Chapter 13, Problem 5PSA

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 B Company and K Company.

Explanation of Solution

(a)

Formula to calculate current ratio is,

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

Current ratio of B Company:

Given info,

Current assets are $155,440
Current liabilities are $61,340

Substitute $155,440 for current assets and $61,340 for current liabilities.

$\begin{array}{c}\text{Current ratio}=\frac{\$155,440}{\$61,340}\\ =2.53\end{array}$

Thus current ratio is 2.53.

Working notes:

$\begin{array}{l}\text{Current}\text{assets}\text{=}\text{Cash+Accounts}\text{}\text{receivable+Current notes receivable}\\ \text{+Merchasdise}\text{inventory+Prepaid}\text{expenses}\\ \text{=}\text{\$19,500+\$37,400+\$91,100+\$84,440+\$5,000}\\ \text{=\$155,440}\\ \end{array}$

Likewise, current ratio of K Company:

$\begin{array}{c}\text{Current ratio}=\frac{\$238,050}{\$93,300}\\ =2.55\end{array}$

Thus, current ratio is 2.55.

(b)

Formula to calculate acid test ratio is,

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

Acid test ratio of B Company:

Given info,

Cash is $19,500.
Accounts receivables are $37,400
Current liabilities are $61,340.

Substitute $19,500 for cash, $37,400 for accounts receivable and $61,340 for current liabilities.

$\begin{array}{c}\text{Acid}\text{test}\text{ratio}=\frac{\text{\$19,500+\$0+\$37,400}}{\text{\$61,340}}\\ =\frac{\$56,900}{\$61,340}\\ \text{=0}\text{.93}\end{array}$

Thus, acid test ratio is 0.93

Likewise, acid test ratio of K Company:

$\begin{array}{c}\text{Acid}\text{test}\text{ratio}=\frac{\text{\$34,000+\$0+\$57,400}}{\text{\$93,300}}\\ =\frac{\$91,400}{\$93,300}\\ \text{=0}\text{.98}\end{array}$

Thus, acid test ratio is 0.98.

(c)

Formula to calculate accounts receivable turnover is,

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

Accounts receivable turnover of B Company:

Given info,

Net sales are $770,000.
Accounts receivable is 37,400.

Substitute $770,000 for net sales and $37,400 for accounts receivable.

$\begin{array}{c}\text{Accounts receivable turnover}=\frac{\$770,000}{\text{\$37,400}}\\ =20.59\end{array}$

Thus, accounts receivable turnover is 20.59.

Likewise, accounts receivable turnover of K Company:

$\begin{array}{l}\text{Accounts receivable turnover}\text{=}\frac{\$880,200}{\text{\$57,400}}\\ =15.33\end{array}$

Thus, accounts receivable turnover is 15.33.

(d)

Formula to calculate inventory turnover is,

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

Inventory turnover of B Company

Given info,

Cost of goods sold is $585,100.
Inventory is $84,440

Substitute $585,100 for cost of goods sold and $84,440.

$\begin{array}{l}\text{Inventory turnover}\text{=}\frac{\$585,100}{\$84,440}\\ =6.93\end{array}$

Thus, inventory turnover is 6.93.

Likewise, inventory turnover of K Company:

$\begin{array}{l}\text{Inventory turnover}\text{=}\frac{\$632,500}{\$132,500}\\ =4.77\end{array}$

Thus, inventory turnover is 4.77

(e)

Formula to calculate day’s sales in inventory is,

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

Day’s sales in inventory of B Company

Given info,

Inventory at the end of the year is $84,440
Cost of goods sold is $585,100

Substitute $585,100 for cost of goods sold and $84,440 for inventory at the end of the year.

$\begin{array}{c}\text{Day’s sales in inventory}\text{=}\left(\frac{\$84,440}{\$858,100}\right)\times 365\\ =36\end{array}$

Thus, day’s sales inventory is 36 day

Likewise, day’s sales in inventory of K Company:

$\begin{array}{c}\text{Day's}\text{sales}\text{in}\text{inventory}\text{=}\left(\frac{\$132,500}{\$632,500}\right)\times 365\\ =76.46\end{array}$

Thus, inventory turnover is 76.46 days

(f)

Formula to calculate day’s sales uncollected is,

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

Day’s sales uncollected of B Company

Given info,

Accounts receivable is $37,400.
Net sales are $770,000.

Substitute $37,400 for accounts receivable and $770,000 for net sales.

$\begin{array}{c}\text{Day's}\text{sales}\text{uncollected}=\left(\frac{\$37,400}{\$770,000}\right)\times 365\\ =17.73\end{array}$

Thus, day’s sales uncollected are 17.73 days.

Likewise, day’s sales uncollected of K Company:

$\begin{array}{c}\text{Day's}\text{sales}\text{uncollected}\text{=}\left(\frac{\$57,400}{\$880,200}\right)\times 365\\ =23.80\end{array}$

Thus, day’s sales uncollected is 23.80 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,

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

Profit margin ratio of B Company

Given info,

Net income is $162,200.
Net sales are $770,000.

Substitute $162,200for net income and $770,000for net sales.

$\begin{array}{c}\text{Profit margin ratio}=\frac{\$162,200}{\$770,000}\times 100\\ =21.06\%\end{array}$

Thus, profit margin ratio is 21.06%.

Likewise, profit margin ratio of K Company:

$\begin{array}{c}\text{Profit margin ratio}=\frac{\$210,400}{\$880,200}\times 100\\ =24\%\end{array}$

Thus, profit margin ratio is 24%.

(b)

Formula to calculate total assets turnover ratio is,

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

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

Total assets turnover ratio of B Company

Given info,

Net sales are $770,000.
Assets in the beginning of the year are $398,000.
Assets at the end of the year are $445,440.

Substitute $770,000for net sales and $398,000for assets in the beginning of the year and $445,440 at the end of the year.

$\begin{array}{c}\text{Total assets turnover ratio}=\frac{\$770,000}{\left(\frac{\$398,000+\$445,440}{2}\right)}\\ =\frac{\$770,000}{\$421,720}\\ =1.83\end{array}$

Thus, total assets turnover ratio is 1.83.

Likewise, total assets turnover ratio of K Company:

$\begin{array}{c}\text{Total assets turnover ratio}=\frac{\$880,200}{\left(\frac{\$382,500+\$542,250}{2}\right)}\\ =\frac{\$880,200}{\$462,375}\\ =1.90\end{array}$

Thus, total assets turnover ratio is 1.90

(c)

Formula to calculate return on total assets ratio is,

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

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

Return on total assets ratio of B Company

Given info,

Net income is $162,200.
Assets in the beginning of the year are $398,000.
Assets at the end of the year are $445,440.

Substitute $162,200 for net income and $398,000for assets in the beginning of the year and $445,440at the end of the year.

$\begin{array}{c}\text{Return on total assets ratio}=\frac{\$162,200}{\left(\frac{\$398,000+\$445,440}{2}\right)}\\ =\frac{\$162,200}{\$421,720}\\ =0.38\end{array}$

Thus, return on total assets ratio is 0.38

Likewise, return on total assets ratio of K Company:

$\begin{array}{c}\text{Return on total assets ratio}=\frac{\$210,400}{\left(\frac{\$382,500+\$542,450}{2}\right)}\\ =\frac{\$210,400}{\$462,475}\\ =0.45\end{array}$

Thus, return on total assets ratio is 0.45

(d)

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

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

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

Return on common stockholder’s equity of B Company

Given info,

Net income is $162,200.
Common stock in the beginning of the year is $180,000.
Common stock at the end of the year is $180,000.

Substitute $162,200 for net income and $180,000 for common stock in the beginning of the year and $180,000 at the end of the year.

$\begin{array}{c}\text{Return on common stockholder’s equity}\text{=}\frac{\text{\$162,200-}\$0}{\left(\frac{\$180,000+\$180,000}{2}\right)}\times 100\\ =\frac{\$162,200}{\$180,000}\times 100\\ =90.11\%\end{array}$

Thus, return on common stockholder’s equity is 90.11%.

Likewise, return on common stockholder’s equity of K Company:

$\begin{array}{c}\text{Return on common stockholder’s equity}\text{=}\frac{\text{\$210,400-}\$0}{\left(\frac{\$206,000+\$206,000}{2}\right)}\times 100\\ =\frac{\$210,400}{\$206,000}\times 100\\ =102.14\%\end{array}$

Thus, return on common stockholder’s equity is 102.14%.

(e)

Formula to calculate price earnings ratio is,

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

Price earnings ratio of B Company

Given info,

Market value per share is $75.
Earning per share is $4.51.

Substitute $75 for market value per share and $4.51 for earnings per share.

$\begin{array}{c}\text{Price}\text{earning}\text{ratio}\text{=}\frac{\$75}{\text{\$4}\text{.51}}\\ =16.63\end{array}$

Thus, price earning ratio is 16.63.

Likewise, price earning ratio of K Company:

$\begin{array}{c}\text{Price}\text{earning}\text{ratio}\text{=}\frac{\$75}{\text{\$5}\text{.11}}\\ =14.68\end{array}$

Thus, price earning ratio is 14.68.

(f)
Formula to calculate dividend yield is,

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

Dividend yield of B Company

Given info,

Cash dividend per share is $3.81.
Market price per share is $75.

Substitute $75 for market price per share and $3.81 for annual cash dividend per share.

$\begin{array}{c}\text{Dividend}\text{yield}\text{=}\frac{\$3.81}{\text{\$75}}\\ =0.051\end{array}$

Thus, dividend yield is 0.051.

Likewise, dividend yield of K Company:

$\begin{array}{c}\text{Dividend}\text{yield}\text{=}\frac{\$3.93}{\text{\$75}}\\ =0.052\end{array}$

Thus, dividend yield is 0.052.