Chapter 16, Problem 12QP

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 12QP

Solution:

The cash collection of Quarter 1(Q1) is $5,850.

The cash collection of Quarter 2(Q2) is $6,750.

The cash collection of Quarter 3(Q3) is $7,150.

The cash collection of Quarter 4(Q4) is $6,300.

Explanation of Solution

Given information:

The collection period is 45 days, Sales of Q1 is $6,100, Sales of Q2 is $7,400, Sales of Q3 is $6,900, and Sales of Q4 is $5,700. The beginning accounts receivable is $2,800.

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):

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q1}\\ =\frac{1}{2}\times \$6,100\\ =\$3,050\end{array}$

Hence, the ending accounts receivable of Q1 is $3,050.

Compute the cash collection for Q1:

$\begin{array}{c}\text{Cash collections of Q1}=\text{Beginning accounts receivable}+\text{Sales of Q1}-\text{Ending accounts receivable}\\ =\$2,800+\$6,100-\$3,050\\ =\$5,850\end{array}$

Hence, the cash collection for Q1 is $5,850.

Compute the ending accounts receivable for Q2:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q2}\\ =\frac{1}{2}\times \$7,400\\ =\$3,700\end{array}$

Hence, the ending accounts receivable of Q2 is $3,700.

Compute the cash collection for Q2:

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

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q2}-\text{Ending accounts receivable}\\ =\$3,050+\$7,400-\$3,700\\ =\$6,750\end{array}$

Hence, the cash collection for Q2 is $6,750.

Compute the ending accounts receivable for Q3:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q3}\\ =\frac{1}{2}\times \$6,900\\ =\$3,450\end{array}$

Hence, the ending accounts receivable of Q3 is $3,450.

Compute the cash collection for Q3:

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

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q3}-\text{Ending accounts receivable}\\ =\$3,700+\$6,900-\$3,450\\ =\$7,150\end{array}$

Hence, the cash collection for Q3 is $7,150.

Compute the ending accounts receivable for Q 4:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q4}\\ =\frac{1}{2}\times \$5,700\\ =\$2,850\end{array}$

Hence, the ending accounts receivable is $2,850.

Compute the cash collection for Q4:

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

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q4}-\text{Ending accounts receivable}\\ =\$3,450+\$5,700-\$2,850\\ =\$6,300\end{array}$

Hence, the cash collection for Q4 is $6,300.

b)

Summary Introduction

To determine: The cash collections 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 12QP

Solution:

The cash collection of Quarter 1(Q1) is $6,866.67.

The cash collection of Quarter 2(Q2) is $6,966.66.

The cash collection of Quarter 3(Q3) is $7,066.67.

The cash collection of Quarter 4(Q4) is $6,100.

Explanation of Solution

Given information:

The collection period is 60 days, Sales of Q1 is $6,100, Sales of Q2 is $7,400, Sales of Q3 is $6,900, and Sales of Q4 is $5,700.

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):

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q1}\\ =\frac{1}{3}\times \$6,100\\ =\$2,033.33\end{array}$

Hence, the ending accounts receivable is $2,033.33.

Compute the cash collection for Q1:

$\begin{array}{c}\text{Cash collections of Q1}=\text{Beginning accounts receivable}+\text{Sales of Q1}-\text{Ending accounts receivable}\\ =\$2,800+\$6,100-\$2,033.33\\ =\$6,866.67\end{array}$

Hence, the cash collection for Q1 is $6,866.67.

Compute the ending accounts receivable for Q2:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q2}\\ =\frac{1}{3}\times \$7,400\\ =\$2,466.67\end{array}$

Hence, the ending accounts receivable of Q2 is $2,466.67.

Compute the cash collection for Q2:

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

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q2}-\text{Ending accounts receivable}\\ =\$2,033.33+\$7,400-\$2,466.67\\ =\$6,966.66\end{array}$

Hence, the cash collection for Q2 is $6,966.66.

Compute the ending accounts receivable for Q3:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q3}\\ =\frac{1}{3}\times \$6,900\\ =\$2,300\end{array}$

Hence, the ending accounts receivable of Q3 is $2,300

Compute the cash collection for Q3:

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

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q3}-\text{Ending accounts receivable}\\ =\$2,466.67+\$6,900-\$2,300\\ =\$7,066.67\end{array}$

Hence, the cash collection for Q3 is $7,066.67.

Compute the ending accounts receivable for Q4:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q4}\\ =\frac{1}{3}\times \$5,700\\ =\$1,900\end{array}$

Hence, the ending accounts receivable of Q4 is $1,900.

Compute the cash collection for Q4:

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

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q4}-\text{Ending accounts receivable}\\ =\$2,300+\$5,700-\$1,900\\ =\$6,100\end{array}$

Hence, the cash collection for Q4 is $6,100.

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 12QP

Solution:

The cash collection of Quarter 1(Q1) is $4,833.33.

The cash collection of Quarter 2(Q2) is $6,533.34.

The cash collection of Quarter 3(Q3) is $7,233.33.

The cash collection of Quarter 4(Q4) is $6,500.

Explanation of Solution

Given information:

The collection period is 30 days, Sales of Q1 is $6,100, Sales of Q2 is $7,400, Sales of Q3 is $6,900, and Sales of Q4 is $5,700.

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):

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q1}\\ =\frac{2}{3}\times \$6,100\\ =\$4,066.67\end{array}$

Hence, the ending accounts receivable is $4,066.67

Compute the cash collection for Q1:

$\begin{array}{c}\text{Cash collections of Q1}=\text{Beginning accounts receivable}+\text{Sales of Q1}-\text{Ending accounts receivable}\\ =\$2,800+\$6,100-\$4,066.67\\ =\$4,833.33\end{array}$

Hence, the cash collection for Q1 is $4,833.33.

Compute the ending accounts receivable for Q2:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q2}\\ =\frac{2}{3}\times \$7,400\\ =\$4,933.33\end{array}$

Hence, the ending accounts receivable of Q2 is $4,933.33

Compute the cash collection for Q2:

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

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q2}-\text{Ending accounts receivable}\\ =\$4,066.67+\$7,400-\$4,933.33\\ =6,533.34\end{array}$

Hence, the cash collection for Q2 is $6,533.34.

Compute the ending accounts receivable for Q3:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q3}\\ =\frac{2}{3}\times \$6,900\\ =\$4,600\end{array}$

Hence, the ending accounts receivable of Q3 is $4,600

Compute the cash collection for Q3:

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

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q3}-\text{Ending accounts receivable}\\ =\$4,933.33+\$6,900-\$4,600\\ =\$7,233.33\end{array}$

Hence, the cash collection for Q3 is $7,233.33.

Compute the ending accounts receivable for Q 4:

$\begin{array}{c}\text{Ending accounts receivable}=\text{Total collection period}\times \text{Sales of Q4}\\ =\frac{2}{3}\times \$5,700\\ =\$3,800\end{array}$

Hence, the ending accounts receivable is $3,800.

Compute the cash collection for Q4:

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

$\begin{array}{c}\text{Cash collection}=\text{Beginning accounts receivable}+\text{Sales of Q4}-\text{Ending accounts receivable}\\ =\$4,600+\$5,700-\$3,800\\ =\$6,500\end{array}$

Hence, the cash collection for Q4 is $6,500.