The breakeven values of the three input variables that are highly uncertain

Full Answer Section

• Pricing: The price at which the product or service can be sold, considering competition and customer price sensitivity.
• Production costs: The costs of raw materials, labor, manufacturing, and other expenses involved in producing the product or service.  
• Operating costs: The costs of running the business, such as rent, utilities, marketing, and administrative expenses.  
• Interest rates: The cost of borrowing money for financing the project.  
• Exchange rates: The value of currencies involved in international transactions.  

2. Define the Range of Possible Values for Each Variable

For each of the three uncertain variables, estimate a range of possible values, including a most likely value, a pessimistic value (worst-case scenario), and an optimistic value (best-case scenario). This range can be based on historical data, market research, expert opinions, or other relevant information.

3. Create a Base Case Model

Develop a base case model that represents the most likely scenario, using the most likely values for all input variables. This model will serve as the starting point for the sensitivity analysis.

4. Vary Each Variable Individually

For each of the three uncertain variables, create a series of scenarios by varying its value across the range of possible values while holding the other two variables constant at their base case values. For example, if market demand is one of the uncertain variables, you might create scenarios with low demand, medium demand, and high demand.

5. Calculate the Outcome for Each Scenario

Calculate the outcome (e.g., profit, net present value, etc.) for each scenario, using the appropriate formulas or models.

6. Analyze the Results

Analyze the results to see how the outcome changes as each variable is varied. This can be done by creating a tornado diagram, a spider chart, or a sensitivity analysis table.

7. Identify Breakeven Values

For each variable, identify the breakeven value, which is the value at which the outcome reaches a critical threshold (e.g., zero profit, zero net present value, etc.). This can be done by interpolation or by using a goal-seeking tool in a spreadsheet program.

Example

Let's say you are analyzing a project with the following three uncertain variables:

• Market demand (range: 10,000 to 30,000 units)
• Selling price (range: $20 to $40 per unit)
• Production cost (range: $10 to $20 per unit)

You would create a base case model with the most likely values for each variable (e.g., market demand = 20,000 units, selling price = $30 per unit, production cost = $15 per unit) and calculate the profit. Then, you would vary each variable individually while holding the others constant and calculate the profit for each scenario. For example, you might create scenarios with low demand (10,000 units), medium demand (20,000 units), and high demand (30,000 units) while keeping the selling price and production cost at their base case values.

By analyzing the results, you can identify the breakeven values for each variable. For example, you might find that the breakeven value for market demand is 15,000 units, meaning that if the demand falls below 15,000 units, the project will become unprofitable.

Sample Answer

To determine the breakeven values of the three most uncertain input variables, we need to conduct a sensitivity analysis. This involves systematically changing the value of each variable while holding the others constant and observing the impact on the outcome (e.g., profit, net present value, etc.).

Here's a general approach to conducting a sensitivity analysis and finding breakeven values:

1. Identify the Three Most Uncertain Input Variables

Based on your knowledge of the project or system being analyzed, identify the three input variables that have the highest degree of uncertainty and are likely to have a significant impact on the outcome. These could be factors like:

• Market demand: The size of the potential customer base and their willingness to purchase the product or service.