Chapter 13, Problem 3CP

To determine

Compute the given ratios of Company AEO and Company UO and compare those ratios

Answer to Problem 3CP

Compute the given ratios of the Company AEO and Company UO.

		Company AEO		Company UO
Ratio	Formula	Calculation	Result	Calculation	Result
Return on Equity (ROE)	$\frac{\text{Net}\text{Income}}{\text{Average}\text{Total}\text{Stockholder'}\text{Equity}}$	$\frac{\$151,705}{\left(\$1,416,851+\$1,351,071\right)÷2}$	11%	$\frac{\$185,251}{\left(\$1,066,268+\$1,411,548\right)÷2}$	15%
Earnings per share (EPS)	$\frac{\text{Net}\text{Income}}{\left(\begin{array}{l}\text{Weighted Average Number of }\\ \text{common Shares Outstanding}\end{array}\right)}$	As given in income statement	$0.78	As given in income statement	$1.20
Net profit margin	$\frac{\text{Net}\text{Income}}{\text{Net Sales Revenue}}$	$\frac{\$151,705}{\$3,159,818}$	4.8%	$\frac{\$185,251}{\$2,473,801}$	7.5%
Inventory turnover	$\frac{\text{Cost of Goods Sold}}{\text{Average Inventory}}$	$\frac{\$2,031,477}{\left(\$378,426+\$301,208\right)÷2}$	6.0 times	$\frac{\$1,613,265}{\left(\$250,073+\$229,561\right)÷2}$	6.7 times
Current ratio	$\frac{\text{Current}\text{Assets}}{\text{Current}\text{Liabilities}}$	$\frac{\$1,287,488}{\$405,401}$	3.2 times	$\frac{\$596,992}{\$233,466}$	2.6 times
Debt-to-equity ratio	$\frac{\text{Total}\text{Liabilities}}{\text{Total}\text{Stockholder's}\text{Equity}}$	$\frac{\$405,401+\$128,550}{\$1,139,746}$	0.38 times	$\frac{\$417,440}{\$1,066,268}$	0.39 times
Price/Earnings (P/E) ratio	$\frac{\text{Market Price per Share}}{\text{Earnings}\text{per Share}}$	$\frac{\$20}{\$0.78}$	25.6  times	$\frac{\$35}{\$1.2}$	29.2 times
Dividend yield ratio	$\frac{\text{Dividend per Share}}{\text{ Market Price per Share}}$	$\frac{\$0.44}{\$20}$	2.2%	No dividends were paid	0%

Table (1)

Compare the ratios of Company AEO and UO.

	Company AEO	Company UO	Industry Average
Return on equity	11.0%	15.0%	13.6%
Earnings per share	$0.78	$1.20	N/A
Net profit margin	4.8%	7.5%	5.4%
Inventory turnover	3.2	2.6	2.7
Current ratio	6.0	6.7	4.9
Debt-to-Equity	0.38	.39	.70
Price earnings	25.6	29.2	16.1
Dividend yield	2.2%	0%	1.5%

Table (1)

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.

$\text{Return on Equity}\text{=}\frac{\text{Net}\text{Income}}{\text{Average}\text{Total}\text{Stockholder'}\text{Equity}}$

Return on equity of the Company AEO is 11.0% and the Company UO is 15.0 %.

Earnings per share:

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.

$\text{EPS}\text{=}\frac{\text{Net}\text{Income}}{\left(\text{Weighted Average Number of common Shares Outstanding}\right)}$

The earnings per share of the Company AEO are $0.78 and the Company UO is $1.20.

Profit margin:

Profit margin ratio is used to determine the percentage of net income that is being generated per dollar of revenue or sales.

$\text{Net profit margin}\text{=}\frac{\text{Net}\text{Income}}{\text{Net Sales Revenue}}$

Net profit margin of the Company AEO is 4.8% and the Company UO is 7.5%.

Inventory turnover ratio:

Inventory turnover ratio is used to determine the number of times inventory used or sold during the particular accounting period.

$\text{Inventory Turnover Ratio =}\frac{\text{Cost of Goods Sold }}{\text{Average Inventory}}$

Inventory turnover ratio of the Company AEO is 6.0 and the Company UO is 6.7%.

Current ratio:

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

$\text{Current ratio}\text{=}\frac{\text{Current}\text{Assets}}{\text{Current}\text{Liabilities}}$

Current ratio of the Company AEO is 3.2 and the Company UO is 2.6 times.

Debt-equity ratio:

The debt-to-equity ratio indicates that the company’s debt as a proportion of its stockholders’ equity.

$\text{Debt-equity ratio}\text{=}\frac{\text{Total}\text{Liabilities}}{\text{Total}\text{Stockholder's}\text{Equity}}$

Debt-to-Equity ratio of the Company AEO is 0.38 and the Company UO is 0.39 times.

Price/Earnings Ratio: It depicts the relation of market price of a share to earnings per share of that company. The price/earnings ratio presents 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.

$\text{Price/Earnings Ratio}\text{=}\frac{\text{Market Price per Share }}{\text{Earnings per Share}}$

Price/Earnings ratio of the Company AEO is 25.6 and the Company UO is 29.2 times.

Dividend yield: This is the ratio which measures the amount of dividends paid relative to the market price.

$\text{Dividend Yield Ratio}\text{=}\frac{\text{Dividends per Share}}{\text{ Market Price per Share}}$

Dividend yield ratio of the Company AEO is 2.2% and the Company UO is nil.

The above ratio analysis indicates that the Company UO is performing above the industry average and Company AEO is under performing the industry average. Since the price earnings’ ratio of company AEO is high, the investors have high expectations on the future performance of Company AEO than Company UO.