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To determine whether the road construction project is expected to be completed on budget, under budget, or over budget, we can use Cost Variance (CV) and Cost Performance Index (CPI).[ CPI = \frac{EV}{AC} ]

Step 1: Calculate the Cost Performance Index (CPI)

[ CPI = \frac{4,500,000}{9,000,000} = 0.5 ]

A CPI of 0.5 indicates that for every dirham spent, the project is only earning 0.5 dirhams of value.[ AC = 9,000,000 \text{ AED} ]

Step 3: Calculate the Cost Variance (CV)

[ CV = EV - AC = 4,500,000 - 9,000,000 = -4,500,000 \text{ AED} ]

A negative CV means the project is over budget by AED 4,500,000.So, the Earned Value (EV) for the project after 10 weeks is:

[ EV = 30% \times 15,000,000 = 4,500,000 \text{ AED} ]

Step 2: Calculate the Actual Cost (AC)

The actual cost spent after 10 weeks is AED 9,000,000, as provided in the scenario.Cost Performance Index (CPI) CPI is a ratio that indicates the cost efficiency of the project.Cost Variance (CV) Cost Variance is a measure of the difference between the Earned Value (EV) and the Actual Cost (AC).### Conclusion:

• The Cost Variance (CV) is negative (AED -4,500,000), meaning the project is over budget.### 1.### 2.

To determine whether the road construction project is expected to be completed on budget, under budget, or over budget, we can use Cost Variance (CV) and Cost Performance Index (CPI). These two metrics are part of the Earned Value Management (EVM) approach, which helps evaluate a project's financial performance.

1. Cost Variance (CV)

Cost Variance is a measure of the difference between the Earned Value (EV) and the Actual Cost (AC). It helps determine if the project is under or over budget.

[
CV = EV - AC
]

Where:

• 
  EV (Earned Value): The value of the work actually completed by a specific time.


• 
  AC (Actual Cost): The actual cost incurred to perform the work by that specific time.

Step 1: Calculate the Earned Value (EV)

We know that the total project cost is AED 15,000,000, and the project was planned to complete 10% of the work each week. After 10 weeks, 30% of the work has been completed. So, the Earned Value (EV) for the project after 10 weeks is:

[
EV = 30% \times 15,000,000 = 4,500,000 \text{ AED}
]

Step 2: Calculate the Actual Cost (AC)

The actual cost spent after 10 weeks is AED 9,000,000, as provided in the scenario.

[
AC = 9,000,000 \text{ AED}
]

Step 3: Calculate the Cost Variance (CV)

[
CV = EV - AC = 4,500,000 - 9,000,000 = -4,500,000 \text{ AED}
]

A negative CV means the project is over budget by AED 4,500,000.

2. Cost Performance Index (CPI)

CPI is a ratio that indicates the cost efficiency of the project. It shows how well the project is performing relative to its budget. A CPI greater than 1 indicates the project is under budget, while a CPI less than 1 indicates the project is over budget.

[
CPI = \frac{EV}{AC}
]

Step 1: Calculate the Cost Performance Index (CPI)

[
CPI = \frac{4,500,000}{9,000,000} = 0.5
]

A CPI of 0.5 indicates that for every dirham spent, the project is only earning 0.5 dirhams of value. This is a sign that the project is significantly over budget.

Conclusion:

• The Cost Variance (CV) is negative (AED -4,500,000), meaning the project is over budget.


• The Cost Performance Index (CPI) is 0.5, indicating that the project is not cost-efficient and is likely to end up over budget.

So, the road construction project is expected to be over budget.