Chapter 13, Problem 6.1GAP

To determine

Introduction:

Accounting ratio helps in comparing two or more financial data of the financial statements of the company. It is used by various parties to measure the performance of the companies.

To find:

All the possible ratios.

Answer to Problem 6.1GAP

		Company R	Company C
1	Net profit margin	10.0%	12.50%
2	Gross profit percentage	40.00%	46.42%
3	Fixed asset turnover	1.45	1.75
4	Return on equity	14.54	16.82
5	Earnings per share	$3.33	$3.33
6	P/E ratio	$4.20	$3.30
7	Account receivable turnover ratio	15.68	18.66
8	Inventory turnover ratio	4.68	4.76
9	Current ratio	2.75	8.80
10	Debt-to-assets ratio	2.28	2.92

Explanation of Solution

1. Profit margin ratio is calculated by dividing net income by the net sales. It helps in calculating the net income as a percentage of revenue.

Formula used:

$\text{Profit margin ratio}=\frac{Net\text{ income}}{\begin{array}{l}Total\text{ revenue}\\ \end{array}}\times 100$

	Company R	Company C
Net income	$80,000	$35,000
Total revenue	$800,000	$280,000
Net profit margin	10.0%	12.50%

2. Gross profit percentage helps the company to compare gross margin to the net sales. This ratio tells the profitability at which company sells its inventory.

Formula used:

$\text{Gross profit percentage}=\frac{Netsales-COGS\text{ or }(Gross\text{ profit)}}{Netsales}\times 100$

	Company R	Company C
Net sales (1)	$800,000	$280,000
COGS (2)	$480,000	$150,000
Gross profit (1 − 2)	$320,000	$130,000
Gross profit percentage	40.00%	46.42%

3. Asset turnover ratio calculates the ability of a company to generate sales with the fixed assets. A decline in the ratio means company has overinvested the amount in the fixed assets.

To calculate average stockholder’s equity:

$Net\text{ a}verage\text{ fixed assets}=\frac{\text{ Net fixed assets at the beginning + Net fixed assets at the end}}{2}$

The ending value of assets is taken as the values of their averages.

Formula used:

$Fixed\text{ assets turover}=\frac{Net\text{ revenue}}{Average\text{ net fixed assets}}$

	Company R	Company C
Net revenue	$800,000	$280,000
Average net fixed assets	$550,000	$160,000
Fixed asset turnover	1.45	1.75

4. Return on equity measure the profit earned using capital provided by the shareholders of a firm or in other words we can say that ROI measures the effectiveness with which a company uses the assets to create profits.

To calculate average stockholder’s equity:

$Averageequity=\frac{equity\text{ at the beginning + equity at the end}}{2}$

Formula Used to calculate return on equity:

$\text{Return }onequity=\frac{Netincome}{Average\text{ shareholder's }equity}\times 100$

	Company R	Company C
Net income	$80,000	$35,000
Average stockholder’s equity	$\begin{array}{l}=\frac{\$570,000+\$530,000}{2}\\ =\$550,000\end{array}$	$\begin{array}{l}=\frac{\$202,000+\$214,000}{2}\\ =\$208,000\end{array}$
Return on equity	14.54	16.82

• Ending equity = Capital stock + additional paid in capital

5. Earnings per share (EPS) is that part of the profit of the company which is allocated to common stock per share. Earnings per share acts as an indicator of a company's profitability.

Formula used:

$Earningpershareratio=\frac{Netincome-\text{Preferred }dividends}{Average\text{ numbers of common shares outstanding}}$

	Company R	Company C
Net income	$80,000	$35,000
Average numbers of common share outstanding.	24,000 shares (480,000÷20)	10,500 (210,000÷20)
Preferred dividends.	$0	$0
Earnings per share.	$3.33	$3.33

6. Price earnings ratio is calculated by dividing market value per share with earning per share. This ratio is used by the investors to find the value of company’s share and helps in making the comparison.

Formula used to calculate P/E ratio:

$\mathrm{P}\text{rice earning ratio=}\frac{Marketvaluepershare}{Earningpershare}$

	Company R	Company C
Market value per share	$14.00	$11.00
Earnings per share	$3.33	$3.33
P/E ratio	$4.20	$3.30

7. Receivable turnover ratio measures the number of times a company collects its accounts receivable.

To calculate Average account receivables

$Av\text{erage account receivable= }\frac{\text{Opening account receivable+ closing account receivable}}{2}$

To calculate account receivable turnover ratio:

$Accounts\text{ Receivable Turn-over ratio=}\frac{Netcreditsalesornetsales}{Averageaccount\text{ Receivable}}$

	Company R	Company C
Net credit sales or net sales	$800,000	$280,000
Average account receivables	$\begin{array}{l}=\frac{\$47,000+\$55,000}{2}\\ =\$51,000\end{array}$	$\begin{array}{l}=\frac{\$16,000+\$14,000}{2}\\ =\$15,000\end{array}$
Account receivable turnover ratio	15.68	18.66

8. Inventory turnover ratio measures the number of times a company has sold its inventory.

To calculate average inventory:

$\text{Average Inventory = }\frac{Openinginventory+cl\text{osing inventory}}{2}$

To calculate inventory turnover ratio:

$\text{Inventory turnover ratio= }\frac{\mathrm{Cos}\text{t of goods sold}}{Average\text{ inventory}}$

	Company R	Company C
Cost of goods sold	$480,000	$150,000
Average inventory	$\begin{array}{l}=\frac{\$95,000+\$110,000}{2}\\ =\$102,500\end{array}$	$\begin{array}{l}=\frac{\$38,000+\$25,000}{2}\\ =\$31,500\end{array}$
Inventory turnover ratio	4.68	4.76

9. Current ratio is the ratio of current assets to current liabilities

$Currentratio=\frac{Currentassets}{Currentliabilities}$

	Company R	Company C
Current Assets	$330,000	$132,000
Current liabilities	$120,000	$ 15,000
Current ratio	2.75	8.80

Current assets = Cash + Accounts receivable + inventory + Other assets

Current Assets of company R = $25,000 + $55,000 + $110,000 + $140,000

= $330,000

Current Assets of company C=$45,000 + $16,000 + $25,000 + 46,000

= $132,000

10. Debt-to-asset ratio calculates the proportion of total assets financed by the creditors. If the ratio is higher, it means that the financing strategy of the company is risky.

Formula used:

$Debt\text{ to total asset ratio}=\frac{Total\text{ liabilities}}{Total\text{ Asset}}$

	Company R	Company C
Total assets	$880,000	$292,000
Total liabilities (current liabilities+ Notes payable (long-term) + borrowed loan)	$385,000	$100,000
Debt-to-assets ratio	2.28	2.92