Problem
A construction company is planning their projects for the year 2021. The company is considering the construction of a certain number of 1,000 m’ buildings. 1312018, the company has built 5 similar buildings but with smaller areas, and the material costs associated with those 5 buildings are as shown in the following table:
Buddmg e Cast (3D) 1 700 83,200 2 747 87,800 3 780 90,400 4 810 93,100 5 845 95,500
The material cost index values are displayed in the following table: Year Cost 2017 345 2018 355 2019 357 2020 360 2021 362
The Correct Answer and Explanation is:
To determine the estimated material cost of a 1,000 m² building in 2021, we must analyze the cost trends of the smaller buildings, normalize them using the cost index, and then project that trend forward using the cost index for 2021.
Step 1: Standardize historical costs using Cost Index
We are given:
| Building | Area (m²) | Cost (USD) | Year | Index |
|---|---|---|---|---|
| 1 | 700 | 83,200 | 2018 | 355 |
| 2 | 747 | 87,800 | 2018 | 355 |
| 3 | 780 | 90,400 | 2018 | 355 |
| 4 | 810 | 93,100 | 2018 | 355 |
| 5 | 845 | 95,500 | 2018 | 355 |
Since all buildings were built in 2018, we will normalize the costs to a base year and then adjust them to 2021 using the index.
Let’s calculate the cost per square meter for each building in 2018:
- B1: 83,200 / 700 = 118.86
- B2: 87,800 / 747 ≈ 117.51
- B3: 90,400 / 780 ≈ 115.90
- B4: 93,100 / 810 ≈ 114.94
- B5: 95,500 / 845 ≈ 113.02
The cost per m² decreases as the building size increases — a common occurrence due to economies of scale.
Now we fit a linear trend to the cost/m² data.
Let’s approximate the trend with linear regression. For simplicity, we can observe that:
- When area increases by 145 m² (from 700 to 845), cost/m² drops from 118.86 to 113.02
- That’s a drop of ≈ 5.84 across 145 m² → slope ≈ -0.0403
We use point-slope form to estimate cost/m² for a 1,000 m² building:
- Using Building 5: Cost/m² = 113.02 + (1000 – 845) × (-0.0403)
- = 113.02 – 6.24 = 106.78 (in 2018)
Step 2: Adjust cost to 2021 using the material cost index
Use ratio of indices: 362 (2021) / 355 (2018) = 1.0197
So, 2021 cost/m² = 106.78 × 1.0197 ≈ 108.89
Total cost for a 1,000 m² building = 108.89 × 1,000 = $108,890
✅ Final Answer: $108,890
Explanation (300+ words):
The construction company wishes to estimate the material cost of constructing a 1,000 m² building in 2021 based on data from 2018. The best approach involves adjusting historical cost data using material cost indices to account for inflation, and extrapolating trends to a larger building size.
First, we calculate the unit cost (cost per m²) for each of the 5 smaller buildings built in 2018. This gives insight into how the cost behaves relative to the size of the building. As expected, we observe that the cost per m² decreases as the size increases — a standard result of economies of scale, where larger projects benefit from bulk purchases and fixed cost dilution.
We then estimate a linear trend to predict the cost per m² for a building size of 1,000 m². This method provides a simple yet effective forecast, considering only a modest extrapolation from 845 m² (the largest building) to 1,000 m². Using the slope derived from cost/m² versus area, we predict a base 2018 cost per m² of about 106.78 USD for the 1,000 m² building.
Next, we apply index-based cost adjustment to translate this 2018 cost to 2021 values. Using the ratio of the material cost indices (362 in 2021 vs. 355 in 2018), we adjust the predicted cost by about 1.97%, yielding a final 2021 cost per m² of approximately 108.89 USD.
Multiplying by the area (1,000 m²), we estimate the total material cost for the proposed building to be $108,890. This systematic method provides a reasonable and industry-standard approach for cost forecasting using historical data and material indices.