Activity ratios measure how efficiently a company performs day-to-day tasks, such us the collection of receivables and management of inventory.
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Short-term Activity Ratios (Summary)
Based on: 10-Q (reporting date: 2025-09-30), 10-Q (reporting date: 2025-06-30), 10-Q (reporting date: 2025-03-31), 10-K (reporting date: 2024-12-31), 10-Q (reporting date: 2024-09-30), 10-Q (reporting date: 2024-06-30), 10-Q (reporting date: 2024-03-31), 10-K (reporting date: 2023-12-31), 10-Q (reporting date: 2023-09-30), 10-Q (reporting date: 2023-06-30), 10-Q (reporting date: 2023-03-31), 10-K (reporting date: 2022-12-31), 10-Q (reporting date: 2022-09-30), 10-Q (reporting date: 2022-06-30), 10-Q (reporting date: 2022-03-31), 10-K (reporting date: 2021-12-31), 10-Q (reporting date: 2021-09-30), 10-Q (reporting date: 2021-06-30), 10-Q (reporting date: 2021-03-31).
- Receivables Turnover
- The receivables turnover ratio exhibits notable fluctuations over the observed periods. Starting at 10.04 in early 2021, it generally increased with occasional dips, reaching a peak above 13 in several quarters, including the first quarter of 2023 and again towards the end of 2024 and into 2025. This upward trend indicates an improvement in the company's efficiency in collecting receivables, signifying faster conversion of credit sales into cash. However, some periods, such as the end of 2021, saw a temporary decline, suggesting variability in collection effectiveness.
- Payables Turnover
- The payables turnover ratio demonstrates significant volatility throughout the timeline. The ratio decreased sharply from 23.16 in early 2021 to a low of 10.87 by the end of 2021, followed by a steady recovery and increase peaking at 32.37 mid-2024. This pattern implies changing payment behavior, ranging from slower payments to vendors during certain periods to more rapid settlement in others. The high turnover ratios in mid-2024 suggest the company accelerated vendor payments, which could reflect increased liquidity or changes in supplier agreements.
- Working Capital Turnover
- The working capital turnover ratio shows extreme variability, with some values appearing anomalously high, such as 1646.62 in early 2022 and 191.48 mid-2025. These extremes may indicate either data inconsistencies or extraordinary operational events impacting working capital usage. Aside from these spikes, the ratio generally exhibits a downward trend from a high of 129.39 in mid-2021 to moderately lower values around 20 to 30 in subsequent periods, suggesting fluctuating but overall reduced efficiency in using working capital for generating sales over time. The variability reflects changes in current asset and liability management or shifts in sales volume.
- Average Receivable Collection Period
- The average receivable collection period decreased from 36 days in early 2021 to around 28-30 days during 2023 and beyond, indicating an improvement in collection efficiency. The period lengthened temporarily in late 2021 to 51 days but otherwise shows a consistent downward trend toward faster receivables turnover. This shortened collection timeframe supports the previously noted increase in receivables turnover ratio, reflecting effective credit management and perhaps tighter collection policies.
- Average Payables Payment Period
- The average payables payment period fluctuates between about 11 to 34 days, with the longest period appearing near the end of 2021 (34 days). Since that peak, the payment period generally decreased to around 12-14 days in 2023 and subsequent years. This suggests a shift toward quicker payment of liabilities, which aligns with the increase in payables turnover ratio observed in recent periods. Faster vendor payments may indicate improved cash availability or strategic decisions to maintain favorable supplier relationships.
Turnover Ratios
Average No. Days
Receivables Turnover
| Sep 30, 2025 | Jun 30, 2025 | Mar 31, 2025 | Dec 31, 2024 | Sep 30, 2024 | Jun 30, 2024 | Mar 31, 2024 | Dec 31, 2023 | Sep 30, 2023 | Jun 30, 2023 | Mar 31, 2023 | Dec 31, 2022 | Sep 30, 2022 | Jun 30, 2022 | Mar 31, 2022 | Dec 31, 2021 | Sep 30, 2021 | Jun 30, 2021 | Mar 31, 2021 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Selected Financial Data (US$ in millions) | |||||||||||||||||||||||||
| Revenue | |||||||||||||||||||||||||
| Accounts receivable, net of allowance | |||||||||||||||||||||||||
| Short-term Activity Ratio | |||||||||||||||||||||||||
| Receivables turnover1 | |||||||||||||||||||||||||
| Benchmarks | |||||||||||||||||||||||||
| Receivables Turnover, Competitors2 | |||||||||||||||||||||||||
| FedEx Corp. | |||||||||||||||||||||||||
| Union Pacific Corp. | |||||||||||||||||||||||||
| United Airlines Holdings Inc. | |||||||||||||||||||||||||
| United Parcel Service Inc. | |||||||||||||||||||||||||
Based on: 10-Q (reporting date: 2025-09-30), 10-Q (reporting date: 2025-06-30), 10-Q (reporting date: 2025-03-31), 10-K (reporting date: 2024-12-31), 10-Q (reporting date: 2024-09-30), 10-Q (reporting date: 2024-06-30), 10-Q (reporting date: 2024-03-31), 10-K (reporting date: 2023-12-31), 10-Q (reporting date: 2023-09-30), 10-Q (reporting date: 2023-06-30), 10-Q (reporting date: 2023-03-31), 10-K (reporting date: 2022-12-31), 10-Q (reporting date: 2022-09-30), 10-Q (reporting date: 2022-06-30), 10-Q (reporting date: 2022-03-31), 10-K (reporting date: 2021-12-31), 10-Q (reporting date: 2021-09-30), 10-Q (reporting date: 2021-06-30), 10-Q (reporting date: 2021-03-31).
1 Q3 2025 Calculation
Receivables turnover
= (RevenueQ3 2025
+ RevenueQ2 2025
+ RevenueQ1 2025
+ RevenueQ4 2024)
÷ Accounts receivable, net of allowance
= ( + + + )
÷ =
2 Click competitor name to see calculations.
The quarterly financial data reveals several notable trends in revenue, accounts receivable, and receivables turnover ratios over the observed periods.
- Revenue
- Revenue demonstrates a consistent upward trajectory throughout the periods, growing from $2,903 million in the first quarter of 2021 to $13,467 million by the third quarter of 2025. This steady increase indicates sustained business expansion and successful revenue generation strategies. Although the growth pace varies slightly between quarters, the overall trend is strongly positive.
- Accounts Receivable, Net of Allowance
- The net accounts receivable balance shows an overall increasing trend, rising from $1,075 million in the first quarter of 2021 to $3,773 million by the third quarter of 2025. There are some fluctuations noted, including a significant jump from $1,333 million in the third quarter of 2021 to $2,439 million in the fourth quarter of 2021. This growth pattern may reflect expanded sales volume and possibly extended credit terms. Attention should be given to the relationship between revenue growth and accounts receivable levels to monitor collection efficiency.
- Receivables Turnover Ratio
- The receivables turnover ratio, which measures how efficiently the company collects its receivables, fluctuates moderately across the periods with a low of 7.16 in the fourth quarter of 2021 and peaks near 13.59 in the second quarter of 2023. Despite these fluctuations, the ratio generally maintains values above 10 after 2021, indicating relatively strong collection performance. A lower ratio in late 2021 corresponds with a sharp rise in accounts receivable, suggesting a temporary decline in collection efficiency during that period. The subsequent improvement and stabilization suggest corrective measures or normalization in credit management.
In summary, the data indicates continuous revenue growth accompanied by increasing receivables, with overall efficient receivables management as reflected by the turnover ratio. Periods with higher accounts receivable balances and lower turnover ratios merit close monitoring to ensure collection processes remain effective and do not adversely impact liquidity.
Payables Turnover
| Sep 30, 2025 | Jun 30, 2025 | Mar 31, 2025 | Dec 31, 2024 | Sep 30, 2024 | Jun 30, 2024 | Mar 31, 2024 | Dec 31, 2023 | Sep 30, 2023 | Jun 30, 2023 | Mar 31, 2023 | Dec 31, 2022 | Sep 30, 2022 | Jun 30, 2022 | Mar 31, 2022 | Dec 31, 2021 | Sep 30, 2021 | Jun 30, 2021 | Mar 31, 2021 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Selected Financial Data (US$ in millions) | |||||||||||||||||||||||||
| Cost of revenue, exclusive of depreciation and amortization | |||||||||||||||||||||||||
| Accounts payable | |||||||||||||||||||||||||
| Short-term Activity Ratio | |||||||||||||||||||||||||
| Payables turnover1 | |||||||||||||||||||||||||
| Benchmarks | |||||||||||||||||||||||||
| Payables Turnover, Competitors2 | |||||||||||||||||||||||||
| FedEx Corp. | |||||||||||||||||||||||||
| United Airlines Holdings Inc. | |||||||||||||||||||||||||
| United Parcel Service Inc. | |||||||||||||||||||||||||
Based on: 10-Q (reporting date: 2025-09-30), 10-Q (reporting date: 2025-06-30), 10-Q (reporting date: 2025-03-31), 10-K (reporting date: 2024-12-31), 10-Q (reporting date: 2024-09-30), 10-Q (reporting date: 2024-06-30), 10-Q (reporting date: 2024-03-31), 10-K (reporting date: 2023-12-31), 10-Q (reporting date: 2023-09-30), 10-Q (reporting date: 2023-06-30), 10-Q (reporting date: 2023-03-31), 10-K (reporting date: 2022-12-31), 10-Q (reporting date: 2022-09-30), 10-Q (reporting date: 2022-06-30), 10-Q (reporting date: 2022-03-31), 10-K (reporting date: 2021-12-31), 10-Q (reporting date: 2021-09-30), 10-Q (reporting date: 2021-06-30), 10-Q (reporting date: 2021-03-31).
1 Q3 2025 Calculation
Payables turnover
= (Cost of revenue, exclusive of depreciation and amortizationQ3 2025
+ Cost of revenue, exclusive of depreciation and amortizationQ2 2025
+ Cost of revenue, exclusive of depreciation and amortizationQ1 2025
+ Cost of revenue, exclusive of depreciation and amortizationQ4 2024)
÷ Accounts payable
= ( + + + )
÷ =
2 Click competitor name to see calculations.
The financial data reveals several notable trends regarding cost of revenue, accounts payable, and payables turnover over the observed periods.
- Cost of Revenue (exclusive of depreciation and amortization)
- The cost of revenue exhibits a consistent upward trajectory throughout the timeline. Beginning at approximately $1.71 billion in the first quarter of 2021, it escalates steadily, reaching around $8.1 billion by the third quarter of 2025. This persistent increase reflects growth in operational expenses associated with generating revenue, suggesting expansion in business activities or rising costs.
- Accounts Payable
- Accounts payable values demonstrate variability yet generally trend upwards across the same period. Starting at $232 million in early 2021, there is an initial fluctuation, with a notable rise from $429 million in mid-2021 to a peak of approximately $1.12 billion by the third quarter of 2025. This pattern indicates increasing short-term liabilities or extended supplier credit terms in line with growing operational scale.
- Payables Turnover Ratio
- The payables turnover ratio, which measures the efficiency in paying suppliers, shows fluctuations initially but settles into a relatively stable range in later periods. It starts at 23.16 in the first quarter of 2021, declines irregularly reaching a low point around 10.87 by the end of 2021, then recovers and peaks over 32 by mid-2024. After this peak, it slightly decreases but remains between approximately 26 and 32 through 2025. This suggests improved or maintained efficiency in managing payables following early volatility.
Overall, the data points to growth in operational scale reflected by rising costs and payables. Despite initial fluctuations in payables turnover, the company appears to achieve stable management of supplier payments in the latter periods. The increases in cost of revenue and accounts payable correspond with the company's expanding activities, and the relatively high payables turnover ratio in recent quarters indicates consistent turnover and possibly strong supplier relations or favorable payment terms.
Working Capital Turnover
| Sep 30, 2025 | Jun 30, 2025 | Mar 31, 2025 | Dec 31, 2024 | Sep 30, 2024 | Jun 30, 2024 | Mar 31, 2024 | Dec 31, 2023 | Sep 30, 2023 | Jun 30, 2023 | Mar 31, 2023 | Dec 31, 2022 | Sep 30, 2022 | Jun 30, 2022 | Mar 31, 2022 | Dec 31, 2021 | Sep 30, 2021 | Jun 30, 2021 | Mar 31, 2021 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Selected Financial Data (US$ in millions) | |||||||||||||||||||||||||
| Current assets | |||||||||||||||||||||||||
| Less: Current liabilities | |||||||||||||||||||||||||
| Working capital | |||||||||||||||||||||||||
| Revenue | |||||||||||||||||||||||||
| Short-term Activity Ratio | |||||||||||||||||||||||||
| Working capital turnover1 | |||||||||||||||||||||||||
| Benchmarks | |||||||||||||||||||||||||
| Working Capital Turnover, Competitors2 | |||||||||||||||||||||||||
| FedEx Corp. | |||||||||||||||||||||||||
| Union Pacific Corp. | |||||||||||||||||||||||||
| United Airlines Holdings Inc. | |||||||||||||||||||||||||
| United Parcel Service Inc. | |||||||||||||||||||||||||
Based on: 10-Q (reporting date: 2025-09-30), 10-Q (reporting date: 2025-06-30), 10-Q (reporting date: 2025-03-31), 10-K (reporting date: 2024-12-31), 10-Q (reporting date: 2024-09-30), 10-Q (reporting date: 2024-06-30), 10-Q (reporting date: 2024-03-31), 10-K (reporting date: 2023-12-31), 10-Q (reporting date: 2023-09-30), 10-Q (reporting date: 2023-06-30), 10-Q (reporting date: 2023-03-31), 10-K (reporting date: 2022-12-31), 10-Q (reporting date: 2022-09-30), 10-Q (reporting date: 2022-06-30), 10-Q (reporting date: 2022-03-31), 10-K (reporting date: 2021-12-31), 10-Q (reporting date: 2021-09-30), 10-Q (reporting date: 2021-06-30), 10-Q (reporting date: 2021-03-31).
1 Q3 2025 Calculation
Working capital turnover
= (RevenueQ3 2025
+ RevenueQ2 2025
+ RevenueQ1 2025
+ RevenueQ4 2024)
÷ Working capital
= ( + + + )
÷ =
2 Click competitor name to see calculations.
The analysis of the available financial data reveals notable fluctuations and trends across the key metrics of working capital, revenue, and working capital turnover ratios over a time span of multiple quarterly periods.
- Working Capital
- Working capital exhibited significant volatility throughout the observed quarters. Initial values started positive but quickly shifted into negative territory as seen around the period ending December 31, 2021. Subsequently, the metric oscillated between positive and negative values, with some quarters demonstrating substantial positive working capital peaks, such as in mid-2023 and late 2024. The largest values occurred in mid-2024 and late 2024, indicating periods of increased liquidity or operational efficiency. However, several quarters also reflected notably reduced or negative working capital levels, pointing to potential short-term liquidity challenges or variances in current asset and liability management.
- Revenue
- Revenue displayed a clear, consistent upward trajectory across all quarters, reflecting steady growth in the company's top-line performance. Starting from approximately $2.9 billion in early 2021, revenue generally increased quarter over quarter without significant declines, culminating in approximately $13.5 billion by the third quarter of 2025. This steady increase suggests ongoing market expansion, enhanced sales capacity, or rising demand for the company's offerings.
- Working Capital Turnover
- The working capital turnover ratio showed considerable dispersion and irregularity. In some early quarters, especially around mid-2021, the ratios reached extremely high values, such as over 129 and a peak of 1,646 in the first quarter of 2022, indicating very efficient use of working capital relative to revenue during those periods or potential distortions due to near-zero or negative working capital. Conversely, several quarters recorded much lower ratios, suggesting less efficient utilization of working capital, including values dropping below 10 in some instances. The inconsistency across quarters implies volatility in how effectively the working capital supports revenue generation, which may stem from varying operational cycles, seasonal factors, or the impact of significant balance sheet fluctuations.
In summary, the revenue growth trajectory is positive and stable, indicating robust sales performance. However, the working capital availability and its turnover rates are highly variable, suggesting fluctuating short-term liquidity and operational efficiency. These discrepancies underscore areas where improvements in working capital management could further stabilize financial performance and enhance operational execution.
Average Receivable Collection Period
| Sep 30, 2025 | Jun 30, 2025 | Mar 31, 2025 | Dec 31, 2024 | Sep 30, 2024 | Jun 30, 2024 | Mar 31, 2024 | Dec 31, 2023 | Sep 30, 2023 | Jun 30, 2023 | Mar 31, 2023 | Dec 31, 2022 | Sep 30, 2022 | Jun 30, 2022 | Mar 31, 2022 | Dec 31, 2021 | Sep 30, 2021 | Jun 30, 2021 | Mar 31, 2021 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Selected Financial Data | |||||||||||||||||||||||||
| Receivables turnover | |||||||||||||||||||||||||
| Short-term Activity Ratio (no. days) | |||||||||||||||||||||||||
| Average receivable collection period1 | |||||||||||||||||||||||||
| Benchmarks (no. days) | |||||||||||||||||||||||||
| Average Receivable Collection Period, Competitors2 | |||||||||||||||||||||||||
| FedEx Corp. | |||||||||||||||||||||||||
| Union Pacific Corp. | |||||||||||||||||||||||||
| United Airlines Holdings Inc. | |||||||||||||||||||||||||
| United Parcel Service Inc. | |||||||||||||||||||||||||
Based on: 10-Q (reporting date: 2025-09-30), 10-Q (reporting date: 2025-06-30), 10-Q (reporting date: 2025-03-31), 10-K (reporting date: 2024-12-31), 10-Q (reporting date: 2024-09-30), 10-Q (reporting date: 2024-06-30), 10-Q (reporting date: 2024-03-31), 10-K (reporting date: 2023-12-31), 10-Q (reporting date: 2023-09-30), 10-Q (reporting date: 2023-06-30), 10-Q (reporting date: 2023-03-31), 10-K (reporting date: 2022-12-31), 10-Q (reporting date: 2022-09-30), 10-Q (reporting date: 2022-06-30), 10-Q (reporting date: 2022-03-31), 10-K (reporting date: 2021-12-31), 10-Q (reporting date: 2021-09-30), 10-Q (reporting date: 2021-06-30), 10-Q (reporting date: 2021-03-31).
1 Q3 2025 Calculation
Average receivable collection period = 365 ÷ Receivables turnover
= 365 ÷ =
2 Click competitor name to see calculations.
- Receivables Turnover
- The receivables turnover ratio demonstrates fluctuating trends across the periods analyzed. Initially, the ratio showed a moderate increase from 10.04 to 11.13 during the first three quarters of 2021, indicating a slight improvement in the efficiency of collecting receivables. However, a notable decline occurred in the fourth quarter of 2021 dropping to 7.16, suggesting a significant slowdown in collection efficiency during that period. Following this dip, the ratio recovered steadily through 2022 and 2023, reaching values as high as 13.59, implying a strengthened capacity to convert receivables into cash. The turnover ratio then exhibited some volatility in late 2023 and 2024 but resumed an upward trend by early 2025, stabilizing at around 13.15. This overall pattern reveals periods of both inefficiency and recovery, with longer-term improvement in receivables management.
- Average Receivable Collection Period
- The average receivable collection period inversely correlates with the receivables turnover ratio, displaying an initial improvement from 36 days in the first quarter of 2021 to 33 days by Q3 2021. A sharp increase to 51 days in Q4 2021 coincides with the low receivables turnover ratio, highlighting slower collection during that timeframe. Post this apex, the collection period reduced consistently to between 27 and 30 days throughout much of 2022 and 2023, reflecting improved cash flow timing and collection processes. Some minor fluctuations occurred in late 2023 and 2024, with days outstanding moving between 28 and 35 but trending downward again by early 2025 to approximately 28 days. This suggests enhanced efficiency and tighter credit control practices over the long term, maintaining a relatively shorter receivable cycle compared to earlier periods.
- Summary
- The data signals a volatile but improving management of receivables over the years analyzed. After a period of diminished efficiency in late 2021 marked by a steep increase in collection days and a drop in turnover ratio, the company managed to enhance its receivables turnover and reduce the collection period considerably. Despite some variability in recent quarters, the general trend points to strengthened operational effectiveness in managing credit sales and converting receivables into cash, which should benefit the company’s liquidity position in subsequent reporting periods.
Average Payables Payment Period
| Sep 30, 2025 | Jun 30, 2025 | Mar 31, 2025 | Dec 31, 2024 | Sep 30, 2024 | Jun 30, 2024 | Mar 31, 2024 | Dec 31, 2023 | Sep 30, 2023 | Jun 30, 2023 | Mar 31, 2023 | Dec 31, 2022 | Sep 30, 2022 | Jun 30, 2022 | Mar 31, 2022 | Dec 31, 2021 | Sep 30, 2021 | Jun 30, 2021 | Mar 31, 2021 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Selected Financial Data | |||||||||||||||||||||||||
| Payables turnover | |||||||||||||||||||||||||
| Short-term Activity Ratio (no. days) | |||||||||||||||||||||||||
| Average payables payment period1 | |||||||||||||||||||||||||
| Benchmarks (no. days) | |||||||||||||||||||||||||
| Average Payables Payment Period, Competitors2 | |||||||||||||||||||||||||
| FedEx Corp. | |||||||||||||||||||||||||
| United Airlines Holdings Inc. | |||||||||||||||||||||||||
| United Parcel Service Inc. | |||||||||||||||||||||||||
Based on: 10-Q (reporting date: 2025-09-30), 10-Q (reporting date: 2025-06-30), 10-Q (reporting date: 2025-03-31), 10-K (reporting date: 2024-12-31), 10-Q (reporting date: 2024-09-30), 10-Q (reporting date: 2024-06-30), 10-Q (reporting date: 2024-03-31), 10-K (reporting date: 2023-12-31), 10-Q (reporting date: 2023-09-30), 10-Q (reporting date: 2023-06-30), 10-Q (reporting date: 2023-03-31), 10-K (reporting date: 2022-12-31), 10-Q (reporting date: 2022-09-30), 10-Q (reporting date: 2022-06-30), 10-Q (reporting date: 2022-03-31), 10-K (reporting date: 2021-12-31), 10-Q (reporting date: 2021-09-30), 10-Q (reporting date: 2021-06-30), 10-Q (reporting date: 2021-03-31).
1 Q3 2025 Calculation
Average payables payment period = 365 ÷ Payables turnover
= 365 ÷ =
2 Click competitor name to see calculations.
- Payables Turnover Ratio
- The payables turnover ratio demonstrates notable fluctuations across the observed periods. Initially, the ratio was relatively high at 23.16 in March 2021, followed by a significant dip to 15.26 in June 2021, and then a rapid recovery to 24.8 by September 2021. The ratio experienced another sharp decline reaching a low of 10.87 in December 2021 before progressively increasing in subsequent quarters. From early 2022 onwards, the ratio generally showed an upward trend, peaking around 32.37 in June 2024. In the last few reported periods, the ratio slightly declined but remained relatively stable in the high 20s to low 30s range. This pattern indicates variability in the rate at which payables are settled, with a general improvement in turnover efficiency in recent quarters.
- Average Payables Payment Period (Days)
- The average payables payment period exhibits an inverse relationship to the payables turnover ratio, as expected. Starting with a low of 16 days in March 2021, the payment period increased to 24 days by June 2021, then sharply decreased to 15 days in September 2021 before rising substantially to 34 days by December 2021. From 2022 forward, the payment period gradually shortened, reaching a low of 11 days multiple times between March 2024 and December 2024. The most recent periods show a slight increase back to around 13-14 days. This suggests that after a phase of extended payment durations, the company improved its payment timeliness, maintaining relatively quick settlements in more recent quarters.
- Overall Insights
- The data reveals a cyclical pattern in payment behavior, with notable volatility during 2021. The initial period showed inconsistent payment efficiency, with the company fluctuating between longer and shorter payment cycles. The trend from 2022 onward indicates a strategic effort to accelerate payables settlement, reflected by a rising payables turnover ratio and declining payment periods. Although some minor setbacks occur toward the end of the dataset, the company consistently maintains a relatively higher turnover ratio and shorter average payment period compared to earlier years. This pattern indicates improved liquidity management and supplier relations over time.