Chapter 16, Problem 1P

### Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250

Chapter
Section

### Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250
Textbook Problem

# CASH CONVERSION CYCLE Parramore Corp has $12 million of sales,$3 million of inventories, $3.25 million of receivables, and$1.25million of payables. Its cost of goods sold is 75% of sales, and it finances working capital with bank loans at an 8%rate. What is Parramore’s cash conversion cycle (CCC)? If Parramore could lower its inventories and receivables by 10% each and increase its payables by 10%, all without affecting sales or cost of goods sold, what would be the new CCC, how much cash would be freed up, and how would that affect pretax profits?

Summary Introduction

To determine: The cash conversion cycle, the new cash conversion cycle, the amount of cash that would be freed up and the effect on pretax profits.

Introduction:

Cash Conversion Cycle:

The cash conversion cycle refers to the time period which starts from the production of the products to selling of the products and lasts until the time the customer receives the cash.

Explanation

Given information:

The amount of sales is $12 million. The amount of inventories is$3 million.

The amount of receivables is $3.25 million. The amount of payables is$1.25 million.

Cost of goods sold is 75% of sales.

The rate of interest on bank loans is 8%.

Calculation of the cash conversion cycle:

The formula to calculate the cash conversion cycle is,

CashāConversionāCycle=Inventoryāconversionāperiod+AverageācollectionāperiodāPaymentādeferralāperiod

Substitute 60.83 days for inventory conversion period, 73 days for the average collection period and 30.41 days for the payables deferral period (refer working note) in the above formula.

CashāConversionāCycle=121.67Ā days+98.85Ā daysā50.69Ā days=169.83ādays

The cash conversion cycle is 169.83 days or 170 days.

Now,

The inventories are reduced by 10%.

The receivables are reduced by 10%.

The payables are increased by 10%.

Calculation of the new cash conversion cycle:

The formula to calculate the cash conversion cycle is,

CashāConversionāCycle=Inventoryāconversionāperiod+AverageācollectionāperiodāPaymentādeferralāperiod

Substitute 109.5 days for inventory conversion period, 88.97 days for the average collection period and 55.76 days for the payables deferral period (refer working note) in the above formula.

CashāConversionāCycle=109.5Ā days+88.97Ā daysā55.76Ā days=143ādays

The new cash conversion cycle is 143 days.

Calculation of the total amount of cash freed up:

The formula to calculate the total amount of cash freed up is,

Totalācashāfreedāup=Cashāfreedāupāforāinventory+Cashāfreedāupāforāaccountsāreceivable+Cashāfreedāupāforāaccountsāpayable

Substitute $300,082.14 for cash freed up for inventory,$324,821.89 for cash freed up for accounts receivable and (-$125,013.68) for cash freed up for accounts payable (refer working note) in the above formula. Totalācashāfreedāup=$300,082.14+$324,821.89+($125,013.68)=$499,890.35 The total cash freed up is$499,890.35.

Calculation of the pre-tax profit:

The formula to calculate the pre-tax profit is,

Pre-taxāprofit=TotalāfreedāupācashĆInterestārate

Substitute $499,890.35 for the total cash freed up and 8% for the interest rate in the above formula. Pre-taxāprofit=$499,890.35Ć8%=$39,991.228 The pre-tax profit is$39,991.228.

Working note:

Calculation of the cost of goods sold:

Costāofāgoodsāsold=SalesĆCostāofāgoodsāsoldāpercentage=$12,000,000Ć75%=$9,000,000

The cost of goods sold is $9,000,000. Calculation of the inventory conversion period: Inventoryāconversionāperiod=InventoryCostāofāgoodsāsoldāperāday=$3,000,000$9,000,000365=$2,000,000$32,876.71=121.67ādays The inventory conversion period is 121.67 days. Calculation of the average collection period: Averageācollectionāperiod=AccountsāreceivableSalesāperāday=AccountsāreceivableSales365=$3,250,000$12,000,000365=98.85ādays The average collection period is 98.85 days. Calculation of the payable deferral period: Paymentādeferralāperiod=AccountsāpayableCostāofāgoodsāsoldāperāday=AccountsāpayableCostāofāgoodsāsold365=$1,250,000\$9,000,000365=50

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