Class 12 Accountancy Part-2 Chapter 3 Ratio Analysis

Key Concept: Accounting Ratio - Current Ratio

c) 2 : 1
[Solution Description]
The current ratio is calculated by dividing current assets by current liabilities.
$\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}} = \frac{300{,}000}{150{,}000} = 2 : 1$

Key Concept: Gross Profit Ratio

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Gross Profit Ratio formula is indeed $\frac{\text{Gross Profit}}{\text{Revenue from Operations}} \times 100$, so the Assertion is true. The Reason is also correct because converting ratios to percentages standardizes comparisons. Moreover, the Reason correctly explains why multiplication by 100 is done for the ratio.

Key Concept: Comparative Analysis

a) Current Ratio includes inventory while Quick Ratio does not.
[Solution Description]
The key differences between Current Ratio and Quick Ratio lie in their definitions, components, reliability, and ideal values.
- **Current Ratio** includes all current assets and measures the ability to pay liabilities within a year.
- **Quick Ratio** excludes inventory and prepaid expenses, focusing on immediate liquidity.
From the syllabus, Quick Ratio is more reliable as it represents true liquidity, and its ideal value is 1:1 compared to 2:1 for Current Ratio.

Key Concept: Working Capital Turnover Ratio

b) 4.36 times
[Solution Description]
First, calculate Working Capital = Current Assets - Current Liabilities = \$8,50,000 - \$3,00,000 = \$5,50,000.
Now, Working Capital Turnover Ratio = $\frac{\text{Revenue from Operations}}{\text{Working Capital}} = \frac{24,00,000}{5,50,000} \approx 4.36$ times.

Key Concept: Advantages of Ratio Analysis

b) It enables inter-firm comparison by normalizing data
[Solution Description]
Converting absolute profits into ratios (e.g., net profit ratio) allows meaningful comparison between firms of different sizes. Without ratios, a firm with higher absolute profit might appear better even if its profitability relative to revenue is lower.

Key Concept: Liquidity Ratios - Current Ratio

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a current ratio of 3:1 is better than 1.5:1, which is true as it shows higher liquidity. The reason explains why a higher ratio is better (more assets to cover liabilities), which correctly explains the assertion. Both are true and the reason properly explains the assertion.

Key Concept: Net Credit Purchases Calculation

c) \$350,000
[Solution Description]
The formula for Net Credit Purchases is:
$\text{Net Credit Purchases} = \text{Total Purchases} - \text{Cash Purchases} - \text{Purchases Returns}$
Substituting the given values:
$\text{Net Credit Purchases} = \$500,000 - \$100,000 - \$50,000 = \$350,000$

Key Concept: Expression of Ratio

b) 25\%
[Solution Description]
The gross profit ratio is calculated by dividing gross profit by revenue from operations and multiplying by 100.
$\text{Gross Profit Ratio} = \left( \frac{150,000}{600,000} \right) \times 100 = 25\%$

Key Concept: Liquidity Ratios

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The assertion states that a current ratio of 2:1 is ideal, which is correct as per standard financial norms. The reason explains that the current ratio measures the ability to convert current assets into cash to pay liabilities, which is also true. However, the reason does not directly explain why 2:1 is the ideal ratio; it only describes what the ratio measures. Hence, both are true, but the reason does not correctly explain the assertion.

Key Concept: Meaning and Nature of Ratio, Liquidity Ratios

d) Assertion is false, but Reason is true.
[Solution Description]
The Assertion states that the current ratio must always be greater than 1 for liquidity. However, this is not strictly true as some industries or companies with strong cash flow management may operate with a current ratio slightly below 1 and still maintain liquidity. The Reason correctly explains that a current ratio less than 1 means current liabilities exceed current assets, but this does not necessarily imply insolvency if the company can manage its short-term obligations effectively. Therefore, the Assertion is false, but the Reason is true.

Key Concept: Trade Receivables Turnover Ratio

c) 10 times
[Solution Description]
The Trade Receivables Turnover Ratio is calculated using the formula:
$\text{Trade Receivables Turnover Ratio} = \frac{\text{Credit Revenue from Operations}}{\text{Average Trade Receivables}}$
Substituting the given values:
$\text{Trade Receivables Turnover Ratio} = \frac{500,000}{50,000} = 10 \text{ times}$

Key Concept: Trade Receivables Turnover Ratio, Average Collection Period

b) 4 times; 91 days
[Solution Description]
The Trade Receivables Turnover Ratio is calculated as:
$\text{Trade Receivables Turnover Ratio} = \frac{\text{Credit Revenue from Operations}}{\text{Average Trade Receivables}} = \frac{12,00,000}{3,00,000} = 4 \text{ times}$.
The Average Collection Period is:
$\text{Average Collection Period} = \frac{365}{\text{Trade Receivables Turnover Ratio}} = \frac{365}{4} = 91.25 \text{ days}$ rounded to 91 days.

Key Concept: Liquidity Ratios, Combined Effect

a) Purchase of inventory on credit
[Solution Description]
We need a transaction that leaves $\frac{\text{Current Assets}}{\text{Current Liabilities}}$ unchanged but reduces $\frac{\text{Quick Assets}}{\text{Current Liabilities}}$.
1. **Option a)** Purchase of inventory on credit: Increases both current assets (inventory) and current liabilities equally, keeping the current ratio at 2:1. However, since inventory is not a quick asset, the quick ratio decreases to $\frac{10,000}{10,000 + x}$.
2. **Option b)** Prepayment of insurance: Converts cash (quick asset) to prepaid expense (not quick asset), reducing quick assets without changing current liabilities. But this also affects the current ratio as total current assets remain the same (only composition changes).
3. **Option c)** Settlement of a current liability using cash: Reduces both current assets and current liabilities, potentially increasing the current ratio (e.g., paying \$5,000: $\frac{20,000 - 5,000}{10,000 - 5,000} = 3:1$).
4. **Option d)** Receipt of cash from a debtor: No effect on either ratio as cash and receivables are both quick assets.
Thus, the correct answer is option a).

Key Concept: Limitations of Ratio Analysis

b) It lacks context and cannot indicate financial position alone
[Solution Description]
A single ratio provides limited information because its significance depends on the context. For example, a high current ratio may seem good, but if the quick ratio is low, it indicates inventory issues. Hence, analyzing multiple ratios together gives a clearer picture of financial health.

Key Concept: Debt to Equity Ratio

b) 0.67
[Solution Description]
The debt to equity ratio is calculated as:
$Debt\ to\ Equity\ Ratio = \frac{Long-term\ Debts}{Shareholders’\ Funds} = \frac{\$400,000}{\$600,000} = 0.67$

Key Concept: Liquid Ratio Components

b) Inventory and prepaid expenses
[Solution Description]
Liquid assets are calculated as Current Assets minus Inventory and Prepaid Expenses. This exclusion is because inventory cannot be readily converted into cash and prepaid expenses are not convertible into cash at all.

Key Concept: Quick Ratio, Inventory Calculation

c) 1.8 : 1
[Solution Description]
Quick Ratio is calculated as $\frac{\text{Liquid Assets}}{\text{Current Liabilities}}$. Liquid Assets = Current Assets - Inventory - Prepaid Expenses = \$350,000 - \$150,000 - \$20,000 = \$180,000. So, Quick Ratio = $\frac{180,000}{100,000} = 1.8 : 1$.

Key Concept: Current Ratio, Working Capital

b) \$100,000
[Solution Description]
The current ratio is given by:
$Current\ Ratio = \frac{Current\ Assets}{Current\ Liabilities}$.
Given Current Ratio = 3:1 and Current Liabilities = \$50,000.
So, $3 = \frac{Current\ Assets}{50,000}$.
Therefore, Current Assets = 3 * \$50,000 = \$150,000.
Working Capital = Current Assets - Current Liabilities = \$150,000 - \$50,000 = \$100,000.

Key Concept: Trade Receivables Turnover Ratio

b) 1.5 months
[Solution Description]
The formula for Average Collection Period using the Trade Receivables Turnover Ratio is:
$\text{Average Collection Period} = \frac{12 \text{ months}}{\text{Trade Receivables Turnover Ratio}}$
Given:
$\text{Trade Receivables Turnover Ratio} = 8$
Substituting the value:
$\text{Average Collection Period} = \frac{12}{8} = 1.5 \text{ months}$

Key Concept: Effect of Transactions on Quick Ratio

b) Sale of goods at cost.
[Solution Description]
The quick ratio improves when quick assets increase or current liabilities decrease. Selling goods at cost increases cash (a quick asset) while reducing inventory (not part of quick assets). Selling goods at profit further increases quick assets due to additional profit. Purchasing goods on credit does not affect quick assets but increases current liabilities, reducing the ratio.

Key Concept: Understanding EPS Components

c) Preference dividend
[Solution Description]
The formula for EPS is:
$\text{EPS} = \frac{\text{Net Profit after Tax and Preference Dividend}}{\text{Number of Equity Shares}}$
Here, preference dividend is subtracted from net profit after tax to compute profit available for equity shareholders. Dividends on equity shares are not part of this calculation.

Key Concept: Liquidity Ratios

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a current ratio of 2:1 is ideal, which is correct as it indicates the firm has twice the current assets compared to current liabilities, providing a safety margin. The reason explains that this ratio ensures sufficient current assets to meet liabilities, which is true and directly explains why a 2:1 ratio is ideal. Therefore, both assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Trade Receivables Turnover Ratio

c) 7 times
[Solution Description]
First, calculate Credit Revenue from Operations:
$\text{Credit Revenue from Operations} = \text{Revenue from Operations} - \text{Cash Revenue from Operations}$
$= 6,00,000 - (0.30 \times 6,00,000) = 6,00,000 - 1,80,000 = \$\ 4,20,000$
Next, calculate Average Trade Receivables:
$\text{Average Trade Receivables} = \frac{\text{Opening Trade Receivables} + \text{Closing Trade Receivables}}{2}$
$= \frac{50,000 + 70,000}{2} = \$\ 60,000$
Now, compute the Trade Receivables Turnover Ratio:
$\text{Trade Receivables Turnover Ratio} = \frac{\text{Credit Revenue from Operations}}{\text{Average Trade Receivables}}$
$= \frac{4,20,000}{60,000} = 7 \text{ times}$

Key Concept: Meaning of Ratio

b) An arithmetical expression of the relationship between two related items
[Solution Description]
A ratio is an arithmetical expression of the relationship between two related or inter-dependent items. It is found by dividing one number into another, where the numerator and denominator must be logically related.

Key Concept: Introduction to Ratios: Meaning and Nature of Ratio

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Solution: The assertion states that the ratio of 6 to 3 is 2:1, which is true because $\frac{6}{3} = 2$, so the ratio is 2:1. The reason states that a ratio is calculated by dividing the first quantity by the second quantity, which is also true and correctly explains how the ratio in the assertion was derived. Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: Helpful to Management

b) Controlling liquidity and working capital.
[Solution Description]
Ratio analysis aids management in controlling the firm's financial position by evaluating liquidity ratios like the Current Ratio ($\frac{\text{Current Assets}}{\text{Current Liabilities}}$), which measures short-term solvency. This helps in making informed decisions regarding working capital management.

Key Concept: Net Profit Ratio Calculation

c) 20\%
[Solution Description]
To calculate the Net Profit Ratio, use the formula:
$\text{Net Profit Ratio} = \frac{\text{Net Profit}}{\text{Revenue from Operations}} \times 100$
Given:
Net Profit = \text{\$}50,000
Revenue from Operations = \text{\$}250,000
Substituting the values:
$\text{Net Profit Ratio} = \frac{50,000}{250,000} \times 100 = 20\%$

Key Concept: Current Ratio, Quick Ratio

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
To analyze this:
1. Let us assume initial Current Assets = \$100,000 and Current Liabilities = \$50,000, giving a Current Ratio of 2:1.
2. If the company pays off a short-term loan of \$20,000 using cash:
- Revised Current Assets = \$100,000 - \$20,000 = \$80,000
- Revised Current Liabilities = \$50,000 - \$20,000 = \$30,000
- New Current Ratio = \$80,000 / \$30,000 ≈ 2.67:1
3. The Assertion is true as the Current Ratio increases.
4. The Reason correctly explains why the ratio increases because reducing current liabilities (while also reducing current assets by the same amount for a higher ratio) leads to an improved Current Ratio.
Thus, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Quick Ratio Analysis

b) 1.33:1
[Solution Description]
The formula for Quick Ratio is:
$\text{Quick Ratio} = \frac{\text{Quick Assets}}{\text{Current Liabilities}}$
Here, Quick Assets are already given as \text{\$}80,000.
Therefore, Quick Ratio = $\frac{\text{\$}80,000}{\text{\$}60,000}$ = 1.33:1

Key Concept: Assertion-Reason

a)
[Solution Description]
The Assertion states that a higher Trade Receivables Turnover Ratio indicates better efficiency in collecting receivables, which is true as it shows the company collects payments more frequently. The Reason correctly defines the formula for the ratio: $\text{Trade Receivables Turnover Ratio} = \frac{\text{Credit Revenue from Operations}}{\text{Average Trade Receivables}}$, and this formula directly explains why the Assertion is true because the ratio quantifies collection efficiency.

Key Concept: Advantages of Ratio Analysis, Limitations of Ratio Analysis

d) Assertion is false, but Reason is true.
[Solution Description]
The Assertion states that ratio analysis is comprehensive as it includes both quantitative and qualitative factors, but this is false because ratio analysis is primarily based on quantitative data and ignores qualitative aspects like employee morale and management quality. The Reason claims that qualitative factors can be accurately quantified and included in ratio analysis, which is also false since qualitative factors are subjective and cannot be precisely measured or incorporated into ratios. Thus, both the Assertion and Reason are false.

Key Concept: Debt to Total Assets Ratio

d) 35\%
[Solution Description]
First, calculate Long-term Debts:
$\text{Long-term Debts} = \text{Long-term Borrowings} + \text{Long-term Provisions}$
$\text{Long-term Debts} = \$300,000 + \$50,000 = \$350,000$
Debt to Total Assets Ratio:
$\text{Debt to Total Assets Ratio} = \frac{\text{Long-term Debts}}{\text{Total Assets}}$
$\text{Debt to Total Assets Ratio} = \frac{\$350,000}{\$1,000,000} = 0.35$ or 35\%
The correct answer is option d).

Key Concept: Window dressing

b) It can artificially inflate current assets to improve the current ratio.
[Solution Description]
Window dressing involves manipulating financial statements to present a better position than reality. For instance, a company may show higher closing inventory to artificially inflate current assets, improving the current ratio ($\frac{\text{Current Assets}}{\text{Current Liabilities}}$), but this does not reflect the true liquidity position.

Key Concept: Quick Ratio

b) 2 : 1
[Solution Description]
First, calculate Quick Assets:
$\text{Quick Assets} = \text{Current Assets} - \text{Inventory} - \text{Prepaid Expenses} = 120,000 - 30,000 - 10,000 = \$80,000$
Then, the Quick Ratio is:
$\text{Quick Ratio} = \frac{\text{Quick Assets}}{\text{Current Liabilities}} = \frac{80,000}{40,000} = 2 : 1$

Key Concept: Current Ratio, Liquid Ratio

b) 2 : 1
[Solution Description]
First, calculate the liquid assets by subtracting inventory from current assets:
$\text{Liquid Assets} = \text{Current Assets} - \text{Inventory} = 250,000 - 50,000 = 200,000$
Then, calculate the liquid ratio using:
$\text{Liquid Ratio} = \frac{\text{Liquid Assets}}{\text{Current Liabilities}} = \frac{200,000}{100,000} = 2 : 1$

Key Concept: Liquidity Ratios, Current Ratio and Quick Ratio

c) Efficient working capital management
[Solution Description]
The current ratio of 3:1 indicates that current assets are three times the current liabilities, which is higher than the ideal ratio of 2:1. The quick ratio of 1.5:1, being above the ideal 1:1, shows sufficient liquidity. This implies the firm has efficient working capital management with adequate current and liquid assets to cover short-term obligations.

Key Concept: Expression of Ratio in Proportion

c) 3 : 1
[Solution Description]
The current ratio is calculated by dividing current assets by current liabilities:
$\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}} = \frac{150,000}{50,000} = 3 : 1$

Key Concept: Working Capital Turnover Ratio

c) $\text{Working Capital Turnover Ratio} = \frac{\text{Revenue from Operations}}{\text{Working Capital}}$
[Solution Description]
The Working Capital Turnover Ratio measures how efficiently a company utilizes its working capital to generate revenue. The formula is:
$\text{Working Capital Turnover Ratio} = \frac{\text{Revenue from Operations}}{\text{Working Capital}}$
where Working Capital = Current Assets – Current Liabilities.

Key Concept: Net Profit Formula Understanding

c) $\text{Gross Profit} + \text{Other Income} - \text{Indirect Expenses} - \text{Tax}$
[Solution Description]
The Net Profit is calculated as:
$\text{Net Profit} = \text{Gross Profit} + \text{Other Income} - \text{Indirect Expenses} - \text{Tax}$
This formula accounts for all income and expenses to determine the final net profit.

Key Concept: Working Capital Concept, Current Assets and Liabilities

b) \$40,000
[Solution Description]
Working Capital is calculated as Current Assets minus Current Liabilities. The given Current Assets are \$1,20,000 and Current Liabilities are \$80,000.
$\text{Working Capital} = 1,20,000 - 80,000 = \$40,000$

Key Concept: Profitability Ratios, Operating Ratio

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
Operating Ratio is calculated as:
$\text{Operating Ratio} = \frac{\text{Cost of Revenue from Operations + Operating Expenses}}{\text{Revenue from Operations}} \times 100$
A lower operating ratio indicates better efficiency since it means the company spends less on operating expenses relative to revenue. Therefore, the Assertion is true. The Reason explains what the operating ratio measures but does not directly justify why a lower ratio indicates efficiency. Hence, both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

Key Concept: Current Ratio, Quick Ratio, Implications

b) Inventory constitutes a major part of current assets.
[Solution Description]
The quick ratio excludes inventory, so a low quick ratio (0.8:1) compared to the current ratio (1.5:1) suggests that the firm heavily relies on inventory to meet short-term obligations. This could lead to liquidity issues if inventory cannot be sold quickly.
The difference between the ratios ($1.5 - 0.8 = 0.7$) highlights the significant portion of current assets tied up in inventory.

Key Concept: Proprietary Ratio, Debt to Equity Ratio

c) 0.95
[Solution Description]
Calculate Proprietary Ratio = $\frac{Shareholders' Funds}{Total Assets} = \frac{4,00,000}{7,00,000} = 0.57:1$
Calculate Debt to Equity Ratio = $\frac{Long-term Debts}{Shareholders' Funds} = \frac{1,50,000}{4,00,000} = 0.38:1$
Sum = 0.57 + 0.38 = 0.95

Key Concept: Debt to Equity Ratio

b) 0.4
[Solution Description]
To calculate the debt to equity ratio, divide the company's long-term debts by its shareholders' funds. Given long-term debts = \$500,000 and shareholders' funds = \$1,250,000.
$\text{Debt to Equity Ratio} = \frac{\text{Long-term Debts}}{\text{Shareholders' Funds}} = \frac{500,000}{1,250,000} = 0.4$
The debt to equity ratio is 0.4.

Key Concept: Average Collection Period, Trade Receivables Turnover Ratio

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
To verify the Assertion and Reason, let's analyze them step by step. First, the formula for Average Collection Period in months is indeed $\frac{12}{\text{Trade Receivables Turnover Ratio}}$. Given that the Trade Receivables Turnover Ratio is 6 times, substituting this into the formula: $\frac{12}{6} = 2$ months. Therefore, both the Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Trade Receivables Turnover Ratio

c) 6 times
[Solution Description]
First calculate average trade receivables:
$\text{Average Trade Receivables} = \frac{\text{Opening Debtors} + \text{Closing Debtors}}{2} = \frac{\text{\$}80,000 + \text{\$}1,20,000}{2} = \text{\$}1,00,000$
Now calculate the turnover ratio:
$\text{Trade Receivables Turnover Ratio} = \frac{\text{Credit Sales}}{\text{Average Trade Receivables}} = \frac{\text{\$}6,00,000}{\text{\$}1,00,000} = 6 \text{ times}$

Key Concept: Components of Current Ratio

c) Trade Investments
[Solution Description]
Current Assets include items like Current Investments, Inventories (excluding Loose Tools and Spare Parts), Trade Receivables, Cash and Bank Balance, Short-term Loans and Advances, and Other Current Assets. Non-current investments, such as Trade Investments, are not part of Current Assets.

Key Concept: Liquidity Ratios, Quick Ratio, Current Ratio

c) \$90,000
[Solution Description]
Given:
$\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}} = 4:1$
$\text{Quick Ratio} = \frac{\text{Liquid Assets}}{\text{Current Liabilities}} = 2.5:1$
First, find Current Assets:
$\text{Current Assets} = 4 \times \text{Current Liabilities} = 4 \times 60,000 = 240,000$
Next, find Liquid Assets:
$\text{Liquid Assets} = 2.5 \times \text{Current Liabilities} = 2.5 \times 60,000 = 150,000$
Finally, Inventory is the difference between Current Assets and Liquid Assets:
$\text{Inventory} = \text{Current Assets} - \text{Liquid Assets} = 240,000 - 150,000 = 90,000$

Key Concept: Average Collection Period, Credit Revenue from Operations

c) 61 days
[Solution Description]
To find the average collection period:
1. Formula:
$\text{Average Collection Period} = \left( \frac{\text{Average Trade Receivables}}{\text{Credit Revenue from Operations}} \right) \times 365$
2. Substitute values:
$\text{Average Collection Period} = \left( \frac{25,000}{150,000} \right) \times 365$
3. Simplify fraction:
$\frac{25,000}{150,000} = \frac{1}{6}$
4. Calculate days:
$\frac{1}{6} \times 365 = 60.83 \approx 61 \text{ days}$

Key Concept: Average Trade Receivables Calculation

c) \$50,000
[Solution Description]
Given:
- Opening Trade Receivables = \$40,000
- Closing Trade Receivables = \$60,000
- Formula:
$\text{Average Trade Receivables} = \frac{\text{Opening Trade Receivables} + \text{Closing Trade Receivables}}{2}$
Substituting the values:
$\text{Average Trade Receivables} = \frac{\$40,000 + \$60,000}{2} = \$50,000$

Key Concept: Quick Ratio

d) Inventories
[Solution Description]
Quick Assets are current assets that can be quickly converted into cash and do not include inventory or prepaid expenses. Therefore, inventories are excluded.

Key Concept: Inventory Turnover Ratio Calculation

d) 5 times
[Solution Description]
The formula for Inventory Turnover Ratio is:
$\text{Inventory Turnover Ratio} = \frac{\text{Cost of Revenue from Operations}}{\text{Average Inventory}}$
Substituting the values:
$\text{Inventory Turnover Ratio} = \frac{50,000}{10,000} = 5 \text{ times}$

Key Concept: Liquidity and Solvency Ratios

b) Quick Ratio: 1.38; Debt to Equity Ratio: 0.6
[Solution Description]
First calculate Quick Ratio:
Liquid Assets = Current Assets - Inventories - Prepaid Expenses
$= 800,000 - 200,000 - 50,000 = 550,000$
Quick Ratio = Liquid Assets / Current Liabilities
$= 550,000 / 400,000 = 1.375$
Now calculate Debt to Equity Ratio:
Debt to Equity Ratio = Long-term Debts / Shareholders' Funds
$= 600,000 / 1,000,000 = 0.6$

Key Concept: Trade Payables Turnover Ratio

c) 3.44 times
[Solution Description]
Net Credit Purchases = Total Purchases – Cash Purchases – Purchases Returns = Rs.8,00,000 – Rs.2,00,000 – Rs.50,000 = Rs.5,50,000. Average Trade Payables = (Opening Creditors + Closing Creditors)/2 = (Rs.1,50,000 + Rs.1,70,000)/2 = Rs.1,60,000. Trade Payables Turnover Ratio = Rs.5,50,000 / Rs.1,60,000 ≈ 3.44 times.

Key Concept: Working Capital Turnover Ratio, Efficiency Analysis

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that a company with a Working Capital Turnover Ratio of 8 times is more efficient than one with 5 times. This is true because the ratio measures how efficiently working capital is used to generate revenue. A higher ratio means better utilization. The Reason explains that the ratio calculates the turnover of working capital to generate revenue and that a higher ratio indicates greater efficiency. This is also correct and directly explains the Assertion. Therefore, both the Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Operating Ratio

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The assertion states that a lower operating ratio indicates better operational efficiency, which is correct as per the significance mentioned in the syllabus. The reason explains what the operating ratio measures, which is also accurate. However, the reason does not explain why a lower ratio indicates better efficiency; it merely defines the ratio. Thus, both are true but the reason does not correctly explain the assertion.

Key Concept: Advantages and Limitations of Ratio Analysis: Different accounting policies

b) The return on assets ratio will be incomparable due to different depreciation expenses affecting net profit and asset values.
[Solution Description]
The straight-line method results in a constant annual depreciation expense, whereas the written-down value method results in higher depreciation in earlier years. This affects profit trends and asset valuation over time, making direct comparison of profitability and efficiency ratios like Return on Assets (ROA) misleading unless adjustments are made.

Key Concept: Debt to Equity Ratio

c) 0.83 : 1
[Solution Description]
To calculate the Debt to Equity Ratio, we use the formula:
$\text{Debt to Equity Ratio} = \frac{\text{Long-term Debts}}{\text{Shareholders’ Funds}}$
Here, Long-term Debts = Long-term Borrowings + Long-term Provisions = \$200,000 + \$50,000 = \$250,000.
Shareholders’ Funds = \$300,000.
Therefore, the ratio is:
$\frac{\$250,000}{\$300,000} = 0.83 : 1$

Key Concept: Trade Receivables Turnover Ratio

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Trade Receivables Turnover Ratio is calculated as $\frac{\text{Credit Revenue from Operations}}{\text{Average Trade Receivables}}$. A higher ratio means the company is collecting its receivables more frequently, indicating efficient credit management. The Reason correctly explains why a higher ratio reflects better efficiency, as it directly measures the speed of converting credit sales to cash.

Key Concept: Liquid Ratio, Current Ratio

b) \$1,080,000
[Solution Description]
Current Ratio = Current Assets/Current Liabilities
1.8 = Current Assets/\$200,000 → Current Assets = \$360,000
Inventory = Current Assets - Liquid Assets = \$360,000 - \$180,000 = \$180,000
Inventory Turnover Ratio = Cost of Goods Sold/Average Inventory
6 = Cost of Goods Sold/\$180,000
Cost of Goods Sold = 6 × \$180,000 = \$1,080,000

Key Concept: Trade Payables Turnover Ratio

c) 3.5 times
[Solution Description]
First, calculate Net Credit Purchases:
$\text{Net Credit Purchases} = \text{Total Purchases} - \text{Cash Purchases} - \text{Purchases Returns} = 500,000 - 100,000 - 50,000 = \$350,000$
Next, compute Average Trade Payables:
$\text{Average Trade Payables} = \frac{\text{Opening Trade Payables} + \text{Closing Trade Payables}}{2} = \frac{80,000 + 120,000}{2} = \$100,000$
Finally, calculate the Trade Payables Turnover Ratio:
$\text{Trade Payables Turnover Ratio} = \frac{\text{Net Credit Purchases}}{\text{Average Trade Payables}} = \frac{350,000}{100,000} = 3.5 \text{ times}$

Key Concept: Current Ratio

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The current ratio is indeed calculated as $\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}}$. A ratio of 1.5:1 means the company's current assets are 1.5 times its current liabilities, indicating sufficient liquidity. Both the assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Profitability and Efficiency Ratios

b) Gross Profit Ratio: 40\%; Price Earning Ratio: 20
[Solution Description]
First calculate Gross Profit Ratio:
Gross Profit = Revenue - Cost of Revenue
$= 5,000,000 - 3,000,000 = 2,000,000$
Gross Profit Ratio = (Gross Profit/Revenue) × 100
$= (2,000,000/5,000,000) × 100 = 40\%$
Now calculate Price Earning Ratio:
Net Profit before Tax = Gross Profit - Operating Expenses - Interest
$= 2,000,000 - 1,000,000 - 100,000 = 900,000$
Net Profit after Tax = 900,000 - 300,000 = 600,000
EPS = Net Profit after Tax / Number of Shares
$= 600,000 / 500,000 = 1.2$
Price Earning Ratio = Market Price / EPS
$= 24 / 1.2 = 20$

Key Concept: Assertion-Reason

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Assertion (A) is true because a higher Debt to Equity Ratio means the firm relies more on borrowed funds rather than shareholders’ equity, increasing financial risk. Reason (R) is also true as this ratio is calculated using the formula: $\text{Debt to Equity Ratio} = \frac{\text{Long-term Debts}}{\text{Shareholders’ Funds}}$. Moreover, Reason (R) correctly explains Assertion (A) because the higher the ratio, the more dependent the firm is on external debt, leading to higher financial risk.

Key Concept: Interest Coverage Ratio

c) 9 times
[Solution Description]
First, calculate Net Profit before Tax:
Let Net Profit before Tax = $100$
Less: Tax ($40\%$) = $40$
Net Profit after Tax = $60$
If Net Profit after Tax is \$9,60,000, then:
$\text{Net Profit before Tax} = \frac{100}{60} \times 9,60,000 = 16,00,000$
Add Interest ($10\%$ of \$20,00,000 = \$2,00,000):
$\text{Net Profit before Interest and Tax} = 16,00,000 + 2,00,000 = 18,00,000$
Interest Coverage Ratio:
$\frac{18,00,000}{2,00,000} = 9 \text{ times}$

Key Concept: Effect on Current Ratio

c) 3.5:1
[Solution Description]
Given initial Current Assets = \$300,000, Current Liabilities = \$100,000, and repayment amount = \$20,000. The new Current Assets = \$300,000 - \$20,000 = \$280,000. New Current Liabilities = \$100,000 - \$20,000 = \$80,000. The new current ratio is calculated as $\frac{\$280,000}{\$80,000} = 3.5:1$.

Key Concept: Expression of Ratio

c) 3 : 1
[Solution Description]
The current ratio is calculated as Current Assets divided by Current Liabilities:
$\text{Current Ratio} = \frac{\$150,000}{\$50,000} = 3 : 1$

Key Concept: Quick Ratio Calculation

c) 1.1 : 1
[Solution Description]
To calculate the Quick Ratio, first determine the Liquid Assets:
$\text{Liquid Assets} = \text{Current Assets} - \text{Inventories} - \text{Prepaid Expenses}$
$\text{Liquid Assets} = \$100,000 - \$40,000 - \$5,000 = \$55,000$
Now, apply the formula for Quick Ratio:
$\text{Quick Ratio} = \frac{\text{Liquid Assets}}{\text{Current Liabilities}} = \frac{\$55,000}{\$50,000} = 1.1 : 1$

Key Concept: Profitability Ratios

c) 20\%
[Solution Description]
The net profit ratio is given by:
$\text{Net Profit Ratio} = \frac{\text{Net Profit}}{\text{Revenue from Operations}} \times 100$
Substituting the given values:
$\text{Net Profit Ratio} = \frac{1,20,000}{6,00,000} \times 100 = 20\%$
Therefore, the net profit ratio is 20\%.

Key Concept: Liquid Assets Identification

a) Accounts Receivable
[Solution Description]
Liquid Assets are calculated as:
$\text{Liquid Assets} = \text{Current Assets} - \text{Inventories} - \text{Prepaid Expenses}$
Therefore, only assets that are easily convertible to cash within a short period are considered. Among the options, Accounts Receivable is part of Current Assets but not excluded, hence it is included in Liquid Assets.

Key Concept: Gross Profit Ratio Calculation

b) 20\%
[Solution Description]
First, calculate the Gross Profit using the formula:
$\text{Gross Profit} = \text{Revenue from Operations} - \text{Cost of Revenue from Operations}$
$\text{Gross Profit} = \Rs.8,00,000 - \Rs.6,40,000 = \Rs.1,60,000$
Now, compute the Gross Profit Ratio:
$\text{Gross Profit Ratio} = \frac{\text{Gross Profit}}{\text{Revenue from Operations}} \times 100 = \frac{1,60,000}{8,00,000} \times 100 = 20\%$

Key Concept: Trade Payables Turnover Ratio with Missing Data

c) 5 times
[Solution Description]
Since opening trade payables are not given, we use closing trade payables for calculation.
Trade Payables Turnover Ratio = Net Credit Purchases / Closing Trade Payables
$= 450,000 / 90,000 = 5$ times

Key Concept:

b) 1.5 : 1
[Solution Description]
The quick ratio is calculated using the formula:
$\text{Quick Ratio} = \frac{\text{Liquid Assets}}{\text{Current Liabilities}}$
Here, liquid assets are current assets minus inventory (\$200,000 - \$50,000 = \$150,000). Current liabilities are \$100,000. Thus,
$\text{Quick Ratio} = \frac{150,000}{100,000} = 1.5 : 1$

Key Concept: Current Ratio, Liquid Ratio

b) 1.13:1
[Solution Description]
First calculate Current Ratio = $\frac{Current Assets}{Current Liabilities} = \frac{3,00,000}{1,50,000} = 2:1$
Then calculate Liquid Ratio = $\frac{Current Assets - Inventory - Prepaid Expenses}{Current Liabilities} = \frac{3,00,000 - 1,50,000 - 20,000}{1,50,000} = 0.87:1$
Difference = 2 - 0.87 = 1.13

Key Concept: Working Capital Concept

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Working capital is indeed calculated as the difference between current assets and current liabilities, which makes the Assertion true. The Reason is also true because working capital indicates the company's operational efficiency and short-term financial health by showing the funds available to meet its short-term obligations and run daily operations. Moreover, the Reason correctly explains why working capital is important (due to its role in day-to-day operations), making it a valid explanation for the Assertion.

Key Concept: Inventory Turnover Ratio, Working Capital Turnover Ratio

a) 25 times and 4.5 times
[Solution Description]
Step 1: Cost of Revenue from Operations = Cost of Material Consumed + Change in Inventories (Finished Goods) = \Rs.7,20,000 + \Rs.30,000 = \Rs.7,50,000.
Step 2: Since only the change in inventory is given, we assume Closing Inventory is \Rs.30,000 higher than Opening Inventory. However, exact average cannot be calculated; hence, we use an assumed ratio.
Step 3: Approximate Inventory Turnover Ratio = Cost of Revenue from Operations / Average Inventory ≈ \Rs.7,50,000 / \Rs.30,000 = 25 times (assuming average inventory as change value).
Step 4: Working Capital = Current Assets - Current Liabilities = \Rs.6,50,000 - \Rs.2,50,000 = \Rs.4,00,000.
Step 5: Working Capital Turnover Ratio = Revenue from Operations / Working Capital = \Rs.18,00,000 / \Rs.4,00,000 = 4.5 times.

Key Concept: Net Profit Ratio

b) $\text{Net Profit Ratio} = \left( \frac{\text{Net Profit}}{\text{Revenue from Operations}} \right) \times 100$
[Solution Description]
The Net Profit Ratio is calculated using the formula:
$\text{Net Profit Ratio} = \left( \frac{\text{Net Profit}}{\text{Revenue from Operations}} \right) \times 100$
This ratio measures profitability relative to revenue.

Key Concept: Impact on Current Ratio

b) Decreases to 1.7
[Solution Description]
Initial current assets were:
$\text{Current Ratio} = \frac{\text{Current Assets}}{100,000} = 2 \implies \text{Current Assets} = 200,000$
After decreasing current assets by \$30,000:
$\text{New Current Assets} = 200,000 - 30,000 = 170,000$
The new current ratio is:
$\frac{170,000}{100,000} = 1.7$
Thus, the current ratio decreases.

Key Concept: Debt to Equity Ratio: Shareholders’ Funds Calculation

d) Current Liabilities
[Solution Description]
Shareholders’ Funds include share capital (equity and preference), reserves, and surplus. Current Liabilities are obligations due within a year and are not part of Shareholders’ Funds.

Key Concept: Quick Ratio

c) 1.5 : 1
[Solution Description]
The Quick Ratio is calculated as $\text{Quick Ratio} = \frac{\text{Quick Assets}}{\text{Current Liabilities}}$. Here, it is $\frac{90,000}{60,000} = 1.5 : 1$.

Key Concept: Reliability of Ratios Depends on Correctness of Data

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that incorrect financial statement data leads to unreliable ratios, which is true as ratios are calculated from such data. The reason correctly explains this dependency by stating that ratio accuracy relies on correct financial data. Thus, both are true, and the reason is the correct explanation of the assertion.

Key Concept: Liquid Ratio, Current Assets, Inventories

b) 1.5 : 1
[Solution Description]
To find the Quick Ratio, we use the formula:
$\text{Quick Ratio} = \frac{\text{Current Assets} - \text{Inventories}}{\text{Current Liabilities}}$
Substituting the given values:
$\text{Quick Ratio} = \frac{120,000 - 30,000}{60,000} = \frac{90,000}{60,000} = 1.5 : 1$

Key Concept: Debt to Equity Ratio

b) 0.5 : 1
[Solution Description]
Debt to Equity Ratio = Long-term Debts / Shareholders’ Funds. Given: Long-term Debts = \$300,000; Shareholders’ Funds = \$600,000.
Substituting the values: Debt to Equity Ratio = \$300,000 / \$600,000 = 0.5.
Therefore, the debt to equity ratio is 0.5:1.

Key Concept: Trade Receivables Turnover Ratio

b) 6 times
[Solution Description]
The trade receivables turnover ratio is calculated using:
$\text{Trade Receivables Turnover Ratio} = \frac{\text{Credit Revenue from Operations}}{\text{Average Trade Receivables}}$
Compute average trade receivables:
$\text{Average Trade Receivables} = \frac{\text{Opening Trade Receivables} + \text{Closing Trade Receivables}}{2} = \frac{\$20,000 + \$30,000}{2} = \$25,000$
Now, substitute into the formula:
$\text{Trade Receivables Turnover Ratio} = \frac{\$150,000}{\$25,000} = 6\, \text{times}$
The trade receivables turnover ratio is 6 times.

Key Concept: Operating Ratio, Operating Profit Ratio

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
To analyze the assertion and reason:
1. **Assertion Analysis**: A lower operating ratio implies that a smaller proportion of revenue is consumed by operating costs, leaving a larger margin for non-operating expenses and profits. Hence, it does indicate higher operational efficiency. However, profitability is not solely dependent on operational efficiency but also on non-operating factors (e.g., taxes, interest). Thus, the assertion is partially true but oversimplified.
2. **Reason Analysis**: The operating ratio and operating profit ratio are indeed complementary. The formula shows:
$\text{Operating Ratio} + \text{Operating Profit Ratio} = 100\%$
This relationship is mathematically accurate, making the reason true.
3. **Conclusion**: While both statements are true, the reason does not correctly explain the assertion because operational efficiency does not guarantee higher profitability due to external factors.

Key Concept: Effect on Current Ratio

c) Increases
[Solution Description]
Initial current ratio is $\frac{\$120,000}{\$40,000} = 3:1$. After paying \$10,000, new Current Assets = \$110,000, new Current Liabilities = \$30,000. New current ratio becomes $\frac{\$110,000}{\$30,000} = 3.67:1$. Thus, the ratio improves.

Key Concept: Components of Current Assets, Quick Ratio

c) 1 : 1
[Solution Description]
To find the quick ratio, subtract inventory and prepaid expenses from current assets to get quick assets. Then divide by current liabilities.
Step 1: Calculate Quick Assets
$\text{Quick Assets} = \text{Current Assets} - \text{Inventory} - \text{Prepaid Expenses} = `1,50,000 - `60,000 - `10,000 = `80,000$
Step 2: Compute Quick Ratio
$\text{Quick Ratio} = \frac{\text{Quick Assets}}{\text{Current Liabilities}} = \frac{`80,000}{`80,000} = 1 : 1$

Key Concept: Ratio in Fraction Form, Real-World Application

c) 48,500
[Solution Description]
The ratio of defective items is $\frac{3}{100}$, so the ratio of non-defective items is $\frac{97}{100}$. Multiply this by the total items produced: $50,000 \times \frac{97}{100} = 48,500$.

Key Concept: Liquidity Ratios

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The assertion states that a current ratio of 1.5 indicates sufficient liquidity, which is true because a ratio above 1 means current assets exceed current liabilities. The reason correctly defines the current ratio as measuring the ability to cover current liabilities with current assets. However, while both are true, the reason does not explain why 1.5 specifically indicates sufficient liquidity—it only defines the ratio. Hence, the correct answer is option b).

Key Concept: Trade Receivables Turnover Ratio

b) Credit Revenue from Operations / Average Trade Receivables
[Solution Description]
The Trade Receivables Turnover Ratio is calculated by dividing the credit revenue from operations by the average trade receivables (debtors + bills receivable).

Key Concept: Working Capital Turnover Ratio

d) 5 times
[Solution Description]
The Working Capital Turnover Ratio is calculated as:
$\text{Working Capital Turnover Ratio} = \frac{\text{Revenue from Operations}}{\text{Working Capital}} = \frac{500,\!000}{100,\!000} = 5 \text{ times}$

Key Concept: Trade Receivables Turnover Ratio, Gross Profit Ratio

b) 3.75 times
[Solution Description]
1. Calculate Revenue from Operations using Gross Profit Ratio:
$\text{Gross Profit} = 20\% \text{ of Revenue from Operations}$
$\text{Cost of Revenue from Operations} = 80\% \text{ of Revenue from Operations}$
$Rs.6,00,000 = 80\% \times \text{Revenue from Operations}$
$\text{Revenue from Operations} = \frac{Rs.6,00,000}{0.8} = Rs.7,50,000$
2. Calculate Credit Revenue from Operations:
$\text{Credit Revenue from Operations} = 60\% \times Rs.7,50,000 = Rs.4,50,000$
3. Calculate Trade Receivables Turnover Ratio:
$\text{Trade Receivables Turnover Ratio} = \frac{\text{Credit Revenue from Operations}}{\text{Average Trade Receivables}}$
$= \frac{Rs.4,50,000}{Rs.1,20,000} = 3.75 \text{ times}$

Key Concept: Conceptual, Formula-based

b) 1.4 : 1
[Solution Description]
To calculate the Quick Ratio, subtract Inventory and Prepaid Expenses from Current Assets to get Liquid Assets. Then divide this by Current Liabilities.
Step 1: Calculate Liquid Assets = Current Assets - Inventory - Prepaid Expenses
$Liquid\ Assets = 200,000 - 50,000 - 10,000 = 140,000$
Step 2: Compute Quick Ratio = Liquid Assets / Current Liabilities
$Quick\ Ratio = \frac{140,000}{100,000} = 1.4 : 1$

Key Concept: Solvency Ratios

b) The firm's ability to meet long-term obligations
[Solution Description]
The Debt to Equity Ratio assesses a firm's ability to meet its long-term obligations by comparing Long-term Debts to Shareholders’ Funds.
$\text{Debt to Equity Ratio} = \frac{\text{Long-term Debts}}{\text{Shareholders’ Funds}}$
It indicates the safety of the principal amount for long-term lenders. The correct answer is option b).

Key Concept: Trade Payables Turnover Ratio, Average Payment Period

b) 4 times
[Solution Description]
Net Credit Purchases = Total Purchases - Cash Purchases - Purchase Returns
$= 800,000 - 150,000 - 50,000 = 600,000$
Average Trade Payables = (Opening Trade Payables + Closing Trade Payables)/2
$= (120,000 + 180,000)/2 = 150,000$
Trade Payables Turnover Ratio = Net Credit Purchases / Average Trade Payables
$= 600,000 / 150,000 = 4$ times

Key Concept: Working Capital Turnover Ratio

c) 4 times
[Solution Description]
Using the formula:
$\text{Working Capital Turnover Ratio} = \frac{\text{Revenue from Operations}}{\text{Working Capital}} = \frac{200,000}{50,000} = 4 \text{ times}$

Key Concept: Quick Ratio

b) 0.83:1
[Solution Description]
The Quick Ratio is calculated as $\frac{\text{Quick Assets}}{\text{Current Liabilities}} = \frac{50,000}{60,000} \approx 0.83:1$.

Key Concept: Inventory Turnover Ratio

b) The efficiency of asset utilisation for generating revenue from operations
[Solution Description]
The Inventory Turnover Ratio measures how efficiently a company manages its inventory by comparing the cost of goods sold to the average inventory during a period. A higher ratio indicates better efficiency in converting inventory into sales.

Key Concept: Components of Current Liabilities, Liquidity Ratios

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
To verify the assertion, first calculate the total current liabilities:
$\text{Current Liabilities} = 50{,}000 + 30{,}000 + 10{,}000 + 5{,}000 = 95{,}000$
The current ratio is given by $\frac{\text{Current Assets}}{\text{Current Liabilities}}$. For the current ratio to be greater than 1, current assets must exceed \$95,000. Hence, the assertion is true.
The reason correctly lists the components of current liabilities, confirming it's true. However, while both are true, the reason does not explain why the assertion holds (it merely defines current liabilities). Thus, Reason is NOT the correct explanation of Assertion.

Key Concept: Current Ratio, Dividend Payment

a) Improves the current ratio
[Solution Description]
Initial current ratio = $\frac{\$500,000}{\$250,000} = 2:1$. After paying the dividend:
New Current Assets = \$500,000 - \$50,000 = \$450,000
New Current Liabilities = \$250,000 - \$50,000 = \$200,000
New Current Ratio = $\frac{\$450,000}{\$200,000} = 2.25:1$
Since the ratio increases from 2:1 to 2.25:1, the current ratio improves.

Key Concept: Working Capital Turnover Ratio

c) 15 times
[Solution Description]
Working Capital = Current Assets - Current Liabilities = \$250,000 - \$125,000 = \$125,000
Working Capital Turnover Ratio = Revenue from Operations/Working Capital = \$1,875,000/\$125,000 = 15 times

Key Concept: Average Collection Period

b) 60 days
[Solution Description]
First calculate trade receivables turnover ratio:
$\text{Trade Receivables Turnover Ratio} = \frac{\text{Credit Sales}}{\text{Average Trade Receivables}} = \frac{\text{\$}9,00,000}{\text{\$}1,50,000} = 6 \text{ times}$
Now calculate collection period:
$\text{Average Collection Period} = \frac{360 \text{ days}}{\text{Trade Receivables Turnover Ratio}} = \frac{360}{6} = 60 \text{ days}$

Key Concept: Introduction to Ratios

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the ratio of current assets to current liabilities is a liquidity ratio, which is true as it falls under the classification of Liquidity Ratios. The reason given is also true because this ratio indeed assesses the firm's capacity to pay off its short-term liabilities with its short-term assets. Moreover, the reason correctly explains the assertion since liquidity ratios are specifically designed to evaluate short-term financial health.

Key Concept: Working Capital Turnover Ratio

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that a high Working Capital Turnover Ratio indicates efficient utilization of working capital for generating revenue from operations. This is true as per the significance of the ratio explained in the syllabus. The Reason states that the Working Capital Turnover Ratio evaluates the efficiency of the entire working capital, not just inventory, which is also true and correctly explains why a high ratio indicates efficient utilization of working capital. Thus, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Current Ratio, Liquidity Ratios

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that an increase in current liabilities with unchanged current assets leads to a decrease in the current ratio. This is true because the current ratio formula is $\text{Current Assets} / \text{Current Liabilities}$. If current liabilities increase and current assets stay the same, the denominator increases, reducing the ratio. The reason correctly defines the current ratio formula and supports the assertion by explaining why the ratio decreases. Hence, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: Inventory Turnover Ratio

b) 6.67
[Solution Description]
The Inventory Turnover Ratio is calculated as:
$\text{Inventory Turnover Ratio} = \frac{\text{Cost of Revenue from Operations}}{\text{Average Inventory}}$
First, find Average Inventory:
$\text{Average Inventory} = \frac{\text{Opening Inventory} + \text{Closing Inventory}}{2} = \frac{50{,}000 + 70{,}000}{2} = 60{,}000$
Now, calculate the ratio:
$\text{Inventory Turnover Ratio} = \frac{400{,}000}{60{,}000} \approx 6.67$

Key Concept: Current Ratio

c) $\frac{\text{Current Assets}}{\text{Current Liabilities}}$
[Solution Description]
The Current Ratio is calculated by dividing Current Assets by Current Liabilities. The formula is:
$\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}}$

Key Concept: Window Dressing

c) It makes ratios unreliable for decision-making
[Solution Description]
Window dressing involves manipulating accounts to present a better financial position than reality. This distortion makes ratios unreliable because they no longer reflect the actual financial performance or position of the company, leading to misleading conclusions about management effectiveness.

Key Concept: Proprietary Ratio

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a higher proprietary ratio indicates better financial stability, which is true as per the syllabus notes. The reason explains that this is because a higher ratio signifies greater financing through shareholders' funds rather than creditors, which aligns with the syllabus explanation that a higher ratio is favorable for creditors. Therefore, both statements are true, and the reason correctly explains the assertion.

Key Concept: Liquid Ratio

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The quick ratio, also known as the acid-test ratio, is calculated by dividing liquid assets (current assets minus inventories and prepaid expenses) by current liabilities. A ratio of 1.5:1 indicates that the firm has \$1.50 in liquid assets for every \$1 of current liabilities, which is generally considered a healthy liquidity position. The Reason correctly explains why this ratio is important: it assesses the firm's ability to meet short-term obligations without selling inventory, as inventory may take time to convert to cash. Therefore, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Working Capital, Current Ratio

b) Current assets \$480,000, Current liabilities \$360,000
[Solution Description]
Let current assets be $4x$ and current liabilities be $3x$.
Working capital is calculated as:
$\text{Working Capital} = \text{Current Assets} - \text{Current Liabilities} = 4x - 3x = x = 120,000$
Therefore:
$\text{Current Assets} = 4x = 480,000$
$\text{Current Liabilities} = 3x = 360,000$

Key Concept: Impact of Analyst’s Ability and Bias

c) Because the analyst may not consider the quality of current assets.
[Solution Description]
A high current ratio ($\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}}$) does not necessarily indicate strong liquidity if the quality of current assets is poor (e.g., obsolete inventory). An analyst may overlook this aspect due to bias or lack of knowledge.

Key Concept: Limitations of Ratio Analysis

c) Differing accounting policies
[Solution Description]
Different accounting policies for depreciation or stock valuation can lead to varying profit calculations, making profitability ratios incomparable across firms.

Key Concept: Current Ratio Interpretation

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion states that a company with a current ratio of 3:1 is always financially healthier than one with 1.5:1. While the reason correctly points out that a higher current ratio indicates better liquidity, it also highlights that an excessively high ratio (like 3:1) may indicate inefficiency—meaning it's not "always" healthier. Thus, the assertion is false because higher ratios can sometimes be detrimental due to idle assets, while the reason is true as it explains the implications of the current ratio accurately.
Therefore:
- Assertion is false (as higher ratio doesn't always mean better health).
- Reason is true (it correctly explains the trade-off).
The correct relationship is that the assertion is false, but the reason is true.

Key Concept: Working Capital Concept

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
Negative working capital occurs when current liabilities exceed current assets ($\text{Current Liabilities} > \text{Current Assets}$). While this situation can indicate potential liquidity problems, it does not necessarily mean the company is always in financial distress. Some companies, like those with strong cash conversion cycles (e.g., retailers), may operate efficiently with negative working capital by quickly converting inventory into cash. Therefore, while the Reason correctly explains the condition of negative working capital, the Assertion makes an absolute claim ("always") which is not universally true. Thus, both statements are true, but the Reason does not fully justify the Assertion.

Key Concept: Sale of Fixed Assets

c) 2.03:1
[Solution Description]
The current ratio is calculated as $\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}}$. Initially, the current ratio is $\frac{\$200,000}{\$100,000} = 2:1$. After selling the fixed asset for \$3,000, the cash (a current asset) increases by \$3,000, making the new current assets \$203,000. The current liabilities remain unchanged. Thus, the new current ratio is $\frac{\$203,000}{\$100,000} = 2.03:1$.

Key Concept: Return on Investment, Capital Employed Calculation

c) 27.69\%
[Solution Description]
To calculate ROI, we first determine the Capital Employed using the formula:
$\text{Capital Employed} = \text{Fixed Assets} + \text{Working Capital}$.
Working Capital is calculated as $\text{Current Assets} - \text{Current Liabilities} = \$3,00,000 - \$1,50,000 = \$1,50,000$.
Therefore, Capital Employed = \$5,00,000 + \$1,50,000 = \$6,50,000.
Now, ROI is calculated as $\frac{\$1,80,000}{\$6,50,000} \times 100 = 27.69\%$.

Key Concept: Liquidity Ratios

b) 2
[Solution Description]
The current ratio is calculated using the formula:
$\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}}$
Substituting the given values:
$\text{Current Ratio} = \frac{500,000}{250,000} = 2$
The current ratio of the company is 2.

Key Concept: EPS, Bonus Issue, Preference Dividend

b) \$11.50
[Solution Description]
1. Adjust the number of shares due to the bonus issue:
$\text{New Number of Shares} = 10,000 + 10,000 = 20,000$
2. Deduct Preference Dividend:
$\text{Profit available for Equity Shareholders} = \$250,000 - \$20,000 = \$230,000$
3. Calculate Adjusted EPS:
$\text{Adjusted EPS} = \frac{\$230,000}{20,000} = \$11.50$

Key Concept: Current Ratio, Short-Term Financial Health

c) 4.0
[Solution Description]
After paying \$100,000 from cash:
$\text{New Current Assets} = \$500,000 - \$100,000 = \$400,000.$
$\text{New Current Liabilities} = \$200,000 - \$100,000 = \$100,000.$
The new current ratio is:
$\frac{\$400,000}{\$100,000} = 4.$

Key Concept: Expression of Ratio - Times

c) 4 times
[Solution Description]
The inventory turnover ratio is calculated as:
$\text{Inventory Turnover Ratio} = \frac{\text{Net Sales}}{\text{Average Inventory}} = \frac{8,00,000}{2,00,000} = 4 \text{ times}$

Key Concept: Trade Payables Turnover Ratio

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that the Trade Payables Turnover Ratio measures how efficiently a firm pays its suppliers, which is correct. The Reason provides the correct formula for calculating this ratio, which is also accurate and explains the Assertion. Therefore, both Assertion and Reason are true, and Reason correctly explains the Assertion.

Key Concept: Current Ratio Interpretation

d) 2 : 1
[Solution Description]
The current ratio is calculated by dividing current assets by current liabilities. Here, $\text{Current Ratio} = \frac{200,000}{100,000} = 2:1$.

Key Concept: Trade Receivables Turnover Ratio

c) 1.5 months
[Solution Description]
The formula for Average Collection Period when Trade Receivables Turnover Ratio is given:
$\text{Average Collection Period} = \frac{12 \text{ months}}{\text{Trade Receivables Turnover Ratio}}$
Substituting the value:
$\text{Average Collection Period} = \frac{12}{8} = 1.5 \text{ months}$

Key Concept: Working Capital Calculation

b) \$35,000
[Solution Description]
Working Capital is calculated as:
$\text{Working Capital} = \text{Current Assets} - \text{Current Liabilities}$
Substituting the given values:
$\text{Working Capital} = 60,000 - 25,000 = 35,000$

Key Concept: Gross Profit Ratio Interpretation

b) Cost of Revenue from Operations has decreased
[Solution Description]
An increase in Gross Profit Ratio with constant Revenue from Operations implies that the Cost of Revenue from Operations has decreased. The formula for Gross Profit Ratio is:
$\text{Gross Profit Ratio} = \frac{\text{Gross Profit}}{\text{Revenue from Operations}} \times 100$
If Revenue from Operations stays the same but the ratio increases, Gross Profit must have increased due to lower costs.

Key Concept: Trade Receivables Turnover Ratio, Gross Profit Ratio

c) Rs.1,75,000
[Solution Description]
1. Calculate Revenue from Operations (RFO):
Given Gross Profit Ratio is 25\%, so Cost of RFO is 75\% of RFO.
$\frac{100}{75} \times 10,00,000 = Rs.13,33,333.33$
2. Calculate Credit Revenue from Operations:
Let Credit RFO be Rs.100, then Cash RFO is Rs.33.33.
Total RFO is Rs.133.33.
$\frac{100}{133.33} \times 13,33,333.33 = Rs.10,00,000$
3. Let Opening Trade Receivables = x.
Closing Trade Receivables = x + 50,000.
Average Trade Receivables = $\frac{x + (x + 50,000)}{2} = x + 25,000$.
4. Using Trade Receivables Turnover Ratio:
$5 = \frac{10,00,000}{x + 25,000}$
$x + 25,000 = \frac{10,00,000}{5} = 2,00,000$
$x = 2,00,000 - 25,000 = Rs.1,75,000$

Key Concept: Current Ratio

c) $\text{Current Assets} / \text{Current Liabilities}$
[Solution Description]
The Current Ratio measures a company's ability to pay short-term obligations using its current assets. The formula is:
$\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}}$

Key Concept: No Suitable Standards, Effect of Personal Bias

c) No suitable standards and analyst bias lead to inconsistent interpretations.
[Solution Description]
The lack of precise terminology or standard definitions for calculating ratios (e.g., net profit before vs. after tax) leads to inconsistent interpretations. Additionally, personal bias or methodology differences between analysts can result in varying conclusions despite using the same financial data.

Key Concept: Trade Receivables Turnover Ratio

c) Efficiency in collecting credit sales from customers
[Solution Description]
The Trade Receivables Turnover Ratio measures how efficiently a company collects its credit sales from customers. It is calculated as:
$\text{Trade Receivables Turnover Ratio} = \frac{\text{Credit Revenue from Operations}}{\text{Average Trade Receivables}}$
A higher ratio indicates quicker collection of receivables.

Key Concept: Net Profit Ratio, Tax Calculation

b) 28\%
[Solution Description]
First, calculate Tax:
$\text{Tax} = Rs.2,80,000 \times 30\% = Rs.84,000$
Now, Net Profit after Tax:
$\text{Net Profit} = Rs.2,80,000 - Rs.84,000 = Rs.1,96,000$
Net Profit Ratio:
$\frac{Rs.1,96,000}{Rs.7,00,000} \times 100 = 28\%$

Key Concept: Working Capital Turnover Ratio

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion states that a higher Working Capital Turnover Ratio indicates better efficiency in utilizing working capital, which is correct as per the significance mentioned in the syllabus. The Reason provides the formula for the ratio, which is also correct. However, the Reason does not explain why a higher ratio indicates better efficiency; it only states the formula. Therefore, both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

Key Concept: Return on Investment Calculation

b) 28.57\%
[Solution Description]
First, calculate Capital Employed:
$\text{Capital Employed} = \text{Fixed Assets} + \text{Current Assets} - \text{Current Liabilities} = \$500,000 + \$300,000 - \$100,000 = \$700,000$
Then compute ROI:
$\text{ROI} = \frac{\text{Net Profit before Interest and Tax}}{\text{Capital Employed}} \times 100 = \frac{\$200,000}{\$700,000} \times 100 = 28.57\%$

Key Concept: Liquidity Ratios, Solvency Ratios

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion states that a high current ratio always indicates strong liquidity and financial health. However, this is not necessarily true because the current ratio ($\frac{\text{Current Assets}}{\text{Current Liabilities}}$) includes all current assets, some of which may not be easily convertible to cash (e.g., obsolete inventory). The Reason correctly points out this limitation by highlighting that the current ratio ignores the quality of current assets. Therefore, while both statements are true, the Reason explains why the Assertion is not always valid.

Key Concept: EPS, Face Value, Multiple Classes of Shares

c) \$5.87
[Solution Description]
1. Calculate Preference Dividend:
$\text{Preference Dividend} = 12\% \times (4,000 \times \$50) = \$24,000$
2. Calculate Profit available for Equity Shareholders:
$\text{Profit available} = \$200,000 - \$24,000 = \$176,000$
3. Calculate EPS:
$\text{EPS} = \frac{\$176,000}{30,000} = \$5.87$

Key Concept: Current Ratio Calculation

b) \$60,000
[Solution Description]
Current Ratio $= \frac{Current Assets}{Current Liabilities}$
Given, Current Ratio $= 3:1$ and Current Assets $= \$1,80,000$
Let Current Liabilities be $x$.
Then, $\frac{1,80,000}{x} = 3$
Solving for $x$, we get $x = \frac{1,80,000}{3} = 60,000$.
Thus, the current liabilities are \$60,000.

Key Concept: Gross Profit Ratio

b) 25\%
[Solution Description]
The formula for Gross Profit Ratio is:
$\text{Gross Profit Ratio} = \frac{\text{Gross Profit}}{\text{Revenue from Operations}} \times 100$
Substituting the given values:
$\text{Gross Profit Ratio} = \frac{200,000}{800,000} \times 100 = 25\%$
The answer is $25\%$.

Key Concept: Meaning of Ratio, Expression of Ratio

d) Assertion is false, but Reason is true.
[Solution Description]
The Assertion states that it is meaningful to calculate the ratio between the number of students and teacher salaries because they are both related to an educational institution. However, according to the meaning of ratio, a ratio must exist only between two numerical values of the same kind. While both the number of students and teacher salaries are related to the school, they are not the same kind of quantity (one is a count of individuals, and the other is a financial measure). Therefore, the Assertion is false.
The Reason correctly explains that a ratio must involve two numerical values of the same kind to be meaningful, which aligns with the definition provided in the syllabus. Hence, the Reason is true.
Therefore, the Assertion is false, but the Reason is true.

Key Concept: Accounting policies limitation

b) Different accounting policies can affect comparability
[Solution Description]
Different firms may follow different accounting policies (e.g., straight-line vs. written-down value depreciation or FIFO vs. LIFO inventory valuation), making their ratios less comparable. This does not mean ratios ignore size or are unrelated to financial statements.

Key Concept: Impact of Inventory Reduction on Liquid Ratio

a) Increases from 1.25 : 1 to 1.67 : 1
[Solution Description]
Initial Liquid Ratio:
$\text{Liquid Ratio} = \frac{25{,}000}{20{,}000} = 1.25 : 1$
After reducing inventory by \$5,000 and paying off liabilities, Liquid Assets remain unchanged (\$25,000 - \$5,000 + \$5,000 = \$25,000). New Current Liabilities:
$20{,}000 - 5{,}000 = 15{,}000$
New Liquid Ratio:
$\text{Liquid Ratio} = \frac{25{,}000}{15{,}000} \approx 1.67 : 1$
The ratio improves due to lower Current Liabilities.

Key Concept: Gross Profit Ratio with Purchases Data

c) 35\%
[Solution Description]
First, compute the Cost of Revenue from Operations:
$\text{Cost of Revenue from Operations} = \text{Opening Inventory} + \text{Net Purchases} + \text{Direct Expenses} - \text{Closing Inventory}$
$\text{Cost of Revenue from Operations} = \Rs.50,000 + \Rs.2,00,000 + \Rs.40,000 - \Rs.30,000 = \Rs.2,60,000$
Next, calculate Gross Profit:
$\text{Gross Profit} = \text{Revenue from Operations} - \text{Cost of Revenue from Operations} = \Rs.4,00,000 - \Rs.2,60,000 = \Rs.1,40,000$
Finally, compute the Gross Profit Ratio:
$\text{Gross Profit Ratio} = \frac{1,40,000}{4,00,000} \times 100 = 35\%$

Key Concept: Conceptual, Limited Meaning of Single Ratio Without Other Ratios

b) The company's liquidity is overstated due to high inventory levels.
[Solution Description] The current ratio is $\text{Current Assets / Current Liabilities} = 3:1$, suggesting good liquidity. However, the quick ratio, which excludes inventory ($\text{(Current Assets - Inventory) / Current Liabilities} = 0.8:1$), is low. This indicates that most of the current assets are tied up in inventory, which may not be easily convertible to cash. Thus, despite a high current ratio, the company's short-term solvency is weak due to excessive inventory.

Key Concept: Liquidity Ratios: Conversion of Debentures

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The quick ratio is calculated as Quick Assets divided by Quick Liabilities. When debentures are converted into shares, it is a non-cash transaction that does not impact either quick assets (which exclude inventory and prepaid expenses) or quick liabilities (short-term obligations). Thus, the quick ratio remains unaffected. The Assertion is true because the ratio does not change, and the Reason correctly explains why this happens.

Key Concept: Current Ratio

c) 3.00
[Solution Description]
First, calculate the initial current ratio:
$\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}} = \frac{500,000}{200,000} = 2.5$
After paying \$50,000, the new current assets are:
$500,000 - 50,000 = 450,000$
The new current liabilities are:
$200,000 - 50,000 = 150,000$
The new current ratio is:
$\frac{450,000}{150,000} = 3$

Key Concept: Expression of Ratio

b) 4 times
[Solution Description]
The inventory turnover ratio is calculated by dividing the cost of goods sold by the average inventory:
$\text{Inventory Turnover Ratio} = \frac{\text{Cost of Goods Sold}}{\text{Average Inventory}} = \frac{Rs.5,00,000}{Rs.1,25,000} = 4 \text{ times}$

Key Concept: Ratio in Fraction Form

b) $\frac{5}{2}$
[Solution Description]
The ratio of total assets to total liabilities is given by dividing total assets by total liabilities:
$\frac{\text{Total Assets}}{\text{Total Liabilities}} = \frac{500,000}{200,000} = \frac{5}{2}$