Cost-benefit analysis isn't always clear-cut. Sensitivity analysis and risk assessment help us understand how changes in key variables might affect our results. By tweaking inputs and running different scenarios, we can get a better grip on the uncertainties.

These techniques give us a range of possible outcomes instead of just one answer. They help decision-makers understand potential risks and rewards, making it easier to choose the best course of action in an uncertain world.

Sensitivity and Scenario Analysis

Evaluating Uncertainty in Cost-Benefit Analysis

• Sensitivity analysis systematically changes variables in a model to determine the effects of such changes and identify the most sensitive variables
• Involves changing one variable at a time while holding others constant to see how sensitive the outcome is to each variable (discount rate, costs, benefits)
• Scenario analysis creates different scenarios by changing multiple variables simultaneously to assess their combined impact on the project's net present value or other outcome measures
• Considers best-case, worst-case, and most likely scenarios to provide a range of possible outcomes and help decision-makers understand potential risks and rewards (optimistic, pessimistic, baseline scenarios)

Break-Even Analysis and Uncertainty

• Break-even analysis determines the point at which total costs equal total benefits, indicating the minimum level of benefits needed for the project to be worthwhile
• Calculates the break-even point by setting net present value to zero and solving for the unknown variable, such as the minimum number of users for a public service
• Uncertainty refers to the lack of precise knowledge about the values of costs and benefits in a cost-benefit analysis
• Arises from incomplete information, measurement errors, and the inherent variability of key parameters (discount rates, project lifespan, externalities)
• Sensitivity analysis, scenario analysis, and break-even analysis help address uncertainty by exploring how changes in assumptions affect the results and inform decision-making under uncertainty

Risk Assessment Techniques

Quantifying Risk through Monte Carlo Simulation

• Risk assessment involves identifying, analyzing, and evaluating potential risks that could impact the costs, benefits, or overall success of a project or policy
• Monte Carlo simulation is a computerized mathematical technique that accounts for risk in quantitative analysis and decision-making
• Involves defining a range of possible values for uncertain variables and randomly sampling from those ranges to generate a large number of scenarios (thousands of iterations)
• Produces a probability distribution of potential outcomes, allowing analysts to quantify the likelihood of different results and identify key sources of risk (normal distribution, skewed distribution)

Expected Value and Probability Distributions

• Probability distribution shows the likelihood of different values occurring for an uncertain variable, based on historical data, expert judgment, or statistical analysis
• Common probability distributions include normal (bell-shaped curve), uniform (equal probability for all values), and triangular (minimum, most likely, maximum values)
• Expected value is the sum of all possible values of a variable, weighted by their respective probabilities
• Represents the average outcome over a large number of trials or scenarios, helping decision-makers compare and rank alternatives based on their expected costs and benefits
• Combining Monte Carlo simulation with probability distributions provides a comprehensive risk assessment by generating a range of potential outcomes and their associated probabilities (5th percentile, 95th percentile)