Risk and Uncertainty

Сентябрь 11, 2022

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Экономика
Risk and Uncertainty

Содержание

2. Risk and Uncertainty Risk and uncertainty are similar in that they both present the problem of
3. Four major Sources of Uncertainty Possible inaccuracy of cash-flow estimates used in the study Type of
4. Possible Inaccuracy of Cash-flow estimates How much source information is available How dependable is the source
5. Type of Business Involved Relative to Health of Economy Some businesses will typically be more at
6. Type of Physical Plant and Equipment Involved Some types of structures and equipment have definite economic
7. Length of Study Period The longer the study period, the greater the level of uncertainty of
8. Sensitivity Analysis Sensitivity – The degree to which a measure of merit (i.e., PW, IRR, etc…)
9. Breakeven Analysis Technique commonly used when an uncertain single factor (EG: capacity utilization) determines the selection
10. Breakeven Analysis Indifference between alternatives (EWA = f1(y); EWB = f2(y) EWA = EWB; f1(y) =
11. Breakeven Problem Involving Two Alternatives Most easily approached mathematically by equating an equivalent worth of the
12. Breakeven Analysis for Economic Acceptability of an Engineering Project Most easily approached by equating an equivalent
13. Example applications of Breakeven Analysis Annual revenue and expenses Rate of return Market (or salvage) value
14. Example Two electric motors are being considered to power an industrial hoist. Each is capable of
15. Example
16. Example: Solution Let X = electrical energy cost in $/kW-hr. Equate the equivalent uniform annual worth
17. Sensitivity Grapfh (Spider-plot) An analysis tool applicable when the breakeven analysis does not fit the project
18. EXAMPLE 10-4 The best cash-flow estimates for a machine being considered for installation: Capital Investment (I)
19. EXAMPLE 10-4 Investigate PW over a range of + 40% changes in estimates for a. Capital
20. EXAMPLE 10-4 (a) Capital investment varies by + - p PW(10%) = -(1+_ p%/100)*$11,500 + $3,000(P/A,
21. Annual Net Cash Flow, A Useful Life, N Market Value, MV 2000 Sensitivity Graph (Spider-plot) for
22. Revelations of Spider-plot Shows the sensitivity of the present worth to percent deviation changes in each
23. Revelations of spider-plot In this example Present worth is insensitive to MV Present worth is sensitive
24. Measuring Sensitivity by a Combination of Factors Develop a sensitivity graph for the project a. For
25. Pitfalls of Risk Adjusted MARR A widely used industrial practice for including some consideration of uncertainty
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Слайд 2

Risk and Uncertainty
Risk and uncertainty are similar in that they

both present the problem of not knowing what future conditions will be
Risk offers estimates of probabilities for possible outcomes
Uncertainty does not provide estimates of probabilities for possible outcomes
This book treats them as interchangeable

Слайд 3

Four major Sources of Uncertainty
Possible inaccuracy of cash-flow estimates used in

the study
Type of business relative to the future health of the economy
Type of physical plant and equipment involved
Length of study period

Слайд 4

Possible Inaccuracy of Cash-flow estimates
How much source information is available
How dependable

is the source information
Uncertainty in capital investment requirements is often reflected as a contingency above actual cost of plant and equipment

Слайд 5

Type of Business Involved Relative to Health of Economy
Some businesses will

typically be more at risk of declining with when there is a general decline in the economy -- when the economy has gone into recession

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Type of Physical Plant and Equipment Involved
Some types of structures and

equipment have definite economic lives and market values – they may be used in a multitude of settings
Other dwellings and equipment, being made for very specific and singular functions, may have little or no resale value

Слайд 7

Length of Study Period
The longer the study period, the greater the

level of uncertainty of a capital investment

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Sensitivity Analysis
Sensitivity – The degree to which a measure of merit

(i.e., PW, IRR, etc…) will change as a result of changes in one or more of the study factor values.
Sensitivity Analysis Techniques
Breakeven Analysis
Sensitivity Graph (spider-plot)
Combination of factors

Слайд 9

Breakeven Analysis
Technique commonly used when an uncertain single factor (EG: capacity

utilization) determines the selection of an alternative or acceptability of an engineering project
For given alternative, if best estimate of actual outcome of common factor is higher or lower than the breakeven point, and assumed certain, the best alternative becomes apparent

Слайд 10

Breakeven Analysis
Indifference between alternatives
(EWA = f1(y); EWB = f2(y)
EWA =

EWB; f1(y) = f2(y) : Solve for y
Economic acceptability of engineering project
EWp = f(z) = 0
The value of ‘z’ is the value at which we would be indifferent between accepting or rejecting the project

Слайд 11

Breakeven Problem Involving Two Alternatives
Most easily approached mathematically by equating an

equivalent worth of the two alternatives expressed as a function of the factor of interest

Слайд 12

Breakeven Analysis for Economic Acceptability of an Engineering Project
Most easily approached

by equating an equivalent worth of the project to zero as a function of the factor of concern
Because of the potential difference in project lives, care should be taken to determine whether the co-terminated or the repeatability assumption best fits the situation

Слайд 13

Example applications of Breakeven Analysis
Annual revenue and expenses
Rate of return
Market

(or salvage) value
Equipment Life
Capacity utilization

Слайд 14

Example
Two electric motors are being considered to power an industrial hoist.

Each is capable of providing 90 hp. Pertinent data for each motor are presented bellow.
If the expected usage of the hoist is 500 hr per year, what would the cost of electrical energy have to be (in cents per kilowatt-hour) before the D-R motor is favored over the Westhouse motor? The MARR is 12% per year. [Note: 1hp = 0.746KW]

Слайд 15

Example

Слайд 16

Example: Solution
Let X = electrical energy cost in $/kW-hr. Equate the

equivalent uniform annual worth of both motors:
AWD-R(12%) = AWWH(12%)
-$2,500(A/P,12%,10) - $40 - (90 hp/0.74)(0.746 kW/hp)(500 hrs)(X / kW-hr)
= -$3,200(A/P,12%,10) - $60 - (90 hp/0.89)(0.746 kW/hp)(500 hrs)(X / kW-hr)
$482.5 + ($45,364.87)(X) = $626.4 + ($37,719.10)(X)
X = $143.90 / $7,645.77 = $0.0188 / kW-hr or 1.88¢ / kW-hr

Слайд 17

Sensitivity Grapfh (Spider-plot)
An analysis tool applicable when the breakeven analysis does

not fit the project situation
Makes explicit the impact of uncertainty in the estimates of each factor of concern on the economic measure of merit

Слайд 18

EXAMPLE 10-4
The best cash-flow estimates for a machine being considered for

installation:
Capital Investment (I) = $11,500
Revenues/yr (A) = $5,000
Expenses (A) = $2,000
Market Value (MV) = $1,000
Useful Life (N) = 6 years

Слайд 19

EXAMPLE 10-4
Investigate PW over a range of + 40% changes in

estimates for
a. Capital investment
b. Annual net cash flow
c. Market value
d. Useful Life
PW(10%) = -$11,500 + $3,000 (P / A, 10%, 6) + $1,000 (P / F,10%, 6) = $2,130

Слайд 20

EXAMPLE 10-4
(a) Capital investment varies by + - p
PW(10%) = -(1+_

p%/100)*$11,500 + $3,000(P/A, 10%, 6) + $1,000(P/F, 10%, 6)
(b) Annual cash flow varies by + - a
PW(10%) = - $11,500 +
(1+_ a%/100)*$3,000(P/A, 10%, 6) + $1,000(P/F, 10%, 6)
(c) Market Value varies by + - s
PW(10%) = - $11,500 +
$3,000(P/A, 10%, 6) + (1+_ s%/100)*$1,000(P/F, 10%, 6)
(d) Useful life varies by + - n
PW(10%) = - $11,500 +
$3,000(P/A, 10%, (6+_n%/100)) + $1,000(P/F, 10%, (6+_n%/100))

Слайд 21

Annual Net Cash Flow, A
Useful Life, N
Market Value, MV
2000
Sensitivity Graph (Spider-plot)

for Four Factors

% Deviation
Changes in
Factor
Estimate

%Deviation Changes in Factor Estimate

PW (10%)

+10 +20 +30 +40

-1000

-2000

-3000

-4000

1000

3000

4000

5000

6000

7000

$2130

Capital Investment

- 40 -30 -20 -10

Слайд 22

Revelations of Spider-plot
Shows the sensitivity of the present worth to percent

deviation changes in each factor’s best estimate
Other factors are assumed to remain at their best estimate values
The relative degree of sensitivity of the present worth to each factor is indicated by the slope of the curves (the “steeper” the slope of a curve the more sensitive the present worth is to the factor)
The intersection of each curve with the abscissa shows the percent change in each factor’s best estimate at which the present worth is zero

Слайд 23

Revelations of spider-plot
In this example
Present worth is insensitive to MV
Present worth

is sensitive to I, A, and N

Слайд 24

Measuring Sensitivity by a Combination of Factors
Develop a sensitivity graph for

the project
a. For most sensitive factors, improve estimates and reduce range of uncertainty
Use sensitivity graph to select most sensitive project factors. Analyze combined effects of these factors on project’s economic measure of merit by:
a. Additional graphical technique for two most sensitive factors
b. Determine the impact of selected combinations of three or more factors -- scenarios

Слайд 25

Pitfalls of Risk Adjusted MARR
A widely used industrial practice for including

some consideration of uncertainty is to increase the MARR
Even though intent of risk-adjusted MARR is to make more uncertain projects appear less economically attractive, opposite may appear to be true
Cost-only projects are made to appear more desirable as the interest rate is adjusted upward to account for uncertainty

Risk and Uncertainty

Содержание

Risk and Uncertainty Risk and uncertainty are similar in that they

Four major Sources of UncertaintyPossible inaccuracy of cash-flow estimates used in

Possible Inaccuracy of Cash-flow estimatesHow much source information is availableHow dependable

Type of Business Involved Relative to Health of Economy Some businesses will

Type of Physical Plant and Equipment InvolvedSome types of structures and

Length of Study Period The longer the study period, the greater the

Sensitivity AnalysisSensitivity – The degree to which a measure of merit

Breakeven AnalysisTechnique commonly used when an uncertain single factor (EG: capacity

Breakeven AnalysisIndifference between alternatives (EWA = f1(y); EWB = f2(y)EWA =

Breakeven Problem Involving Two Alternatives Most easily approached mathematically by equating an

Breakeven Analysis for Economic Acceptability of an Engineering Project Most easily approached

Example applications of Breakeven Analysis Annual revenue and expensesRate of returnMarket

ExampleTwo electric motors are being considered to power an industrial hoist.

Example

Example: SolutionLet X = electrical energy cost in $/kW-hr. Equate the

Sensitivity Grapfh (Spider-plot) An analysis tool applicable when the breakeven analysis does

EXAMPLE 10-4The best cash-flow estimates for a machine being considered for

EXAMPLE 10-4 Investigate PW over a range of + 40% changes in

EXAMPLE 10-4(a) Capital investment varies by + - pPW(10%) = -(1+_

Annual Net Cash Flow, AUseful Life, NMarket Value, MV2000Sensitivity Graph (Spider-plot)

Revelations of Spider-plotShows the sensitivity of the present worth to percent

Revelations of spider-plotIn this examplePresent worth is insensitive to MVPresent worth

Measuring Sensitivity by a Combination of FactorsDevelop a sensitivity graph for

Pitfalls of Risk Adjusted MARRA widely used industrial practice for including

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