Model Answer
0 min readIntroduction
In project management, particularly in construction and real estate, adhering to deadlines and quality standards is crucial. Penalties are often incorporated into contracts to incentivize timely completion and adherence to specifications. This question assesses the ability to apply statistical reasoning to a real-world business problem, specifically calculating the probability of avoiding penalties and estimating potential financial liabilities. Understanding these risks is vital for effective project planning and financial forecasting within a company. The question implicitly assumes a probabilistic model governing the completion of triplexes.
Understanding the Penalty Conditions
The question, as presented, is incomplete. It lacks the crucial information regarding the conditions under which penalty fees are levied. We need to *assume* a scenario to proceed. Let's assume the following:
- The company is building 50 triplexes.
- Each triplex has a deadline for completion.
- A penalty is incurred for each triplex not completed by its deadline.
- The probability of completing a single triplex by its deadline is 90% (0.9). This is an assumed value.
- The penalty fee for each delayed triplex is $10,000 (this is also an assumed value).
Based on these assumptions, we can proceed with the calculations.
Calculating the Probability of No Penalty
The company will not have to pay any penalty fees if *all* 50 triplexes are completed by their respective deadlines. Since the completion of each triplex is assumed to be independent of the others, we can calculate the probability of this event by multiplying the probabilities of completing each individual triplex on time.
Probability of completing all 50 triplexes on time = (Probability of completing one triplex on time)^50 = (0.9)^50
Calculating this value:
(0.9)^50 ≈ 0.00515
Therefore, the probability that the company will not have to pay penalty fees is approximately 0.515%.
Calculating the Expected Penalty Fee
To calculate the expected penalty fee, we first need to determine the expected number of delayed triplexes. This can be calculated as:
Expected number of delayed triplexes = Total number of triplexes * Probability of a single triplex being delayed = 50 * (1 - 0.9) = 50 * 0.1 = 5
Now, we can calculate the expected penalty fee:
Expected penalty fee = Expected number of delayed triplexes * Penalty fee per delayed triplex = 5 * $10,000 = $50,000
Therefore, the company is expected to pay a penalty fee of approximately $50,000 if the total number of triplexes to be built is 50.
Sensitivity Analysis
It's important to note that these calculations are highly sensitive to the assumed probability of completing a single triplex on time (0.9) and the penalty fee ($10,000). If these values change, the results will change significantly. For example, if the probability of on-time completion is 80% (0.8), the expected penalty fee would be much higher.
| Probability of On-Time Completion | Probability of No Penalty | Expected Number of Delayed Triplexes | Expected Penalty Fee ($) |
|---|---|---|---|
| 0.9 | 0.00515 | 5 | 50,000 |
| 0.8 | 0.00133 | 10 | 100,000 |
| 0.95 | 0.0769 | 2.5 | 25,000 |
Conclusion
In conclusion, based on the assumed probability of 90% on-time completion for each triplex and a $10,000 penalty per delay, the probability of avoiding penalties is approximately 0.515%, and the expected penalty fee is $50,000. This highlights the importance of accurate project planning, risk assessment, and contingency planning. A sensitivity analysis demonstrates how changes in key assumptions can significantly impact the financial outcome. Further investigation into the factors affecting completion rates and potential mitigation strategies would be beneficial.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.