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Engineering Economic Analysis: Slide 1
Massachusetts Institute of Technology^ 3.080 Econ & Enviro Issues In Materials Selection Randolph Kirchain Department of Materials Science & EngineeringMassachusetts Institute of TechnologyDepartment of Materials Science & Engineering
Engineering Economics:
Comparing Financial Characteristics of Design Options
Engineering Economic Analysis: Slide 2
Massachusetts Institute of Technology^ 3.080 Econ & Enviro Issues In Materials Selection Randolph Kirchain Department of Materials Science & EngineeringMassachusetts Institute of TechnologyDepartment of Materials Science & Engineering
Engineering Econ Example: Comparing Alternatives
BIG
DIG
Where Should You Build? Far or Near
Figure by MIT OCW.
Example: Comparing Alternatives
Cost Site A Site B Cost to build @ site $250,000 $500, Monthly Costs Average Hauling Distance 6 5 miles Hauling Expense $15 $15 /mile Shipments 250 250 /month Total Monthly Cost $22,500 $18,
Monthly Savings $3,
Massachusetts Institute of TechnologyMassachusetts Institute of Technology^ 3.080 Econ & Enviro Issues In Materials Selection Department of Materials Science & EngineeringDepartment of Materials Science & Engineering Randolph Kirchain Engineering Economic Analysis: Slide 3
Example: Comparing Alternatives
- Simple payback:
- Site B is preferred after 5 years ($500,000 − $250,000) (^) ≈ 67 months $3,750 / month
- Considering reasonable business assumptions (15% discount rate) - Site B is preferred after > 12 years
How do we come up with such a difference? …
Massachusetts Institute of TechnologyMassachusetts Institute of Technology^ 3.080 Econ & Enviro Issues In Materials Selection Department of Materials Science & EngineeringDepartment of Materials Science & Engineering Randolph Kirchain Engineering Economic Analysis: Slide 4
Cost Concepts: Nomenclature
- Capital
- Wealth (money or property) that can be used to produce more wealth
- Sunk cost
- Expense which has happened in the past. No relevance to alternatives being considered.
- Opportunity cost
- Cost / value of the best rejected alternative
- Fixed cost
- Magnitude does NOT vary with changes in level of activity (output) -- over some range of activity - Insurance - Management and administrative salaries - Licenses
- Variable cost
- Magnitude DOES vary with level of activity (output) Massachusetts Institute of TechnologyMassachusetts Institute of Technology^ 3.080 Econ & Enviro Issues In Materials Selection Department of Materials Science & EngineeringDepartment of Materials Science & Engineering Randolph Kirchain Engineering Economic Analysis: Slide 8
Engineering Economy
- Objective – Evaluation
- How to compare the economic value of alternative design options?
vs
$20k $25k (^) $350 / Month Lease
vs
Figure by MIT OCW.
Massachusetts Institute of TechnologyMassachusetts Institute of Technology^ 3.080 Econ & Enviro Issues In Materials Selection Department of Materials Science & EngineeringDepartment of Materials Science & Engineering Randolph Kirchain Engineering Economic Analysis: Slide 9
Determining Equivalence:
Issue - Value over time
- Money now has a different value than the same amount at a different date - Would you prefer $75 today or $80 in one year? - It depends – Rate of return on investment
- Proper name: Discount Rate, i or r
- Future benefits / costs are reduced (ie, “discounted”) to compare with present
Massachusetts Institute of TechnologyMassachusetts Institute of Technology^ 3.080 Econ & Enviro Issues In Materials Selection Department of Materials Science & EngineeringDepartment of Materials Science & Engineering Randolph Kirchain Engineering Economic Analysis: Slide 10
Return on Capital
- Why consider return on capital?
- For most engineering projects, capital must be tied up for some period of time - Purchase a piece of equipment - Fund a research project
- Revenues from the use of capital
- Provides incentive to forego using the capital today for consumption
- Provides incentive to take on risk of losing capital
- Opportunity cost (of capital)
- Profit available from the use of capital in some other alternative
- Frequent engineering economy question: Does the return on capital exceed the opportunity cost?
Massachusetts Institute of TechnologyMassachusetts Institute of Technology^ 3.080 Econ & Enviro Issues In Materials Selection Department of Materials Science & EngineeringDepartment of Materials Science & Engineering Randolph Kirchain Engineering Economic Analysis: Slide 11
Engineering Economic Analysis: Slide 14
Massachusetts Institute of Technology^ 3.080 Econ & Enviro Issues In Materials Selection Randolph Kirchain Department of Materials Science & EngineeringMassachusetts Institute of TechnologyDepartment of Materials Science & Engineering
How does Capital Change in Value with Time?
Compound Interest
- Compound interest
- Interest earned (charged) for a period is based on
- Remaining principal plus
- Accumulated (unpaid) interest at the beginning of the period I (^) n (Interest in Period n) = Pn i Pn = Principal in period n i = interest rate per period = (^) ∑ n n
I I
Cash Flow Diagram
P
?
Magnitude 0
…
Engineering Economic Analysis: Slide 15
3.080 Econ & Enviro Issues In Materials Selection Randolph Kirchain
n
F
?
Time
Massachusetts Institute of TechnologyDepartment of Materials Science & EngineeringMassachusetts Institute of TechnologyDepartment of Materials Science & Engineering
Formulae for N Periods –
Single Payments
Future Amount = P (1 + i )N^ = P (caf) F
caf ≡ Compound Amount Factor P … Common notation:^0 1 2 3 n-1^ n
F = P(F/P, i%, N)
Massachusetts Institute of TechnologyMassachusetts Institute of Technology^ 3.080 Econ & Enviro Issues In Materials Selection Department of Materials Science & EngineeringDepartment of Materials Science & Engineering Randolph Kirchain Engineering Economic Analysis: Slide 16
Formulae for N Periods –
Single Payments
Present Amount =
F F
= F
caf (1+ i ) N
P
1/caf ≡ Present Worth Factor … 0 1^2 3 n-1 n
Common notation:
P = F(P/F, i%, N)
Massachusetts Institute of TechnologyMassachusetts Institute of Technology^ 3.080 Econ & Enviro Issues In Materials Selection Department of Materials Science & EngineeringDepartment of Materials Science & Engineering Randolph Kirchain Engineering Economic Analysis: Slide 17
Engineering Economic Analysis: Slide 20
Massachusetts Institute of Technology^ 3.080 Econ & Enviro Issues In Materials Selection Randolph Kirchain Department of Materials Science & EngineeringMassachusetts Institute of TechnologyDepartment of Materials Science & Engineering
Relating a Uniform Series of Payments to P or F
- Uniform series of payments – often called an Annuity
- By convention:
- P at time 0
- A at end of period
- F at end of period
Therefore:
- 1 st^ A, 1 period after P
- Last A, coincident with F
A A A A
…
A
n-1 n
P
?
F
?
Engineering Economic Analysis: Slide 21
Massachusetts Institute of Technology^ 3.080 Econ & Enviro Issues In Materials Selection Randolph Kirchain Department of Materials Science & EngineeringMassachusetts Institute of TechnologyDepartment of Materials Science & Engineering
Derive Uniform Series Compound Amount Factor
- How do we find the present value (PV) of N payments @ $A?
- Subtract the PV of an infinite series of payments starting at N+ from the PV of an infinite series of payments starting at 1
A A A
…
P A
N-1 N
A A A
…
P A
N-1 N
A
…
A
A
N+
…
P
N-1 N
A
…
A
A
N+
Engineering Economic Analysis: Slide 22
3.080 Econ & Enviro Issues In Materials Selection Randolph Kirchain
Formulas for N Periods
Finite Series of Equal Payments
a) Future Value (F)
b) Payment (A)
= P (crf)
crf = Capital Recovery Factor
×
N N = P [(1+r)^ ] [(1 + r) -1]
r
A A A A
…
P
A
n-1 n
=^ +
∑ (1^ )
[(1 ) - 1]
N (^) i
i N
A r
A r r
Massachusetts Institute of TechnologyDepartment of Materials Science & EngineeringMassachusetts Institute of TechnologyDepartment of Materials Science & Engineering
