To determine the weighted-average accumulated expenditures for 2025, we need to take into account the timing of the expenditures and weigh each expenditure based on the fraction of the year it was outstanding. Here is a step-by-step solution:
1. Identify the expenditures and their dates in 2025:
- January 2, 2025: \[tex]$592,000
- September 1, 2025: \$[/tex]1,806,000
- December 31, 2025: \[tex]$1,806,000
2. Calculate the fraction of the year each expenditure was outstanding:
- For January 2, 2025, the expenditure is outstanding for the entire year, which is \(\frac{12}{12} = 1\).
- For September 1, 2025, the expenditure is outstanding from September 1st to December 31st, which is 4 months. The fraction of the year is:
\[
\frac{4}{12} = \frac{1}{3}
\]
- For December 31, 2025, the expenditure is only outstanding on that specific day and does not contribute to the weighted average for that year. Thus the fraction is:
\[
\frac{0}{12} = 0
\]
3. Calculate the weighted-average accumulated expenditures:
- Multiply each expenditure by its respective fraction of the year:
\[
\text{Weighted expenditure for January 2, 2025} = 592,000 \times 1 = 592,000
\]
\[
\text{Weighted expenditure for September 1, 2025} = 1,806,000 \times \frac{1}{3} = 1,806,000 \times 0.3333 \approx 602,000
\]
\[
\text{Weighted expenditure for December 31, 2025} = 1,806,000 \times 0 = 0
\]
4. Sum the weighted expenditures to find the total weighted-average accumulated expenditures for 2025:
\[
592,000 + 602,000 + 0 = 1,194,000
\]
Thus, the weighted-average accumulated expenditures for 2025 are \$[/tex]1,194,000.
