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CHAPTER 27
CASH MANAGEMENT
Answers to Concepts Review and Critical Thinking Questions
Question 9 discusses another reason.
2. If it has too much cash it can pay a dividend, or, more likely in the current financial environment, buy
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
actually does, and the firm is, therefore, receiving interest on funds it has already spent.
8. a. About the only disadvantage to holding T-bills are the generally lower yields compared to
alternative money market investments.
b. Some ordinary preferred stock issues pose both credit and price risks that are not consistent with
most short-term cash management plans.
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 that
doing so increases the firm’s cash cycle.
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
loan, and the grocery store is harmed because it could have earned interest on the money instead of
loaning it to you.
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.
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
2. a. The disbursement float is the average daily checks written times the average number of days for
the checks to clear, so:
Disbursement float = 4($13,200)
Disbursement float = $52,800
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b. The new collection float will be:
Collection float = 1(–$23,800)
Collection float = –$23,800
3. a. The collection float is the average daily checks received times the average number of days for
the checks to clear, so:
Collection float = 3($14,700)
Collection float = $44,100
b. The firm should pay no more than the amount of the float, or $44,100, to eliminate the float.
4. a. Total float = 4($9,200) + 5($2,400)
Total float = $48,800
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:
5. The average daily collections are the number of checks received times the average value of a check,
so:
Average daily collections = $127(4,950)
Average daily collections = $628,650
The present value of the lockbox service is the average daily receipts times the number of days the
collection is reduced, so:
PV = (2 day reduction)($628,650)
PV = $1,257,300
The daily cost is a perpetuity. The present value of the cost is the daily cost divided by the daily interest
rate. So:
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:
Average daily float = [.70(5,850)($50)(2) + .30(5,850)($75)(3)]/30
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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:
Weighted average delay = 2[.70(5,850)($50)/$336,375] + 3[.30(5,850)($75)/$336,375]
Weighted average delay = 2.39 days
c. The most the firm should pay is the total amount of the average float, or $26,813.
d. The average daily interest rate is:
1.07 = (1 + R)365
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:
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6
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:
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 two payments early. So, the savings are the cash
balance reduction of $283,800 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:
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
10. The benefit of the new arrangement is the $2.7 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:
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:
PV = 2(750)($570)
PV = $855,000
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:
Daily interest rate = 1.051/365 – 1
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9
APPENDIX 27A
1. a. Decrease. This will lower the trading costs, which will cause a decrease in the target cash balance.
b. Decrease. This will increase the holding cost, which will cause a decrease in the target cash
balance.
c. Increase. This will increase the amount of cash that the firm has to hold in non-interest bearing
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:
Holding cost = ($1,300)(.05)
Holding cost = $65.00
The trading costs are the total cash needed times the replenishing costs, divided by the average daily
balance times two, so:
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The target cash balance using the BAT model is:
4. a. The opportunity costs are the amount transferred times the interest rate, divided by two, so:
Opportunity cost = ($1,500)(.05)/2
Opportunity cost = $37.50
The trading costs are the total cash balance times the trading cost per transaction, divided by the
amount transferred, so:
5. The total cash needed is the cash shortage per month times twelve months, so:
Total cash = 12($140,000)
Total cash = $1,680,000
The target cash balance using the BAT model is:
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:
Securities sold = $80,000 – 43,000
7. The target cash balance using the Miller-Orr model is:
C* = L + (3/4 × F × 2/R]1/3
C* = $1,500 + [3/4($40)($70)2/.00021]1/3
C* = $2,387.90
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:
Daily rate = 1.071/365 – 1
Daily rate = .000185, or .0185% per day
10. Using the BAT model and solving for R, we get:
C* = [(2T × F)/R]1/2
