# Approaches to sensitivity analysis

Sensitivity analysis should be undertaken using two approaches: scenario analysis and switching values.

## Scenario analysis - testing “what if”

Scenarios are useful in considering how options may be affected by future uncertainty. Scenarios should be chosen to draw attention to the major uncertainties and assumptions on which the success of the proposal depends.

Are there any variables (such as exchange rates, salary costs, demand drivers, timing or assumptions) that materially influence the net benefits? These key variables should be identified using the risk and uncertainty process above.

The scenario analysis should then focus on asking “what if” questions and recalculating the expected Net Present Value for several scenarios. For example, what if one or more sensitive/key variables were changed by ±10%, or ±50%, or whatever is a realistic and possible variation. What if related Government policy altered or critical legislation is not passed? If these events occur, should the proposal proceed? Under what circumstances does the preferred option change? A common approach is to test three scenarios:

1. pessimistic or conservative scenario
2. most probable or base scenario, and
3. optimistic scenario.

## Switching values

This is a “what if” scenario test that highlights how much a given variable (eg an uncertain cost, benefit or key assumption) would have to change to alter the choice of the preferred option. Judgements may be necessary to model how the change would alter the choice of the preferred option.

Examples of variables that are likely to impact on the robustness of the choice of the preferred option may include growth of real wages, forecast revenues, demand, prices, and/or assumptions about the transfer of risk. An understanding of how costs fall into fixed, step, variable and semi-variable categories can also help in understanding the sensitivity of the costs of given options.

The table over the page is an example of an off-shore procurement of capital assets valued at \$US23.9 million at an exchange rate of \$NZ0.66 (based on option 3 in Table 2 above) and with different exchange rate and price discount scenarios.

Sensitivity Testing of Option 3 Conservative Scenario Base Scenario Optimistic Scenario
Exchange Rate (\$NZ per US\$) \$0.60 \$0.66 \$0.75
Negotiated purchase price discount 10% 15% 25%
Resultant Net Present Value (NPV) \$29 \$35 \$40

Various ‘what if’ scenarios can be constructed by varying the two factors, exchange rate and price discount. The resulting impacts on the overall options analysis and the robustness of the preferred option can then be considered.

In the example above and keeping the purchase price discount constant at 15%, the analyst also determines that a worsening in the exchange rate is sufficient to change the choice of the preferred option from option 3 to option 4. The exchange rate of \$0.60 is then a ‘switching value’. Switching value analysis is an important input to the decision on whether or not a proposal should proceed. These risks need to be clearly highlighted to decision-makers to enable them to accurately assess the degree of robustness of the preferred option.