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Sagot :
Sure, let's go through the detailed, step-by-step calculations for determining the Trade Receivables Turnover Ratio and Inventory Turnover Ratio for the year 2022:
### Trade Receivables Turnover Ratio:
1. Revenue from Operations (Sales):
- For the year 2022, the sales amount is given as \[tex]$3,600,000. 2. Trade Receivables: - Trade Receivables on 1st January 2022: \$[/tex]540,000
- Trade Receivables on 31st December 2022: \[tex]$650,000 3. Average Trade Receivables: - To find the average trade receivables for the year 2022, we use the formula: \[ \text{Average Trade Receivables} = \frac{\text{Trade Receivables at Start} + \text{Trade Receivables at End}}{2} \] Plugging in the values: \[ \text{Average Trade Receivables} = \frac{540,000 + 650,000}{2} = \frac{1,190,000}{2} = 595,000 \] 4. Trade Receivables Turnover Ratio: - The Trade Receivables Turnover Ratio is calculated as: \[ \text{Trade Receivables Turnover Ratio} = \frac{\text{Sales}}{\text{Average Trade Receivables}} \] Using the given sales and the average trade receivables: \[ \text{Trade Receivables Turnover Ratio} = \frac{3,600,000}{595,000} \approx 6.05 \] ### Inventory Turnover Ratio: 1. Inventory: - Inventory on 1st January 2022: \$[/tex]700,000
- Inventory on 31st December 2022: \$940,000
2. Gross Profit Margin:
- The gross profit margin given is 25%. This means that the cost of goods sold (COGS) is 75% of the sales.
3. Cost of Goods Sold (COGS):
- To find COGS, we calculate:
[tex]\[ \text{COGS} = \text{Sales} \times (1 - \text{Gross Profit Margin}) \][/tex]
Substituting the given values:
[tex]\[ \text{COGS} = 3,600,000 \times (1 - 0.25) = 3,600,000 \times 0.75 = 2,700,000 \][/tex]
4. Average Inventory:
- To find the average inventory for the year 2022, we use the formula:
[tex]\[ \text{Average Inventory} = \frac{\text{Inventory at Start} + \text{Inventory at End}}{2} \][/tex]
Plugging in the values:
[tex]\[ \text{Average Inventory} = \frac{700,000 + 940,000}{2} = \frac{1,640,000}{2} = 820,000 \][/tex]
5. Inventory Turnover Ratio:
- The Inventory Turnover Ratio is calculated as:
[tex]\[ \text{Inventory Turnover Ratio} = \frac{\text{COGS}}{\text{Average Inventory}} \][/tex]
Using the computed COGS and the average inventory:
[tex]\[ \text{Inventory Turnover Ratio} = \frac{2,700,000}{820,000} \approx 3.29 \][/tex]
### Final Results:
- Trade Receivables Turnover Ratio for 2022: approximately 6.05 times.
- Inventory Turnover Ratio for 2022: approximately 3.29 times.
These ratios provide insight into the company's efficiency in managing its receivables and inventory. A higher Trade Receivables Turnover Ratio indicates that the company is efficient in collecting its receivables, while a higher Inventory Turnover Ratio indicates that the company is efficiently managing its inventory levels.
### Trade Receivables Turnover Ratio:
1. Revenue from Operations (Sales):
- For the year 2022, the sales amount is given as \[tex]$3,600,000. 2. Trade Receivables: - Trade Receivables on 1st January 2022: \$[/tex]540,000
- Trade Receivables on 31st December 2022: \[tex]$650,000 3. Average Trade Receivables: - To find the average trade receivables for the year 2022, we use the formula: \[ \text{Average Trade Receivables} = \frac{\text{Trade Receivables at Start} + \text{Trade Receivables at End}}{2} \] Plugging in the values: \[ \text{Average Trade Receivables} = \frac{540,000 + 650,000}{2} = \frac{1,190,000}{2} = 595,000 \] 4. Trade Receivables Turnover Ratio: - The Trade Receivables Turnover Ratio is calculated as: \[ \text{Trade Receivables Turnover Ratio} = \frac{\text{Sales}}{\text{Average Trade Receivables}} \] Using the given sales and the average trade receivables: \[ \text{Trade Receivables Turnover Ratio} = \frac{3,600,000}{595,000} \approx 6.05 \] ### Inventory Turnover Ratio: 1. Inventory: - Inventory on 1st January 2022: \$[/tex]700,000
- Inventory on 31st December 2022: \$940,000
2. Gross Profit Margin:
- The gross profit margin given is 25%. This means that the cost of goods sold (COGS) is 75% of the sales.
3. Cost of Goods Sold (COGS):
- To find COGS, we calculate:
[tex]\[ \text{COGS} = \text{Sales} \times (1 - \text{Gross Profit Margin}) \][/tex]
Substituting the given values:
[tex]\[ \text{COGS} = 3,600,000 \times (1 - 0.25) = 3,600,000 \times 0.75 = 2,700,000 \][/tex]
4. Average Inventory:
- To find the average inventory for the year 2022, we use the formula:
[tex]\[ \text{Average Inventory} = \frac{\text{Inventory at Start} + \text{Inventory at End}}{2} \][/tex]
Plugging in the values:
[tex]\[ \text{Average Inventory} = \frac{700,000 + 940,000}{2} = \frac{1,640,000}{2} = 820,000 \][/tex]
5. Inventory Turnover Ratio:
- The Inventory Turnover Ratio is calculated as:
[tex]\[ \text{Inventory Turnover Ratio} = \frac{\text{COGS}}{\text{Average Inventory}} \][/tex]
Using the computed COGS and the average inventory:
[tex]\[ \text{Inventory Turnover Ratio} = \frac{2,700,000}{820,000} \approx 3.29 \][/tex]
### Final Results:
- Trade Receivables Turnover Ratio for 2022: approximately 6.05 times.
- Inventory Turnover Ratio for 2022: approximately 3.29 times.
These ratios provide insight into the company's efficiency in managing its receivables and inventory. A higher Trade Receivables Turnover Ratio indicates that the company is efficient in collecting its receivables, while a higher Inventory Turnover Ratio indicates that the company is efficiently managing its inventory levels.
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