Math Problem Statement

The bond indenture for the 10-year, 8% debenture bonds, dated January 2, 20Y8, required working capital of $200,000, a current ratio of 2.0, and a quick ratio of 1.0 at the end of each calendar year until the bonds mature. At December 31, 20Y9, the three measures were computed as follows:

Current assets:           Cash

$120,000         Temporary investments

150,000         Accounts receivable (net)

240,000         Inventories

190,000         Prepaid expenses

50,000         Intangible assets

30,000         Property, plant, and equipment

540,000           Total current assets (net)     $1,320,000     Current liabilities:           Accounts and short-term notes payable

$440,000         Accrued liabilities

160,000           Total current liabilities     (600,000)     Working capital     $ 720,000   2.

Current ratio

2.2   $1,320,000 ÷ $600,000

Quick ratio

1.5   $660,000 ÷ $440,000

a.  There are errors in the calculation of the three measures of current position analysis. Determine the correct amounts. Round ratios to two decimal places.

Working capital

$fill in the blank 1

Current ratio   fill in the blank 2

Quick ratio   fill in the blank 3

Solution

To correct the errors in the calculations for working capital, current ratio, and quick ratio, we need to accurately follow the formulas and use the appropriate values from the financial data provided.

1. Working Capital

Working capital is calculated as follows: Working Capital=Total Current AssetsTotal Current Liabilities\text{Working Capital} = \text{Total Current Assets} - \text{Total Current Liabilities}

From the dataTo correct the errors in the calculations for working capital, current ratio, and quick ratio, we need to accurately follow the formulas and use the appropriate values from the financial data provided.

1. Working Capital

Working capital is calculated as follows: Working Capital=Total Current AssetsTotal Current Liabilities\text{Working Capital} = \text{Total Current Assets} - \text{Total Current Liabilities}

From the

  • Total Current Assets = $120,000 (Cash) + $150,000 (Temporary Investments) + $240,000 (Accounts Receivable) + $190,000 (Inventories) + $50,000 (Prepaid Expenses) = $750,000
  • Total Current Liabilities = $440,000 (Accounts and Short-term Notes Payable) + $160,000 (Accrued Liabilities) = $600,000

Thus, \text{Working Capital} = $750,000 - $600,000 = $150,000

2. Current Ratio

The current ratio is calculated as follows: Current Ratio=Total Current AssetsTotal Current Liabilities\text{Current Ratio} = \frac{\text{Total Current Assets}}{\text{Total Current Liabilities}}

Using the values calculated: \text{Current Ratio} = \frac{$750,000}{$600,000} = 1.25

3. Quick Ratio

The quick ratio is calculated by excluding inventories and prepaid expenses from current assets: Quick Assets=Cash+Temporary Investments+Accounts Receivable\text{Quick Assets} = \text{Cash} + \text{Temporary Investments} + \text{Accounts Receivable} = $120,000 + $150,000 + $240,000 = $510,000

Quick Ratio=Quick AssetsTotal Current Liabilities\text{Quick Ratio} = \frac{\text{Quick Assets}}{\text{Total Current Liabilities}} = \frac{$510,000}{$600,000} = 0.85

Summary of Correct Calculations

  1. Working Capital: $150,000
  2. Current Ratio: 1.25
  3. Quick Ratio: 0.85

Questions for Further Understanding:

  1. What are the implications of a lower than required quick ratio for the company?
  2. How can the company improve its working capital position?
  3. Why is it important to meet the current ratio and quick ratio requirements stipulated in the bond indenture?
  4. What impact could failing to meet these financial covenants have on the company's bonds?
  5. How do changes in current liabilities affect the working capital?
  6. How does the composition of current assets (cash vs. receivables vs. inventories) impact liquidity ratios?
  7. What strategies can a company use to maintain its current and quick ratios within the required limits?
  8. How do seasonal variations in sales and expenses impact the calculation of these ratios?

Tip:

Regularly monitoring and managing accounts receivable and inventory levels can significantly impact a company's liquidity ratios and overall financial health.

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Math Problem Analysis

Mathematical Concepts

Financial Analysis
Working Capital Management
Liquidity Ratios

Formulas

Working Capital = Total Current Assets - Total Current Liabilities
Current Ratio = Total Current Assets / Total Current Liabilities
Quick Ratio = Quick Assets / Total Current Liabilities

Theorems

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Suitable Grade Level

Professional