Chapter 13, Problem 13.6CP

1)

To determine

The Net profit margin ratio for Company A and Company B

Explanation of Solution

Net Profit margin Ratio:

This ratio gauges the operating profitability by quantifying the amount of income earned from business operations from the sales generated.

Following is the calculation of Net profit margin ratio for Company A

$\begin{array}{c}\text{Net}\text{profit}\text{margin}\text{ratio=}\frac{\text{Net}\text{income}}{\text{Revenues}}\text{×100}\\ \text{=}\frac{\text{\$45,000}}{\text{\$450,000}}\text{×100}\\ \text{=10\%}\end{array}$

Following is the calculation of Net profit margin ratio for Company B

$\begin{array}{c}\text{Net}\text{profit}\text{margin}\text{ratio=}\frac{\text{Net}\text{income}}{\text{Revenues}}\text{×100}\\ \text{=}\frac{\text{\$90,000}}{\text{\$810,000}}\text{×100}\\ \text{=11}\text{.11\%}\end{array}$

Thus, the net profit margin ratio for Company A and Company B is 10% and 4.3%

To determine

The Gross profit percentage ratio for Company A and Company B

Explanation of Solution

Gross Profit Percentage:

Gross profit is the financial ratio that shows the relationship between the gross profit and net sales. It represents gross profit as a percentage of net sales. Gross Profit is the difference between the net sales revenue, and the cost of goods sold. It can be calculated by dividing gross profit and net sales.

Following is the calculation of Gross profit percentage ratio for Company A

$\begin{array}{c}\text{Gross}\text{profit}\text{percentage}\text{ratio=}\frac{\left(\begin{array}{l}\text{Net}\text{sales}\text{revenue-}\\ \text{cost}\text{of}\text{goods}\text{sold}\end{array}\right)}{\text{Net}\text{sales}\text{revenue}}\text{×100}\\ \text{=}\frac{\left(\text{\$450,000-\$245,000}\right)}{\text{\$450,000}}\text{×100}\\ \text{=}\frac{\text{\$205,000}}{\text{\$450,000}}\text{×100}\\ \text{=45}\text{.56\%}\end{array}$

Following is the calculation of Gross profit percentage ratio for Company B

$\begin{array}{c}\text{Gross}\text{profit}\text{percentage}\text{ratio=}\frac{\left(\begin{array}{l}\text{Net}\text{sales}\text{revenue-}\\ \text{cost}\text{of}\text{goods}\text{sold}\end{array}\right)}{\text{Net}\text{sales}\text{revenue}}\text{×100}\\ \text{=}\frac{\left(\text{\$810,000-\$405,000}\right)}{\text{\$810,000}}\text{×100}\\ \text{=}\frac{\text{\$405,000}}{\text{\$810,000}}\text{×100}\\ \text{=50\%}\end{array}$

Thus, the gross profit percentage ratio for Company A and Company B is 45.56% and 50%

To determine

The fixed asset turnover ratio for Company A and Company B

Explanation of Solution

Fixed Asset turnover:

Fixed asset turnover is a ratio that measures the productive capacity of the fixed assets to generate the sales revenue for the company. Thus, it shows the relationship between the net sales and the average total fixed assets.

Following is the fixed asset turnover ratio for Company A

$\begin{array}{c}\text{Fixed}\text{asset}\text{trunover=}\frac{\text{Net}\text{revenue}}{\text{Average}\text{net}\text{fixed}\text{assets}}\\ \text{=}\frac{\text{\$450,000}}{\text{\$180,000}}\\ \text{=2}\text{.50}\end{array}$

Following is the fixed asset turnover ratio for Company B

$\begin{array}{c}\text{Fixed}\text{asset}\text{trunover=}\frac{\text{Net}\text{revenue}}{\text{Average}\text{net}\text{fixed}\text{assets}}\\ \text{=}\frac{\text{\$810,000}}{\text{\$300,000}}\\ \text{=2}\text{.70}\end{array}$

Thus, the fixed asset turnover ratio for company A and company B IS 2.50 and 2.70

To determine

The return on equity ratio for Company A and Company B

Explanation of Solution

Return on equity ratio:

Rate of return on equity ratio is used to determine the relationship between the net income available for the common stockholders’ and the average common equity that is invested in the company.

Following is the return on equity ratio for the Company A

$\begin{array}{c}\text{Return}\text{on}\text{equity=}\frac{\left(\begin{array}{l}\text{Net}\text{income-}\\ \text{preferred}\text{dividends}\end{array}\right)}{\text{Average}\text{common}\text{stockholders'}\text{equity}}\text{×100}\\ \text{=}\frac{\left(\text{\$45,000-0}\right)}{\text{\$355,500(1)}}\text{×100}\\ \text{=19}\text{.11\%}\end{array}$

Working note:

Calculate the average stockholders’ equity

$\begin{array}{c}\text{Average}\text{common}\text{stockholders'}\text{equity=}\frac{\left(\begin{array}{l}\text{Opening}\text{common}\text{stockholders'}\text{equity+}\\ \text{Closing}\text{common}\text{stock}\text{holders'}\text{equity}\end{array}\right)}{\text{2}}\\ \text{=}\frac{\text{\$231,000+\$240,000}}{\text{2}}\\ \text{=\$235,500}\end{array}$ (1)

Following is the return on equity ratio for the Company B

$\begin{array}{c}\text{Return}\text{on}\text{equity=}\frac{\left(\begin{array}{l}\text{Net}\text{income-}\\ \text{preferred}\text{dividends}\end{array}\right)}{\text{Average}\text{common}\text{stockholders'}\text{equity}}\text{×100}\\ \text{=}\frac{\left(\text{\$90,000-0}\right)}{\text{\$410,000(2)}}\text{×100}\\ \text{=21}\text{.95\%}\end{array}$

Working note:

$\begin{array}{c}\text{Average}\text{common}\text{stockholders'}\text{equity=}\frac{\left(\begin{array}{l}\text{Opening}\text{common}\text{stockholders'}\text{equity+}\\ \text{Closing}\text{common}\text{stock}\text{holders'}\text{equity}\end{array}\right)}{\text{2}}\\ \text{=}\frac{\text{\$440,000+\$380,000}}{\text{2}}\\ \text{=\$410,000}\end{array}$ (2)

Thus, the return on equity ratio for Company A and Company B is 19.11% and 21.95%

To determine

The earnings per share ratio of Company A and Company B

Explanation of Solution

Earnings per share ratio:

Earnings per share help to measure the profitability of a company. Earnings per share are the amount of profit that is allocated to each share of outstanding stock.

Following is the Earnings per share ratio of Company A

$\begin{array}{c}\text{Earnings}\text{per}\text{share}\text{ratio=}\frac{\text{\$45,000}}{\text{15,000shares(3)}}\\ \text{=\$3}\end{array}$

Working note:

Calculate the number of shares outstanding for company A

$\text{Number}\text{of}\text{shares}\text{outstanding=}\frac{\text{Total}\text{value}\text{of}\text{common}\text{stock}}{\begin{array}{l}\text{Par}\text{value}\text{of}\text{each}\text{stock}\\ \text{=}\frac{\text{\$150,000}}{\text{\$10}}\\ \text{=\$15,000}\end{array}}$ (3)

Following is the Earnings per share ratio of Company B

$\begin{array}{c}\text{Earnings}\text{per}\text{share}\text{ratio=}\frac{\text{\$90,000}}{\text{20,000shares(4)}}\\ \text{=\$4}\text{.50}\end{array}$

Working note:

Calculate the number of shares outstanding for Company B

$\text{Number}\text{of}\text{shares}\text{outstanding=}\frac{\text{Total}\text{value}\text{of}\text{common}\text{stock}}{\begin{array}{l}\text{Par}\text{value}\text{of}\text{each}\text{stock}\\ \text{=}\frac{\text{\$200,000}}{\text{\$10}}\\ \text{=\$20,000}\end{array}}$ (3)

Thus, the Earnings per share ratio of Company A and Company B is $3 and $4.50

To determine

The price/Earnings ratio of Company A and Company B

Explanation of Solution

Price/Earnings Ratio:

The price/earnings ratio shows the market value of the amount invested to earn $1 by a company. It is major tool to be used by investors before the decisions related to investments in a company.

Following is the price/earnings ratio of Company A

$\begin{array}{c}\text{Price/Earnings}\text{ratio=}\frac{\text{Stock}\text{price}}{\text{Earnings}\text{per}\text{share}}\\ \text{=}\frac{\text{\$18}}{\text{\$3}}\\ \text{=6}\end{array}$

Following is the price/earnings ratio of Company B

$\begin{array}{c}\text{Price/Earnings}\text{ratio=}\frac{\text{Stock}\text{price}}{\text{Earnings}\text{per}\text{share}}\\ \text{=}\frac{\text{\$27}}{\text{\$4}\text{.50}}\\ \text{=6}\end{array}$

Thus, the price/earnings ratio of Company A and Company B is 6 and 6

To determine

The receivables turnover ratio for Company A

Explanation of Solution

Receivables turnover ratio:

Receivables turnover ratio is mainly used to evaluate the collection process efficiency. It helps the company to know the number of times the accounts receivable is collected in a particular time period. This ratio is determined by dividing credit sales and sales return.

Following is the receivables turnover ratio for Company A

$\begin{array}{c}\text{Receivables}\text{turnover}\text{ratio=}\frac{\text{Net}\text{sales}\text{revenue}}{\text{Average}\text{net}\text{receivables}}\\ \text{=}\frac{\text{\$450,000}}{\text{\$30,000(5)}}\\ \text{=15}\end{array}$

Following is the number of days a company A takes to collect accounts receivables.

$\begin{array}{c}\text{Days}\text{to}\text{collect=}\frac{\text{365}}{\text{Receivables}\text{turnover}\text{ratio}}\\ \text{=}\frac{\text{365}}{\text{15}\text{.0}}\\ \text{=24}\text{.33}\end{array}$

Working note:

Calculate the average net receivables

$\begin{array}{c}\text{Average}\text{net}\text{receivables=}\frac{\left(\begin{array}{l}\text{Opening}\text{net}\text{receivables+}\\ \text{Closing}\text{net}\text{receivables}\end{array}\right)}{\text{2}}\\ \text{=}\frac{\text{\$20,000+\$40,000}}{\text{2}}\\ \text{=\$30,000}\end{array}$ (5)

Following is the receivables turnover ratio for Company B

$\begin{array}{c}\text{Receivables}\text{turnover}\text{ratio=}\frac{\text{Net}\text{sales}\text{revenue}}{\text{Average}\text{net}\text{receivables}}\\ \text{=}\frac{\text{\$810,000}}{\text{\$34,000(6)}}\\ \text{=23}\text{.82}\end{array}$

Following is the number of days a company B takes to collect accounts receivables.

$\begin{array}{c}\text{Days}\text{to}\text{collect=}\frac{\text{365}}{\text{Receivables}\text{turnover}\text{ratio}}\\ \text{=}\frac{\text{365}}{23.82}\\ \text{=15}\text{.32}\end{array}$

Thus, the receivables turnover ratio for company A and company b is 15 and 23.82

To determine

The inventory turnover ratio for Company A and Company B

Explanation of Solution

Inventory Turnover Ratio:

This ratio is a financial metric used by a company to quantify the number of times inventory is used or sold during the accounting period.

Following is the inventory turnover ratio for Company A

$\begin{array}{c}\text{Inventory}\text{turnover}\text{ratio=}\frac{\text{Cost}\text{of}\text{goods}\text{sold}}{\text{Average}\text{inventory}}\\ \text{=}\frac{\text{\$245,000}}{\text{\$96,000(7)}}\\ \text{=2}\text{.55}\end{array}$

Following is the number of days a company A takes to sell its inventory

$\begin{array}{c}\text{Days}\text{to}\text{sell=}\frac{\text{365}}{\text{Inventory}\text{turnover}\text{ratio}}\\ \text{=}\frac{\text{365}}{\text{2}\text{.55}}\\ \text{=143}\text{.14}\end{array}$

Working note:

Calculate the average inventory

$\begin{array}{c}\text{Average}\text{inventory=}\frac{\left(\begin{array}{l}\text{Opening}\text{inventory+}\\ \text{Closing}\text{inventory}\end{array}\right)}{\text{2}}\\ \text{=}\frac{\text{\$92,000+\$100,000}}{\text{2}}\\ \text{=}\frac{\text{\$192,000}}{\text{2}}\\ \text{=\$96,000}\end{array}$ (7)

Following is the inventory turnover ratio for Company B

$\begin{array}{c}\text{Inventory}\text{turnover}\text{ratio=}\frac{\text{Cost}\text{of}\text{goods}\text{sold}}{\text{Average}\text{inventory}}\\ \text{=}\frac{\text{\$405,000}}{\text{\$42,500(8)}}\\ \text{=9}\text{.53}\end{array}$

Following is the number of days a company B takes to sell its inventory

$\begin{array}{c}\text{Days}\text{to}\text{sell=}\frac{\text{365}}{\text{Inventory}\text{turnover}\text{ratio}}\\ \text{=}\frac{\text{365}}{9.53}\\ \text{=38}\text{.30}\end{array}$

Working note:

Calculate the average inventory

$\begin{array}{c}\text{Average}\text{inventory=}\frac{\left(\begin{array}{l}\text{Opening}\text{inventory+}\\ \text{Closing}\text{inventory}\end{array}\right)}{\text{2}}\\ \text{=}\frac{\text{\$45,000+\$40,000}}{\text{2}}\\ \text{=}\frac{\text{\$85,000}}{\text{2}}\\ \text{=\$42,500}\end{array}$ (8)

To determine

The current ratio of Company A

Explanation of Solution

Current ratio:

Current ratio is used to determine the relationship between current assets and current liabilities. The ideal current ratio is 2:1.

Following is the current ratio of Company A

$\begin{array}{c}\text{Current}\text{ratio=}\frac{\text{Current}\text{assets}}{\text{Current}\text{liabilities}}\\ \text{=}\frac{\text{\$175,000(9)}}{\text{\$100,000}}\\ \text{=1}\text{.75}\end{array}$

Working note:

Calculate the current assets of Company A

$\begin{array}{c}\text{Current}\text{assets=Cash+Accounts}\text{receivables+Inventory}\\ \text{=\$35,000+\$40,000+\$100,000}\\ \text{=\$175,000}\end{array}$ (9)

Following is the current ratio of Company B

$\begin{array}{c}\text{Current}\text{ratio=}\frac{\text{Current}\text{assets}}{\text{Current}\text{liabilities}}\\ \text{=}\frac{\text{\$92,000(10)}}{\text{\$50,000}}\\ \text{=1}\text{.84}\end{array}$

Working note:

Calculate the current assets of Company B

$\begin{array}{c}\text{Current}\text{assets=Cash+Accounts}\text{receivables+Inventory}\\ \text{=\$22,000+\$30,000+\$40,000}\\ \text{=\$92,000}\end{array}$ (10)

Thus, the current ratio of Company A and Company B is 1.75 and 1.84

To determine

The debt-to-assets ratio of Company A and Company B

Explanation of Solution

Debt to Asset Ratio:

Debt to asset ratio is the ratio between total asset and total liability of the company. Debt ratio reflects the finance strategy of the company. It is used to evaluate company’s ability to pay its debts. Higher debt ratio implies the higher financial risk.

Following is the debt-to-asset ratio of Company A

$\begin{array}{c}\text{Debt-to-asset}\text{ratio=}\frac{\text{Total}\text{liabilities}}{\text{Total}\text{assets}}\\ \text{=}\frac{\text{\$160,000}}{\text{\$400,000}}\\ \text{=0}\text{.40}\end{array}$

Following is the debt-to-asset ratio of Company B

$\begin{array}{c}\text{Debt-to-asset}\text{ratio=}\frac{\text{Total}\text{liabilities}}{\text{Total}\text{assets}}\\ \text{=}\frac{\text{\$420,000}}{\text{\$800,000}}\\ \text{=0}\text{.53}\end{array}$

Thus, the debt-to-asset ratio of Company A and Company B is 0.40 and 0.53

2)

To determine

To prepare: Comparative written evaluation of ratio analyses between the two companies and to conclude with own recommendation of choices.

Explanation of Solution

The difference of amount for the Company A and Company B is not given so evaluation of ratio analysis is not possible . But, it is assumed that amount of slight differences are minor.

Following is the comparative evaluation of profitability ratio analyses for the current year

Particulars	Company A	Company B
Net profit margin ratio	10%	11.11%
Gross profit percentage ratio	45.56%	50%
Fixed asset turnover ratio	2.50	2.70
Earnings per share	$3	$4.50
Return on equity	19.11%	21.95%

Table (1)

From the above table it is concluded that Company B is more profitable that Company A as its profitability ratios are higher for the current year