to accelerate a project by crashing will cost $20000, the change will have the following benefits: 25% chance of $15,000 benefit, 25% chance of $20,000 bebefit, 39% chance of $10,000 loss, 20% chance of no benefit. What is the weighted average benefit of making the change and would you recommend implementing the change
To calculate the weighted average benefit of making the change, we need to calculate the expected value of each outcome and then multiply it by the corresponding probability.
Let's break down the calculations for each outcome:
1. Benefit 1: $15,000 with a 25% chance
Expected value of benefit 1 = $15,000 * 0.25 = $3,750
2. Benefit 2: $20,000 with a 25% chance
Expected value of benefit 2 = $20,000 * 0.25 = $5,000
3. Loss: $10,000 with a 39% chance
Expected value of loss = -$10,000 * 0.39 = -$3,900 (negative sign indicates loss)
4. No benefit: $0 with a 20% chance
Expected value of no benefit = $0 * 0.20 = $0
Now, we can calculate the weighted average benefit by summing up the expected values:
Weighted average benefit = (expected value of benefit 1 + expected value of benefit 2) / total probability
Weighted average benefit = ($3,750 + $5,000 + (-$3,900) + $0) / 1
Weighted average benefit = $4,850 / 1
Weighted average benefit = $4,850
The weighted average benefit is $4,850.
Now, whether to recommend implementing the change depends on the specific context and decision-making criteria. If the $4,850 average benefit is considered substantial compared to the $20,000 cost of crashing the project, it may be worth considering. However, it's important to consider other factors such as risk tolerance, project goals, and potential negative consequences of crashing the project. Additionally, it may be helpful to conduct a more comprehensive analysis, such as a cost-benefit analysis, to support the decision-making process.