option A (Lump Sum) Option B (Installment Plan)
0 1 2 3 25 104 M 7.92 M 7.92 M 7.92 M 7.92 M
5
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.

6
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.
• Interest is the cost of moneya cost to the
  borrower and an earning to the lender

7
Delaying Consumption
8
(No Transcript)
9
(No Transcript)
10
Which Repayment Plan?
End of Year Receipts Payments Payments
Plan 1 Plan 2
Year 0 20,000.00 200.00 200.00
Year 1 5,141.85 0
Year 2 5,141.85 0
Year 3 5,141.85 0
Year 4 5,141.85 0
Year 5 5,141.85 30,772.48
The amount of loan 20,000, origination fee 200, interest rate 9 APR (annual percentage rate) The amount of loan 20,000, origination fee 200, interest rate 9 APR (annual percentage rate) The amount of loan 20,000, origination fee 200, interest rate 9 APR (annual percentage rate) The amount of loan 20,000, origination fee 200, interest rate 9 APR (annual percentage rate)
11
Cash Flow Diagram
12
End-of-Period Convention
Interest Period
0
1
End of interest period
Beginning of Interest period
1
0
13
Methods of Calculating Interest

• 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.

14
Simple 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
15
Simple Interest Formula
16
Compound Interest

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  withdrawn.

17
Compound 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 86.40 1,166.40
3 1,166.40 93.31 1,259.71
18
Compounding Process
1,080
1,166.40
0
1,259.71
1
1,000
2
3
1,080
1,166.40
19
1,259.71
2
1
0
3
1,000
20
Compound Interest Formula
21
Some Fundamental Laws
The Fundamental Law of Engineering Economy
22
Compound Interest

• The greatest mathematical discovery of all
  time,
• Albert Einstein

23
Practice Problem Warren Buffetts Berkshire
Hathaway

• Went public in 1965 18 per share
• Worth today (August 22, 2003) 76,200
• Annual compound growth 24.58
• Current market value 100.36 Billion
• If he lives till 100 (current age 73 years as of
  2003), his companys total market value will be ?

24
Market Value

• Assume that the companys stock will continue to
  appreciate at an annual rate of 24.58 for the
  next 27 years.

25
EXCEL Template

• 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 2003, the total US population would
  be close to
• 275 millions. If the total sum would be
  distributed equally
• among the population, how much would each
  person receive?

26
Excel Solution
FV(8,377,0,1) 3,988,006,142,690
27
Excel Worksheet
A B C
1 P 1
2 i 8
3 N 377
4 FV
5
FV(8,377,0,1) 3,988,006,142,690
28
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?

29
Solution
F
0 1 2 3 4 5
6 7 8 9 10
100
200
30
Practice problem

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

?
1,210
1
4
0
2
3
1,500
1,000
1,000
31
?
1,210
0
1
3
2
4
1,000
1,000
1,500
1,100
1,000
2,981
1,210
2,100
2,310
1,500
-1,210
1,100
2,710
32
Solution
End 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