Chapter 4, Problem 15P

RETURN ON EQUITY AND QUICK RATIO Lloyd Inc. has sales of $200,000, a net income of $15,000, and the following balance sheet:

The new owner thinks that inventories are excessive and can be lowered to the point where the current ratio is equal to the industry average, 25×, without affecting sales or net income. If inventories are sold and not replaced (thus reducing the current ratio to 25×); if the funds generated are used to reduce common equity (stock can be repurchased at book value); and if no other changes occur, by how much will the ROE change? What will be the firm’s new quick ratio?

Summary Introduction

To identify: The change in return on equity and new quick ratio.

Quick Ratio: A part of liquidity ratios, quick ratio reflects the ability to oblige the short term debts of a company. It is calculated based on the liquid assets and current liabilities; a company has in an accounting period.

Return on Equity: Return on equity represents the amount earned as return by equity share holders; it can be calculated by dividing earnings available for equity share holders to total equity capital.

Explanation of Solution

Computation of return on equity

Items required for the calculation of return on equity are net income and common equity.

Given,

Net income is $15,000.

Common equity is $200,000.

Formula to calculate return on equity ratio,

$\text{ROE}=\frac{\text{Net}\text{income}}{\text{Common}\text{equity}}$

Where,

• ROE is return on equity.

Substitute $15,000 for net income and $200,000 for common equity in the above formula,

$\begin{array}{c}\text{ROE}=\frac{\$15,000}{\$200,000}\\ =0.075\end{array}$

Hence, the return on equity is 0.075 or 7.5%.

Compute the quick ratio

Given,

The current assets are $210,000.

The inventories are $150,000.

The current liabilities are $50,000.

Formula to compute quick ratio,

$\text{Quick}\text{ratio}=\frac{\text{Current}\text{assets}-\text{Inventories}}{\text{Current}\text{liabilities}}$

Substitute $210,000 for current assets, $150,000 for inventories and $50,000 for current liabilities in the above formula,

$\begin{array}{c}\text{Quick}\text{ratio}=\frac{\text{\$210,000}-\text{\$150,000}}{\text{\$50,000}}\\ =\frac{\$60,000}{\$50,000}\\ =1.2\text{times}\end{array}$

The quick ratio is 1.2 times.

In order to compute new quick ratio, old current ratio, new current assets and new return on equity need to calculate.

Computation of old current ratio

The items required for the calculation of current ratio are current liabilities and current assets.

Given,

Current assets are $210,000.

Current liabilities are $50,000.

Formula to calculate current ratio,

$\text{Current}\text{ratio}=\frac{\text{Current}\text{assets}}{\text{Current}\text{liabilities}}$

Substitute $210,000 for current assets and $50,000 for current liabilities in the above formula,

$\begin{array}{c}\text{Current}\text{ratio}=\frac{\$210,000}{\$50,000}\\ =4.2\text{times}\end{array}$

Hence, old current ratio is 4.2 times.

The new current ratio which is required to take is 2.5 times.

Compute the change in assets due to the current ratio as 2.5 times.

The current liabilities are $50,000. (Given)

The current ratio is 2.5 times.

Formula to calculate new current assets derives from the formula of current ratio,

$\begin{array}{c}\text{Current}\text{ratio}=\frac{\text{Current}\text{assets}}{\text{Current}\text{liabilities}}\\ \text{Current}\text{assets}=\text{Current}\text{ratio}\times \text{Current}\text{liabilities}\end{array}$

Substitute $50,000 for current liabilities and 2.5 for current ratio in the above formula,

$\begin{array}{c}\text{Current}\text{assets}=2.5\times \$50,000\\ =\$125,000\end{array}$

The new current assets are $125,000.

The difference between the currents assets refers the value of sold inventory.

Compute the sold inventory due to change in current assets

The current assets are $210,000. (Given)

The new current assets are $125,000. (Calculated)

Formula to calculate the sold inventory,

$\text{Sold}\text{inventory}=\text{Old}\text{current}\text{assets}-\text{New}\text{current}\text{assets}$

Substitute $210,000 for old current assets and $125,000 for new current assets in the above formula,

$\begin{array}{c}\text{Sold}\text{inventory}=\$210,000-\$125,000\\ =\$85,000\end{array}$

The value of inventor is curtailed by the $85,000.

Compute the balance inventory

The total inventory is $150,000. (Given)

The sold inventory is $85,000. (Calculated)

Formula to calculate the balance inventory,

$\text{Balance}\text{Inventory}=\text{Inventory}-\text{Sold}\text{Inventory}$

Substitute $150,000 for inventory and $85,000 for sold inventory in the above formula,

$\begin{array}{c}\text{Balance}\text{inventory}=\$150,000-\$85,000\\ =\$65,000\end{array}$

The balanced inventory is $65,000.

Due to the sale the cash balance would also decrease by 65,000.

Computation of cash balance after the sale of inventory

Cash balance is $10,000.

The sale of inventory is $65,000.

Formula to calculate the new cash balance,

$\text{New}\text{cash}\text{balance}=\text{Old}\text{cash balance}-\text{Sold}\text{inventory}$

Substitute $10,000 for old balance and $65,000 for sold inventory in the above formula,

$\begin{array}{c}\text{New}\text{cash}\text{balance}=\$65,000-\$10,000\\ =\$55,000\end{array}$

The cash balance after the sale of inventory is $55,000.

From the cash balance after sale of inventory, equity can be bought back. So the level of cash balance will reduce and equity will reduce by $65,000.

Compute the reduced equity:

The equity balance is $200,000. (Given)

The buyback equity share is $65,000. (Calculated)

Formula to calculate the reduced capital,

$\text{Reduced}\text{equity}\text{shares}=\text{Total}\text{equity}\text{shares}-\text{Buyback}\text{shares}$

Substitute $200,000 for total equity shares and $65,000 for buyback shares in the above formula,

$\begin{array}{c}\text{Reduced}\text{equity}\text{shares}=\$200,000-\$65,000\\ =\$135,000\end{array}$

The reduced equity shares are $135,000.

Compute the new return on equity

The net income is $15,000. (Given)

The equity value is $135,000. (Calculated)

Formula to calculate the return on equity,

$\text{ROE}=\frac{\text{Net}\text{income}}{\text{Common}\text{equity}}$

Where,

• ROE is return on equity.

Substitute $15,000 for net income and $135,000 for common equity in the above formula,

$\begin{array}{c}\text{ROE}=\frac{\$15,000}{\$135,000}\\ =0.1111\end{array}$

Hence, the return on equity is 0.1111 or 11.11%.

Compute the new quick ratio

The new current assets are $125,000.

The new inventories are $65,000.

The current liabilities are $50,000.

Formula to calculate quick ratio,

$\text{Quick}\text{ratio}=\frac{\text{Current}\text{assets}-\text{Inventories}}{\text{Current}\text{liabilities}}$

Substitute $125,000 for current assets, $65,000 for inventories and $50,000 for current liabilities in the above formula,

$\begin{array}{c}\text{Quick}\text{ratio}=\frac{\text{\$125,000}-\text{\$65,000}}{\text{50,000}}\\ =\frac{\$60,000}{\$50,000}\\ =1.2\text{times}\end{array}$

The new quick ratio is 1.2 times.

Quick ratio has remained same as there is no other current asset has changed except inventory and inventory is not the part of the terms used for the calculation of quick ratio.

Conclusion

Hence, the change in return on equity is 11.11% and there is no change in quick ratio and it is 1.2 times.