Engineering Economics

1
Engineering Economics Management

• Civi 322/Engi 303
• Chapters 3-4

Read Chapter 2 for a better understanding of
financial statements.
2
Engineering Economy

• Do benefits exceed costs of an engineering
  design/project?
• Requires systematic evaluation of costs and
  benefits of various alternatives

3
Basic Principles

• Develop the alternatives
• decision (choice) lies among alternatives
• Focus on the incremental differences
• only the incremental differences in expected
  future outcomes among the alternatives are
  relevant
• Use a consistent viewpoint
• Use a common unit of measure

4
Basic Principles

• Consider all relevant criteria
• maximum monetary return, etc.
• Make uncertainty explicit
• uncertainty inherent in estimating
• Revisit your decisions
• validation

5
Economic Analysis Procedure

• Recognize, formulate, and evaluate problem
• Develop feasible alternatives
• Develop cash flows for each alternative
• Select criteria
• Analyze and compare alternatives
• Select preferred alternative
• Monitor performance and evaluate results

6
Additional factors

• Ignore sunk costs
• Use a common planning horizon
• Include the time value of money
• Consider separable decisions separately
• Include intangible consequences

7
Cost-Volume Relations

• Volume
• activity with strong influence on cost
• inputs or outputs e.g. automobiles produced
• Fixed Costs
• cost of providing basic operating capacity
• Variable Costs
• have close relationship to volume

8

• Semi-Variable Costs
• neither fixed nor variable auto depreciation
• Average Unit Cost
• per unit activity cost
• variable cost per unit volume is constant
• fixed cost varies with changes in volume
• Marginal/Incremental Costs
• added cost of an additional unit of output
• Recurring and Nonrecurring Costs
• Direct and Indirect Costs

9

• Sunk Cost
• cost that has occurred in the past and has no
  relevance to estimates of future revenues
• Opportunity Cost
• cost of the foregone opportunity
• Life-Cycle Cost
• all costs related to a system during its life span

10
Economic Environment

• Price-Demand Relationship

• Perfect Competition
• Product Substitution

p a - bD
Price
Monopoly Oligopoly
Units of Demand
11
Total Revenue Function
TR Price x Demand Substitute p a -
bD TR aD - bD2 Demand that will produce max
revenue? dTR/dD a-2bD 0 D a/2b How would
you guarantee that D maximizes total revenue?
Total Revenue
Da/2b
Demand
Maximum profits may not be obtained by
maximizing revenue
12
Breakeven Point
CT CF Cv Cv (cv) (D) where cv is the
variable cost per unit
Total Revenue
Max Profit
Case 1 Demand is function of price D1 , D2
breakeven points Total Rev Total Cost D
Optimal demand for maximum profit Profit(loss)
total revenue - total costs (aD-bD2) - (CF
cvD) Take derivative and set to zero Optimal D

CT
Profit
Cost and Revenue
Cv
CF
D1
D2
D
Volume (Demand)
How would you check profit maxima vs. profit
minima? How would you calculate economic
breakeven points?
13
Breakeven Point
Case 2
TR
Total revenue total cost
When price is independent of demand
Breakeven Point
Profit
CT
Cost and Revenue
Loss
Variable Costs
CF

Fixed Costs
D
CF (p-cv)
Volume (Demand)
D
14
Average Unit Cost Function
Fixed Component
Avg Unit Cost, Cu
Average Unit Cost
When total variable costs are a linear function
of demand CV cvD then, average unit cost
is Cu
Variable Component
Volume (Demand)
15
Cost-Driven Design Optimization

• Maintain a life-cycle viewpoint
• Initial investment costs
• Operation and maintenance expenses
• Future annual expenses
• Environmental and social consequences
• Minimum life-cycle cost goal is achieved largely
  in
• the early stages of design

16
Design Optimization Steps

• Identify the primary design variable
• Formulate a cost model
• Set the first derivative of the cost equal to
  zero
• Solve for the optimum value of the continuous
  design variable
• Verify for global minimum

17
Interest Time Value of Money

• Interest
• Cost of having money available for use
• Time Value of Money
• The economic value of a sum depends on when it is
  received
• distinguish between earning potential over time
  and decrease in value due to inflation

18

• Interest Based Transactions
• Examples borrowing, investing, purchasing on
  credit
• Elements
• Principal, P initial amount of money borrowed
  or invested
• Interest Rate, i cost of money expressed as a
  percentage
• per period of time
• Interest Period, how frequently interest is
  calculated
• Number of Interest Periods, N duration of
  transactions
• Future Amount, F cumulative effect of interest
  rate over
• periods of interest
• An end-of-period payment or receipt
• Vn equivalent sum of money at the end of period
  n

19
Cash Flow Diagrams
15,000
2000
Positive net Cash flow (receipts)
13,000 is net positive cash flow
1
2
4
5
3
Time ( of interest periods)
0
Negative net Cash Flow (payments)
End-of-Period Convention place all cash flow
transactions at the end of the period
20
Interest Formulation
Simple Interest
Compound Interest
After N periods, the total accumulated value F
will grow to
21
Economic Equivalence

• Which one would you prefer?
• 20,000 today
• 50,000 ten years from now
• 8,000 each year for the next ten years
• We need to compare their economic worth!
• Economic equivalence exists between cash flows if
• they have the same economic effect.
• Convert cash flows into an equivalent cash flow
  at
• any point in time

22
Equivalence Principles

• Use a common time basis
• Equivalent cash flows are equivalent at any
  common point in time
• Use the present time present worth
• Use some future point in time future worth
• Equivalence depends on interest rate
• Changing the interest rate destroys equivalence

23
Equivalence Principles

• Requires conversion of multiple payment cash
  flows to a single cash flow
• Equivalence is maintained regardless of the point
  of view

24
Types of Cash Flows

• Single cash flow
• Uniform series (most common)
• Linear gradient series
• Geometric gradient series
• Irregular series

25
Single Cash Flow
F
Compounding Process
P
Discounting Process
PPresent equivalent value
AAnnual equivalent value
F Future equivalent value
26
Uneven Payment Series
Find the present worth of any uneven stream of
payments by calculating the present value of
each individual payment and summing the
results Future worth can then be calculated by
using the interest formula
P5
P1
P6
P2
P3
P0
P4
0
Years
27
Equal Payment Series
F
N-1
1
2
3
0
N
A
A
A
A
A
A
Subtracting two above equations from each other
yields
28
Sinking Fund Factor Find A, given F, I, N
Capital Recovery (Annuity) Factor Find
A, given P, I, N
Present Worth Factor Find P, given A, I, N
29
Linear Gradient Series
(N-1)G
A1
2G
G
Uniform Series
0
N-1
0
1
2
N
Composite Series uniform series linear gradient
Find P, given A1, G, I, N
30
Gradient to Uniform Series Conversion
Find A, given G, I, N Substitute the Gradient
Series Present Worth Factor into Capital
Recovery Factor.
(N-1)G
(N-2)G
A
A
A
A
A
A
2G
G
N
(N-1)G
0
1
2
0
1
2
N-1
N
Future Worth Factor
31
Geometric Gradient Series

• Particularly relevant to construction costs
• Cash flows increase by a constant (g) compound
  growth
• Example price changes due to inflation

Present Worth, Pn, of any Cash Flow An
A1(1g)N-1
A1(1g)
A1
If ig, then P?
0
1
3
N
2
N-1
g gt 0
P
Find P, given A1, g, i, N
32
Rate-of-Return Analysis
How do you determine the rate of growth of your
investments? What is the rate of return on
investment in an engineering project?