Problem 20-2 Float

a.
                                           Firm's        Bank's
                                          checkbook      records
                                          __________   __________
       Day 1     Deposit $1,200,000;
                 write check for
                 $1,600,000.             -$  400,000   $1,200,000

       Day 2     Write check
                 for $1,600,000.         -$2,000,000   $1,200,000

       Day 3     Write check 
                 for $1,600,000.         -$3,600,000   $1,200,000

       Day 4     Write check 
                 for $1,600,000.         -$5,200,000   $1,200,000

       Day 5     Write check for
                 $1,600,000; deposit
                 $1,600,000.             -$5,200,000   $1,200,000

After the firm has reached a steady state, it must deposit $1,600,000
each day to cover the checks written four days earlier.

b.	The firm has four days of float.

c.	The firm should try to maintain a balance on the bank's records of $1,200,000.  
On its own books it will have a balance of minus $5,200,000.

d.	For any level of sales, the firm will probably have a higher rate of return 
on assets and equity if it can reduce its total assets.  By using float, SSC can 
reduce its cash account, by (4 H $1,600,000) - $1,200,000 = $5,200,000.  However, 
they actually can reduce equity and debt by $6,000,000 as the firm has gross float
 of $6,400,000 - $400,000 (increase in the amount deposited in the bank) 
= $6,000,000, so earnings per share will be higher.  In terms of the Du Pont 
system, the rate of return on equity will be higher because of the reduction 
in total assets.

Problem 20-3 Lockbox System

a.	Presently, HGC has 5 days of collection float; under the lockbox system, this would drop to 2 days.

                         $1,400,000 H 5 days       = $7,000,000 
                         $1,400,000 H 2 days       =  2,800,000 
                                                     $4,200,000

HGC can reduce its cash balances by the $4,200,000 reduction in negative float.

b.	0.10($4,200,000) = $420,000 = the value of the lockbox system on an annual basis.

c.	$420,000/12 = $35,000 = maximum monthly charge HGC can pay for the lockbox system.

Problem 20-7 Receivables

a.	0.4(10) + 0.6(40) = 28 days.

b.	$900,000/360 = $2,500 sales per day.
$2,500(28) = $70,000 = Average receivables.

c.	0.4(10) + 0.6(30) = 22 days.  $900,000/360 = $2,500 sales per day.
$2,500(22) = $55,000 = Average receivables.

Sales may also decline as a result of the tighter credit.  
This would further reduce receivables.  Also, some customers 
may now take discounts further reducing receivables.