Question

The Fried Green Tomatoes Restaurant has increased its operating cycle from 95.4 days to 99.7 days while the cash cycle has decreased by 1.9 days. How have these changes affected the accounts payable period?


Multiple Choice

Increase of 2.4 days


Increase of 4.3 days


Decrease of 2.4 days


Increase of 6.2 days


Decrease of 6.2 days

Answer 1

To determine how the changes in the operating cycle and cash cycle have affected the accounts payable period, we can use the following relationships:

1. **Operating Cycle** (OC) = Inventory Period (IP) + Accounts Receivable Period (ARP)
2. **Cash Cycle** (CC) = Operating Cycle (OC) - Accounts Payable Period (AP)

Given:

- The operating cycle increased from 95.4 days to 99.7 days.
- The cash cycle decreased by 1.9 days.

Let's define the following:

- Let \( OC_1 = 95.4 \) days (initial operating cycle).
- Let \( OC_2 = 99.7 \) days (new operating cycle).
- Let \( CC_1 \) = initial cash cycle.
- Let \( CC_2 = CC_1 - 1.9 \) days (new cash cycle).
- Let \( AP_1 \) = initial accounts payable period.
- Let \( AP_2 \) = new accounts payable period.

From the cash cycle formula:

\[
CC = OC - AP
\]

Initially:

\[
CC_1 = OC_1 - AP_1
\]

Thus:

\[
AP_1 = OC_1 - CC_1
\]

Now for the new state:

\[
CC_2 = OC_2 - AP_2
\]
\[
AP_2 = OC_2 - CC_2
\]

Substituting \( CC_2 = CC_1 - 1.9 \):

\[
AP_2 = OC_2 - (CC_1 - 1.9)
\]

Substituting \( OC_2 \) and \( OC_1 \):

\[
AP_2 = 99.7 - (CC_1 - 1.9)
\]

To find \( AP_2 - AP_1 \):

\[
AP_2 - AP_1 = \left(99.7 - (CC_1 - 1.9)\right) - \left(95.4 - CC_1\right)
\]

Simplifying this expression:

\[
AP_2 - AP_1 = 99.7 - CC_1 + 1.9 - 95.4 + CC_1
\]
\[
= 99.7 - 95.4 + 1.9
\]
\[
= 4.3 \text{ days}
\]

Since \( AP_2 - AP_1 \) is positive, the accounts payable period has increased by 4.3 days.

Thus, the answer is:

**Increase of 4.3 days**