Chapter 13, Problem 5PSB

1.

To determine

To compute: (a) current ratio, (b) acid test ratio, (c) accounts receivable turnover (d) inventory turnover (e) day’s sales in inventory (f) day’s sales uncollected of F Company and B Company.

Explanation of Solution

(a)

Formula to calculate current ratio is,

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

F Company

Given info,

Current assets are $205,200.
Current liabilities are $90,500.

Substitute $205,200 for current assets and $90,500 for current liabilities.

$\begin{array}{c}\text{Current ratio}=\frac{\$205,200}{\$90,500}\\ =2.27\end{array}$

Thus, current ratio is 2.27.

Working notes:

Calculation of current assets,
$\begin{array}{c}\text{Current}\text{assets}=\left(\begin{array}{c}\text{Cash}+\text{Accounts}\text{}\text{receivable}+\text{Current notes receivable}\\ +\text{Merchasdise}\text{inventory}+\text{Prepaid}\text{expenses}\end{array}\right)\\ =\text{\$20,000}+\text{\$77,100}+\text{\$11,600}+\text{\$86,800}+\text{\$9,700}\\ =\text{\$205,200}\end{array}$

B Company

$\begin{array}{c}\text{Current ratio}=\frac{\$208,100}{\$97,000}\\ =2.15\end{array}$

Thus, current ratio is 2.15.

(b)

Formula to calculate acid test ratio is,

$\text{Acid}\text{test}\text{ratio}\text{=}\frac{\text{Cash + Short term investments + Accounts receivables}}{\text{Current}\text{Liabilities}}$

F Company:

Given,
Cash is $20,000.
Accounts receivables are $77,100
Current liabilities are $90,500.

Substitute $20,000 for cash, $77,100 for accounts receivable and $90,500 for current liabilities.

$\begin{array}{c}\text{Acid}\text{test}\text{ratio}=\frac{\text{\$20,000+\$0+\$77,100}}{\text{\$90,500}}\\ =\frac{\$97,100}{\text{\$90,500}}\\ \text{=1}\text{.07}\end{array}$

Thus, acid test ratio is 1.07

B Company:

$\begin{array}{c}\text{Acid}\text{test}\text{ratio}=\frac{\text{\$36,500+\$0+\$70,500}}{\text{\$97,000}}\\ =\frac{\$107,000}{\text{\$97,000}}\\ =\text{1}\text{.10}\end{array}$

Thus, acid test ratio is 1.10.

(c)

Formula to calculate accounts receivable turnover is,

$\begin{array}{l}\text{Accounts receivable turnover}=\frac{\text{Net}\text{sales}}{\text{Average accounts}\text{Receivable}}\\ \end{array}$

$\text{Average}\text{account}\text{receivable}=\left(\frac{\begin{array}{l}\text{account}\text{receivable in}\text{the}\text{begning}\text{of}\text{the}\text{year}+\\ \text{account}\text{receivable at}\text{the}\text{end}\text{of}\text{the}\text{year}\end{array}}{\text{2}}\right)$

F Company

Given,
Net sales are $393,600.
Accounts receivable in the beginning of the year is $72,200.
Accounts receivable at the end of the year is $77,100.

Substitute $393,600 for net sales and $72,200 for accounts receivable in the beginning of the year and $77,100 at the end of the year.

$\begin{array}{c}\text{Accounts receivable turnover}\text{=}\frac{\$393,600}{\left(\frac{\text{\$72,200+\$77,100}}{2}\right)}\\ =\frac{\$393,600}{\$74,650}\\ =5.27\end{array}$

Thus, accounts receivable turnover is 5.27.

B Company:

$\begin{array}{c}\text{Accounts receivable turnover}\text{=}\frac{\$667,500}{\left(\frac{\text{\$73,300+\$70,500}}{2}\right)}\\ =\frac{\$667,500}{\$71,900}\\ =9.28\end{array}$

Thus, accounts receivable turnover is 9.28.

(d)

Formula to calculate inventory turnover is,

$\begin{array}{l}\text{Inventory turnover}=\frac{\text{Cost}\text{of}\text{goods}\text{sold}}{\text{Average Inventory}}\\ \end{array}$

$\text{Average}\text{inventory}=\left(\frac{\begin{array}{l}\text{Inventory in}\text{the}\text{begning}\text{of}\text{the}\text{year +}\\ \text{Inventory at}\text{the}\text{end}\text{of}\text{the}\text{year}\end{array}}{\text{2}}\right)$

F Company

Given,
Cost of goods sold is $290,600.
Inventory in the beginning of the year is $105,100.
Inventory at the end of the year is $86,800.

Substitute $290,600 for cost of goods sold and $105,100 for inventory in the beginning of the year and $86,800 at the end of the year.

$\begin{array}{c}\text{Inventory turnover}\text{=}\frac{\$290,600}{\left(\frac{\$105,100+\$86,800}{2}\right)}\\ =\frac{\$290,600}{\$95,950}\\ =3.03\end{array}$

Thus, inventory turnover is 3.03.

B Company:

$\begin{array}{c}\text{Inventory turnover}\text{=}\frac{\$480,000}{\left(\frac{\$80,500+\$82,000}{2}\right)}\\ =\frac{\$480,000}{\$81,250}\\ =5.91\end{array}$

Thus, inventory turnover is 5.91.

(e)

Formula to calculate day’s sales in inventory is,

$\text{Day’s sales in inventory =}\left(\frac{\text{Inventory}\text{at}\text{the}\text{end}\text{of}\text{the}\text{year}}{\text{Cost}\text{of}\text{goods}\text{sold}}\right)\times 365$

F Company

Given,
Inventory at the end of the year is $86,800.
Cost of goods sold is $290,600.

Substitute $290,600 for cost of goods sold and $86,800 for inventory at the end of the year.

$\begin{array}{c}\text{Day’s sales in inventory}=\left(\frac{\$86,800}{\$290,600}\right)\times 365\\ =109.02\end{array}$

Thus, day’s sales inventory is 109.02 day

B Company:

$\begin{array}{c}\text{Day's}\text{sales}\text{in}\text{inventory}=\left(\frac{\$82,000}{\$480,000}\right)\times 365\\ =62.35\end{array}$

Thus, inventory turnover is 62.35 days

(f)

Formula to calculate day’s sales uncollected is,

$\begin{array}{l}\text{Day's}\text{sales}\text{uncollected}=\left(\frac{\text{Accounts}\text{Receivable}}{\text{Net}\text{Sales}}\right)\times 365\\ \end{array}$

F Company

Given,
Accounts receivable is $77,100.
Net sales are $393,600.

Substitute $77,100 for accounts receivable and $393,600 for net sales.

$\begin{array}{c}\text{Day's}\text{sales}\text{uncollected}=\left(\frac{\$77,100}{\$393,600.}\right)\times 365\\ =77.5\end{array}$

Thus, day’s sales uncollected are 77.5 days.

B Company:

$\begin{array}{c}\text{Day's}\text{sales}\text{uncollected}\text{=}\left(\frac{\$70,500}{\$667,500}\right)\times 365\\ =38.55\end{array}$

Thus, day’s sales uncollected is 38.55 days

2.

To determine

To compute: (a) profit margin ratio (b) total assets turnover ratio,(c) return on total assets ratio (d) return on common stockholder’s equity (e) price earnings ratio (f) dividend yields of B Company and K Company.

Explanation of Solution

(a)

Formula to calculate Profit margin ratio is,

$\text{Profit margin ratio}=\frac{\text{Net}\text{income}}{\text{Net}\text{sales}}\times 100$

F Company

Given,
Net income is $33,850.
Net sales are $393,600.

Substitute $33,850 for net income and $393,600 for net sales.

$\begin{array}{c}\text{Profit}\text{margin ratio}\text{=}\frac{\$33,850}{\$393,600}\times 100\\ =8.6\%\end{array}$

Thus, profit margin ratio is 8.6%.

B Company:

$\begin{array}{c}\text{Profit margin ratio}=\frac{\$61,700}{\$667,500}\times 100\\ =9.24\%\end{array}$

Thus, profit margin ratio is 9.24%.

(b)

Formula to calculate total assets turnover ratio is,

$\text{Total assets turnover ratio}=\frac{\text{Net}\text{sales}}{\text{Average}\text{total}\text{assets}}$

$\text{Average}\text{total}\text{assets}=\left(\frac{\begin{array}{l}\text{Assets in}\text{the}\text{begning}\text{of}\text{the}\text{year}+\\ \text{Assets}\text{at}\text{the}\text{end}\text{of}\text{the}\text{year}\end{array}}{\text{2}}\right)$

F Company

Given,
Net sales are $393,600.
Assets in the beginning of the year are $383,400.
Assets at the end of the year are $382,100.

Substitute $393,600 for net sales and $383,400 for assets in the beginning of the year and $382,100 at the end of the year.

$\begin{array}{c}\text{Total assets turnover ratio}=\frac{\$393,600}{\left(\frac{\$383,400+\$382,100}{2}\right)}\\ =\frac{\$393,600}{\$382,750}\\ =1.03\end{array}$

Thus, total assets turnover ratio is 1.03.

B Company:

$\begin{array}{c}\text{Total assets turnover ratio}\text{=}\frac{\$667,500}{\left(\frac{\$443,000+\$460,400}{2}\right)}\\ =\frac{\$667,500}{\$451,700}\\ =1.48\end{array}$

Thus, total assets turnover ratio is 1.48.

(c)

Formula to calculate return on total assets ratio is,

$\text{Return on total assets ratio}=\frac{\text{Net Income}}{\text{Average}\text{total}\text{assets}}$

$\text{Average}\text{total}\text{assets}=\left(\frac{\begin{array}{l}\text{Assets in}\text{the}\text{begning}\text{of}\text{the}\text{year}+\\ \text{Assets}\text{at}\text{the}\text{end}\text{of}\text{the}\text{year}\end{array}}{\text{2}}\right)$

F Company

Given,
Net income is $33,850.
Assets in the beginning of the year are $383,400.
Assets at the end of the year are $382,100.

Substitute $33,850 for net income and $383,400 for assets in the beginning of the year and $382,100 at the end of the year.

$\begin{array}{c}\text{Return on total assets ratio}=\frac{\$33,850}{\left(\frac{\$383,400+\$382,100}{2}\right)}\\ =\frac{\$33,850}{\$382,750}\\ =0.09\end{array}$

Thus, return on total assets ratio is 0.09

B Company:

$\begin{array}{c}\text{Return on total assets ratio}=\frac{\$61,700}{\left(\frac{\$443,000+\$460,400}{2}\right)}\\ =\frac{\$61,700}{\$451,700}\\ =0.14\end{array}$

Thus, return on total assets ratio is 0.14

(d)

Formula to calculate return on common stockholder’s equity is,

$\text{Return on common stockholder’s equity}=\frac{\text{Net}\text{income}-\text{Preferred}\text{dividends}}{\text{Average}\text{common stockholder’s equity}}\times 100$

$\text{Average}\text{common}\text{stock}=\left(\frac{\begin{array}{l}\text{Common stock in}\text{the}\text{begning}\text{of}\text{the}\text{year +}\\ \text{Common stock}\text{at}\text{the}\text{end}\text{of}\text{the}\text{year}\end{array}}{\text{2}}\right)$

F Company

Given,
Net income is $33,850.
Common stock in the beginning of the year is $133,000.
Common stock at the end of the year is $133,000.

Substitute $33,850 for net income and $133,000 for common stock in the beginning of the year and $133,000 at the end of the year.

$\begin{array}{c}\text{Return on common stockholder’s equity}\text{=}\frac{\$33,850\text{-}\$0}{\left(\frac{\$133,000+\$133,000}{2}\right)}\times 100\\ =\frac{\$33,850}{\$133,000}\times 100\\ =25.45\%\end{array}$

Thus, return on common stockholder’s equity is 25.45%.

B Company:

$\begin{array}{c}\text{Return on common stockholder’s equity}\text{=}\frac{\text{\$61,700-}\$0}{\left(\frac{\$141,000+\$141,000}{2}\right)}\times 100\\ =\frac{\$61,700}{\$141,000}\times 100\\ =43.76\%\end{array}$

Thus, return on common stockholder’s equity is 43.76%.

(e)

Formula to calculate price earnings ratio is,

$\text{Price}\text{earnings}\text{ratio}\text{=}\frac{\text{market}\text{value}\text{per}\text{share}}{\text{earnings}\text{per}\text{share}}$

F Company

Given,
Market value per share is $25.
Earnings per share are $1.27.

Substitute $25 for market value per share and $1.27 for earnings per share.

$\begin{array}{c}\text{Price}\text{earning}\text{ratio}\text{=}\frac{\$25}{\text{\$1}\text{.27}}\\ =19.69\end{array}$

Thus, price earning ratio is $19.69.

B Company:

$\begin{array}{c}\text{Price}\text{earning}\text{ratio}\text{=}\frac{\$25}{\text{\$2}\text{.19}}\\ =11.42\end{array}$

Thus, price earning ratio is $11.42.

(f)

Formula to calculate dividend yield is,

$\text{Dividend yield}\text{=}\frac{\text{Annual}\text{cash}\text{dividends}\text{per}\text{share}}{\text{Market}\text{price}\text{per}\text{share}}$

F Company

Given,
Cash dividend per share is $1.50.
Market price per share is $25.

Substitute $25 for market price per share and $1.50 for annual cash dividend per share.

$\begin{array}{c}\text{Dividend}\text{yield}=\frac{\$1.50}{\text{\$25}}\\ =0.06\end{array}$

Thus, dividend yield is $0.06.

B Company:

$\begin{array}{c}\text{Dividend}\text{yield}=\frac{\$1.50}{\text{\$25}}\\ =0.06\end{array}$

Thus, dividend yield is $0.06.