Understanding the Current Ratio and its Changes

The current ratio is a key liquidity ratio that measures a company's ability to pay off its short-term liabilities with its short-term assets. It is calculated using the formula:

\(\text{Current Ratio} = \frac{\text{Current Assets (CA)}}{\text{Current Liabilities (CL)}}\)

A higher current ratio generally indicates better short-term financial health, meaning the company has more assets than liabilities to cover its short-term debts.

Analyzing the Scenario: Initial Current Ratio 2:1

We are given an initial situation where the current ratio is 2:1. This means that the Current Assets are twice the amount of the Current Liabilities. We can represent this as:

\(\frac{\text{CA}}{\text{CL}} = \frac{2}{1}\)

Let's assume initial Current Assets are \(\text{CA}_1\) and initial Current Liabilities are \(\text{CL}_1\). So, \(\text{CA}_1 = 2 \times \text{CL}_1\).

Effect of an Equal Increase in Current Assets and Current Liabilities

The question states that there is an equal increase in both Current Assets and Current Liabilities. Let this equal increase be represented by the amount '\(x\)', where \(x > 0\).

The new Current Assets (\(\text{CA}_2\)) will be \(\text{CA}_1 + x\).

The new Current Liabilities (\(\text{CL}_2\)) will be \(\text{CL}_1 + x\).

The new Current Ratio will be:

\(\text{New Current Ratio} = \frac{\text{CA}_2}{\text{CL}_2} = \frac{\text{CA}_1 + x}{\text{CL}_1 + x}\)

Using an Example to Illustrate the Change

Let's use simple numbers based on the initial 2:1 ratio. Assume initial \(\text{CL}_1 = 100\) units. Then initial \(\text{CA}_1 = 2 \times 100 = 200\) units.

Initial Current Ratio = \(\frac{200}{100} = 2\)

Now, let's assume an equal increase of \(x = 50\) units in both Current Assets and Current Liabilities.

• New Current Assets (\(\text{CA}_2\)) = \(200 + 50 = 250\) units
• New Current Liabilities (\(\text{CL}_2\)) = \(100 + 50 = 150\) units

The New Current Ratio is:

\(\text{New Current Ratio} = \frac{250}{150} = \frac{25}{15} = \frac{5}{3} \approx 1.67\)

Comparing the initial ratio (2) with the new ratio (\(\approx 1.67\)), we can see that the current ratio has decreased.

Mathematical Explanation

Let the initial ratio be \(\frac{\text{CA}_1}{\text{CL}_1} = R\). Here, \(R = 2\), so \(\text{CA}_1 = R \times \text{CL}_1\).

The new ratio is \(\frac{\text{CA}_1 + x}{\text{CL}_1 + x}\).

Substitute \(\text{CA}_1 = R \times \text{CL}_1\):

\(\text{New Ratio} = \frac{R \times \text{CL}_1 + x}{\text{CL}_1 + x}\)

We want to compare this with the original ratio \(R\). Let's subtract \(R\) from the new ratio:

\(\frac{R \times \text{CL}_1 + x}{\text{CL}_1 + x} - R = \frac{R \times \text{CL}_1 + x - R \times (\text{CL}_1 + x)}{\text{CL}_1 + x}\)

\(= \frac{R \times \text{CL}_1 + x - R \times \text{CL}_1 - R \times x}{\text{CL}_1 + x}\)

\(= \frac{x - R \times x}{\text{CL}_1 + x} = \frac{x(1 - R)}{\text{CL}_1 + x}\)

In our case, the initial ratio \(R = 2\). So, \(1 - R = 1 - 2 = -1\).

The difference becomes \(\frac{x(-1)}{\text{CL}_1 + x} = \frac{-x}{\text{CL}_1 + x}\).

Since \(x > 0\) (equal increase) and \(\text{CL}_1 > 0\) (initial liability must be positive), the denominator \(\text{CL}_1 + x\) is positive. The numerator \(-x\) is negative.

Therefore, the difference \(\frac{-x}{\text{CL}_1 + x}\) is negative.

This means the New Ratio - Original Ratio < 0, which implies the New Ratio < Original Ratio.

So, when the initial current ratio is greater than 1 (\(R > 1\), as is the case with 2:1), an equal increase in both current assets and current liabilities will lead to a decrease in the current ratio.

Conclusion

Based on both the numerical example and the mathematical analysis, when the current ratio is initially 2:1 (which is > 1) and there is an equal increase in both current assets and current liabilities, the resulting current ratio will be lower than the original ratio.

Revision Table: Current Ratio Concepts

Additional Information: Ratio Analysis Context

The current ratio is just one of several financial ratios used to analyze a company's performance and health. It falls under the category of liquidity ratios.

• Liquidity Ratios: These ratios measure a company's ability to meet its short-term obligations. Examples include the current ratio, quick ratio, and cash ratio.
• Solvency Ratios: These measure a company's ability to meet its long-term obligations. Examples include the debt-to-equity ratio and times interest earned ratio.
• Activity Ratios: These measure how efficiently a company is using its assets. Examples include inventory turnover and accounts receivable turnover.
• Profitability Ratios: These measure a company's ability to generate earnings. Examples include net profit margin and return on assets.

Understanding how changes in financial statement items impact these ratios is crucial for financial analysis and decision-making. The behavior observed with the current ratio (decreasing when equal amounts are added to numerator and denominator if the original ratio is > 1) is a common mathematical property of fractions greater than 1.