Solutions to Chapter 20
Cash and Inventory Management
1.
Ledger balance = starting balance – payments + deposits
Ledger balance = $250,000 – $20,000 – $60,000 + $45,000 = $215,000
The payment float is the outstanding total of not-yet-cleared checks written by the
firm, which equals $60,000 in this case.
The net float is: $60,000 – $45,000 = $15,000
2.
3.
4.
a.
Payment float = $625,000 – $600,000 = $25,000
Availability float = $625,000 – $550,000 = $75,000
b.
The company can earn interest on these funds.
c.
Payment float increases. The bank’s ledger balance and available balance
increase by the same amount.
a.
Payment float =
$20,000  6 = $120,000
Availability float = $22,000  3 = $ 66,000
Net float =
$ 54,000
b.
If availability float were reduced by one day, then interest could be earned on
$22,000. Annual interest earnings would be: 0.06  $22,000 = $1,320
The present value of the earnings, if the reduction in float were permanent,
would be $22,000.
a.
The lock-box reduces collection float by:
400 payments per day  $2,000 per payment  2 days = $1,600,000
Daily interest saved is: 0.00015  $1,600,000 = $240
The bank charge each day is: 400 payments per day  $0.40 per payment = $160
The lock-box is worthwhile; interest earnings exceed the bank charges.
b.
Break-even occurs when interest earned equals the bank fees:
0.00015  [400  $2,000  Days saved] = $160  Days saved = 1.33
20-1
5.
payment float; availability float; net float; concentration banking; wire transfer;
depository transfer check; lock-box banking.
20-2
6.
7.
a.
Collection float decreases by: $15,000 per day  2 days saved = $30,000
b.
Daily interest saving = 0.0002  30,000 = $6
c.
Monthly savings = 30  $6 = $180
This is the maximum fee Sherman’s should pay.
a.
The lock box will collect an average of: $300,000/30 = $10,000 per day
The money will be available three days earlier; this will increase the cash
available to JAC by $30,000. Thus, JAC will be better off accepting the
compensating balance offer: $25,000 is tied up in the compensating balance,
but the lock-box frees up $30,000.
b.
Let x equal the average check size for break-even. Then the number of checks
written per month is (300,000/x) and the monthly cost of the lockbox is:
(300,000/x)  0.10
The alternative is the compensating balance of $25,000; its monthly cost is the
lost interest, which is equal to:
$25,000  (0.06/12)
These costs are equal if:
($300,000/x)  0.10 = $25,000  (0.06/12)  x = $240
If the average check size is greater than $240, then paying per check is less
costly; if the average size is less than $240, then the compensating balance
arrangement is less costly.
c.
In part (a), we compared balances with balances: how many dollars are made
available to JAC compared to the number of dollars required to be kept in the
bank. In part (b), one cost is compared to another. The interest forgone by
holding the compensating balances is compared to the cost of processing
checks, and so here we need to know the interest rate.
8.
Total compensating balances increase by $100,000. However, collection float
decreases by $1 million. Opening the new account increases funds on which the
firm can earn interest by $900,000. The firm should open the account.
9.
a.
Optimal initial cash balance, from the Baumol model, equals:
2  300,000  20
 $20,000
0.03
The firm should sell securities for cash: $300,000/$20,000 = 15 times per year
20-3
b.
The average cash balance is: $20,000/2 = $10,000
10. Sales = 200 units per month
Carrying cost = $1 per month per gem
Order cost = $20
Economic order quantity 
2  200  20
 89.4
1
The economic order quantity is only about 90 gems, which is less than one-half of a
month’s sales. The firm should place smaller but more frequent orders.
11. Order cost = $40
Sales = 200 pounds per week
Carrying cost = 0.05 per pound per week
Economic order quantity 
2  200  20
 400
0.05
Patty should restock less frequently. The optimal order size is 400 pounds, meaning
that she should reorder every other week.
12. a.
Orders per month
Total order cost
Average inventory
Total carrying costs
Total inventory costs
b.
EOQ 
100
10
$300
$50
$75
$375
Order Size
200
300
5
4
$150
$120.0
$100
$125.0
$150
$187.5
$300
$307.5
2  purchases  cost per order

carrying cost
400
2
$60
$250
$375
$435
2  1,000  30
 200
1.50
The order size of 200 does in fact minimize total costs.
13. a.
b.
EOQ 
2  purchases  cost per order

carrying cost
2  7,200  250
 600
0.20  50
Total costs = order costs + carrying costs
7,200  
600 

  250 
   0.20  50 
  $6,000
600  
2 

20-4
14. If the firm takes the discount, it obtains the goods at a lower price, but is obligated to
place larger orders than the optimal order size derived in the previous problem. Total
inventory-related costs will increase, possibly by more than the price discount.
If the firm places an order of 1,800 units, its total costs are as follows. (We continue to
assume carrying costs are 20% of the purchase price, which has fallen by 1% to:
0.99  $50
Total costs = order costs + carrying costs
7,200  
1,800 

  250 
   0.20  50  0.99 
  $9,910
1,800  
2 

Therefore, inventory costs have increased by: $9,910  $6,000 = $3910 (compared to
the result in the previous problem)
The reduction in the purchase cost is: 0.01  50  $7,200 = $3600
Therefore, the firm saves less from the discount than the increase in inventory costs.
The firm should reject the discount.
15. EOQ 
2  sales  cost per order
carrying cost
If order cost falls by a factor of 50, then the economic order quantity falls by a factor
of approximately 7. So you should order one-seventh as many goods, but 7 times as
often.
16. This problem is a straightforward application of the Baumol model. The optimal
initial cash balance is:
2  100,000  10
 $20,000
0.005
This implies that the average number of transfers per month is:
$100,000/$20,000 = 5.0
17. While the firm pays less for its payment to clear through the ACH system, the
system speeds up the clearing process. In the process, the firm loses payment float,
and the interest it could be earning on that float. If the payment is large enough, it
might be better to pay more for the clearing service, but continue to earn interest for
an extra day or so.
18. The cost of a wire transfer is $10, and cash is available the same day. The cost of a
check is $0.80 plus the loss of interest for three days, or:
20-5
$0.80 + [0.06  (3/365)  (amount transferred)]
Setting this equal to $10 and solving, we find the minimum amount transferred
is $18,656.
19. a.
Knob collects $182.5 million per year, or (assuming 365 days per year)
$0.5 million per day. If the float is reduced by three days, then Knob gains
by increasing average balances by $1.5 million.
b.
The line of credit can be reduced by $1.5 million, so that annual interest
savings equals:
$1.5 million  0.06 = $0.09 million = $90,000
c.
20. a.
The cost of the old system is $40,000 plus the opportunity cost of the extra
float ($90,000), or $130,000 per year. The cost of the new system is
$100,000. Therefore, Knob will save $30,000 a year by switching to the new
system.
The interest rate, the cost of each security transaction, and the day-to-day
variability of cash flows.
b.
The firm should restore its cash balance to the return point, which is the lower
limit plus one-third of the spread between the upper and lower limits.
c.
The firm would minimize the expected number of times its cash balance hits
either of the limit points by restoring the cash balance to the halfway point
between the limits. The forgone interest earnings that result from holding cash
balances, however, is another (opportunity) cost that the firm would like to
control. This consideration reduces the optimal level to which cash should be
restored. The return point that best trades off these costs turns out to be one-third
of the spread between the upper and lower limits. By using a return point below
the halfway point between the upper and lower limits, the firm increases the
transaction frequency but earns more interest. This minimizes the sum of
transaction costs plus costs of forgone interest.
21. Annual cash disbursements = $80  52 = $4160
Cost per transaction = $0.10
Interest rate = 0.03 per year
Economic order quantity 
2  4,160  0.10
 167
0.03
a.
You should go to the bank about once every 2 weeks ($167/$80 = 2.09).
b.
You should withdraw $167 at a time.
20-6
c.
Your average cash on hand is: $167/2 = $83.50
22. With an increase in the rate of interest, the opportunity cost of holding cash
increases. This decreases cash balances relative to sales.
20-7
23. The economic order quantity is proportional to the square root of sales. Since the
average inventory level equals order quantity divided by 2, inventory level is also
proportional to the square root of sales. Similarly, the average cash balance is
proportional to the square root of disbursements, which in turn ought to be about
proportional to production. Therefore, both cash and inventories should increase by
the square root of 2. A percentage of sales model predicts that both cash and
inventories would double. The percentage of sales models do not capture the
nonlinear relationships in these two components of current assets.
24. a.
In the 28-month period encompassing September 1976 through December 1978,
there are 852 days (365 + 365 + 30 + 31 + 30 + 31). Thus, Merrill Lynch
disbursed, per day:
$1.25 billion/852 = $1,467,000
b.
Remote disbursement delayed the payment of:
1.5 days  1,467,000 per day = $2,200,500
from day 0 to day 852 (i.e., remote disbursing shifted the stream of daily
payments back by 1.5 days). At an annual interest rate of 8%, a 28-month
delay in the payment of $2,200,500 is worth:
PV  $2.2005 million 
$2.2005 million
 0.362 million  $362,000
1.08 28 / 12
c.
If the benefits are permanent, the net benefit is the immediate cash inflow, or
$2,200,500.
d.
Merrill Lynch disbursed $1,467,000 each day. The 1.5 day delay is worth:
$1,467,000  1.5  (0.08/365) = $482.30
Merrill Lynch writes an average of: 365,000/852 = 428.4 checks per day
Therefore, Merrill Lynch would have been justified in incurring additional
costs of: $482.30/428.4 = $1.126 per check
20-8