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8/3/2019 Engineering Economics Sp06
1/18
Engineering Economics
.
Rajeev Bansal
February 1, 2006
8/3/2019 Engineering Economics Sp06
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Engineering Economics
Why is it important?
Value and Interest
Cash Flow Diagrams and Patterns Equivalence of Cash Flow Patterns
Evaluating Alternatives
Break-Even Analysis
Income Tax and Depreciation
Inflation
Conclusion
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Why do we care about
Engineering Economics? Engineering designs are intended to produce good
results.
They are accompanied by undesirables (costs). If outcomes are evaluated in dollars, and good is
defined as profit, then decisions will be guided by
engineering economics.
This process maximizes goodness only if all
outcomes are anticipated and can be monetized.
$
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Value and Interest
The value of money depends on the
amount and when it is received or spent.
1 2
$1000
$1166
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
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Cash Flow Diagrams
P-Pattern1 2 3 n
present
F-Pattern1 2 3 n
future
A-Pattern1 2 3 n
annual
G-Pattern1 2 3 n
gradient
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Equivalence of Cash Flow
PatternsTo Find Given Multiply By Formula
F P
P F
A P
A G
n
iPF )/(
n
iFP )/(
n
iPA
)/(
n
iGA )/(
ni)1(
+
ni)1(
1
+
1)1(
)1(
+
+n
n
i
ii
1)1(
1
+
ni
n
i
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Example: A new circuit board component insertion tool will
save $50,000 in production costs each year and will have a
life of seven years. What is the highest price that can be
justified for the tool using a 12% interest rate?
Solution:
1 2 3 74 5 6
P
50k 50k 50k 50k 50k 50k 50k
k
Aii
iAAPP
n
n
228$000,50$56.4
000,50$)12.01(12.0
1)12.01(
)1(
1)1()/(
7
7
%127
==+
+=
++
==
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Evaluating Alternatives
Annual Equivalent Cost Comparisons
Present Equivalent Cost Comparisons
Incremental Approach
Rate of Return Comparisons
Benefit/Cost Comparisons
Minimum Attractive Rate of Return (MARR): The lowest rate of return
that the organization will accept.
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Annual Equivalent Cost
Comparison Incomes are converted to an A-pattern.
Costs are converted to an A-pattern.
The costs are subtracted from the incomes todetermine the ANEV.
Mutually Exclusive Alternatives choose the one
with highest ANEV Independent Alternatives choose all with positive
ANEV
ANEV: Annual Net Equivalent Value
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Example: A new circuit board component insertion tool is
needed. Which should you buy?
Solution: The ANEV is calculated for each:
kkkk
kFAkkPAANEV
9.539.1208.35
30)/(20220)/( %1010%10
10
=+=+=
Model Price Annual Maintenance Salvage Value Life
JACO $220k $20k $30k 10 years
Cheepo $100k $35k 0 5 years
JACO:
k
kkPAANEV
4.61$
35100)/( %105
==Cheepo:
JACO
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Present Equivalent Cost
Comparison Incomes and costs are converted to P-patterns.
The costs are subtracted from the incomes to
determine the PNEV. Mutually Exclusive Alternatives choose the one
with highest PNEV
Independent Alternatives choose all with positivePNEV
PNEV: Present Net Equivalent Value, also called life cycle cost,
present worth, capital cost, and venture worth.
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Incremental Approach
For a set of mutually exclusive alternatives, only
the differences in amounts need to be considered.
kkkkk
kFPkFPkAPkPNEV
9.45$6.111.622.92120
30)/(100)/(15)/(120 %1010%10
5%10
10
=+++=+++=
Model Price Annual Maintenance Salvage Value Life
JACO $220k $20k $30k 10 years
Cheepo $100k $35k 0 5 years
JACO- Cheepo:
JACO
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Rate of Return Method
ANEV or PNEV is formulated
From this, we solve for the interest rate that will
give zero ANEV or PNEV This interest rate is the ROR of the alternative
For mutually exclusive alternatives, the one with
the highest ROR is chosen For independent alternatives, all with a ROR
greater than MARR are accepted
ROR: Rate of Return on Investment
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Benefit/Cost Comparisons
The benefit/cost ratio is determined from
For mutually exclusive alternatives, the one
with the highest B/C is chosen.
For independent alternatives, all with B/C >
1 are accepted.
The MARR is used to determine the denominator (cost).
costinitialofequivalentannual
benefitsannualnetuniform=C
B
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Break-Even Analysis
Break-even point: the value of an independentvariable such that two alternatives are equallyattractive.
For values above the break-even point, onealternative is preferred.
For values below the break-even point, the other is
preferred. Break-even analysis is useful when dealing with a
changing variable (such as MARR).
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Income Tax and Depreciation
Businesses pay the IRS a tax:
Depreciation: method of charging the initial cost ofan asset against more than one year.
An asset is depreciable if :
It is used to produce income,
Has a life greater than one year, but
Decays, wears out, becomes obsolete, or gets used up.
=ondepreciati-paidinterest-
costsoperating-revenuegrossRTAX
ACRS: Accelerated Cost Recovery System, used by IRS since 1980.
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Inflation
The buying power of money changes with time.
Inflation, if anticipated, can be put to good use by
fixing costs and allowing income to rise by Entering long-term contracts for materials or wages
Purchasing materials long before they are needed
Stockpiling product for sale later.
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Conclusion
For-profit enterprises exist to make money.
Non-profit entities also make decisions to
maximize the goodness of outcomes byassigning dollar values.
Your engineering decisions will be shaped
by economics.
$
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