Chapter 5, Problem 5.15P

Requirement – 1

To determine

Financial ratio:

The financial ratios examine the performance of the company, and used in comparing own business with other same business. It indicates the relationship of two or more items of financial statements.

To determine:  The Company that appears more efficient in collecting its accounts receivable and managing its inventory out of the two companies. 

Explanation of Solution

Calculations of ratios are as follows:

Company	Inventory turnover ratio	Average collection period	Inventory turnover ratio	Average days in inventory
J	6.37 times (1)	57 days (3)	3.39 times (5)	108  days (7)
P	5.15 times (2)	71days (4)	1.68 times (6)	217  days (8)

Table (1)

Working Notes:

1. Calculate the accounts receivable turnover ratio for Company J.

$\begin{array}{c}\text{Accounts Receivable Turnover Ratio = }\frac{\text{Net credit sales}}{\text{Average accounts receivable}}\\ \text{ = }\frac{\$41,862}{\text{\$6,574}}\\ \text{ = 6}\text{.37 Times}\\ \end{array}$ (1)

2. Calculate the accounts receivable turnover ratio for Company P.

$\begin{array}{c}\text{Accounts Receivable Turnover Ratio = }\frac{\text{Net credit sales}}{\text{Average accounts receivable}}\\ \text{=}\frac{\$45,188}{\$8,775}\\ \text{=5}\text{.15}\text{times }\end{array}$ (2)

3. Calculate the Average collection period for Company J.

$\begin{array}{c}\text{Average collection period = }\frac{\text{Days in accounting period}}{\text{ Receivables turnover}}\\ \text{ = }\frac{365}{6.37}\\ =57\text{Days}\end{array}$ (3)

4. Calculate the Average collection period for Company P.

$\begin{array}{c}\text{Average collection period = }\frac{\text{Days in accounting period}}{\text{ Receivables turnover}}\\ \text{ = }\frac{365}{5.5}\\ =71\text{Days}\end{array}$ (4)

5. Calculate the inventory turnover ratio for Company J.

$\begin{array}{c}\text{ Inventory Turnover Ratio = }\frac{\text{Cost of goods sold}}{\text{Average Inventory}}\\ \text{ = }\frac{\$12,176}{\$3,588}\\ =3.39\text{Times}\end{array}$ (5)

6. Calculate the inventory turnover ratio for Company P.

$\begin{array}{c}\text{Inventory Turnover Ratio = }\frac{\text{Cost of goods sold}}{\text{Average Inventory}}\\ \text{ = }\frac{\text{\$9,832}}{\$5,837}\\ =1.68\text{Times}\end{array}$ (6)

7. Calculate the average days in inventory for Company J.

$\begin{array}{c}\text{Average days in inventory = }\frac{\text{Days in accounting period}}{\text{Inventory Turnover}}\\ =\frac{\text{365}}{\text{3}\text{.39}}\\ =108\text{ Days}\end{array}$ (7)

8. Calculate the average days in inventory for Company P.

$\begin{array}{c}\text{Average days in inventory = }\frac{\text{Days in accounting period}}{\text{Inventory Turnover}}\\ \text{ = }\frac{365}{1.68}\\ =217\text{Days}\end{array}$ (8)

Conclusion

• Based on Accounts receivable ratio, the Company J collects their credit receivables within 57 days which is less than 14 days of Company P. Hence, Company J is preferable.
• Based on Inventory turnover ratio, Company J sells its inventory twice more than Company P. Hence, the Company J is preferable.

Requirement – 2

To determine

The Company that appears more efficient in greater earnings.

Explanation of Solution

Return on assets

It evaluates the efficiency of company’s assets. It reports the profit earned as the percentage of total assets used in the business. A company’s rate of return on total assets reflects its ability to optimize the use of total assets.

Company	Rate of Return on Assets
J	14.90% (9)
p	1.40% (10)

Table (2)

Working Notes:

1. Calculate the Rate of return on assets for Company J.

$\begin{array}{c}\text{Rate on return of assets = }\frac{\text{Net income}}{\text{Total assets}}\\ \text{ = }\frac{\text{\$7,197}}{\$48,263}\\ =14.90\%\end{array}$ (9)

2. Calculate the Rate of return on assets for Company P.

$\begin{array}{c}\text{Rate on return of assets = }\frac{\text{Net income}}{\text{Total assets}}\\ \text{ = }\frac{\text{\$1,639}}{\$116,775}\\ =1.4\%\end{array}$ (10)

Conclusion

Return on assets reports the overall profitability of the company. In this case, Company J has higher rate of profitability compared to Company P.

Requirement – 3

To determine

The more efficient company in respective of rate of return on assets with similar combination of profit margin and turnover.

Explanation of Solution

Profit Margin:

Profit margin reflects the portion of net income in the net sales. It is a profitability measure tool that is used to evaluate the net income a business earns on every dollar of net sales.

Company	Rate of Return on Assets
J	14.90% (11)
p	1.40% (12)

Table (3)

Working Notes:

1. Calculate the rate of return on assets for Company J.

$\begin{array}{c}\text{Rate of return on assets = Profit Margin }\times \text{ Asset Turnover}\\ \text{= }\frac{\text{Net income}}{\text{Net sales}}\times \frac{\text{Net sales}}{\text{Total assets}}\\ =\frac{\$7,197}{\text{\$41,862}}\times \frac{\text{\$41,862}}{\text{\$48,263}}\\ =\text{}17.19\%\times 0.867\text{Times}\\ \text{=}\text{14}\text{.9\%}\end{array}$ (11)

2. Calculate the rate of return on assets for Company P.

$\begin{array}{c}\text{Rate of return on assets = Profit Margin }\times \text{ Asset Turnover}\\ \text{= }\frac{\text{Net income}}{\text{Net sales}}\times \frac{\text{Net sales}}{\text{Total assets}}\\ =\frac{\text{\$1,639}}{\text{\$45,188}}\times \frac{\$45,188}{\text{\$116,775}}\\ =3.63\%\times 0.387\text{Times}\\ \text{=1}\text{.4\%}\end{array}$ (12)

Conclusion

In this case, the profit margin and assets turnover for Company J is comparatively higher than Company P; hence Company J is more efficient.

Requirement – 4

To determine

The Company that appears more efficient in higher rate of return.

Explanation of Solution

Company	Rate of return on shareholders' equity
J	26.80% (13)
p	2.50% (14)

Table (4)

Working Notes:

Calculate the Rate of return on shareholders’ equity for J.

$\begin{array}{c}\text{Rate of return on sharedolders' equity = }\frac{\text{Net income}}{\text{Shareholders' equity}}\\ =\frac{\$7,197}{\$26,869}\\ =26.8\%\end{array}$ (13)

Calculate the Rate of return on shareholders’ equity for P.

$\begin{array}{c}\text{Rate of return on sharedolders' equity = }\frac{\text{Net income}}{\text{Shareholders' equity}}\\ =\frac{\text{\$1,639}}{\$65,377}\\ =\text{}\text{}\text{}\text{}2.5\%\end{array}$ (14)

Conclusion

In this case, Company J provides higher rate of return on shareholders’ equity compared to Company P; hence Company J is more efficient.

Requirement – 5

To determine

The Company that appears more efficient in equity multiplier.

Explanation of Solution

Equity multiplier shareholders’ equity

Equity multiplier shareholders’ equity is used to measure the company’s financial leverage. If equity multiplier ratio is high it indicates high debt, if the ratio is low it indicates low debt to the company.

$\text{Equity multiplier shareholders equity = }\frac{\text{Total assets}}{\text{Shareholders' equity}}$

Company	Equity multiplier shareholders' equity
J	1.80 (15)
p	1.79 (16)

Table (5)

Working Notes:

1. Calculate the equity multiplier shareholders’ equity for Company J.

$\begin{array}{c}\text{Equity multiplier shareholders' equity = }\frac{\text{Total Assets}}{\text{Sharedolders' equity}}\\ =\frac{\text{\$48,263}}{\$26,869}\\ =1.80\end{array}$ (15)

2. Calculate the equity multiplier shareholders’ equity for Company P.

$\begin{array}{c}\text{}\text{Equity multiplier shareholders' equity = }\frac{\text{Total Assets}}{\text{Sharedolders' equity}}\\ \text{ =}\frac{\text{\$116,775}}{\text{\$65,377}}\\ =1.79\end{array}$ (16)

Conclusion

In this case, both the companies are having similar equity multipliers; it indicates both the companies’ equities are higher than the return on assets.