Chapter 27, Problem 4QP

Float and Weighted Average Delay Your neighbor goes to the post office once a month and picks up two checks, one for $9,700 and one for 52,600. The larger check takes four days to clear after it is deposited; the smaller one takes five days.

a. What is the total float for the month?

b. What is the average daily float?

c. What arc the average daily receipts and weighted average delay?

Summary Introduction

To compute: The total amount of company’s float.

Float:

Float is defined as the difference between the balance shown in ledger of the company and the balance that is available at the bank. Available balance refers to the balance that is shown by the banks of that particular company.

Explanation of Solution

Given,

Larger cheque is of $9,700.

The days for clearing the cheque are 4 days.

Smaller cheque is of $2,600.

The days for clearing the smaller check are 5 days.

Formula to calculate total amount of company’s float,

$\text{Total}\text{amount}\text{of}\text{company's}\text{float}=\left(\begin{array}{l}\text{Total}\text{float}\text{of}\text{larger}\text{check}\\ +\text{Total}\text{float}\text{of}\text{smaller}\text{check}\end{array}\right)$

Substitute $38,800 for total float of larger check and $13,000 for total float of smaller cheque.

$\begin{array}{c}\text{Total}\text{amount}\text{of}\text{company's}\text{float}=\$38,800+\$13,000\\ =\$51,800\end{array}$

Total amount of company’s float is $51,800.

Working notes:

Computation of total float of larger check,

$\begin{array}{c}\text{Total}\text{float}=\frac{\text{Total}\text{amount}\times \text{Clearing}\text{days}}{1}\\ =\$9,700\times 4\\ =\$38,800\end{array}$

Total float of larger cheque is $38,800.

Computation of total float of smaller check,

$\begin{array}{c}\text{Total}\text{float}=\frac{\text{Total}\text{amount}\times \text{Clearing}\text{days}}{1}\\ =\frac{\$2,600\times 5}{1}\\ =\$13,000\end{array}$

Total amount of total float is $13,000.

Conclusion

Hence, the total amount of company’s float is $51,800.

Summary Introduction

To compute: The average daily float.

Explanation of Solution

Number of days in a month is 30.

Formula to calculate average total float,

$\text{Average}\text{total}\text{float}=\frac{\text{Amount}\text{of}\text{total}\text{float}}{\text{Number}\text{of}\text{days}\text{in}\text{a}\text{month}}$

Substitute $51,800 for amount of total float and 30 for number of days in a month.

$\begin{array}{c}\text{Average}\text{total}\text{float}=\frac{\$51,800}{30}\\ =\$1,727\end{array}$

Average total float is $1,727.

Conclusion

Hence, the average total float is $1,727.

Summary Introduction

To compute: The average daily receipts and weighted average delay.

Explanation of Solution

Total amount received from post office is $12,300.

Number of days in a month is 30.

Formula to calculate average daily receipts,

$\text{Average}\text{daily}\text{receipts}=\frac{\text{Total amount received from post office}}{\text{Number of days in a month}}$

Substitute $12,300 for total amount received from post office and 30 for number of days in a month.

$\begin{array}{c}\text{Average}\text{daily}\text{receipts}=\frac{\$12,300}{30}\\ =\$410\end{array}$

Hence, average daily receipts are $410.

Formula to calculate weighted average delay,

$\text{Weighted}\text{average}\text{delay}=\left[\begin{array}{c}\left(\begin{array}{l}\left(\frac{\text{Larger check}}{\text{Total amount received from post office}}\right)\\ \times \left(\text{Days for clearing the cheque}\right)\end{array}\right)\\ +\left(\begin{array}{c}\left(\frac{\text{Smaller check}}{\text{Total amount received from post office}}\right)\\ \times \left(\text{Days for clearing the cheque}\right)\end{array}\right)\end{array}\right]$

Substitute $9,700 for larger check, $12,300 for total amount received from post office, 4 for clearing the larger check, $2,600 for smaller check and 5 for days for clearing the smaller check.

$\begin{array}{c}\text{Weighted}\text{average}\text{delay}=\left(\frac{\$9,700}{\$12,300}\times 4\right)+\left(\frac{\$2,600}{\$12,300}\times 5\right)\\ =3.15+1.05\\ =4.2\end{array}$

Weighted average delay is 4.2.

Working notes:

Given,

Larger check is of $9,700.

Smaller check is of $2,600.

Computation of total amount received from post office,

$\begin{array}{c}\text{Total}\text{amount}\text{received}\text{from}\text{post}\text{office}=\left(\begin{array}{l}\text{Amount}\text{of}\text{larger}\text{check}\\ +\text{Amount}\text{of}\text{smaller}\text{check}\end{array}\right)\\ =\$9,700+\$2,600\\ =\$12,300\end{array}$

Total amount received from post office is $12,300.

Conclusion

Hence, the average daily receipts and weighted average delay is $410 and 4.2 respectively.