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, we need to multiply the probability of each outcome by its corresponding benefit or loss, and then sum them up.
Let's calculate the weighted average benefit step-by-step:
1. Calculate the expected benefit for each outcome:
- Benefit of $15,000 with a 25% chance: $15,000 x 0.25 = $3,750
- Benefit of $20,000 with a 25% chance: $20,000 x 0.25 = $5,000
- Loss of $10,000 with a 39% chance: -$10,000 x 0.39 = -$3,900 (Note: negative value indicates a loss)
- No benefit with a 20% chance: $0 x 0.20 = $0
2. Calculate the total expected benefit:
$3,750 + $5,000 - $3,900 + $0 = $4,850
The weighted average benefit of making the change is $4,850.
As for whether or not to recommend implementing the change, it depends on the specific context of the project and the tolerance for risk. On one hand, the weighted average benefit is positive, indicating a potential gain. On the other hand, there is a 39% chance of a $10,000 loss. If the potential loss outweighs the benefit, or if the level of risk is considered too high, it might be advisable to proceed with caution or seek alternative options. Decision-making in such cases often involves considering additional factors beyond just the numbers.