Chapter 16, Problem 12QP

a)

Summary Introduction

To determine: The cash collection for each four quarters, when the collection period is 45days.

Introduction:

Cash collection is the amount collected through business. It is a task of accounts receivables.

Average cash collection period is the number of days taken to collect the cash from the customers.

$\text{Cash collection period}=\frac{\text{Number of days or months in a year }}{\text{Debtors turnover}}$

Answer to Problem 12QP

The cash collection for each quarters are Quarter 1 is $4,050, Quarter 2 is $4,750, Quarter 3 is $5,000 and Quarter 4 is $4,400.

Explanation of Solution

Given information:

Accounts receivable at the beginning of the year is $1900, and the collection period is 45 days.

Compute the cash collection for each four quarters:

Note: All the receivables, which are outstanding, will be collected in the current year.

Compute the ending receivables for quarter 1:

$\begin{array}{c}\text{Ending receivables}=\frac{90-45}{90}\\ =\frac{45}{90}\\ \text{Ending receivables}=\frac{1}{2}\text{of current sales}\end{array}$

Therefore, the ending receivable will be half of the current year sales.

$\begin{array}{c}\text{Ending receivables}=\frac{1}{2}\left(\$4300\right)\\ =\$2,150\end{array}$

Hence, the ending receivables are $2,150.

Compute the cash collection for quarter 1:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$1900+\$4,300-\$2,150\\ =\$4,050\end{array}$

Hence, the cash collected for the quarter 1 is $4,050.

Compute the ending receivables for quarter 2:

$\begin{array}{c}\text{Ending receivables}=\frac{1}{2}\text{of current sales}\\ =\frac{1}{2}\left(\$5,200\right)\\ =\$2,600\end{array}$

Hence, the ending receivables are $2,600.

Compute the cash collection for quarter 2:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$2,150+\$5,200-\$2,600\\ =\$4,750\end{array}$

Hence, the cash collected for the quarter 2 is $4,750.

Compute the ending receivables for quarter 3:

$\begin{array}{c}\text{Ending receivables}=\frac{1}{2}\text{of current sales}\\ =\frac{1}{2}\left(\$4800\right)\\ =\$2,400\end{array}$

Hence, the ending receivables are $2,400.

Compute the cash collection for quarter 3:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$2,600+\$4,800-\$2,400\\ =\$5,000\end{array}$

Hence, the cash collected for the quarter 1 is $5,000.

Compute the ending receivables for quarter 4:

$\begin{array}{c}\text{Ending receivables}=\frac{1}{2}\text{of current sales}\\ =\frac{1}{2}\left(\$4,000\right)\\ =\$2,000\end{array}$

Hence, the ending receivables are $2,000.

Compute the cash collection for quarter 4:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$2,400+\$4,000-\$2,000\\ =\$4,400\end{array}$

Hence, the cash collected for the quarter 1 is $4,400.

b)

Summary Introduction

To determine: The cash collection for each four quarters, when the collection period is 60 days.

Answer to Problem 12QP

The cash collection for each quarter: Quarter 1 is $4,767, Quarter 2 is $4,900, Quarter 3 is $4,933, and Quarter 4 is $4,267.

Explanation of Solution

Given information:

Accounts receivables at the beginning of the year are $1,900 and the collection period is 60 days.

Compute the cash collection for each four quarters:

Note: All the receivables, which are outstanding, will be collected in the current year.

Compute the ending receivables for quarter 1:

$\begin{array}{c}\text{Ending receivables}=\frac{90-60}{90}\\ =\frac{30}{90}\\ \text{Ending receivables}=\frac{1}{3}\text{of current sales}\end{array}$

Therefore, the ending receivable will be half of the current year sales.

Compute ending receivables for quarter 1:

$\begin{array}{c}\text{Ending receivables}=\frac{1}{3}\left(\$4,300\right)\\ =\$1,433\end{array}$

Hence, the ending receivables are $1,433.

Compute the cash collection for quarter 1:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$1,900+\$4,300-\$1,433\\ =\$4,767\end{array}$

Hence, the cash collected for the quarter 1 is $4,767.

Compute ending receivables for quarter 2:

$\begin{array}{c}\text{Ending receivables}=\frac{1}{3}\text{of current sales}\\ =\frac{1}{3}\left(\$5,200\right)\\ =\$1,733.33\end{array}$

Hence, the ending receivables are $1,733.33.

Compute the cash collection for quarter 2:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$1,433+\$5,200-\$1,733\\ =\$4,900\end{array}$

Hence, the cash collected for the quarter 2 is $4,900.

Compute the ending receivables for quarter 3:

$\begin{array}{c}\text{Ending receivables}=\frac{1}{3}\text{of current sales}\\ =\frac{1}{3}\left(\$4800\right)\\ =\$1,600\end{array}$

Hence, the ending receivables are $1,600.

Compute the cash collection for quarter 3:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$1,733+\$4,800-\$1,600\\ =\$4,933\end{array}$

Hence, the cash collected for the quarter 1 is $4,933.

Compute the ending receivables for quarter 4:

$\begin{array}{c}\text{Ending receivables}=\frac{1}{3}\text{of current sales}\\ =\frac{1}{3}\left(\$4,000\right)\\ =\$1,333\end{array}$

Hence, the ending receivables are $1,333.

Compute the cash collection for quarter 4:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$1,600+\$4,000-\$1,333\\ =\$4,267\end{array}$

Hence, the cash collected for the quarter 1 is $4,267.

c)

Summary Introduction

To determine: The cash collection for each four quarters, when the collection period is 30 days.

Introduction:

Cash collection is the amount collected through business. It is a task of accounts receivables.

Average cash collection period is the number of days taken to collect the cash from the customers.

$\text{Cash collection period}=\frac{\text{Number of days or months in a year }}{\text{Debtors turnover}}$

Answer to Problem 12QP

The cash collections for each quarter are Quarter 1 is $3,333, Quarter 2 is $4,600, Quarter 3 is $5,067, and Quarter 4 is $4,533.

Explanation of Solution

Given information:

Accounts receivable at the beginning of the year is $1900, and the collection period is 30 days.

Compute the cash collection for each four quarters:

Note: All the receivables, which are outstanding, will be collected in the current year.

Compute the ending receivables for quarter 1:

$\begin{array}{c}\text{Ending receivables}=\frac{90-30}{90}\\ =\frac{60}{90}\\ =\frac{2}{3}\text{of current sales}\end{array}$

Therefore, the ending receivables will be half of the current year sales.

$\begin{array}{c}\text{Ending receivables}=\frac{2}{3}\left(\$4300\right)\\ =\$2,866.67\end{array}$

Hence, the ending receivables are $2,866.67.

Compute the cash collection for quarter 1:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$1,900+\$4,300-\$2,867\\ =\$3,333\end{array}$

Hence, the cash collected for the quarter 1 is $3,333.

Compute ending receivables for quarter 2:

$\begin{array}{c}\text{Ending receivables}=\frac{2}{3}\text{of current sales}\\ =\frac{2}{3}\left(\$5,200\right)\\ =\$3,466.67\end{array}$

Hence, the ending receivables are $3,466.67.

Compute the cash collection for quarter 2:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$2,867+\$5,200-\$3,467\\ =\$4,600\end{array}$

Hence, the cash collected for the quarter 2 is $4,600.

Compute the ending receivables for quarter 3:

$\begin{array}{c}\text{Ending receivables}=\frac{2}{3}\text{of current sales}\\ =\frac{2}{3}\left(\$4,800\right)\\ =\$3,200\end{array}$

Hence, the ending receivables are $3,200

Compute the cash collection for quarter 3:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$3,467+\$4,800-\$3,200\\ =\$5,067\end{array}$

Hence, the cash collected for the quarter 1 is $5,067.

Compute the ending receivables for quarter 4:

$\begin{array}{c}\text{Ending receivables}=\frac{2}{3}\text{of current sales}\\ =\frac{2}{3}\left(\$4,000\right)\\ =\$2,667\end{array}$

Hence, the ending receivables are $2,667.

Compute the cash collection for quarter 4:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$3,200+\$4,000-\$2,667\\ =\$4,533\end{array}$

Hence, the cash collected for the quarter 1 is $4,533.