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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
  to be received tomorrow”
 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
 Linear gradient series
 Geometric gradient 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

G-Pattern                        “gradient”
             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
            Linear Gradient Series
                                                    (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
           Geometric Gradient Series
•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
          Example: buying a car
            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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posted:9/15/2011
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