Chapter 16, Problem 5QP

a)

Summary Introduction

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

Introduction:

Cash collection is an amount which is recovered from an individual or business. It is a function of a particular company’s accounts receivables.

Answer to Problem 5QP

The cash collection of Quarter 1(Q1) is $565.

The cash collection of Quarter 2(Q2) is $585.

The cash collection of Quarter 3(Q3) is $610.

The cash collection of Quarter 4(Q4) is $715.

Explanation of Solution

Given information:

The collection period is 45 days, Sales of Q1 is $540, Sales of Q2 is $630, Sales of Q3 is $590, and Sales of Q4 is $840. The beginning accounts receivable is $295.

The formula to calculate the cash collection:

$\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales}-\text{Ending receivables}$

Compute the cash collection for each four quarters:

Note: The 45 days collection period indicates that the entire receivables which are outstanding will be collected in the current quarter.

Compute the total collection period:

$\begin{array}{c}\text{Total collection period}=\frac{\left(\begin{array}{l}\text{Total number of days in three quarters}\\ -\text{ Collection period}\end{array}\right)}{\text{Total number of days in the three quarters}}\\ =\frac{\left(90-45\right)}{90}\\ =\frac{45}{90}\\ =\frac{1}{2}\text{of current quarter's sales}\end{array}$

Hence, the half of current quarter’s sales will be collected for 45 days of collection period.

Compute the ending accounts receivable of Quarter 1(Q1):

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q1}\\ =\frac{1}{2}\times \$540\\ =\$270\end{array}$

Hence, the ending accounts receivable is $270.

Compute the cash collection for Q1:

$\begin{array}{c}\text{Cash collections of Q1}=\text{Beginning accounts receivable}+\text{Sales of Q1}-\text{Ending accounts receivable}\\ =\$295+\$540-\$270\\ =\$565\end{array}$

Hence, the cash collection for Q1 is $565.

Compute the ending accounts receivable for Q2:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q2}\\ =\frac{1}{2}\times \$630\\ =\$\text{315}\end{array}$

Hence, the ending accounts receivable of Q2 is $315.

Compute the cash collection for Q2:

Note: The beginning accounts receivable of Q2 will be ending accounts receivable of Q1.

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q2}-\text{Ending accounts receivable}\\ =\$270+\$630-\$315\\ =\$\text{585}\end{array}$

Hence, the cash collection for Q2 is $585.

Compute the ending accounts receivable for Q3:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q3}\\ =\frac{1}{2}\times \$590\\ =\$\text{295}\end{array}$

Hence, the ending accounts receivable of Q3 is $295.

Compute the cash collection for Q3:

Note: The beginning accounts receivable of Q3 will be ending accounts receivable of Q2.

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q3}-\text{Ending accounts receivable}\\ =\$315+\$590-\$295\\ =\$\text{610}\end{array}$

Hence, the cash collection for Q3 is $610.

Compute the ending accounts receivable for Q 4:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q4}\\ =\frac{1}{2}\times \$840\\ =\$420\end{array}$

Hence, the ending accounts receivable is $420.

Compute the cash collection for Q4:

Note: The beginning accounts receivable of Q4 will be ending accounts receivable of Q3.

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q4}-\text{Ending accounts receivable}\\ =\$295+\$840-\$420\\ =\$\text{715}\end{array}$

Hence, the cash collection for Q4 is $715.

b)

Summary Introduction

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

Introduction:

Cash collection is an amount which is recovered from an individual or business. It is a function of a particular company’s accounts receivables.

Answer to Problem 5QP

The cash collection of Quarter 1(Q1) is $655.

The cash collection of Quarter 2(Q2) is $600.

The cash collection of Quarter 3(Q3) is $603.33.

The cash collection of Quarter 4(Q4) is $756.67.

Explanation of Solution

Given information:

The collection period is 60 days, Sales of Q1 is $540, Sales of Q2 is $630, Sales of Q3 is $590, and Sales of Q4 is $840.

Compute the cash collection for each four quarters:

Note: The 60 days collection period indicates that the entire receivables which are outstanding will be collected in the current quarter.

Compute the total collection period:

$\begin{array}{c}\text{Total collection period}=\frac{\left(\begin{array}{l}\text{Total number of days in three quarters}\\ -\text{ Collection period}\end{array}\right)}{\text{Total number of days in the three quarters}}\\ =\frac{\left(90-60\right)}{90}\\ =\frac{30}{90}\\ =\frac{1}{3}\text{of current quarter's sales}\end{array}$

Hence, the one-third of the current quarter’s sales will be collected for 60 days of collection period.

Compute the ending accounts receivable of Quarter 1(Q1):

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q1}\\ =\frac{1}{3}\times \$540\\ =\$180\end{array}$

Hence, the ending accounts receivable is $180.

Compute the cash collection for Q1:

$\begin{array}{c}\text{Cash collections of Q1}=\text{Beginning accounts receivable}+\text{Sales of Q1}-\text{Ending accounts receivable}\\ =\$295+\$540-\$180\\ =\$655\end{array}$

Hence, the cash collection for Q1 is $655.

Compute the ending accounts receivable for Q2:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q2}\\ =\frac{1}{3}\times \$630\\ =\$\text{210}\end{array}$

Hence, the ending accounts receivable of Q2 is $210.

Compute the cash collection for Q2:

Note: The beginning accounts receivable of Q2 will be ending accounts receivable of Q1.

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q2}-\text{Ending accounts receivable}\\ =\$180+\$630-\$210\\ =\$600\end{array}$

Hence, the cash collection for Q2 is $600.

Compute the ending accounts receivable for Q3:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q3}\\ =\frac{1}{3}\times \$590\\ =\$196.67\end{array}$

Hence, the ending accounts receivable of Q3 is $196.67.

Compute the cash collection for Q3:

Note: The beginning accounts receivable of Q3 will be ending accounts receivable of Q2.

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q3}-\text{Ending accounts receivable}\\ =\$210+\$590-\$196.67\\ =\$\text{603}\text{.33}\end{array}$

Hence, the cash collection for Q3 is $603.33.

Compute the ending accounts receivable for Q 4:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q4}\\ =\frac{1}{3}\times \$840\\ =\$\text{280}\end{array}$

Hence, the ending accounts receivable is $420.

Compute the cash collection for Q4:

Note: The beginning accounts receivable of Q4 will be ending accounts receivable of Q3.

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q4}-\text{Ending accounts receivable}\\ =\$196.67+\$840-\$280\\ =\$756.67\end{array}$

Hence, the cash collection for Q4 is $756.67.

c)

Summary Introduction

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

Introduction:

Cash collection is an amount which is recovered from an individual or business. It is a function of a particular company’s accounts receivables.

Answer to Problem 5QP

The cash collection of Quarter 1(Q1) is $475.

The cash collection of Quarter 2(Q2) is $570.

The cash collection of Quarter 3(Q3) is $616.67.

The cash collection of Quarter 4(Q4) is $673.33.

Explanation of Solution

Given information:

The collection period is 30 days, Sales of Q1 is $540, Sales of Q2 is $630, Sales of Q3 is $590, and Sales of Q4 is $840.

Compute the cash collection for each four quarters:

Note: The 30 days collection period indicates that the entire receivables which are outstanding will be collected in the current quarter.

Compute the total collection period:

$\begin{array}{c}\text{Total collection period}=\frac{\left(\begin{array}{l}\text{Total number of days in three quarters}\\ -\text{ Collection period}\end{array}\right)}{\text{Total number of days in the three quarters}}\\ =\frac{\left(90-30\right)}{90}\\ =\frac{60}{90}\\ =\frac{2}{3}\text{of current quarter's sales}\end{array}$

Hence, the two-third of the current quarter’s sales will be collected for 30 days of collection period.

Compute the ending accounts receivable of Quarter 1(Q1):

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q1}\\ =\frac{2}{3}\times \$540\\ =\$\text{360}\end{array}$

Hence, the ending accounts receivable is $360.

Compute the cash collection for Q1:

$\begin{array}{c}\text{Cash collections of Q1}=\text{Beginning accounts receivable}+\text{Sales of Q1}-\text{Ending accounts receivable}\\ =\$295+\$540-\$\text{360}\\ =\$\text{475}\end{array}$

Hence, the cash collection for Q1 is $475.

Compute the ending accounts receivable for Q2:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q2}\\ =\frac{2}{3}\times \$630\\ =\$\text{420}\end{array}$

Hence, the ending accounts receivable of Q2 is $420.

Compute the cash collection for Q2:

Note: The beginning accounts receivable of Q2 will be ending accounts receivable of Q1.

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q2}-\text{Ending accounts receivable}\\ =\$360+\$630-\$\text{420}\\ =\$\text{570}\end{array}$

Hence, the cash collection for Q2 is $570.

Compute the ending accounts receivable for Q3:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q3}\\ =\frac{2}{3}\times \$590\\ =\$\text{393}\text{.33}\end{array}$

Hence, the ending accounts receivable of Q3 is $393.33

Compute the cash collection for Q3:

Note: The beginning accounts receivable of Q3 will be ending accounts receivable of Q2.

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q3}-\text{Ending accounts receivable}\\ =\$420+\$590-\$393.33\\ =\$616.67\end{array}$

Hence, the cash collection for Q3 is $616.67.

Compute the ending accounts receivable for Q 4:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q4}\\ =\frac{2}{3}\times \$840\\ =\$\text{560}\end{array}$

Hence, the ending accounts receivable is $560.

Compute the cash collection for Q4:

Note: The beginning accounts receivable of Q4 will be ending accounts receivable of Q3.

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q4}-\text{Ending accounts receivable}\\ =\$393.33+\$840-\$560\\ =\$673.33\end{array}$

Hence, the cash collection for Q4 is $673.33.