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CHAPTER 27 APPENDIX -
CHAPTER 27
CASH 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. Cash management is associated more with the collection and disbursement of cash. Liquidity
5. Such instruments go by a variety of names, but the key feature is that the dividend adjusts, keeping
6. Net disbursement float is more desirable because the bank thinks the firm has more money than it
7. The firm has a net disbursement float of $500,000. If this is an ongoing situation, the firm may be
8. 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 transaction sizes, which may not be
d. The primary disadvantages of the commercial paper market are the higher default risk
e. The primary disadvantages of RANs is that some possess non-trivial levels of default risk, and
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9. The concern is that excess cash on hand can lead to poorly thought-out management decisions. The
10. A potential advantage is that the quicker payment often means a better price. The disadvantage is
11. This is really a capital structure decision. If the firm has an optimal capital structure, paying off debt
12. 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 amount 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 checks written times the average number of days for
the checks to clear, so:
The collection float is the average daily checks received times the average number of days for
the checks to clear, so:
The net float is the disbursement float plus the collection float, so:
b. The new collection float will be:
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And the new net float will be:
3. a. The collection float is the average daily checks received times the average number of days for
the checks to clear, so:
c. The maximum daily charge the firm should be willing to pay is the collection float times the
daily interest rate, so:
4. a. Total float = 4($9,700) + 5($2,600)
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 total 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 checks received, so:
5. The average daily collections are the number of checks received times the average value of a check,
so:
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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 firm should take the lockbox service. The NPV of the lockbox is the cost plus the present value
of the reduction in collection time, so:
The annual savings excluding the cost would be the future value of the savings minus the costs, 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 check 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:
On average, there is $27,068 that is uncollected and not available to the firm.
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:
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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:
c. The most the firm should pay is the total amount of the average float, or $27,068.
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 amount the average daily float is reduced. Under the
reduced collection time assumption, we get:
7. a. The present value of adopting the system is the number of days collections are reduced times
the average daily collections, so:
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 the average daily collections times the daily interest
rate, minus the transaction cost per day, so:
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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
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:
c. If the company takes the lockbox, it will receive three payments early, with the first payment
occurring today. We can use the daily interest rate from part b, so the savings are:
If the lockbox payments occur at the end of the month, we need the effective monthly interest
rate, which is:
Assuming the lockbox payments occur at the end of the month, the lockbox payments, which
are a perpetuity, will be:
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:
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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 $2.9 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:
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:
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:
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Without the fee, the lockbox system should be accepted. To calculate the NPV of the lockbox with
With the 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 27A
1. a. Decrease. This will lower the trading costs, which will cause a decrease in the target cash
b. Decrease. This will increase the holding cost, 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
f. Either. This depends somewhat on what the fees apply to, but if direct fees are established, then
the compensating balance may be lowered, thus lowering the target cash balance. If, on the
2. The target cash balance using the BAT model is:
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The initial balance should be $2,661.45, and whenever the balance drops to $0, another $2,661.45
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:
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:
The trading costs are the total cash balance times the trading cost per transaction, divided by the
amount transferred, so:
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b. The target cash balance using the BAT model is:
5. The total cash needed is the cash shortage per month times twelve months, so:
The target cash balance using the BAT model is:
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:
7. The target cash balance using the Miller–Orr model is:
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The upper limit is:
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:
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.
As the variance increases, however, the amount of uncertainty increases. When this happens, the
9. The average daily interest rate is:
The target cash balance using the Miller–Orr model is:
The upper limit is:
10. Using the BAT model and solving for R, we get:
C* = [(2T × F) / R]1/2
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