Transcript No Slide Title
Engineering Economics
John Ayers September 17, 2004 .
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
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.
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
Cash Flow Diagrams
P-Pattern 1 2 3 F-Pattern 1 2 3 A-Pattern 1 2 3 G-Pattern 1 2 3 n n n n “present” “future” “annual” “gradient”
Equivalence of Cash Flow Patterns
To Find Given Multiply By Formula F P (
F
/
P
)
i n
P A A F P G (
P
/
F
)
i n
(
A
/
P
)
i n
(
A
/
G
)
i n
( 1
i
)
n
1 ( 1
i
)
n i
( 1
i
)
n
( 1
i
)
n
1
i
1
n
( 1
i
)
n
1
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?
50k 50k 50k 50k 50k 50k 50k Solution: 1 2 3 4 5 6 7 P
P
(
P
/
A
) 12 7 %
A
( 1
i i
( 1 )
n
1
A i
)
n
( 1 0 .
12 ) 7 1 0 .
12 ( 1 0 .
12 ) 7 $ 50 , 000 4 .
56 $ 50 , 000 $ 228
k
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.
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 to determine the ANEV.
• Mutually Exclusive Alternatives – choose the one with highest ANEV • Independent Alternatives – choose all with positive ANEV ANEV: Annual Net Equivalent Value
Example: A new circuit board component insertion tool is needed. Which should you buy? Model Price Annual Maintenance Salvage Value Life JACO Cheepo $220k $100k $20k $35k $30k 0 10 years 5 years Solution: The ANEV is calculated for each: JACO:
ANEV
35 .
8
k
(
A
/ 20
k P
) 10 10 % 1 .
9
k
220
k
53 20 .
9
k k
(
A
/
F
) 10 10 % 30
k
Cheepo:
ANEV
$ 61 .
4
k
(
A
/
P
) 10 5 % 100
k
35
k
JACO
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 positive PNEV PNEV: Present Net Equivalent Value, also called “life cycle cost,” “present worth,” “capital cost,” and “venture worth.”
Incremental Approach
• For a set of mutually exclusive alternatives, only the differences in amounts need to be considered.
Model JACO Cheepo Price $220k $100k Annual Maintenance $20k $35k Salvage Value $30k 0 Life 10 years 5 years JACO- Cheepo:
PNEV
120
k
120
k
92 .
2
k
(
P
62 .
/ 1
A
) 10 10 % 15
k k
11 .
6
k
(
P
$ / 45
F
) 10 5 % .
9
k
100
k
(
P
/
F
) 10 10 % 30
k
JACO
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
Benefit/Cost Comparisons
• The benefit/cost ratio is determined from
B C
uniform net annual benefits annual equivalent of initial cost • 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 numerator (benefits).
Break-Even Analysis
• Break-even point: the value of an independent variable such that two alternatives are equally attractive.
• For values above the break-even point, one alternative 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).
Income Tax and Depreciation
• Businesses pay the IRS a tax:
TAX
R
gross revenue interest paid operating costs depreciati on • Depreciation: method of charging the initial cost of an 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.
ACRS: Accelerated Cost Recovery System, used by IRS since 1980.
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.
Conclusion
• For-profit enterprises exist to make money.
• Non-profit entities also make decisions to maximize the goodness of outcomes by assigning dollar values.
• Your engineering decisions will be shaped by economics.
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