The following information about the operations of Franklin Company is available. The cost of capital for Franklin is 13%. Annual sales $25 million Variable cost ratio 68% Number of days sales...

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4.1. The following information about the operations of Franklin Company is available.
The cost of capital for Franklin is 13%.
Annual sales $25 million
Variable cost ratio 68%
Number of days sales outstanding 73 days
Number of days in payables 30 days
Inventory turnover ratio 4.21
Find the following about Franklin:
A. Inventory period
B. Receivables period
C. Operating cycle
D. Payables period
E. Cash cycle
F. Sales in one operating cycle
G. NPV of its operating cycle
A. 86.70 days, B. 73 days, C. 159.7 days, D. 30 days, E. 129.7 days, F. $10.938 million,
G. $3.005 million ♥
Solution:
A. Inventory period
Formula: Inventory period = 365/Inventory turnover ratio
 365/4.21
 86.70 days
B. Receivables period
Receivables period is otherwise called as the “Average collection period” or
“Number of days sales outstanding”.
In the question, the number of days’ sales outstanding is given as 73 days and
hence the receivables period is also 73 days.
 73 days.
C. Operating cycle
Operating cycle is defined as the time between the firm receives the invoice for
raw materials inventory and the firm receives cash for finished goods sold.
Therefore, as per the definition, we can say that:
Operating cycle = Inventory period + Receivables period
 86.70 days + 73 days
 159.7 days
D. Payables period
Payables period is the time between the receipt of the invoice for raw materials
inventory and the cash payment made to suppliers for the same. It is also called as
the number of days in payable, which is given as 30 days in the question.
Therefore, the answer is also 30 days.
 30 days
E. Cash cycle
The cash cycle is also called as the net operating cycle. This is the time between
cash paid for raw materials and cash received for finished goods sold.
Cash cycle = Inventory period + Receivables period – Payables period
 86.70 days + 73 days – 30 days
 129.7 days

F. Sales in one operating cycle
The annual sales are given, which is for 365 days.
So, we have to find the sales for one operating cycle, which is 159.7 days.
Sales in one operating cycle = $25,000,000 * 159.7/365
 $10,938,356
 The above is written as $10.938 million.
G. NPV of its operating cycle
Step 1: To find the Cost in one operating cycle (Cd)
We have already calculated the Sales in one operating cycle as $10.938 million.
Variable cost ratio = 68%
Therefore, total annual variable cost = Annual sales * Variable cost ratio
 $25 million * 68%
 $17 million
Cost in one operating cycle = Annual costs * Operating cycle in days/365
 $17 million * 159.7/365
 $7,438,082
The above is written as $7.438 million
Step 2: To find the NPV of the operating cycle
Formula:
-Cd Sd
NPV (operating cycle) =
(1 + r)p
+
(1 + r)d

Where:
C = Cost of goods sold in one year
S = Sales in one year
r = Cost of capital
p = Payables period, in years
d = Operating cycle, in years
In the above formula, we have calculated all the required amounts.
Cd = Cost in one operating cycle = $7.438 million (refer step 1)
Sd = Sales in one operating cycle = $10.938 million (refer F)
R = 13% (given)
Payables period, in years = 30/365
Operating cycle, in years = 159.7/365
Substituting the above figures in the formula, we get:
NPV of operating cycle = -7.438 + 10.938
(1+.13)
30/365
(1+.13)
159.7/365
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