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 constructing a 1,000 m² building in 2021, we need to perform cost escalation using index values based on the past data.
Step 1: Understand the Given Data
We are given the material costs for 5 previously built buildings (in m² and cost), and cost indices for the years 2017 to 2021.
| Building | Area (m²) | Cost (\$) |
|---|---|---|
| 1 | 700 | 83,200 |
| 2 | 747 | 87,800 |
| 3 | 780 | 90,400 |
| 4 | 810 | 93,100 |
| 5 | 845 | 95,500 |
Material Cost Index by Year:
| Year | Index |
|---|---|
| 2017 | 345 |
| 2018 | 355 |
| 2019 | 357 |
| 2020 | 360 |
| 2021 | 362 |
Assume these past building costs are in 2018 dollars (as no other reference year is specified and data seems centered around 2018). We will estimate the cost of a 1,000 m² building in 2021 using two major steps:
Step 2: Perform Cost Estimation in 2018 Dollars
We can use linear regression or unit cost approach to estimate the cost of a 1,000 m² building in 2018.
We’ll first calculate cost per square meter (m²) for the given buildings:
| Building | Cost per m² |
|---|---|
| 1 | 83,200 ÷ 700 ≈ 118.86 |
| 2 | 87,800 ÷ 747 ≈ 117.54 |
| 3 | 90,400 ÷ 780 ≈ 115.90 |
| 4 | 93,100 ÷ 810 ≈ 114.94 |
| 5 | 95,500 ÷ 845 ≈ 113.08 |
As area increases, cost per m² decreases due to economies of scale.
Take the trend and estimate cost per m² for 1,000 m².
Assuming a linear trend, extrapolate downward:
Use best fit estimate: ~110 \$/m²
So, estimated cost in 2018 dollars:
1,000 m² × \$110 = \$110,000
Step 3: Escalate Cost to 2021 Dollars
Use material cost index:
$$
\text{Cost in 2021} = \text{Cost in 2018} \times \left( \frac{\text{Index}{2021}}{\text{Index}{2018}} \right)
= 110,000 \times \left( \frac{362}{355} \right)
$$
$$
= 110,000 \times 1.0197 ≈ \boxed{112,167}
$$
✅ Final Answer: \$112,167
Explanation (300+ Words)
This problem involves estimating the future material cost for a larger building based on historical cost data and adjusting for inflation using a material cost index. The first step is to assess the historical trend in construction costs by examining previously built buildings. The cost per square meter decreases as the building size increases, indicating economies of scale—larger buildings tend to have a lower unit cost due to more efficient material usage and labor.
We computed the cost per square meter for the five historical buildings, which ranged from approximately \$119/m² to \$113/m². Extrapolating this trend for a 1,000 m² building—larger than any previously built—we reasonably estimate a cost of \$110/m² in 2018 dollars.
After estimating the 2018 cost (\$110,000), we need to adjust it to reflect 2021 prices using a cost index. The cost index reflects inflation or market price changes in building materials over time. The ratio of the 2021 index (362) to the 2018 index (355) gives the factor by which we increase the 2018 cost. This ratio is approximately 1.0197, meaning material prices have increased by about 1.97% from 2018 to 2021.
Multiplying the 2018 cost (\$110,000) by this factor gives us the estimated 2021 cost: \$112,167. This adjusted cost reflects both size scaling and material cost inflation.
This kind of index-based escalation method is commonly used in engineering economics, construction management, and financial planning for future projects. It ensures that cost estimates account for changes in economic conditions, providing a more realistic projection.