Corporate Finance 公司理财 机械工业出版社 Ross Ch027第27章答案

《Corporate Finance》公司理财

Stephen A.Ross

机械工业出版社

Chapter 27: Cash Management

27.1 Firms need to hold cash to:

a. Satisfy the transaction needs. For example, cash is collected from sales and new

financing and disbursed as wages, salaries, trade debts, taxes and dividends.

b. Maintain compensating balances. A minimum required compensating balance at

banks providing credit service to the firm may impose a lower limit on the level of

cash a firm holds.

27.2 a. Decrease. Examine the Baumol model. As the interest rate (k) increases, the optimal

cash balance must also decrease.

b. Increase. Examine the Baumol model. As brokerage costs (F, the per transaction

costs) rise, the optimal balance increases.

c. Decrease. Clearly, if the bank lowers its compensating balance requirement, a firm

will not be required to hold as much of its assets as cash (assuming that the firm's

cash need for the transaction motive is below the compensating balance requirement).

d. Decreas

e. If the cost of borrowing falls, a firm need not hold as much of its assets as

cash because the cost of running short (borrowing to fill cash needs) is lower.

e. Increase. As a firm’s credit rating falls, its cost to borrow increases. Thus, the firm

cannot as easily afford to run short of cash and its cash balance must be higher.

f. Increase. Introduction of direct banking fees would increase the fixed costs

associated with holding cash. As fixed costs rise, the optimal balance must also rise.

27.3 In order to determine weekly earnings (sometimes the word "return" is used to mean

dollar amounts) on the cash balances, first find the weekly interest rate

.12

r==

.002308

52

and apply this to each of the weekly amounts:

Week Avg Cash Balance $ Earned

1 24,000 55.39

2 34,000 78.47

3 10,000 23.08

4 15,000 34.62

Avg monthly 83,000 191.56

Average annual earnings = 191.56 x 12 = $2,298.72 Note: this assumes interest is not compounded. The question does not specify what compounding assumptions should be made. 27.4 a.

The total amount of cash that will be disbursed during the year is: $345,000 * 12 = $4,140,000 Using the optimal cash balance formula from the Baumol model, 193,243$07.0)000,140,4)(500($2K 2FT *C === $243,193 should be kept as cash. The balance, $556,807 (=$800,000-$243,193), should be invested in marketable securities. b.

The number of times marketable securities will be sold during the next twelve months is $4,140,000 / $243,193 = 17 times 27.5

Start with the Baumol model and solve for Total Costs, T: ()222C*2FT C*K KC*T 2F .075(20 million)25,000$3,000 million ===?=?= 3,000 million Average weekly disbursement 52$57.69 million == 27.6 Use the Miller-Orr formula. The target cash balance = Z*3F 4K L 2

3=+σ

The upper limit = H*=3Z*-2L

The daily opportunity cost = K 10.000211==

Z*$20,000$34,536= H*3(34,536)2(20,000)63,608=-= The target cash level is $34,536, and the upper limit is $63,608. 27.7 a. Since the upper limit, H*, is set by the firms, use that to find Z*: H* = 3Z* - 2L H* - 2L Z* = 3 Then, H 2L 200,0002100,000g g Z *$133,333Gold 33H 2L 300,0002150,000s s Z *$200,000Silver 33++?===++?=== b. Use the Miller/Orr equation for Z*, and solve for variance, 2σ

:

()()()2

33

2

332Z*L

3F Z*L 4K 3F Z*L 4K

Z*L 4K

3F

σσσ==+-=-=

Now, find the variance for Gold Star:

()()G 332G G G G G K 10.000261

133,333100,00040.000261

Z *L 4K /3F 6,444,251

32,000σ==-??=-=≈?

and Silver Star:

()()S 3

32S S S S S K 10.000236

200,000150,00040.000236

Z *L 4K /3F 15,733,333

32,000σ==-??=-=≈?

So, Silver Star Co. has a more volatile daily cash flow.

27.8 Compare the cost and benefit of a lockbox:

Benefit of Lockbox:

Garden Groves daily float = 150 payments per day x $15,000 avg payment

= $2,250,000

27.8 (continued)

Increase in collected cash balance if a 3 day lockbox is installed

= 3 x $2,250,000

= $6,750,000

Since this is a sustained increase in the cash balance, find the annual earnings from

this increase if invested in money-market securities:

Annual earnings = $6,750,000 x 0.075

= $506,250

Cost of Lockbox:

Variable cost $ 0.5 x 150 x 365 = $27,375

Fixed cost = 80,000

Total cost =$107,375

Net benefit of the lockbox = Benefit - Cost

= $506,250 - $107,375

= $398,875

The lockbox system should be installed.

27.9 To make the system profitable, the net earnings of installing the lockbox system must

be non-negative. The lower limit for acceptability is zero profits.

Let N = number of customers per day, and write the benefit and cost of the lock box

in terms of N:

Earnings = ($4,500) (N) (2) (0.06) = $540 x N

Costs: Total Cost = Variable Cost + Fixed Cost

Variable cost = N (365) ($0.25) = $91.25 x N

Fixed cost = $15,000

Total cost = 91.25 N + 15,000

Then, set Earnings = Total Cost, and solve for N: 540 N = 15,000 + 91.25 N N = 33.43 Salisbury Stakes needs at least 34 customers per day for the lockbox system to be profitable.

27.10

Disbursement float = avg daily pymts x avg days to clear = $12,000 x 5 = $60,000 Collection float = avg pymt x availability time = -$15,000 x 3 = -$45,000 Net float = disbursement float - collection float = $60,000 - $45,000 = $15,000 If funds are collected in four days rather than three, disbursement float will not change. Collection float would change to -15,000 x 4 = -$60,000. This change would make the net float equal to zero. 27.11 a.

Reduction in outstanding cash balances = $100,000 x 3 days = $300,000 b.

Return on savings = $300,000 (0.12) = $36,000 c.

Maximum monthly charge = $36,000 / 12 = $3,000 27.12 The cash savings are the earnings from the interest bearing account that otherwise

would not have been received.

The $ Return on the delayed payment is (ignoring compounding)

()$200,000.00043$240

R ??=??= Since the disbursements occur every 2 weeks:

Annual savings = 240 x 26

= $6,240

The Walter Company will save $6,240 per year.

27.13 If the Miller Company divides the eastern region, collections will be accelerated by

one day freeing up $4 million per day. Compensating balances will be increased by

$100,000 [=2($300,000)-$500,000]. The net effect is to have $3,900,000 to invest.

If T-bills pay 7% per year, the annual net savings from the division of the eastern

region is

$3,900,000 x 0.07 = $273,000.

Therefore, Miller should divide the Eastern Region.

27.14 Lockbox Benefit

daily float = 7,500 x 250

= $1,875,000

increased cash = 1.5 days x $1,875,000

= $2,812,500

daily Interest = 2,812,500 x .0003

= $843.75

annual interest = 843.75 x 365

= $307,968.75

Lockbox Cost: = 30,000 + .3 x 250 pymts x 365 days

= $57,375

Net Benefit of Lockbox = Benefit - Cost

= 307,986.75 - 57,375

= $250,593.75

Concentration Banking:

daily float = 1,875,000

increased cash = 1 day x $1,875,000 = $1,875,000

daily interest = 1,875,000 x .0003 = 562.50

annual interest = 562.50 x 365 = $205,312.50

Since there is no other additional cost for Concentration Banking,

compare:

205,312.50: net benefit of concentration

250,593.75: net benefit of lockbox

So the lockbox system is recommended.

27.15 The important characteristics of short-term marketable securities are:

i. maturity

ii. default risk

iii. marketability

iv.taxability

《Corporate Finance》公司理财

Stephen A.Ross

机械工业出版社