Transcript Place of Engineering Economics in the World

Dealing with Uncertainty
Assessing a Project’s Worth under
Uncertainty or Risk
Previously
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In previous lectures, we assumed a high degree
of confidence in all estimated values, that is we
assumed certainty.
In most situations, however, there is doubt as to
the ultimate results that will be obtained from
an investment - there is risk and uncertainty
Risk and Uncertainty
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Caused by lack of precise knowledge regarding future
business conditions, technological developments,
synergies among projects, etc.
Should be made explicit in any analysis
Risk - Variability described by probability distributions
Uncertainty - Probability distributions are not known
Generally the terms are interchangeable
Four major sources of uncertainty
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Inaccuracy of the estimates: cash inflow, savings in
existing operating expenses, capital required
Type of business involved
Type of physical plant and equipment involved
Length of the project and study period
Non-probabilistic Methods for
Describing Project Risk
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Breakeven Analysis
Sensitivity Analysis
Scenario Analysis
Risk-Adjusted MARRs
Reduction of the useful life
Breakeven Analysis
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Commonly used when selection among
alternatives is dependent on a single factor
(e.g., capacity, sales).
Solve for the value of that factor at which the
conclusion is a standoff.
common measures include annual revenues
and expenses, rate of return, market or salvage
value, equipment life, capacity utilization).
Kinds of Breakeven Analysis
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Comparing two alternatives: Find the value of
some parameter that makes the NAW or NPW
equal.
Evaluating a single alternative: Find the value of
some parameter that makes NAW or NPW equal to
zero.
To decide, judge whether the breakeven point can
reasonably be expected.
Breakeven Analysis - Example 1
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Suppose that the market value of Alternative 1 is
known with certainty. What would the market
value of Alternative 2 have to be so that the initial
decision based on this information would be
reversed? Use a MARR of 15% per year
Capital Investment
Annual Revenues
Annual Expenses
Estimated Market Value
Useful Life
Alternative 1
-$4,500
$1,600
-$400
$800
8 years
Alternative 2
-$6,000
$1,850
-$500
$1,200
10 years
Example 1 - cont’d
NAWA = $255
 NAWB = $213
(MV = 1200)
Choose A
 Find Breakeven Point for market value for B
NAWA = NAWB
255 = -$6000 (A/P,15%,10) + $1350 +X(A/F,15%,10)
 Solve for X = 2050
 Decision?
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Example 1 - cont’d
NAW versus Market Value of Alternativ e 2
Alternative 1
$280
Alternative 2
$270
$260
$250
$240
$230
$220
Breakeven Point = $2050
$210
$200
1200
1400
1600
1800
2000
2200
2400
Sensitivity Analysis
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Relative magnitude of change in the measure
of interest caused by one or more changes in
estimated factors
Common technique when one or more factors
are subject to uncertainty.
Assesses the impact of uncertainty in estimates
on study results.
Sensitivity Analysis - Example 2
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A machine is considered for immediate
installation. Because of the new technology built
in, we want to investigate its NPW over a range
of +/-40% in
a) capital investment,
c) market value,
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b) annual net cash flow,
d) useful life.
Use MARR = 10%
Capital Investment
Annual Revenues
Annual Expenses
Estimated Market Value
Useful Life
-$11,500
$5,000
-$2,000
$1,000
6 years
Example 2 - cont’d
Base NPW =
-$11,500 + $3000 (P/A,10%,6) + $1000 (P/F,10%,6) = $2,130
 a) When capital invest. varies by +/- p%,
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NPW = - (1 + p/100) ($11,500) + …
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(linear function)
b) When revenues vary by +/- a%,
NPW = … + (1 + a/100) ($3000)(P/A,10%,6) + … (linear function)
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c) When market value varies by +/- s%,
NPW = … + (1 + s/100) ($1000) (P/F,10%,6) (linear function)
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d) When the useful life varies by +/- n%,
NPW = … + $3000(P/A,10%,(1 + n/100)(6))
+ $1000 (P/F,10%, (1 + n/100) (6)) (nonlinear function)
Example 2 - Spider Chart
Initial Investment
Market Value
Annual Net Cashflow
Useful Life
8000
6000
4000
2000
0
-60%
-40%
-20%
0%
20%
40%
60%
-2000
-4000
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Observation: Solution is most sensitive to …
Sensitivity analysis is useful for identifying factors that
need to be estimated more carefully
Considering Several Factors: Scenario
Analysis
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also called optimistic-pessimistic estimation
used to establish a range of values for the
measure of interest
typically, the optimistic estimate has 1 chance
out of 20 to be exceeded by the actual outcome
and the pessimistic estimate has 19 chances
out of 20 to be exceeded by the actual outcome
Scenario Analysis - Example 3
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An ultrasound inspection device for which
optimistic, most likely and pessimistic estimates
are found below. The MARR is 8%.
Optimistic
Most
(O)
Likely (M)
Capital Invest.
-$150,000
-$150,000
Annual Revenues $110,000
$70,000
Annual Expenses -$20,000
-$43,000
Market Value
$0
$0
Useful Life
18 years
10 years
NAW
$73,995
$4,650
Pessimistic
(P)
-$150,000
$50,000
-$57,000
$0
8 years
-$33,100
Making Decisions
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Compare
NAW(O) = 74,000 , NAW(M) = 4500, NAW(P) = -3300
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Decision:
– If NAW(O) < 0 then
» Reject
– If NAW(P) > 0 then
» Accept
– Else
» Do more analysis or let the boss decide
Analyze all Combinations (NAW in $000s)
Annual Expenses
M
Life
O
Life
Annual
Revenues
O
M
P
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O
74
34
14
M
68
28
8
P
64
24
4
O
51
11
-9
M P
45 41
5
1
-15 -19
NAW > $50,000 for 4 out 27 combinations
NAW < $0 for 9 out of 27 combinations
Decision?
P
Life
O
37
-3
-23
M
31
-9
-29
P
27
-13
-33
Risk-adjusted MARRs
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Involves the use of higher MARRs for
alternatives that are classified as highly
uncertain and lower MARRs for projects with
fewer uncertainties
Widely used in practice
Risk-adjusted MARRs - Example 4
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Two alternatives, both affected by uncertainty to
different degrees. The firm’s risk-free MARR is
10%.
Alternative
End-ofYear, k
0
1
2
3
4
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P
Q
-$160,000
$120,000
$60,000
$0
$60,000
-$160,000
$20,827
$60,000
$120,000
$60,000
Alternative P is thought to be more uncertain
than Alternative Q.
At 10%, both alternatives have the same NPW
Decision?
Example 4 - cont’d
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Using prescribed risk-adjusted MARRs of
20% for P and 17% for Q, we get
NPWP = $10,602
NPWQ = $8,575
=> Choose Alternative P
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Contradictory result
Example 4 - cont’d
$120,000
$100,000
$80,000
NPW of P
$60,000
NPW of Q
$40,000
$20,000
$0
0%
($20,000)
($40,000)
5%
10%
15%
20%
25%
30%
Risk - adjusted MARRs
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Subject to many pitfalls. One of them is that the
uncertainty in the project is not made explicit.
Not recommended when other techniques can be
used.
Reduction of the useful life
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Estimated project life is reduced by a fixed
percentage and each alternative is evaluated
regarding its acceptability over this reduced life
span
Reduction of the useful life - Example 5
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A proposed new product line has cash flows as below.
Do an after tax analysis with an MARR of 15%
The company ‘s maximum simple payback period is three
years
Decision?
Year (N)
Init. Inv.
Revenues
Expenses
After Tax CF
Cum
ROR(N)
-1
-0.9
0
0
-0.9
-0.9
---
0
-1.1
0
0
-1.1
-2
---
1
0
1.8
-0.8
0.76
-1.24
---
2
0
2
-0.9
0.92
-0.32
---
3
0
2.1
-0.9
0.88
0.56
10%
4
0
1.9
-0.9
0.7
1.26
19%
5
0
1.8
-0.8
0.7
1.96
24%
6
0
1.8
-0.8
0.65
2.61
27%
7
0
1.7
-0.8
0.54
3.15
29%
8
0
1.5
-0.7
0.48
3.63
30%
Example 5 - cont’d
ROR as a function of the useful life
30
Aftertax
ROR
25
20
15
10
5
0
1
2
3
4
5
6
7
Useful Life
8
Reduction of Useful Life
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Heavy emphasis is placed on rapid recovery of
investment capital in the early years of project
Closely related to the discounted payback technique
Neglects cash flows that occur later in life
Not recommended
Summary
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Methods are relatively simple to apply.
They are also somewhat simplistic and imprecise
in cases where we must deal with multifaceted
project uncertainty.
Probability concepts allow us to further analyze
project risk and develop better recommendations.