Decision-Making Steps

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Decision-Making Steps 1. Define problem 2.
Choose objectives 3. Identify alternatives 4.
Evaluate consequences 5. Select 6.
Implement 7. Audit
EGR 403, Jan 99
2
Engineering Economy uses mathematical formulas
to account for the time value of money and to
balance current and future revenues and
costs. Cash flow diagrams depict the timing and
amount of expenses (negative, downward) and
revenues (positive, upward) for engineering
projects.
EGR 403, Jan 99
3
Example on Cash Flow Diagram Draw the cash flow
diagram for a Corolla with the following cash
flow Down payment 1000, refundable security
deposit 225, and first months payment 189
which is due at signing (total 1414). Monthly
payment 189 for 36 month lease (total 6804).
Lease-end purchase option 7382.
EGR 403, Jan 99
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Interest is the return on capital or cost of
using capital. Simple Vs Compound interest
rate Equivalence (page 45) When we are
indifferent as to whether we have a quantity of
money now or the assurance of some other sum of
money in the future, or series of future sums of
money, we say that the present sum of money is
equivalent to the future sum or series of future
sums. Equivalence depends on interest rate
EGR 403, Jan 99
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Notation i Interest rate per payment
period n Number of payment periods P Present
value of a sum of money (time 0) Fn Future
value of a sum of money in year n (end
of year n) Considering Compound interest Single
Payment Compound Amount (FP,i,n) (1i)n
F/P, thus F P(FP, i, n) Single Payment
Present Worth (PF,i,n) 1/(1i)n, thus
P F(PF, i, n)
EGR 403, Jan 99
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Example on P and F 1- An antique piece is
purchased for 10,000 today.  How much will it
be worth in three years if its value increases 8
per year? 2- What sum can you borrow now, at an
8 interest rate, if you can pay back 6,000 in
five years? 3- How long will it take for an
investment of 300 to double considering 8
interest rate? 4- An investment of 2,000 has
been cashed in as 3,436 eight years later. 
What was the interest rate? 5- How much will a
deposit of 400 in a bank be six years from now,
if the interest rate is 12 compounded quarterly?
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Different Methods for Solving Engineering
Economy Problems 1- Mathematical formulas (use
calculator) 2- Engineering Economy functional
notation (use compound interest tables) 3-
Software such as Excel (use defined functions)
EGR 403, Jan 00
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In most Eng. Econ. Formula, there are four
parameters , i.e. F, P, i, and n. If three of
these are known you can find the fourth
one. Specific Situations The required number
of years is not in the compound interest
table There is no compound interest table for
the required interest rate The interest is
compounded for some period other than annually
EGR 403, Jan 00
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Different Skills (Tricks) to Solve Cash Flow
Diagram

• Shift origin (time 0) to an imaginary point of
  time
• Add and subtract imaginary cash flows
• Dissect cash flow diagram

EGR 403, Jan 04
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Notation A A series of n uniform payments at
the end-of-period Considering Compound
interest Uniform series compound amount F
A(FA, i, n) Uniform series sinking fund A
F(AF, i, n) Uniform series capital recovery A
P(AP, i, n) Uniform series present worth P
A(PA, i, n) Deferred annuities

EGR 403, Jan 99
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Example on A 1- You make 12 equal annual
deposits of 2,000 each into a bank account
paying 4 interest per year.  The first deposit
will be made one year from today.  How much
money can be withdrawn from this bank account
immediately after the 12th deposit? 2- Your
parents deposit 7,000 in a bank account for your
education now.  The account earns 6 interest
per year.  They plan to withdraw equal amounts
at the end of each year for five years, starting
one year from now.  How much money would you
receive at the end of each one of the five years?
3- How much should you invest today in order to
provide an annuity of 6,000 per year for seven
years, with the first payment occurring exactly
four years from now? Assume 8 interest rate.
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Notation G Arithmetic gradient series, fix
amount increment at the
end-of-period Considering Compound
interest Arithmetic gradient uniform series A
G(AG, i, n) Arithmetic gradient present
worth P G(PG, i, n)
G 2G 0
1 2 3
EGR 403, Jan 99
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Notation g Geometric gradient series, fix
increment at the end-of-period Considering
Compound interest
A A(1g) A(1g)2 0
1 2 3
EGR 403, Jan 99
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Example on G and g 1- Suppose that certain
end-of-year cash flows are expected to be 2,000
for the second year, 4,000 for the third year,
and 6,000 for the fourth year.  What is the
equivalent present worth if the interest rate is
8?  What is the equivalent uniform annual
amount over four years? 2- Overhead costs of a
firm are expected to be 200,000 in the first
year, and then increasing by 4 each year
thereafter, over a 6-year period.  Find the
equivalent present value of these cash flows
assuming 8 interest rate.
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Types of Interest Rates r Nominal interest
rate per period (compounded as sub
period) mi i Effective interest rate per sub
period (i.e., month) ia Effective interest rate
per year (annum) m Number of compounding sub
periods per period Super period Cash flow less
often than compounding period Sub period Cash
flow more often than compounding period
Continuous Compounding
EGR 403, Jan 99
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Example on Different Interest Rates 1- A credit
card company charges an interest rate of 1.5
per month on the unpaid balance of all
accounts.  What is the nominal rate of return? 
What is the effective rate of return per year?
2- Suppose you have borrowed 3000 now at a
nominal interest rate of 10.  How much is it
worth at the end of the ninth year?     a) If
interest rate is compounded quarterly.     b) If
interest rate is compounded continuously.
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• Timing of cash flow
• End of the period
• Beginning of the period
• Middle of the period
• Continuous during the period

EGR 403, Jan 99
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Example on Different Timing 3- We would like to
find the equivalent present worth of 4,000 paid
sometime in future. Assume 20 interest rate.
    a) How much is the equivalent present worth
if it is paid at the end of the first
year?     b) How much is the equivalent present
worth if it is paid in the middle of
the first year?     c) How much is the
equivalent present worth if it is paid at the
beginning of the first year?     d) How
much is the equivalent present worth if it is
paid continuously during the first
year? Assume continuous compounding
with nominal interest rate of 20.
EGR 403, Jan 04
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Example on Patterns Recognition in Cash Flow
Diagram You have two job offers with the
following salary per year.  Assume you will stay
with a job for four years and the interest rate
is 10.  Which one of the jobs will you select
and why? Year          1                     
2                      3                      4
Job A      50,000         52,500            
55,125         57,881 Job B     
52,000         53,200            
54,400         55,600
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Example on Loan Analysis Assume you borrow
2,000 today, with an interest rate of 10 per
year, to be repaid over five years in equal
amounts (payments are made at the end of each
year). The 2,000 is known as the principal of
the loan. The amount of each payment can be
calculated as below A 2000(AP, 10, 5)
527.6 Each payment consists of two portions
interest over that year and part of the
principal. The following table shows the amount
of each portion for each of the payments. Notice
that as time goes by you will pay less interest
and your payment will cover more of the
principal.
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Loan Analysis

A 2000(AP, 10, 5) 527.6
EGR 403, Jan 2000
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Bond Analysis Bond is issued to raise funds
through borrowing. The borrower will pay
periodic interest (uniform payments A) and a
terminal value (face value F) at the end of
bonds life (maturity date). The timing of the
periodic payments and its amount are also
indicated on each bond. Sometimes the bond's
interest rate (rb), that is a nominal interest
rate, is mentioned instead of the amount of each
payment. The market price of a bond does not
need to be equal to its face value. A F rb
/ m
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Example on Bond A bond pays 100 quarterly.
Bonds face value is 2,000 and its maturity
date is three years from now. a) What is the
bonds interest rate? rb Am/F 100 4 / 2000
20 quarterly b) What is the present worth of
the bond assuming that a nominal interest rate
of 12 compounded quarterly is desirable. i
r/m 12/4 3 per quarter Number of payments
n 34 12 quarters P 100(PA, 3, 12)
2000(PF, 3, 12) 2,398.2
EGR 403, Jan 2000