Math Problem Statement

From the following particulars, estimate the working capital requirements based on the given data for credit periods, annual expenses, and incomes.

Solution

The table appears to list items related to a working capital estimate, with annual estimates and periods for credit allowed. Let me calculate the working capital requirement step-by-step.

Key Concepts:
Working capital is determined by analyzing current assets (cash, debtors, stock, work-in-progress, etc.) and current liabilities (purchases, wages, etc.) based on the periods allowed for credits or durations of payments.

Table Analysis:

  • Cash: ₹50,000 (Immediate asset)
  • Average Stock: ₹6,00,000 (inventory as an asset)
  • Work-In-Progress (WIP): ₹2,00,000 (part of working capital as it is an unfinished asset)
  • Cash Sales: ₹5,00,000 (likely excluded since they are cash transactions)
  • Debtors (Receivables): Credit allowed is 2 months; annual sales ₹30,00,000.
  • Purchase of Materials: Credit allowed is 8 weeks; annual purchases ₹13,00,000.
  • Wages: Credit allowed is 2 weeks; annual wages ₹19,50,000.
  • Rent and Rates: Credit allowed is 3 months; annual rent ₹1,00,000.
  • Salaries: Credit allowed is 1 month; annual salary ₹6,00,000.
  • Miscellaneous Expenses: Credit allowed is 2 months; annual expenses ₹1,20,000.

Step-by-Step Calculation of Working Capital:

1. Debtors (Receivables):

Credit period = 2 months.
Debtors = (Annual Sales × Credit Period) ÷ 12
Debtors = (₹30,00,000 × 2) ÷ 12 = ₹5,00,000

2. Purchase of Materials (Payables):

Credit period = 8 weeks = 2 months.
Materials Payables = (Annual Purchases × Credit Period) ÷ 12
Materials Payables = (₹13,00,000 × 2) ÷ 12 = ₹2,16,667

3. Wages (Outstanding Wages):

Credit period = 2 weeks = 0.5 months.
Outstanding Wages = (Annual Wages × Credit Period) ÷ 12
Outstanding Wages = (₹19,50,000 × 0.5) ÷ 12 = ₹81,250

4. Rent and Rates (Outstanding Rent):

Credit period = 3 months.
Outstanding Rent = (Annual Rent × Credit Period) ÷ 12
Outstanding Rent = (₹1,00,000 × 3) ÷ 12 = ₹25,000

5. Salaries (Outstanding Salaries):

Credit period = 1 month.
Outstanding Salaries = (Annual Salaries × Credit Period) ÷ 12
Outstanding Salaries = (₹6,00,000 × 1) ÷ 12 = ₹50,000

6. Miscellaneous Expenses (Outstanding Misc. Expenses):

Credit period = 2 months.
Outstanding Misc. Expenses = (Annual Expenses × Credit Period) ÷ 12
Outstanding Misc. Expenses = (₹1,20,000 × 2) ÷ 12 = ₹20,000

Total Working Capital:

Now, let’s compute the net working capital:

  • Assets:

    • Cash = ₹50,000
    • Stock = ₹6,00,000
    • Work-In-Progress = ₹2,00,000
    • Debtors = ₹5,00,000

    Total Assets = ₹13,50,000

  • Liabilities:

    • Materials Payables = ₹2,16,667
    • Outstanding Wages = ₹81,250
    • Outstanding Rent = ₹25,000
    • Outstanding Salaries = ₹50,000
    • Outstanding Misc. Expenses = ₹20,000

    Total Liabilities = ₹3,92,917

Net Working Capital = Total Assets - Total Liabilities
Net Working Capital = ₹13,50,000 - ₹3,92,917 = ₹9,57,083


Would you like further clarification or a breakdown of any specific section? Let me know!

Related Questions:

  1. How are credit periods converted into monthly fractions for calculations?
  2. Why is cash sales excluded from working capital requirements?
  3. Can working capital requirements vary for different businesses?
  4. What role does WIP play in determining working capital?
  5. How do short credit periods affect the liabilities calculation?

Tip:

Working capital ensures that a business can meet its short-term obligations, so maintaining an optimal level is key to financial stability. Always monitor both assets and liabilities periodically.

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Math Problem Analysis

Mathematical Concepts

Working Capital Management
Time-based Proportions
Financial Ratios

Formulas

Debtors = (Annual Sales × Credit Period) ÷ 12
Outstanding Expenses = (Annual Expenses × Credit Period) ÷ 12
Net Working Capital = Total Assets - Total Liabilities

Theorems

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Suitable Grade Level

Undergraduate Finance or Accounting