# flow

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```					       Warm-Up Review
 Time Value of Money
 Calculation of Future Value
 Calculation of Current Value
 Simple interests and
compound interests
 Continuous compounding

1
Basics of Time Value of Money
 Interest   rate
 reward for use of capital\$
 usually expressed in % per year

 Simple Interest (self-study)
 Only the principal earns interest

 Interest amount =P • i • n

 Future value = P + P • i • n = P (1 + i • n)

2
Basics of Time Value of Money
 Compound Interest
   Interest on interest
• dependant on compounding period
(yearly, semi-annually, monthly)
   For 2 years:
• Future value = P ( 1+i) + i • P (1+i) = P (1+ i)2
   For n years:
• Future value = P (1+ i)n
• see column 2 of interest tables
3
What is Time Value?
 We  say that money has a time
value because that money can be
invested with the expectation of
earning a positive rate of return
 In other words, “a dollar received
today is worth more than a dollar
 That is because today’s dollar can
be invested so that we have more
than one dollar tomorrow
4
Compound Interest
 Note from the example that the future value is
increasing at an increasing rate
 In other words, the amount of interest earned each
year is increasing
 Year 1: \$10

 Year 2: \$11

 Year 3: \$12.10

 The reason for the increase is that each year you
are earning interest on the interest that was earned
in previous years in addition to the interest on the
original principle amountchange                     5
Interest Formulation

Simple Interest                                    F  Pe       rt
I  (iP)N
F  P  I  P(1 iN)
Compound Interest
P(1  i)  i[P(1  i)]
 P(1  i)(1  i)
 P(1  i) 2
After N periods, the total accumulated value F will grow to

F  P(1  i) N                      F
P
(1  i ) N
6
Continuous Compounding
 There is no reason why we need to stop increasing the
compounding frequency at daily
 We could compound every hour, minute, or second
 We can also compound every instant (i.e.,
continuously):

F  Pe               rt

   Here, F is the future value, P is the present value, r is the
annual rate of interest, t is the total number of years, and e
is a constant

7
Topics Today

 Cash   Flow Diagrams

 Equivalent Issues

 Engineer Decision

8
Cash Flow- expenses and receipts
 Engineering projects generally have economic
consequences that occur over an extended period of
time
 For example, if an expensive piece of machinery is

installed in a plant were brought on credit, the
simple process of paying for it may take several
years
 Each project is described as cash receipts or expenses
at different points in time

9
Categories of Cash Flows
   The expenses and receipts due to engineering
projects usually fall into one of the following
categories:
   First cost: expense to build or to buy and install
   Operations and maintenance (O&M): annual expense,
such as electricity, labor, and minor repairs
   Salvage value: receipt at project termination for sale or
transfer of the equipment (can be a salvage cost)
   Revenues: annual receipts due to sale of products or
services
   Overhaul: major capital expenditure that occurs during
the asset’s life

10
Examples of Cash Inflows & Outflows

   Receipts from customers--operating
activity
   Loans made to other firms--investing
activity
   Dividend payments--financing activity
   Payments to investing activity
   Payments of taxes--operating activity

Slide 14.8             11
Types of Cash Flows
 Single cash flow
 Uniform series
 Irregular series

12
Cash Flow Diagrams
 The  costs and benefits of engineering
projects over time are summarized on a
cash flow diagram.
 Cash flow diagram illustrates the size,
sign, and timing of individual cash
flows, and forms the basis for
engineering economic analysis
 Tool! To show expenses and receipts

13
Cash Flow Diagrams
 Pictorial representation of
engineering economic problem
 incomes and expenditures

 time period

 interest rate

14
Cash Flow diagrams--How
A  cash flow diagram is created by first
drawing a segmented time-based
horizontal line, divided into appropriate
time unit. Each time when there is a
cash flow, a vertical arrow is added 
pointing down for costs and up for
revenues or benefits. The cost flows are
drawn to relative scale

15
Cash Flow Diagrams

P-Pattern                        “present”
1   2   3     n

F-Pattern                         “future”
1   2   3     n

A-Pattern                        “annual”
1   2   3     n

1   2   3     n

16
Cash Flow Diagrams

\$15,000

Positive net Cash flow                           \$2000
(receipts)                 \$13,000 is net positive cash flow

1       2      3      4       5   Time (# of interest periods)
0

Negative net Cash Flow
(payments)

17
Single Cash Flow

F
Compounding Process
P
Discounting Process

F
F  P(1  i)   N                P
(1  i) N
P=Present equivalent value           A=Annual equivalent value
F= Future equivalent value

18
Example: Value and Interest
 The“value” of money depends on the amount
and when it is received or spent.
Example: What amount must be paid to settle a
current debt of \$1000 in two years at an interest
rate of 8% ?

Solution: \$1000 (1 + 0.08) (1 + 0.08) = \$1166
\$1000

1            2

\$1166   19
An Example of Cash Flow Diagram
 Boney  (right) borrowed
\$1,000 from a bank at 8%
interest. Two end-of-year
payments: at the end of the
first year, he will repay half of
the \$1000 principal plus the
interest that is due. At the end
of the second year, he will
repay the remaining half plus
the interest for the second
year.
20
An Example of Cash Flow Diagram
 Cashflow for this problem is:
End of year    Cash flow
0               +\$1000
1               -\$580 (-\$500 - \$80)
2               -\$540 (-\$500 - \$40)

21
Cash Flow Diagram
\$1,000

Time (# of interest periods)
1      2

0

\$540
\$580

22
Uneven Payment Series
Find the present worth of any uneven stream of
payments by calculating the present value of each
individual payment and summing the results

Future worth can then be calculated by using the
interest formula
P5
P1   P2                     P6
P3                            F
P0                     P4             P
(1  i) N
0              Years

23
Equal Payment Series
F

0       1          2          3                 N-1
N

A          A          A       A         A       A

N 1                N2
F  A(1  i)             A(1  i)          ......A(1  i)  A

F  A  A(1 i)  A(1 i) 2 ..... A(1 i) N 1
2                  N
(1  i)F  A(1  i)  A(1  i)  ....  A(1  i)
    N 1
Subtracting two above equations from each other yields:                 (1 i)
        
FA           
N                                              
F(1  i)  F  - A  A(1  i)                                               i     
        
24
(N-1)G
A1
2G
G
Uniform Series

0
0   1         2                  N-1     N

 (1  i) N  iN  1
P  G                   
 i (1  i)
2        N


Composite Series: uniform series + linear gradient
Find P, given A1, G, I, N
25
•Particularly relevant to construction costs
•Cash flows increase by a constant %(g); compound growth
•Example: price changes due to inflation

A1(1+g)N-1    Present Worth, Pn, of any Cash Flow An
Pn  A n (1  i) n  A 1 (1  g) n 1 (1  i) n
A1(1+g)
N  (1  g) n 1
A1                          P   A1                     If i=g, then P=?
0                                   n 1  (1  i) n
1      2 3    N-1 N
g>0
1(1g)N (1i) N 
P
PA                    ....i  g
1
      i g        

Find P, given A1, g, i, N
26
Principal Uses of A Statement of Cash Flows
 Evaluate a business’s ability to produce
positive cash flows in the future.
 Determine whether a company can satisfy
its financial obligations.
 Identify sources of differences between a
business’s net income and its related
(net) cash flow from revenue and expense
transactions.
 Analyze the impact on a business’s
financial condition of its major investing
and financing transactions.

27
Cash-Flow Data Can Be Used to Address

 Will a company generate
sufficient cash to retire a long-
term debt that matures soon?
 Why doesn’t a company’s
record profits translate into
positive cash flows?
 Is a company likely to suspend
(or increase) its dividend
payments?
 How does the composition of a
company’s cash flows compare
to that of its competitors?
28
Three Major Types of Business Activities
   Operating activities: those
transactions and events
related to the production
and delivery of goods
and services.

   Investing activities: include
the making and collecting of loans, the
acquisition and disposal of PP&E assets,
and the purchase and sale of securities
other than trading securities and cash
equivalents.

   Financing activities:
involve obtaining cash from lenders and
repaying those amounts and obtaining cash
from investors and providing them with a
return of and a return on their investments.
Slide 14.7   29
Economic Equivalence
Which one would you prefer?

•\$20,000 today
•\$50,000 ten years from now
•\$ 8,000 each year for the next ten years

We need to   compare their economic worth!
Economic equivalence exists between cash flows if
they have the same economic effect.
Convert cash flows into an equivalent cash flow at
any point in time
30
Equivalence Principles
1   Use a common time basis
   Equivalent cash flows are equivalent at any
common point in time
   Use the present time = present worth
   Use some future point in time = future worth
2   Equivalence depends on interest rate
   Changing the interest rate destroys
equivalence

31
Equivalence Principles
3 Requires conversion
of multiple payment
cash flows to a
single cash flow
4 Equivalence is
maintained
regardless of the
point of view
32
The Decision Making Process
   Define problem
   Choose objectives
   Identify alternatives
   Evaluate consequences
   Select the best
   Implement
   Audit results

33
Making Decisions

Preferences

Politics        People

Facts
research

opinion
Market

Expert
Costs

…

34
57 Chevy   97 Neon   93 Mercedes

Purchase     \$12,000   \$7,000      \$20,000

Operation    200/mth   50/mth      150/mth

Resale      \$13,000   \$5,000      \$20,000

35
Modeling

Real World

Analysis   The Model     Information
for decision
making

36

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 views: 3 posted: 9/15/2011 language: English pages: 36