Chapter 18, Problem 5QP

a)

Summary Introduction

To determine: The cash collection for each four quarters when the collection period is 45 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 5QP

The cash collection for quarter 1 is $670, quarter 2 is $735, quarter 3 is $790, and quarter 4 is $870.

Explanation of Solution

Given information:

Accounts receivable at the beginning of the year is $310, Collection period is 45 days.

Compute cash collection for each four quarters:

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

Compute 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

$\begin{array}{c}\text{Ending receivables}=\frac{1}{2}\left(\$720\right)\\ =\$360\end{array}$

Hence, ending receivables is $360.

Compute cash collection for quarter 1:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$310+\$720-\$360\\ =\$670\end{array}$

Hence, cash collected for the quarter 1 is $670.

Compute ending receivables for quarter 2:

$\text{Ending receivables}=\frac{1}{2}\text{of current sales}$

$\begin{array}{c}\text{Ending receivables}=\frac{1}{2}\left(\$750\right)\\ =\$375\end{array}$

Hence, ending receivables is $375.

Compute cash collection for quarter 2:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$360+\$750-\$375\\ =\$735\end{array}$

Hence, the cash collected for the quarter 2 is $735.

Compute ending receivables for quarter 3:

$\text{Ending receivables}=\frac{1}{2}\text{of current sales}$

$\begin{array}{c}\text{Ending receivables}=\frac{1}{2}\left(\$830\right)\\ =\$415\end{array}$

Hence, the ending receivables is $415.

Compute cash collection for quarter 3:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$375+\$830-\$415\\ =\$790\end{array}$

Hence, the cash collected for the quarter 3 is $790.

Compute ending receivables for quarter 4:

$\text{Ending receivables}=\frac{1}{2}\text{of current sales}$

$\begin{array}{c}\text{Ending receivables}=\frac{1}{2}\left(\$910\right)\\ =\$455\end{array}$

Hence, the ending receivables is $455.

Compute cash collection for quarter 4:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$415+\$910-\$455\\ =\$870\end{array}$

Hence, the cash collected for the quarter 4 is $870.

b)

Summary Introduction

To determine: The cash collection for each four quarters when the collection period is 60 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 5QP

The cash collection for quarter1 is $790, quarter 2 is $740, quarter 3 is $803.24, and quarter 4 is $883.43.

Explanation of Solution

Given information:

Accounts receivables at the beginning of the year are $310, Collection period is 60 days.

Compute cash collection for each four quarters:

Note: All the receivables, which are outstanding, will be collected by this current year

Compute 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 ending receivable will be half of current year sales

$\begin{array}{c}\text{Ending receivables}=\frac{1}{3}\left(\$720\right)\\ =\$240\end{array}$

Hence, the ending receivables is $240

Compute cash collection for quarter 1:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$310+\$720-\$240\\ =\$790\end{array}$

Hence, the cash collected for the quarter 1 is $790

Compute ending receivables for quarter 2:

$\text{Ending receivables}=\frac{1}{3}\text{of current sales}$

$\begin{array}{c}\text{Ending receivables}=\frac{1}{3}\left(\$750\right)\\ =\$250\end{array}$

Hence, the ending receivables is $250

Compute cash collection for quarter 2:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$240+\$750-\$250\\ =\$740\end{array}$

Hence, the cash collected for the quarter 2 is $740.

Compute ending receivables for quarter 3:

$\text{Ending receivables}=\frac{1}{3}\text{of current sales}$

$\begin{array}{c}\text{Ending receivables}=\frac{1}{3}\left(\$830\right)\\ =\$276.67\end{array}$

Hence, ending receivables is $276.67

Compute cash collection for quarter 3:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$250+\$830-\$276.76\\ =\$803.24\end{array}$

Hence, the cash collected for the quarter 3 is $803.24.

Compute ending receivables for quarter 4:

$\text{Ending receivables}=\frac{1}{3}\text{of current sales}$

$\begin{array}{c}\text{Ending receivables}=\frac{1}{3}\left(\$910\right)\\ =\$303.33\end{array}$

Hence, the ending receivables is $303.33

Compute cash collection for quarter 4:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$276.76+\$910-\$303.33\\ =\$883.43\end{array}$

Hence, the cash collected for the quarter 4 is $883.43.

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 5QP

The cash collection for quarter 1 is $550, quarter 2 is $730, quarter 3 is $776.67., and quarter 4 is $856.67

Explanation of Solution

Given information:

Accounts receivables at the beginning of the year are $310, Collection period is 30days.

Compute cash collection for each four quarters:

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

Compute ending receivables for quarter 1:

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

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

$\begin{array}{c}\text{Ending receivables}=\frac{2}{3}\left(\$720\right)\\ =\$480\end{array}$

Hence, the ending receivables is $480.

Compute cash collection for quarter 1:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$310+\$720-\$480\\ =\$550\end{array}$

Hence, the cash collected for the quarter 1 is $550.

Compute ending receivables for quarter 2:

$\text{Ending receivables}=\frac{2}{3}\text{of current sales}$

$\begin{array}{c}\text{Ending receivables}=\frac{2}{3}\left(\$750\right)\\ =\$500\end{array}$

Hence, the ending receivables is $500.

Compute cash collection for quarter 2:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$480+\$750-\$500\\ =\$730\end{array}$

Hence, the cash collected for the quarter 2 is $730.

Compute ending receivables for quarter 3:

$\text{Ending receivables}=\frac{2}{3}\text{of current sales}$

$\begin{array}{c}\text{Ending receivables}=\frac{2}{3}\left(\$830\right)\\ =\$553.33\end{array}$

Hence, the ending receivables is $553.33.

Compute cash collection for quarter 3:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$500+\$830-\$553.33\\ =\$776.67\end{array}$

Hence, the cash collected for the quarter 3 is $776.67.

Compute ending receivables for quarter 4:

$\text{Ending receivables}=\frac{2}{3}\text{of current sales}$

$\begin{array}{c}\text{Ending receivables}=\frac{2}{3}\left(\$910\right)\\ =\$606.67\end{array}$

Hence, the ending receivables is $606.67.

Compute cash collection for quarter 4:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$553.33+\$910-\$606.67\\ =\$856.67\end{array}$

Hence, the cash collected for the quarter 4 is $856.67.