Chapter 16, Problem 12P

a)

Summary Introduction

To determine: Cash conversion cycle of Company S.

Explanation of Solution

Given information:

Last year sales were $3,250,000,

Net profit margin is 7%,

Inventory turnover ratio is 6 times during the year,

DSO of company is 41 days,

Cost of goods sold (COGS) is $1,800,000,

Fixed assets $535,000,

Payables deferral payment period is 45 days.

Calculation of inventory and inventory conversion period:

$\begin{array}{c}\text{Inventory}=\frac{\text{COGS}}{\text{Inventory}\text{turnover}}\\ =\frac{\$1,800,000}{6}\\ =\$300,000\end{array}$

$\begin{array}{c}\text{Inventory conversion period}=\frac{\text{Inventory}}{\frac{\text{COGS}}{365}}\\ =\frac{\$300,000}{\left(\frac{\$1,800,000}{365}\right)}\\ =60.8333\end{array}$

Therefore inventory is $300,000 and inventory conversion period is 60.8333

Calculation of length of cash conversion cycle:

$\begin{array}{c}\text{Cash conversion cycle}=\text{Inventory}\text{conversion}\text{period}+\text{Average}\text{collection}\text{period}\\ -\text{Payables}\text{deferral}\text{period}\\ =60.8+41-4\text{5}\\ =56.8\text{days}\end{array}$

Hence, length of cash conversion cycle is 56.8 days.

b)

Summary Introduction

To determine: Total assets turnover ratio and ROA.

Explanation of Solution

Calculation of total assets:

$\begin{array}{c}\text{DSO}=\frac{\text{Receivables}}{\text{Daily}\text{sales}}\\ \text{Receivables}=\frac{\text{DSO}}{\text{Daily}\text{sales}}\\ =41\left(\frac{\$3,250,000}{365}\right)\\ =\$365,068.49\end{array}$

$\begin{array}{c}\text{Total}\text{assets}=\text{Inventory}+\text{receivables}+\text{fixed assets}\\ =\$300,000+\$365,068.49+\$535,000\\ =\$1,200,068.49\end{array}$

Hence, total assets of company are $1,200,068.49

Calculation of assets turnover ratio:

$\begin{array}{c}\text{Total}\text{assets}\text{turnover}=\frac{\text{Sales}}{\text{Total}\text{assets}}\\ =\frac{\$3,250,000}{\$1,200,068.49}\\ =2.7082\text{times}\end{array}$

Hence assets turnover is 2.7082 times

Calculation of ROA:

$\begin{array}{c}\text{ROA}=\text{Profit}\text{margin}\times \text{total}\text{assets}\text{turnover}\\ =0.07\times 2.7082\\ =18.96\%\end{array}$

Therefore, return on assets is 18.96%

c)

Summary Introduction

To determine: Cash conversion cycle, total assets turnover and ROA if inventory turnover had been 9 for the current year.

Explanation of Solution

Calculation of inventory:

$\begin{array}{c}\text{Inventory }=\frac{\text{COGS}}{\text{Inventory turnover}}\\ =\frac{\$1,800,000}{9}\\ =\$20,000\end{array}$

Therefore, inventory is $20,000

Calculation of inventory conversion period:

$\begin{array}{c}\text{Inventory conversion period}=\frac{\text{Inventory}}{\frac{\text{COGS}}{\text{365}}}\\ =\frac{\text{\$200,000}}{\frac{\text{\$1,800,000}}{\text{365}}}\\ =40.56\text{days}\end{array}$

Therefore,

$\begin{array}{c}\text{Cash conversion cycle}=\text{Inventory}\text{conversion}\text{period}+\text{Average}\text{collection}\text{period}\\ -\text{Payables}\text{deferral}\text{period}\\ =40.6+41-4\text{5}\\ =36.6\text{days}\end{array}$

Cash conversion cycle is 36.6 days.

$\begin{array}{c}\text{Total}\text{assets}=\text{Inventory}+\text{receivables}+\text{fixed assets}\\ =\$200,000+\$365,068.49+\$535,000\\ =\$1,100,068.49\end{array}$

Hence, total assets of company are $1,100,068.49

Calculation of assets turnover ratio:

$\begin{array}{c}\text{Total}\text{assets}\text{turnover}=\frac{\text{Sales}}{\text{Total}\text{assets}}\\ =\frac{\$3,250,000}{\$1,100,068.49}\\ =2.9544\text{times}\end{array}$

Hence assets turnover is 2.9544 times

Calculation of ROA:

$\begin{array}{c}\text{ROA}=\text{Profit}\text{margin}\times \text{total}\text{assets}\text{turnover}\\ =0.07\times 2.9544\\ =20.68\%\end{array}$

Therefore, return on assets is 20.68%