Final answer:
Sensitivity and expected value analyses help in evaluating capital investment proposals by assessing the impact of variable changes and estimating average potential returns. The safest investment has the lowest variation in outcomes, while the riskiest has the highest potential for loss or variability.
Step-by-step explanation:
Sensitivity and expected value analyses are crucial tools for evaluating capital investment proposals. Sensitivity analysis involves assessing how changes in input variables affect a project's outcomes, helping to identify risk factors and measure the impact of uncertainty. Constructing a probability distribution function (PDF) for each investment can illustrate the range of possible outcomes and the likelihood of each. On the other hand, the expected value analysis determines the average outcome by calculating a weighted average of all possible results, factoring in the probability of occurrence of each outcome. This helps in estimating the potential returns of an investment.
To use these analyses properly, one should first estimate the project’s expected value by multiplying each possible outcome by its corresponding probability and summing the products. For example, if a software company has a 10 percent chance of returning a $5 million profit, a 30 percent chance of a $1 million profit, and a 60 percent chance of losing $1 million, the expected value would be calculated accordingly. Once the expected value is determined for each investment option, it allows for comparison based on projected returns. Simultaneously, sensitivity analysis tests how robust these returns are against variations in assumptions or input variables.