ENGR 112

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ENGR 112

• Economic Analysis

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Engineering Economic Analysis

• Evaluates the monetary aspects of the products,
  projects, and processes that engineers design
• Aids in the decision making process when
  alternatives are compared
• Especially useful when resources are limited
• Replace vs. keep
• Build vs. buy

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Time Value of Money

• 1 today is more valuable than 1 a year later
• Engineering economy adjusts for the time value of
  money to balance current and future revenues and
  cost

0
5
10
Years
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Capital vs. Interest

• Capital
• Invested money and resources
• Whoever owns it should expect a return from
  whoever uses it
• Bank lends you money
• Buy a car
• Go to college
• Firm invests in a project
• Buy equipment
• Buy knowledge

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Capital vs. Interest

• Interest
• Return on capital
• Typically expressed as an interest rate for a
  year
• Interest rates are needed to evaluate engineering
  projects!!

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Interest-ing Example

• The engineering group of Baker Designs must
  decide whether to spend 90K (K for thousands) on
  a new project. This project will cost 5K per
  year for operations, and it will increase
  revenues by 20K annually. Both the costs and
  the revenues will continue for 10 years. Should
  the project be done?

Eschenbach, T.G., Engineering Economy Applying
Theory to Practice, Irwin, 1995, p.22
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Types of Interest

• Nomenclature
• P Initial deposit (or principal)
• N Number of years
• i Interest rate per year
• F Future value after N years

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Types of Interest

• Simple Interest
• The interest calculated for N periods is based on
  the initial deposit

F0 P F1 P Pi P(1 i) F2 P Pi
Pi P (1 i i) P (1 2i) Fn P
Pi Pi P (1 i i ) P (1 Ni)
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Types of Interest

• Compound Interest
• Interest type used in engineering economic
  evaluations
• Interest is computed on the current balance that
  has not yet been paid
• Includes accrued interest

F0 P F1 P Pi P (1 i) F2 P1 P1 i
P1 (1i) P (1i) (1i) P (1i)2 Fn
Pn-1 Pn-1 i Pn-1 (1i) P (1i)n-1
(1i) P (1i)n
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Simple vs. Compound Interest

• If 100 is deposited in a savings account, how
  much is in the account at the end of each year
  for 20 years, if interest is deposited in the
  account and no withdrawals are made? Assume a 5
  interest per year.

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Simple vs. Compound Interest
Compound
Simple
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In Class Problem 1

• If 500 is deposited in a savings account, would
  a 5 simple interest rate be better than a 3
  compound interest rate if you were planning to
  keep the money for 3 years? For 35 years?
  Assume that all earned interest is deposited in
  the account and no withdrawals are made.

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Example 1

• Sam Bostro borrows 4000 from his parents for his
  final year of college. He agrees to repay it 3
  years later in one payment to which a 7 compound
  interest rate will be applied.
• a) How much does he repay?
• F (4000)(1 0.07)3 4,900.17
• b) How much of this is interest and how much is
  principal?
• F P I ? P 4,000 I 900.17

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Example 2

• Susan Cardinal deposited 500 in her savings
  account and six years later the account has 600
  in it. What compound rate of interest has Susan
  earned on her capital?
• F P(1i)n ? i F/P1/n 1
• i 600/500 1/6 1 .031
• i 3.1

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In Class Problem 2

• Your friend is willing to loan you 1500 to buy a
  new computer, but you must agree to pay him back
  2500 when you graduate in 4 years? What is the
  compound interest rate you will be paying your
  friend?

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Cash Flow Diagrams

• Pictorial description of when and how much money
  is spent or received
• Summarizes the economic aspects of an engineering
  project

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Cash Flow Categories

• First Cost
• Expense to build or to buy and install
• Operation and maintenance (OM)
• Annual expenses (electricity, labor, minor
  repairs, etc.)
• Salvage value
• Receipt at project termination for sale or
  transfer of equipment
• There can also be a salvage COST

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Cash Flow Categories

• Revenues
• Annual receipts due to sale of products or
  services
• Overhauls
• Major capital expenditures that occurs part way
  through the life of the asset
• Prepaid expenses
• Annual expenses that must be paid in advance
  (e.g., leases, insurance)

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Examples

• Ernies Earthmoving is considering the purchase
  of a piece of heavy equipment. What is the cash
  flow diagram if the following cash flows are
  anticipated?
• First cost 120K
• OM cost 30k per year
• Overhaul cost 35K in year 3
• Salvage value 40K after 5 years
• How would the cash flow diagram change if Ernie
  decides to lease the equipment (at 25K per year)
  instead of purchasing it?

a)
b)
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Solution
40K
a)
30K
30K
30K
30K
30K 35K
120K
b)
25K
30K
25 30K
25 30K
25K 30K
25K 30K 35K
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Frequency of Compounding

• Interest rates are typically specified on an
  annual basis
• However, interest is often compounded more often
• Semiannually
• Quarterly
• Monthly
• Daily

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Frequency of Compounding

• How does that change our formula?
• m of compounding periods per year
• n of compounding periods
• n m x N
• Quarterly? ?
• Monthly? ?

m 4 n 4N ? F P(1i/m)mN P(1i/4)4N
m12 n 12N ? F P(1i/12)12N
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Example

• Suppose you borrow 3000 at the beginning of your
  senior year to meet college expenses. If you make
  no payments for 10 years and then repay the
  entire amount of the loan, including accumulated
  interest, how much money will you owe? Assume
  interest is 6 per year, compounded
• Annually m1 P3,000
• Quarterly m4 N10 years
• Monthly m12 i6 per year
• Daily m365
• How significant is the frequency of compounding?

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Solution

• FA P(1i/1)1N 3000(10.06/1)10 5,372.54
• FQ P(1i/4)4N 3000(10.06/4)40 5,442.05
• FM P(1i/12)12N 3000(10.06/12)120
  5,458.19
• FD P(1i/365)1N 3000(10.06/365)3650
  5,466.08

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Solution
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In Class Problem 3

• You need to borrow 500 to pay for the text books
  you will need for your sophomore level courses.
  Which is the better loan assuming that you will
  pay the entire loan amount plus interest when you
  graduate in 3 years?
• 3.0 compounded annually
• 2.5 compounded quarterly