CP

day, accounts receivable will be $1,000; they will rise to $2,000 by the end of the sec-

ond day; and by January 10, they will have risen to 10($1,000)
$10,000. On Janu-

ary 11, another $1,000 will be added to receivables, but payments for sales made on

January 1 will reduce receivables by $1,000, so total accounts receivable will remain

constant at $10,000. In general, once the firm’s operations have stabilized, this situa-

tion will exist:

(16-5)

 $1,000  10 days 
$10,000.

If either credit sales or the collection period changes, such changes will be reflected in

accounts receivable.

Notice that the $10,000 investment in receivables must be financed. To illustrate,

suppose that when the warehouse opened on January 1, BLC’s shareholders had put

up $800 as common stock and used this money to buy the goods sold the first day. The

$800 of inventory will be sold for $1,000, so BLC’s gross profit on the $800 invest-

ment is $200, or 25 percent. In this situation, the beginning balance sheet would be as

follows:^8

Inventories $800 Common stock $800

Total assets $800 Total liabilities and equity $800

At the end of the day, the balance sheet would look like this:

Accounts receivable $1,000 Common stock $ 800

Inventories 0 Retained earnings 200

Total assets $1,000 Total liabilities and equity $1,000

To remain in business, BLC must replenish inventories. To do so requires that $800 of

goods be purchased, and this requires $800 in cash. Assuming that BLC borrows the

$800 from the bank, the balance sheet at the start of the second day will be as follows:

Accounts receivable $1,000 Notes payable to bank $ 800

Inventories 800 Common stock 800

Retained earnings 200

Total assets $1,800 Total liabilities and equity $1,800

At the end of the second day, the inventories will have been converted to receivables,

and the firm will have to borrow another $800 to restock for the third day.

This process will continue, provided the bank is willing to lend the necessary

funds, until the beginning of the 11th day, when the balance sheet reads as follows:

Accounts receivable $10,000 Notes payable to bank $ 8,000

Inventories 800 Common stock 800

Retained earnings 2,000

Total assets $10,800 Total liabilities and equity $10,800

From this point on, $1,000 of receivables will be collected every day, and $800 of these

funds can be used to purchase new inventories.

This example makes it clear (1) that accounts receivable depend jointly on the level

of credit sales and the collection period, (2) that any increase in receivables must be

Accounts

receivable




Credit sales

per day



Length of

collection period

(^8) Note that the firm would need other assets such as cash, fixed assets, and a permanent stock of inventory.
Also, overhead costs and taxes would have to be deducted, so retained earnings would be less than the fig-
ures shown here. We abstract from these details here so that we may focus on receivables.
Receivables Management 597

592 Working Capital Management