Final answer:
Sensitivity analysis is used to assess the impact of variable changes on a project's financial performance. It involves comparing present costs with the present discounted value of future benefits and understanding the cost production relationship, which is essential in both business and government investment decisions.
Step-by-step explanation:
Sensitivity Analysis in Project Evaluation
The concept of sensitivity analysis revolves around examining how the variation in input variables such as sales forecasts, costs, and discount rates impacts a project's financial performance. In the context of a project that costs $2,040,000 with a 7-year life and no salvage value, one would perform sensitivity analysis by altering these key parameters to assess the project's robustness to different scenarios. As the business must compare the present costs to the present discounted value (PDV) of future benefits, mathematical models play a crucial role in forecasting costs and benefits over time.
Moreover, the principles of PDV stretch far beyond finance, finding applications in government, environmental policies, and even personal finance situations like lottery winnings. In business, costs are often categorized into fixed costs and variable costs. Fixed costs are those that do not change with the level of production, like the initial $160 presented in the hypothetical scenario. As production scales up, variable costs are added, contributing to the total cost which is key in sensitivity analysis.
Understanding the mathematical relationship between output quantity and production cost, as well as incorporating PDV into the analysis, enables businesses and governments to make more informed investment decisions and weigh the merits of projects more accurately.