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Intro to Engineering Economy

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Title: Intro to Engineering Economy


1
Intro to Engineering Economy
  • Objectives
  • Understand the concept of time value of money
  • Illustrate the basic equivalence calculations
  • Understand Project Cash Flows
  • Formulate mutually exclusive alternatives
  • Perform Present Worth Analysis

2
Engineering Economy Decisions
Planning
3
Role of Engineering Economy
  • Understand the Problem
  • Collect all relevant data/information
  • Define the feasible alternatives
  • Evaluate each alternative
  • Select the best alternative
  • Implement and monitor

Tools Present Worth, Future Worth Annual Worth,
Rate of Return Benefit/Cost, Payback, Capitalized
Cost, Value Added
Major Role of Engineering Economy
4
Interest The cost of money
  • Interest rate a percentage that is periodically
    applied and added to an amount of money over a
    specified length of time
  • Interest rate for saving account
  • Interest rate when borrowing money
  • Time value of money
  • A dollar today is worth more than a dollar one or
    more years from now because of the interest
    (profit) it can earn
  • Interest is the cost of money
  • A cost to the borrower and an earning to the
    lender

5
Economic Equivalence
  • Economic Equivalence exits between cash flows
    that have the same economic effect and could be
    traded for one another in the financial market
    place
  • Cash flows can be converted to an equivalent
    cash flow at any point in time
  • Two sums of money at two different points in
    time can be made economically equivalent if we
    consider
  • an interest rate and,
  • No. of time periods between the two sums

Equality in terms of Economic Value
6
Equivalence Illustrated
20,000 is received here
t 1 Yr
t0
21,800 paid back here
  • 20,000 now is not equal in magnitude to 21,800
    1 year from now
  • But, 20,000 now is economically equivalent to
    21,800 one year from now if the interest rate is
    9 per year.
  • If you were told that the interest rate is 9....
  • Which is worth more?
  • 20,000 now or
  • 21,800 one year from now?
  • The two sums are economically equivalent but not
    numerically equal!

7
Simple and Compound Interest
  • A deposit of P dollars with interest rate of i
    for N periods.
  • Simple Interest
  • the practice of charging an interest rate only to
    an initial sum (principal amount).
  • Total interest earned is
  • I (iP)N
  • Total future amount is
  • F PI P(1iN)
  • Compound Interest
  • the practice of charging an interest rate to an
    initial sum and to any previously accumulated
    interest that has not been withdrawn.
  • Total future amount is
  • F PI P(1i)N

8
Ex Compound Interest
For compound interest, with 5 annual interest
rate for 3 years
Owe at t 3 years 1,000 50.00 52.50
55.13 1,157.63
9
Terminology and Symbol
  • P value or amount of money at a time designated
    as the present or time 0.
  • Also, P is referred to as present worth (PW),
    present value (PV), net present value (NPV),
    discounted cash flow (DCF), and capitalized cost
    (CC) dollars
  • F value or amount of money at some future time.
  • Also, F is called future worth (FW) and future
    value (FV) dollars
  • A series of consecutive, equal, end-of-period
    amounts of money.
  • Also, A is called the annual worth (AW) and
    equivalent uniform annual worth (EUAW) dollars
    per year, dollars per month
  • n number of interest periods years, months,
    days
  • i interest rate or rate of return per time
    period percent per year, percent per month
  • t time, stated in periods years, months,
    days, etc

10
Cash Flow
  • CASH INFLOWS
  • Money flowing INTO the firm from outside
  • Upward arrows (?)
  • Revenues, Savings, Salvage Values, etc.
  • CASH OUTFLOWS
  • Disbursements
  • Downward arrows (?)
  • First costs of assets, labor, salaries, taxes
    paid, utilities, rents, interest, etc.
  • NET CASH FLOW
  • two or more receipts and disbursement at the
    same time are summed and shown in a single arrow
  • Cash Inflows Cash Outflows
  • END-OF-PERIOD CONVENTION
  • placing all cash flow transactions at the end of
    an interest period.

11
Types of Cash Flows
  • Single cash flow
  • Equal (uniform) series
  • Linear gradient series
  • Geometric gradient series
  • Irregular series

12
Single-Payment Factors (F/P and P/F)
  • Find F, given P , i, N
  • Single-payment compound amount factor
  • F P (1i)N P (F/P,i,N)
  • Ex If you had 2,000 now an invested it at 10,
    how much would it be worth in 8 years
  • Find P, given F , i , N,
  • Single-payment present worth factor
  • P F (1 i )-N F (P/F,i,N)
  • Ex Suppose that 1,000 is to be received in 5
    years. At an annual interest rate of 12, what is
    the present worth of this amount?

Also see Example 2.1 2.3
13
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14
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15
Example Adapted from Park (2004)
  • A company has borrowed 250,000 to purchase an
    equipment. A loan was offered with 8 interest
    rate per year. The company plans to repay
    installments in equal amounts over the next 6
    years.
  • What is annual installment?
  • What if the repayment is deferred for 1 year,
    what would be the annual installment in this
    case?
  • That is, the 1st loan payment starts at the end
    of year 2 and continues to year 7.

16
Shifted Uniform Series
  • A shifted series is one whose present worth point
    in time is NOT t 0.
  • Shifted either to the left of 0 or to the right
    of t 0.
  • Dealing with a uniform series
  • The PW point is always one period to the left of
    the first series value
  • No matter where the series falls on the time
    line.

i 10
A -500/year
P2
P0
17
Series with other single cash flow
  • It is common to find cash flows that are
    combinations of series and other single cash
    flows.
  • Solve for the series present worth values then
    move to t 0.
  • Solve for the PW at t 0 for the single cash
    flows.
  • Add the equivalent PWs at t 0.
  • Consider

i 10
18
Ex Final Exam (2004)
  • An engineering student who will soon receive his
    B.S. degree is considering continuing his formal
    education by working toward an M.S. degree. The
    student estimates that his average earnings for
    the next 6 years with a B.S. degree will be
    40,000 per year. If he can get an M.S. degree
    in one year, his earnings should average 44,000
    per year for the subsequent 5 years. His
    earnings while working on the M.S. degree will be
    negligible and his additional expenses to be paid
    out over this year will be 10,000. The student
    estimates that his average per-year earnings in
    the two decades following the initial 6-year
    period will be 42,000 and 45,000, if he does
    not stay for an M.S. degree. If he receives an
    M.S. degree his earnings per year in the two
    decades can be stated as 42,000 x and 45,000
    x. The interest rate is assumed at 15.
  • Draw cash flow diagrams for two options working
    and studying. The diagram must be clearly
    labeled.
  • Find the value of x for which the extra
    investment in formal education will pay for
    itself. In other words, find the value of x in
    which the two options (working and studying) are
    break-even and equivalent. Note Use up to 4
    decimal points throughout your calculation.

19
Evaluating Alternatives
  • Revenue/Cost the alternatives consist of cash
    inflow and cash outflows
  • Select the alternative with the maximum economic
    value
  • Service the alternatives consist mainly of cost
    elements
  • Select the alternative with the minimum economic
    value (min. cost alternative)

20
Evaluating Alternatives
  • Independent the decision on any one project has
    no effect on the decision made on another project
  • Mutually exclusive Acceptance of one project
    will automatically rejects all other projects

21
Alternatives
Analysis
Selection
Problem
Execution
22
Evaluating AlternativesPresent Worth Analysis
(PW)
A process of obtaining the equivalent worth of
future cash flows to some point in time
called the Present Worth (PW)
At an interest rate usually equal to or greater
than the Organizations established Minimum
Attractive Rate of Return (MARR).
Step 1 Calculate PW of each alternative at MARR
23
Present Worth Analysis of Equal-Life
Alternatives
Step 1 Calculate PW of each alternative at MARR
  • Ex Assume 2 investment alternatives with the
    same useful life of 4 years. Due to limited
    investment fund, the 2 alternatives are mutually
    exclusive. Based on the following information,
    which one should we select? Assume MARR 10

Also see Ex 5.1
24
Ex PW Analysis (Equal-life)
Consider Machine A Machine B First
Cost 2,500 3,500 Annual Operating Cost
900 700 Salvage Value 200
350 Life 5 years 5 years i 10 per
year
Which alternative should we select?
25
Present Worth Analysis of Different Life
Alternatives
  • Comparison must be made over equal time periods
  • Compare over the least common multiple, LCM, for
    their lives
  • Assume repeatability. Alternative will repeat the
    same manner over each life cycle
  • Cash flow estimates are the same in every life
    cycle
  • Example 3,4, and 6 years. The lowest common
    life is 12 years.
  • Evaluate all over 12 years for a PW analysis.

Also see Ex 5.2
26
Ex PW Analysis (Different-life)
Assume MARR 10 per year.
Which alternative should we select?
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