978-0077861704 Chapter 19 Solutions Manual Part 1

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CHAPTER 19

CASH AND LIQUIDITY MANAGEMENT

Answers to Concepts Review and Critical Thinking Questions

1. Yes. Once a firm has more cash than it needs for operations and planned expenditures, the excess

2. If it has too much cash, it can simply pay a dividend or, more likely in the current financial

4. Historically, it has often been argued that companies held cash to guard against future economic

5. Cash management is associated more with the collection and disbursement of cash. Liquidity

6. Such instruments go by a variety of names, but the key feature is that the dividend adjusts, keeping

8. The firm has a net disbursement float of $500,000. If this is an ongoing situation, the firm may be

9. a. About the only disadvantage to holding T-bills are the generally lower yields compared to

b. Some ordinary preferred stock issues pose both credit and price risks that are not consistent

c. The primary disadvantage of NCDs is the normally large transactions sizes, which may not be

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d. The primary disadvantages of the commercial paper market are the higher default risk

e. The primary disadvantages of RANs are that some possess nontrivial levels of default risk, and

10. The concern is that excess cash on hand can lead to poorly thought-out management decisions. The

11. A potential advantage is that the quicker payment often means a better price. The disadvantage is

12. This is really a capital structure decision. If the firm has an optimal capital structure, paying off debt

13. It is unethical because you have essentially tricked the grocery store into making you an interest-free

Solutions to Questions and Problems

NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple

steps. Due to space and readability constraints, when these intermediate steps are included in this

solutions manual, rounding may appear to have occurred. However, the final answer for each problem is

found without rounding during any step in the problem.

Basic

1. The average daily float is the average value of checks received per day times the average number of

days delay, divided by the number of days in a month. Assuming 30 days in a month, the average

daily float is:

2. a. The disbursement float is the average daily value of checks written times the average number of

days for the checks to clear, so:

The collection float is the average daily value of checks received times the average number of

days for the checks to clear, so:

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The net float is the disbursement float plus the collection float, so:

b. The new collection float will be:

And the new net float will be:

3. a. The collection float is the average daily value of checks received times the average number of

days for the checks to clear, so:

b. The firm should pay no more than the amount of the float, or $57,000, to eliminate the float.

c. The maximum daily charge the firm should be willing to pay is the collection float times the

daily interest rate, so:

b. The average daily float is the total float divided by the number of days in a month. Assuming

30 days in a month, the average daily float is:

c. The average daily receipts are the average daily value of checks received divided by the

number of days in a month. Assuming a 30-day month:

The weighted average delay is the sum of the days to clear a check times the amount of the

check divided by the average daily receipts, so:

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5. The average daily collections are the number of checks received times the average value of a check,

so:

The present value of the lockbox service is the average daily receipts times the number of days the

collection is reduced, so:

The daily cost is a perpetuity. The present value of the cost is the daily cost divided by the daily

interest rate. So:

The NPV of the lockbox is the cost plus the present value of the reduction in collection time, so:

The firm should take the lockbox service.

The annual savings excluding the cost would be the future value of the savings minus the savings,

so:

And the annual cost would be the future value of the daily cost, which is an annuity, so:

So, the annual net savings would be:

6. a. The average daily float is the sum of the percentage each check amount is of the total checks

received times the number of checks received times the amount of the checks times the number

of days until the check clears, divided by the number of days in a month. Assuming a 30-day

month, we get:

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b. The total collections are the sum of the percentage of each check amount received times the

total checks received times the amount of the check, so:

The weighted average delay is the sum of the average number of days a check of a specific

amount is delayed, times the percentage that check amount makes up of the total checks

received, so:

The average daily float is the weighted average delay times the average value of checks

received per day. Assuming a 30-day month, we get:

c. The most the firm should pay is the total amount of the average float, or $21,560.

d. The average daily interest rate is:

The daily cost of float is the average daily float times the daily interest rate, so:

e. The most the firm should pay is the change in the average daily float. Under the reduced

collection time assumption, we get:

So, the most they should pay is the old float minus the new float, or:

7. a. The present value of adopting the system is the number of days collections are reduced times

the average daily collections, so:

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b. The NPV of adopting the system is the present value of the savings minus the cost of adopting

the system. The cost of adopting the system is the present value of the fee per transaction times

the number of transactions. This is a perpetuity, so:

c. The net cash flow is the present value of adopting the system times the daily interest rate, minus

the transaction cost per day, so:

The net cash flow per check is the net cash flow per day divided by the number of checks

received per day, or:

Alternatively, we could find the net cash flow per check as the number of days the system

reduces collection time times the average check amount times the daily interest rate, minus the

transaction cost per check. Doing so, we confirm our previous answer as:

8. a. The reduction in cash balance from adopting the lockbox is the number of days the system

reduces collection time times the average daily collections, so:

b. The dollar return that can be earned is the average daily interest rate times the cash balance

reduction. The average daily interest rate is:

The daily dollar return that can be earned from the reduction in days to clear the checks is:

c. If the company takes the lockbox, it will receive three payments early. So, the savings are the

cash balance reduction of $435,000 in part a.

If the lockbox payments occur at the end of the month, we need the effective monthly interest

rate, which is:

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Assuming the lockbox payments occur at the end of the month, the lockbox payments, which

are a perpetuity, will be:

PV = C / R

It could also be assumed that the lockbox payments occur at the beginning of the month. If so,

we would need to use the PV of a perpetuity due, which is:

PV = C + C / R

Solving for C:

C = (PV × R) / (1 + R)

9. The interest that the company could earn will be the amount of the checks times the number of days

it will delay payment times the number of weeks that checks will be disbursed times the daily

interest rate, so:

10. The benefit of the new arrangement is the $6 million in accelerated collections since the new system

will speed up collections by one day. The cost is the new compensating balance, but the company

will recover the existing compensating balance, so:

The company should proceed with the new system. The savings are the NPV times the annual

interest rate, so:

Intermediate

11. To find the NPV of taking the lockbox, we first need to calculate the present value of the savings.

The present value of the savings will be the reduction in collection time times the average daily

collections, so:

And the daily interest rate is:

Daily interest rate = 1.0551/365 – 1

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The transaction costs are a perpetuity. The cost per day is the cost per transaction times the number

of transactions per day, so the NPV of taking the lockbox is:

Without the annual fee, the lockbox system should be accepted. To calculate the NPV of the lockbox

with the annual fee, we can simply use the NPV of the lockbox without the annual fee and subtract

the additional cost. The annual fee is a perpetuity, so, with the fee, the NPV of taking the lockbox is:

With the annual fee, the lockbox system should not be accepted.

12. The minimum number of payments per day needed to make the lockbox system feasible is the

number of checks that makes the NPV of the decision equal to zero. The average daily interest rate

is:

The present value of the savings is the average payment amount times the days the collection period

is reduced times the number of customers. The costs are the transaction fee and the annual fee. Both

are perpetuities. The total transaction costs are the transaction costs per check times the number of

checks. The equation for the NPV of the project, where N is the number of checks transacted per day,

is:

APPENDIX 19A

1. a. Decrease. This will lower the trading costs, which will cause a decrease in the target cash

c. Increase. This will increase the amount of cash that the firm has to hold in non-interest-bearing

d. Decrease. If the credit rating improves, then the firm can borrow more easily, allowing it to

e. Increase. If the cost of borrowing increases, the firm will need to hold more cash to protect

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f. Either. This depends somewhat on what the fees apply to, but if direct fees are established, then

2. The target cash balance using the BAT model is:

C* = [(2T × F)/R]1/2

3. The holding cost is the average daily cash balance times the interest rate, so:

The trading costs are the total cash needed times the replenishing costs, divided by the average daily

balance times two, so:

The total cost is the sum of the holding cost and the trading cost, so:

The target cash balance using the BAT model is:

C* = [(2T × F) / R]1/2

They should increase their average daily cash balance to:

This would minimize the costs. The new total cost would be:

4. a. The opportunity costs are the amount transferred times the interest rate, divided by two, so:

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The trading costs are the total cash balance times the trading cost per transaction, divided by the

amount transferred, so:

The firm keeps too little in cash because the trading costs are much higher than the opportunity

costs.

b. The target cash balance using the BAT model is:

C* = [(2T × F) / R]1/2

5. The total cash needed is the cash shortage per month times 12 months, so:

The target cash balance using the BAT model is:

C* = [(2T × F) / R]1/2

The company should invest:

of its current cash holdings in marketable securities to bring the cash balance down to the optimal

level. Over the rest of the year, sell securities:

6. The lower limit is the minimum balance allowed in the account, and the upper limit is the maximum

balance allowed in the account. When the account balance drops to the lower limit:

in marketable securities will be sold, and the proceeds deposited in the account. This moves the

account balance back to the target cash level. When the account balance rises to the upper limit, then:

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of marketable securities will be purchased. This expenditure brings the cash level back down to the

7. The target cash balance using the Miller-Orr model is:

C* = L + (3/4 × F × 2 / R]1/3

The upper limit is:

U* = 3 × C* – 2 × L

When the balance in the cash account drops to $1,500, the firm sells:

of marketable securities. The proceeds from the sale are used to replenish the account back to the

optimal target level of C*. Conversely, when the upper limit is reached, the firm buys:

of marketable securities. This expenditure lowers the cash level back down to the optimal level of

8. As variance increases, the upper limit and the spread will increase, while the lower limit remains

unchanged. The lower limit does not change because it is an exogenous variable set by management.

9. The average daily interest rate is:

The target cash balance using the Miller-Orr model is:

C* = L + (3/4 × F × 2 / R]1/3

The upper limit is:

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10. Using the BAT model and solving for R, we get:

C* = [(2T × F)/R]1/2