Chapter 18, Problem 5QP

Calculating Cash Collections [LO3] The Morning Jolt Coffee Company has projected the following quarterly sales amounts for the coming year:

a. Accounts receivable at the beginning of the year are $345. The company has a 45-day collection period. Calculate cash collections in each of the four quarters by completing the following:

b. Rework (a) assuming a collection period of 60 days.

c. Rework (a) assuming a collection period of 30 days.

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 5QP

Q1-$755

Q2-$835

Q3-$890

Q4-$970

Explanation of Solution

Given information:

Accounts receivable at the beginning of the year is $345, 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 ending receivable will be half of the current year sales

$\begin{array}{c}\text{Ending receivables}=\frac{1}{2}\left(\$820\right)\\ =\$410\end{array}$

Hence, ending receivables is $410.

Compute cash collection for quarter 1:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$345+\$820-\$410\\ =\$755\end{array}$

Hence, cash collected for the quarter 1 is $755.

Compute ending receivables for quarter 2:

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

$\begin{array}{c}\text{Ending receivables}=\frac{1}{2}\left(\$850\right)\\ =\$425\end{array}$

Hence, ending receivables is $425.

Compute cash collection for quarter 2:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$410+\$850-\$425\\ =\$835\end{array}$

Hence, cash collected for the quarter 2 is $835.

Compute ending receivables for quarter 3:

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

$\begin{array}{c}\text{Ending receivables}=\frac{1}{2}\left(\$930\right)\\ =\$465\end{array}$

Hence, ending receivables is $465.

Compute cash collection for quarter 3:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$425+\$930-\$465\\ =\$890\end{array}$

Hence, cash collected for the quarter 1 is $890.

Compute ending receivables for quarter 4:

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

$\begin{array}{c}\text{Ending receivables}=\frac{1}{2}\left(\$1010\right)\\ =\$505\end{array}$

Hence, ending receivables is $505.

Compute cash collection for quarter 4:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$465+\$1010-\$505\\ =\$970\end{array}$

Hence, cash collected for the quarter 1 is $970.

Summary Introduction

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

Answer to Problem 5QP

Q1-$891.67

Q2-$840

Q3-$903.33

Q4-$983.33

Explanation of Solution

Given information:

Accounts receivables at the beginning of the year are $345, Collection period is 45 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

$\begin{array}{c}\text{Ending receivables}=\frac{1}{3}\left(\$820\right)\\ =\$273.33\end{array}$

Hence, ending receivables is $273.33.

Compute cash collection for quarter 1:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$345+\$820-\$273.33\\ =\$891.67\end{array}$

Hence, cash collected for the quarter 1 is $891.67.

Compute ending receivables for quarter 2:

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

$\begin{array}{c}\text{Ending receivables}=\frac{1}{3}\left(\$850\right)\\ =\$283.33\end{array}$

Hence, ending receivables is $283.33.

Compute cash collection for quarter 2:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$273.33+\$850-\$283.33\\ =\$840\end{array}$

Hence, cash collected for the quarter 2 is $840.

Compute ending receivables for quarter 3:

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

$\begin{array}{c}\text{Ending receivables}=\frac{1}{3}\left(\$930\right)\\ =\$310\end{array}$

Hence, ending receivables is $310.

Compute cash collection for quarter 3:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$283.33+\$930-\$310\\ =\$903.33\end{array}$

Hence, cash collected for the quarter 1 is $903.33.

Compute ending receivables for quarter 4:

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

$\begin{array}{c}\text{Ending receivables}=\frac{1}{3}\left(\$1010\right)\\ =\$336.67\end{array}$

Hence, ending receivables is $336.67.

Compute cash collection for quarter 4:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$310+\$1010-\$336.67\\ =\$983.33\end{array}$

Hence, cash collected for the quarter 1 is $983.33.

Summary Introduction

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

Answer to Problem 5QP

Q1-$618.33

Q2-$830

Q3-$876.67

Q4-$956.67

Explanation of Solution

Given information:

Accounts receivable at the beginning of the year is $345, Collection period is 30 days.

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 ending receivable will be half of the current year sales

$\begin{array}{c}\text{Ending receivables}=\frac{2}{3}\left(\$820\right)\\ =\$546.67\end{array}$

Hence, ending receivables is $546.67.

Compute cash collection for quarter 1:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$345+\$820-\$546.67\\ =\$618.33\end{array}$

Hence, cash collected for the quarter 1 is $618.33.

Compute ending receivables for quarter 2:

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

$\begin{array}{c}\text{Ending receivables}=\frac{2}{3}\left(\$850\right)\\ =\$566.67\end{array}$

Hence, ending receivables is $566.67.

Compute cash collection for quarter 2:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$546.67+\$850-\$566.67\\ =\$830\end{array}$

Hence, cash collected for the quarter 2 is $830.

Compute ending receivables for quarter 3:

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

$\begin{array}{c}\text{Ending receivables}=\frac{2}{3}\left(\$930\right)\\ =\$620\end{array}$

Hence, ending receivables is $620.

Compute cash collection for quarter 3:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$566.67+\$930-\$620\\ =\$876.67\end{array}$

Hence, cash collected for the quarter 1 is $876.67.

Compute ending receivables for quarter 4:

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

$\begin{array}{c}\text{Ending receivables}=\frac{2}{3}\left(\$1010\right)\\ =\$673.33\end{array}$

Hence, ending receivables is $673.33.

Compute cash collection for quarter 4:

$\begin{array}{c}\text{Cash collection}=\text{Beginning receivables}+\text{Sales}-\text{Ending receivables}\\ =\$620+\$1010-\$673.33\\ =\$956.67\end{array}$

Hence, cash collected for the quarter 1 is $956.67.