Chapter 16, Problem 12P

a)

Summary Introduction

To determine: The length of cash conversion cycle of company B.

Explanation of Solution

Calculation of inventory conversion period:

$\begin{array}{c}\text{Inventory conversion period}=\frac{\text{Inventory}}{\left(\frac{\text{Cost}\text{of}\text{sales}}{\text{365}}\right)}\\ =\frac{\$1,827}{\left(\frac{\$9,890}{365}\right)}\\ =67.4\text{days}\end{array}$

Therefore, inventory conversion period is 67.4 days.

Calculation of receivables conversion period:

$\begin{array}{c}\text{Receivables conversion period}=\frac{\text{Accounts receivables}}{\left(\frac{\text{Net sales}}{\text{365}}\right)}\\ =\frac{\$1,138}{\left(\frac{\$13,644}{365}\right)}\\ =30.4\text{days}\end{array}$

Therefore, receivables conversion period is 30.4 days.

Calculation of length of operating cycle:

$\begin{array}{c}\text{Operating cycle}=\text{Inventory conversion period}+\text{Receivables conversion period}\\ =67.4\text{days}+30.4\text{days}\\ =97.8\text{days}\end{array}$

Therefore, operating cycle is 97.8 days

Calculation of payables deferral period:

$\begin{array}{c}\text{Payables deferral period}=\frac{\text{Accounts payables}}{\left(\frac{\text{cost of sales}}{\text{365}}\right)}\\ =\frac{\$1,166+\$536}{\left(\frac{\$9,890+\$2,264}{365}\right)}\\ =51.1\text{days}\end{array}$

Therefore, payables deferral period is 51.1 days.

Calculation of length of cash conversion cycle:

$\begin{array}{c}\text{Cash conversion cycle}=\text{Opearting cycle}-\text{Payables}\text{deferral period}\\ =97.8\text{days}-51.1\text{days}\\ =46.7\text{days}\end{array}$

Therefore, cash conversion cycle is 46.7 days

b)

Summary Introduction

To determine: Length of the cash conversion cycle.

Explanation of Solution

Calculation of receivables conversion period:

$\begin{array}{c}\text{Receivables conversion period}=\frac{\text{Accounts receivables}}{\left(\frac{\text{Net sales}}{\text{365}}\right)}\\ =\frac{\$1,138}{\left(\frac{\$13,644\times 0.75}{365}\right)}\\ =40.6\text{days}\end{array}$

Therefore, receivables conversion period is 40.6 days.

Calculation of length of operating cycle:

$\begin{array}{c}\text{Operating cycle}=\text{Inventory conversion period}+\text{Receivables conversion period}\\ =67.4\text{days}+40.6\text{days}\\ =108\text{days}\end{array}$

Therefore, operating cycle is 108 days

Calculation of length of cash conversion cycle:

$\begin{array}{c}\text{Cash conversion cycle}=\text{Operating cycle}-\text{Payables}\text{deferral period}\\ =108.0\text{days}-51.1\text{days}\\ =56.9\text{days}\end{array}$

Therefore, cash conversion cycle is 56.9 days

c)

Summary Introduction

To determine: Length of the cash conversion cycle.

Explanation of Solution

Calculation of receivables conversion period:

$\begin{array}{c}\text{Receivables conversion period}=\frac{\text{Accounts receivables}}{\left(\frac{\text{Net sales}}{\text{365}}\right)}\\ =\frac{\$1,138}{\left(\frac{\$13,644\times 0.50}{365}\right)}\\ =60.9\text{days}\end{array}$

Therefore, receivables conversion period is 60.9 days.

Calculation of length of operating cycle:

$\begin{array}{c}\text{Operating cycle}=\text{Inventory conversion period}+\text{Receivables conversion period}\\ =67.4\text{days}+60.9\text{days}\\ =128.3\text{days}\end{array}$

Therefore, operating cycle is 128.3 days

Calculation of length of cash conversion cycle:

$\begin{array}{c}\text{Cash conversion cycle}=\text{Operating cycle}-\text{Payables}\text{deferral period}\\ =128.3\text{days}-51.1\text{days}\\ =77.2\text{days}\end{array}$

Therefore, cash conversion cycle is 77.2 days