Fundamentals of coroprate finance 7th ross westerfield CH20

Chapter20
•Cash and Liquidity
Management

McGraw-Hill/Irwin

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.


Chapter 20 – Index of Sample
Problems
•
•
•
•
•

Slide # 02 - 09
Slide # 10 - 11
Slide # 12 - 16
Slide # 17 - 21
Slide # 22 - 25

Float
Cost of float
Lockbox net present value
BAT model
Miller-Orr model


2: Float

On an average day, your firm receives 50 checks. These checks,
on average, are worth $250 each. The average collection delay is 3
days. Also each day, your firm writes about 25 checks. These
checks are worth an average of $400 and clear your bank in an
average of 6 days.
What is the amount of the collection float?
What is the amount of the disbursement float?
What is the amount of the net float?


3: Float
Collection float = Firm' s available balance - Firm' s book balance
= $0 − (50 × $250 × 3)
= -$37,500
Disbursement float = Firm' s available balance - Firm' s book balance
= (25 × $400 × 6) - $0
= $60,000
Net float = Collection float + Disbursement float
= - $37,500 + $60,000
= $22,500


4: Float
Your firm has decided to contract with only three customers who
each pay you monthly as follows:
Customer
A
B
C

Check Amount
$60,000
$40,000
$50,000

What is the average daily float amount?

Collection delay
4 days
5 days
2 days


5: Float
Item Amount

Delay

Total float

$60,000

×4

= $240,000

$40,000

×5

= $200,000

$50,000

×2

= $100,000

Total:

Average daily float =

$540,000

Total float $540,000
=
= $18,000
Total days
30


6: Float
Your firm has decided to contract with only three customers who
each pay you monthly as follows:
Customer
A
B
C

Check Amount

$60,000
$40,000
$50,000

Collection delay
4 days
5 days
2 days

What is the amount of the average daily receipts?
What is the weighted average delay?


7: Float
Total receipts
Average daily receipts =
Total days
$60,000 + $40,000 + $50,000
=
30
$150,000
=
30
= $5,000


8: Float

Amount

Weight

Delay

Weighted
average delay

$ 60,000

60/150 = .4000

4

.400 × 4 = 1.6000

$ 40,000

40/150 = .2667

5

.2667 × 5 = 1.3335

$ 50,000

50/150 = .3333

2

.3333 × 2 = .6666

$150,000

1.000

Total = 3.6001


9: Float

Average daily float = Average daily receipts × Weighted average delay
= $5,000 × 3.6001
= $18,000.50
= $18,000


10: Cost of float
The Breadwinner Co. receives an average of $1,200 a day in
checks. The average delay in clearing is 4 days. Currently, the
applicable interest rate per day is .03%.
What the is the present value of the float?
What is the most this firm should pay to eliminate its collection
float entirely?
What is the highest daily fee this firm should pay to eliminate its
collection float entirely?


11: Cost of float
What the is the present value of the float?

PV of the float = Total float
= Average daily receipts × Average delay
= $1,200 × 4
= $4,800


12: Cost of float
What is the most this firm should pay to eliminate its
collection float entirely?

Maximum cost = PV of the float = $4,800
What is the highest daily fee this firm should pay to
eliminate its collection float entirely?

Maximum daily fee = Total float × Daily interest rate
= $4,800 × .0003
= $1.44


13: Lockbox net present value
You are considering implementing a lockbox system and have
gathered this information:
Average daily lockbox payments
= 1,200
Average size of payment
= $750
Daily interest rate of Treasury bills
= .01%
Bank charge per check
= $.21

Reduction in mail time
= 1.5 days
Reduction in processing time
= 1.0 day
Reduction in clearing time
= .5 day
What is the NPV of this lockbox arrangement?


14: Lockbox net present value
NPV = Average daily collections × Reduction in delay = (1,200 × $750) × (1.5 + 1 + .5) −

1,200 × $.21
.0001

= $900,000 × 3 − $2,520,000
= $2,700,000 − $2,520,000
= $180,000

See the next slide for another approach.

Daily cost
Daily interest rate


15: Lockbox net present value
Daily cost = 1,200 × $.21 = $252
Daily savings = 1,200 × $750 × (1.5 + 1 + .5) × .0001 = $270
Daily profit = $270 - $252 = $18
$18

NPV of daily profit =
= $180,000
.0001
See the next slide for a slightly different approach.


16: Lockbox
Daily cost = 1,200 × $.21 = $252
PV of daily cost =

$252
= $2,520,000
.0001

Daily savings = 1,200 × $750 × (1.5 + 1 + .5) × .0001 = $270
PV of daily savings =

$270
= $2,700,000
.0001

NPV = $2,700,000 - $2,520,000 = $180,000


17: BAT model
Your firm utilizes $165,000 a week to pay bills. The standard
deviation of these cash flows is $20,000. The fixed cost of
transferring funds is $48 a transfer. The applicable interest rate is
6%. The firm has established a lower cash balance limit of
$100,000. Answer these five questions using the BAT model:

What is the optimal initial cash balance?
What is the optimal average cash balance?
What is the opportunity cost of holding cash?
What is the trading cost of holding cash?
What is the total cost of holding cash?


18: BAT model
What is the optimal initial cash balance?

C* =
=

(2T × F)
R
2 × $165,000 × 52 × $48
.06

$823,680,000
=
.06
= $117,166.55
= $117,167


19: BAT model
What is the optimal average cash balance?

C * $117,167
=

= $58,583.50 = $58,584
2
2
What is the opportunity cost of holding cash?

$58,584 ×.06 = $3,515.04 = $3,515


20: BAT model
What is the trading cost of holding cash?
Optimal initial cash balance $117,167
=
= .7101 weeks
Weekly cash need
$165,000
Total weeks per year 52
= 73.229 This is the number of transfers per year.
Cash balance duration .7101
Cost of transfer × Number of transfers per year = $48 × 73.229 = $3,514.99 = $3,515


21: BAT model
What is the total cost of holding cash?

Total cost = Opportunity cost + Trading cost
= $3,515 + $3,515
= $7,030


22: Miller-Orr model

Your firm utilizes $130,000 a week to pay bills. The standard
deviation of these cash flows is $15,000. The fixed cost of
transferring funds is $51 a transfer. Your firm has established a
lower cash balance limit of $80,000. The weekly interest rate is .
067%. Use the Miller-Orr model to answer these three questions.

What is the optimal initial cash balance?
What is the optimum upper limit?
What is the average cash balance?


23: Miller-Orr model
What is the optimal initial cash balance?
2 1 / 3

3
σ

C* = L +  × F × 
R 
4

2  .33333

3
$15,000


= $80,000 +  × $51×


4
.
00067


= $80,000 + $23,417.26
= $103,417.26
= $103,417


24: Miller-Orr model
What is the optimum upper limit?

U* = (3 × C*) − (2 × L)
= (3 × $103,417) − (2 × $80,000)
= $310,251 − $160,000
= $150,251