Answer :
To prepare a statement showing the working capital needed to finance a level of activity of 5,200 units of output per annum for Sima Ltd., we will compute the needed capital considering the given production costs, stock periods, credit terms, lag in wage payments, and expected cash in hand. Here's the detailed step-by-step solution:
### Given Information:
- Annual Output: [tex]\(5,200\)[/tex] units.
- Costs per Unit:
- Raw Materials: [tex]\(\text{₹} 8\)[/tex]
- Direct Labour: [tex]\(\text{₹} 2\)[/tex]
- Overheads: [tex]\(\text{₹} 6\)[/tex]
- Total Cost: [tex]\(\text{₹} 16\)[/tex]
- Profit: [tex]\(\text{₹} 4\)[/tex]
- Selling Price: [tex]\(\text{₹} 20\)[/tex]
### Stock Periods and Credits:
- Raw Materials in stock: [tex]\(1\)[/tex] month.
- Materials in process: [tex]\(0.5\)[/tex] months.
- Finished goods in stock: [tex]\(6\)[/tex] weeks [tex]\((6/4 = 1.5 \text{ months})\)[/tex]
- Credit allowed by creditors: [tex]\(1\)[/tex] month.
- Credit allowed to debtors: [tex]\(2\)[/tex] months.
- Lag in payment of wages: [tex]\(1.5\)[/tex] weeks [tex]\((1.5/4 = 0.375 \text{ months})\)[/tex]
- Cash in hand and at bank: [tex]\(\text{₹} 7,300\)[/tex]
### Monthly Production Calculation:
Since the annual production is [tex]\(5,200\)[/tex] units, the monthly production rate is:
[tex]\[ \text{Monthly Production} = \frac{5,200 \text{ units}}{12 \text{ months}} = 433.33 \text{ units per month} \][/tex]
### Working Capital Components Calculation:
1. Raw Materials in Stock:
[tex]\[ \text{Raw Materials Stock Value} = \text{Monthly Production} \times \text{Raw Material Cost per Unit} \times \text{Stock Period} \][/tex]
[tex]\[ = 433.33 \times 8 \times 1 = 3,466.67 \text{₹} \][/tex]
2. Materials in Process:
[tex]\[ \text{Materials in Process Value} = \text{Monthly Production} \times \text{Total Cost per Unit} \times \text{Process Period} \][/tex]
[tex]\[ = 433.33 \times 16 \times 0.5 = 3,466.67 \text{₹} \][/tex]
3. Finished Goods in Stock:
[tex]\[ \text{Finished Goods Stock Value} = \text{Monthly Production} \times \text{Total Cost per Unit} \times \text{Finished Goods Stock Period} \][/tex]
[tex]\[ = 433.33 \times 16 \times 1.5 = 10,400.00 \text{₹} \][/tex]
4. Debtors:
[tex]\[ \text{Debtors Value} = \text{Monthly Production} \times \text{Selling Price per Unit} \times \text{Debtors Credit Period} \][/tex]
[tex]\[ = 433.33 \times 20 \times 2 = 17,333.33 \text{₹} \][/tex]
5. Creditors (Negative Working Capital Component):
[tex]\[ \text{Creditors Value} = \text{Monthly Production} \times \text{Raw Material Cost per Unit} \times \text{Credit Period} \][/tex]
[tex]\[ = 433.33 \times 8 \times 1 = 3,466.67 \text{₹} \][/tex]
6. Lag in Payment of Wages:
[tex]\[ \text{Lag in Payment of Wages Value} = \text{Monthly Production} \times \text{Direct Labour Cost per Unit} \times \text{Lag Period in Months} \][/tex]
[tex]\[ = 433.33 \times 2 \times 0.375 = 325.00 \text{₹} \][/tex]
7. Cash in Hand:
[tex]\[ \text{Cash in Hand} = 7,300 \text{₹} \][/tex]
### Total Working Capital Needed:
Finally, the total working capital needed is the sum of all the components above, taking into account that creditors will reduce the necessary working capital:
[tex]\[ \text{Total Working Capital Needed} = \text{Raw Materials Stock Value} + \text{Materials in Process Value} + \text{Finished Goods Stock Value} + \text{Debtors Value} + \text{Lag in Payment of Wages Value} - \text{Creditors Value} + \text{Cash in Hand} \][/tex]
[tex]\[ = 3,466.67 + 3,466.67 + 10,400.00 + 17,333.33 + 325.00 - 3,466.67 + 7,300.00 = 38,825.00 \text{₹} \][/tex]
Thus, the total working capital needed to finance the production activity of Sima Ltd. for the given level of output is [tex]\(\text{₹} 38,825\)[/tex].
### Given Information:
- Annual Output: [tex]\(5,200\)[/tex] units.
- Costs per Unit:
- Raw Materials: [tex]\(\text{₹} 8\)[/tex]
- Direct Labour: [tex]\(\text{₹} 2\)[/tex]
- Overheads: [tex]\(\text{₹} 6\)[/tex]
- Total Cost: [tex]\(\text{₹} 16\)[/tex]
- Profit: [tex]\(\text{₹} 4\)[/tex]
- Selling Price: [tex]\(\text{₹} 20\)[/tex]
### Stock Periods and Credits:
- Raw Materials in stock: [tex]\(1\)[/tex] month.
- Materials in process: [tex]\(0.5\)[/tex] months.
- Finished goods in stock: [tex]\(6\)[/tex] weeks [tex]\((6/4 = 1.5 \text{ months})\)[/tex]
- Credit allowed by creditors: [tex]\(1\)[/tex] month.
- Credit allowed to debtors: [tex]\(2\)[/tex] months.
- Lag in payment of wages: [tex]\(1.5\)[/tex] weeks [tex]\((1.5/4 = 0.375 \text{ months})\)[/tex]
- Cash in hand and at bank: [tex]\(\text{₹} 7,300\)[/tex]
### Monthly Production Calculation:
Since the annual production is [tex]\(5,200\)[/tex] units, the monthly production rate is:
[tex]\[ \text{Monthly Production} = \frac{5,200 \text{ units}}{12 \text{ months}} = 433.33 \text{ units per month} \][/tex]
### Working Capital Components Calculation:
1. Raw Materials in Stock:
[tex]\[ \text{Raw Materials Stock Value} = \text{Monthly Production} \times \text{Raw Material Cost per Unit} \times \text{Stock Period} \][/tex]
[tex]\[ = 433.33 \times 8 \times 1 = 3,466.67 \text{₹} \][/tex]
2. Materials in Process:
[tex]\[ \text{Materials in Process Value} = \text{Monthly Production} \times \text{Total Cost per Unit} \times \text{Process Period} \][/tex]
[tex]\[ = 433.33 \times 16 \times 0.5 = 3,466.67 \text{₹} \][/tex]
3. Finished Goods in Stock:
[tex]\[ \text{Finished Goods Stock Value} = \text{Monthly Production} \times \text{Total Cost per Unit} \times \text{Finished Goods Stock Period} \][/tex]
[tex]\[ = 433.33 \times 16 \times 1.5 = 10,400.00 \text{₹} \][/tex]
4. Debtors:
[tex]\[ \text{Debtors Value} = \text{Monthly Production} \times \text{Selling Price per Unit} \times \text{Debtors Credit Period} \][/tex]
[tex]\[ = 433.33 \times 20 \times 2 = 17,333.33 \text{₹} \][/tex]
5. Creditors (Negative Working Capital Component):
[tex]\[ \text{Creditors Value} = \text{Monthly Production} \times \text{Raw Material Cost per Unit} \times \text{Credit Period} \][/tex]
[tex]\[ = 433.33 \times 8 \times 1 = 3,466.67 \text{₹} \][/tex]
6. Lag in Payment of Wages:
[tex]\[ \text{Lag in Payment of Wages Value} = \text{Monthly Production} \times \text{Direct Labour Cost per Unit} \times \text{Lag Period in Months} \][/tex]
[tex]\[ = 433.33 \times 2 \times 0.375 = 325.00 \text{₹} \][/tex]
7. Cash in Hand:
[tex]\[ \text{Cash in Hand} = 7,300 \text{₹} \][/tex]
### Total Working Capital Needed:
Finally, the total working capital needed is the sum of all the components above, taking into account that creditors will reduce the necessary working capital:
[tex]\[ \text{Total Working Capital Needed} = \text{Raw Materials Stock Value} + \text{Materials in Process Value} + \text{Finished Goods Stock Value} + \text{Debtors Value} + \text{Lag in Payment of Wages Value} - \text{Creditors Value} + \text{Cash in Hand} \][/tex]
[tex]\[ = 3,466.67 + 3,466.67 + 10,400.00 + 17,333.33 + 325.00 - 3,466.67 + 7,300.00 = 38,825.00 \text{₹} \][/tex]
Thus, the total working capital needed to finance the production activity of Sima Ltd. for the given level of output is [tex]\(\text{₹} 38,825\)[/tex].
