Chapter 19, Problem 4QP

a)

Summary Introduction

To calculate: The overall float for a month.

Introduction:

The float is the difference between the bank cash and the book cash, denoting the net effects of checks during the clearing process.

Answer to Problem 4QP

The total float is $71,000.

Explanation of Solution

Given information:

Once in a month, Person X’s neighbor collects two checks; one check for $14,000 and another check for $5,000. The clearing days of the check after it is deposited is 4 days and 3 days for the larger check and smaller check respectively.

Formula to calculate the overall float:

$\text{Total float}=\left[\begin{array}{l}\text{Average number of days for a larger check }\\ \text{to be cleared}\left(\text{Average daily value of larger check}\right)+\\ \text{Average number of days for a smaller check }\\ \text{to be cleared}\left(\text{Average daily value of smaller check}\right)\end{array}\right]$

Calculate the collection float:

$\begin{array}{c}\text{Total float}=\left[\begin{array}{l}\text{Average number of days for a larger check }\\ \text{to be cleared}\left(\text{Average daily value of larger check}\right)+\\ \text{Average number of days for a smaller check }\\ \text{to be cleared}\left(\text{Average daily value of smaller check}\right)\end{array}\right]\\ =4\left(\$14,000\right)+3\left(\$5,000\right)\\ =\$71,000\end{array}$

Hence, the total float is $71,000.

b)

Summary Introduction

To calculate: The average float daily.

Answer to Problem 4QP

The average daily float is $2,366.667.

Explanation of Solution

Given information:

Once in a month, Person X’s neighbor collects two checks; one check for $14,000 and another check for $5,000. The clearing days of the check after it is deposited is 4 days and 3 days for the larger check and smaller check respectively.

Formula to calculate the average daily float:

$\text{Average daily float}=\frac{\text{Total float}}{\text{Number of days in a month}}$

Calculate the average daily float:

$\begin{array}{c}\text{Average daily float}=\frac{\text{Total float}}{\text{Number of days in a month}}\\ =\frac{\$71,000}{30}\\ =\$2,366.666\end{array}$

Hence, the average daily float is $2,366.667.

c)

Summary Introduction

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

Answer to Problem 4QP

The average daily receipts are $633.33 and the weighted average delay is 3.74 days.

Explanation of Solution

Given information:

Once in a month, Person X’s neighbor collects two checks; one check for $14,000 and another check for $5,000. The clearing days of the check after it is deposited is 4 days and 3 days for the larger check and smaller check respectively.

Formula to compute the average daily charge:

$\text{Average daily receipts}=\frac{\left[\begin{array}{l}\text{Average number of days for a larger check }\\ \text{to be cleared}\left(\text{Average daily value of larger check}\right)+\\ \text{Average number of days for a smaller check }\\ \text{to be cleared}\left(\text{Average daily value of smaller check}\right)\end{array}\right]}{\text{Number of days in a month}}$

Compute the average daily charge:

$\begin{array}{c}\text{Average daily receipts}=\frac{\left[\begin{array}{l}\text{Average number of days for a larger check }\\ \text{to be cleared}\left(\text{Average daily value of larger check}\right)+\\ \text{Average number of days for a smaller check }\\ \text{to be cleared}\left(\text{Average daily value of smaller check}\right)\end{array}\right]}{\text{Number of days in a month}}\\ =\frac{\left(\$14,000+\$5,000\right)}{30}\\ =\$633.33\end{array}$

Hence, the average daily charge is $633.33.

Formula to compute the weighted average delay:

$\text{Weighted average delay}=\left[\begin{array}{l}\text{Average number of days for a larger check to be cleared}\\ \left(\frac{\text{Average daily value of larger check}}{\text{Average daily receipts}}\right)+\\ \text{Average number of days for a smaller check to be cleared}\\ \frac{\left(\text{Average daily value of smaller check}\right)}{\text{Average daily receipts}}\end{array}\right]$

Compute the weighted average delay:

$\begin{array}{c}\text{Weighted average delay}=\left[\begin{array}{l}\text{Average number of days for a larger check to be cleared}\\ \left(\frac{\text{Average daily value of larger check}}{\text{Average daily receipts}}\right)+\\ \text{Average number of days for a smaller check to be cleared}\\ \frac{\left(\text{Average daily value of smaller check}\right)}{\text{Average daily receipts}}\end{array}\right]\\ =4\left(\frac{\$14,000}{\$19,000}\right)+3\left(\frac{\$5,000}{\$19,000}\right)\\ =3.74\text{ days}\end{array}$

Hence, the weighted average delay is 3.74 days.