Question

A plant purchased equipment costing $\$500{,}000$ in 2010 (CEPCI = 550). If the CEPCI in 2024 is 800, the estimated current cost of the same equipment is:

• A. $\$727{,}273$
• B. $\$500{,}000$
• C. $\$343{,}750$
• D. $\$800{,}000$

Hint:

Always double-check that the larger index is in the numerator when updating a past cost to a future cost, as price levels generally increase over time due to inflation.
If the estimated cost is lower than the past cost (and there is no deflation), you have likely inverted the ratio.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks us to estimate the current purchase cost of a piece of equipment in the year 2024, given its historical cost in 2010 and the Chemical Engineering Plant Cost Index (CEPCI) values for both years.
This is a standard cost indexing problem used to account for inflation and changing market conditions over time.

Step 2: Key Formula or Approach:
The formula to update historical costs using cost indexes is:
\[ \text{Cost in Year 2} = \text{Cost in Year 1} \times \left(\frac{\text{Index in Year 2}}{\text{Index in Year 1}}\right) \] where in this problem:
Year 1 is 2010.
Year 2 is 2024.
The index used is the CEPCI (Chemical Engineering Plant Cost Index).

Step 3: Detailed Explanation:
Let us identify and list the given numerical values from the problem statement:
- Historical Cost in 2010, \(\text{Cost}_{2010} = \$500,000\)
- CEPCI index in 2010, \(\text{CEPCI}_{2010} = 550\)
- CEPCI index in 2024, \(\text{CEPCI}_{2024} = 800\)
Let us substitute these values into the indexing formula to calculate the estimated cost in 2024:
\[ \text{Cost}_{2024} = \$500,000 \times \left(\frac{800}{550}\right) \] First, calculate the index ratio:
\[ \frac{800}{550} = \frac{80}{55} \approx 1.454545 \] Now, multiply this ratio by the original cost of \(\$500,000\):
\[ \text{Cost}_{2024} = 500,000 \times 1.454545 = 727,272.73 \] Rounding this result to the nearest dollar gives:
\[ \text{Cost}_{2024} \approx \$727,273 \] This result matches Option (A) exactly.

Step 4: Final Answer
The estimated current cost of the equipment is $727,273, which corresponds to option (A).