1. Engineering Economics in Canada
Chapter 11
Dealing with Uncertainty: Sensitivity Analysis

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11.1 Introduction
Most economic evaluations involve estimating project parameters.
E.g. Prices, interest rates, magnitude and timing of cash flows.
Sensitivity analysis develops a better understanding of how uncertainty affects the outcome of the evaluation
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3. Sensitivity Analysis Methods
Sensitivity graphs illustrate the sensitivity of a particular measure to one-at-a-time changes in the uncertain parameters of a project.
Break-even analysis can answer such questions as: “What production level is necessary in order for the PW of a project to be greater than zero?”
Scenario analysis allows us to look at the impact of varying several parameters at a time.
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11.2 Sensitivity Graphs
Sensitivity graphs are used to assess the effect of one-at-a-time changes in key parameter values on a performance measure.
begin with the “base case” where all the estimated parameters values are used to evaluate the project.
then vary parameters above and below the base case one at a time, holding all other variables fixed.
A graph of the changes in a performance measure brought about by these changes is called a sensitivity graph.
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Example 11.1
Corporation C is replacing their current steam plant with a 6-megawatt new plant that will produce both steam and electric power.
Summary data is provided in Table 11.1
What is the present worth of the incremental investment in the cogeneration plant?
What is the impact of a 5% and 10% increase and decrease in each of the parameters of the problem?
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Table 11.1
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Figure 11.1
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8. Benefits and Shortcomings…
the benefits of a sensitivity graph
it can be used to select key parameters in an economic analysis.
It is easy to understand and communicates a lot of information in a single diagram.
The shortcomings of sensitivity graphs
they are valid only over the range of parameter values in the graph.
they do not consider the interaction between two or more parameters.
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11.3 Break-even Analysis
Break-even analysis is the process of varying a parameter of a problem and determining what parameter value causes the performance measure to reach some threshold or “break-even” value.
In Example 11.1, a break-even analysis could answer the question “What MARR will result in a zero present worth?”
This analysis would be particularly useful if they were uncertain about the MARR and wanted to find a threshold MARR above which the project would not be viable.
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Break-even Analysis…
Break-even analysis applied to multiple projects can answer questions like “Over what range of interest rates is project A the best choice?” or “For what output level are we indifferent between two projects?”
The point of doing this analysis is to try to get a better understanding of how sensitive a decision is to changes in the parameters of the problem.
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11. 11.3.1 Break-Even Analysis for a Single Project
break-even analysis can be applied to a single project to illustrate how sensitive a project evaluation is to changes in project parameters.
continue with Example 11.1 to expand upon the information provided by the sensitivity graphs.
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Example 11.2
The present worth of the cogeneration plant is quite sensitive to the savings in electricity costs, the MARR, and the initial costs.
What range of values results in a viable project (i.e., PW > 0)?
What are the “break-even” parameter values which make the present worth of the project zero?
Construct a graph to illustrate the present worth of the project as a function of each parameter.
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Figure 11.2
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Figure 11.3
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Figure 11.4
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16. Example 11.2 …Observations
Figure 11.2 shows the present worth of the project as a function of the MARR. It shows that the break-even MARR is 17.73%.
Figure 11.3 shows that the first cost can be as high as $4 126 350 before the present worth declines to zero.
Figure 11.4 provides a break-even chart for the savings in electrical power costs. Provided that the annual savings are above $849 207, the project is viable. Below this break-even level, the present worth of the project is negative.
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17. 11.3.2 Break-Even Analysis for Multiple Projects
How do changes in parameter values affect which project or projects are chosen?
For multiple independent projects break-even analysis can be carried out on each project independently.
For mutually exclusive projects, the best choice will seldom stand out as clearly superior from all points of view.
The best choice may depend on a particular interest rate, level of output, or first cost.
A break-even comparison can reveal the range over which each alternative is preferred.
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Example 11.3
Westmount Waxworks is considering buying a new wax melter for their line of replicas of statues of government leaders. They have two choices, Finedetail and Simplicity. The proposals are shown in Table 11.3
Which is the preferred supplier
as sales vary from 30 000/year to 200 000/year?
as the “other costs” per unit for the Simplicity model range from $0.45/unit to $0.75/unit?
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Table 11.3
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Figure 11.5
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Figure 11.6
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Example 11.3 Observations
Since 30 000 units per year is the lowest sales will likely be, and sales have averaged 50 000 units per year over the past five years, it appears that the Simplicity wax melter would be the preferred choice, assuming that its “other costs” per unit is $0.55.
We see that the best choice is not sensitive to the “other costs” of the Simplicity wax melter.
It would appear that the Simplicity model is the better choice if sales are at all likely to exceed the break-even sales level of 38 199.
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Summary
Introduction
Sensitivity Graphs
Break-Even Analysis
For a single project
For multiple projects
Scenario Analysis
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