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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 pay a dividend or, more likely in the current financial environment,
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
7. A net disbursement float is more desirable because the bank thinks the firm has more money than it
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:
c. The maximum daily fee 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 total 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
On average, there is $26,712 that is uncollected and not available to the firm.
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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
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:
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
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 daily 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 payments three days earlier. So, the savings
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:
9. The interest that the company could earn will be the amount of the checks times the number of days
10. The benefit of the new arrangement is the $4.5 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:
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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, 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
APPENDIX 19A
1. a. Decrease. This will lower the trading costs, which will cause a decrease in the target cash
balance.
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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:
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
