1. These are firms with relatively long inventory periods and/or relatively long receivables periods. Thus, such firms tend to keep inventory on hand, and they allow customers to purchase on credit and take a relatively long time to pay.
2. These are firms that have a relatively long time between the time purchased inventory is paid for and the time that inventory is sold and payment received. Thus, these are firms that have relatively short payables periods and/or relatively long receivable cycles.
3. a. Use: The cash balance declined by $200 to pay the dividend.
b. Source: The cash balance increased by $500, assuming the goods bought on payables credit were sold for cash.
c. Use: The cash balance declined by $900 to pay for the fixed assets.
d. Use: The cash balance declined by $625 to pay for the higher level of inventory.
e. Use: The cash balance declined by $1,200 to pay for the redemption of debt.
4. Carrying costs will decrease because they are not holding goods in inventory. Shortage costs will probably increase depending on how close the suppliers are and how well they can estimate need. The operating cycle will decrease because the inventory period is decreased.
5. Since the cash cycle equals the operating cycle minus the accounts payable period, it is not possible for the cash cycle to be longer than the operating cycle if the accounts payable is positive. Moreover, it is unlikely that the accounts payable period would ever be negative since that implies the firm pays its bills before they are incurred.
6. It lengthened its payables period, thereby shortening its cash cycle.
7. Their receivables period increased, thereby increasing their operating and cash cycles.
8. It is sometimes argued that large firms “take advantage of” smaller firms by threatening to take their business elsewhere. However, considering a move to another supplier to get better terms is the nature of competitive free enterprise.
9. They would like to! The payables period is a subject of much negotiation, and it is one aspect of the price a firm pays its suppliers. A firm will generally negotiate the best possible combination of payables period and price. Typically, suppliers provide strong financial incentives for rapid payment. This issue is discussed in detail in a later chapter on credit policy.
10. BlueSky will need less financing because it is essentially borrowing more from its suppliers. Among other things, BlueSky will likely need less short-term borrowing from other sources, so it will save on interest expense.
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. a. No change. A dividend paid for by the sale of debt will not change cash since the cash raised from the debt offer goes immediately to shareholders.
b. No change. The real estate is paid for by the cash raised from the debt, so this will not change the cash balance.
c. No change. Inventory and accounts payable will increase, but neither will impact the cash account.
d. Decrease. The short-term bank loan is repaid with cash, which will reduce the cash balance.
e. Decrease. The payment of taxes is a cash transaction.
f. Decrease. The preferred stock will be repurchased with cash.
g. No change. Accounts receivable will increase, but cash will not increase until the sales are paid off.
h. Decrease. The interest is paid with cash, which will reduce the cash balance.
i. Increase. When payments for previous sales, or accounts receivable, are paid off, the cash balance increases since the payment must be made in cash.
j. Decrease. The accounts payable are reduced through cash payments to suppliers.
k. Decrease. Here the dividend payments are made with cash, which is generally the case. This is different from part a where debt was raised to make the dividend payment.
l. No change. The short-term note will not change the cash balance.
m. Decrease. The utility bills must be paid in cash.
n. Decrease. A cash payment will reduce cash.
o. Increase. If marketable securities are sold, the company will receive cash from the sale.
2. The total liabilities and equity of the company are the net book worth, or market value of equity, plus the long-term debt, so:
Total liabilities and equity = $9,300 + 1,900
Total liabilities and equity = $11,200
This is also equal to the total assets of the company. Since total assets are the sum of all assets, and cash is an asset, the cash account must be equal to total assets minus all other assets, so:
Cash = $11,200 – 2,300 – 2,450
Cash = $6,450
We have NWC other than cash, so the total NWC is:
NWC = $2,450 + 6,450
NWC = $8,900
We can find total current assets by using the NWC equation. NWC is equal to:
NWC = CA – CL
$8,900 = CA – $1,250
CA = $10,150
3. a. Increase. If receivables go up, the time to collect the receivables would increase, which increases the operating cycle.
b. Increase. If credit repayment times are increased, customers will take longer to pay their bills, which will lead to an increase in the operating cycle.
c. Decrease. If the inventory turnover increases, the inventory period decreases.
d. No change. The accounts payable period is part of the cash cycle, not the operating cycle.
e. Decrease. If the receivables turnover increases, the receivables period decreases.
f. No change. Payments to suppliers affects the accounts payable period, which is part of the cash cycle, not the operating cycle.
4. a. Increase; Increase. If the terms of the cash discount are made less favorable to customers, the accounts receivable period will lengthen. This will increase both the cash cycle and the operating cycle.
b. Increase; No change. This will shorten the accounts payable period, which will increase the cash cycle. It will have no effect on the operating cycle since the accounts payable period is not part of the operating cycle.
c. Decrease; Decrease. If more customers pay in cash, the accounts receivable period will decrease. This will decrease both the cash cycle and the operating cycle.
d. Decrease; Decrease. Assume the accounts payable period and inventory period do not change. Fewer raw materials purchased will reduce the inventory period, which will decrease both the cash cycle and the operating cycle.
e. Decrease; No change. If more raw materials are purchased on credit, the accounts payable period will tend to increase, which would decrease the cash cycle. We should say that this may not be the case. The accounts payable period is a decision made by the company’s management. The company could increase the accounts payable account and still make the payments in the same number of days. This would leave the accounts payable period unchanged, which would leave the cash cycle unchanged. The change in credit purchases made on credit will not affect the inventory period or the accounts payable period, so the operating cycle will not change.
f. Increase; Increase. If more goods are produced for inventory, the inventory period will increase. This will increase both the cash cycle and operating cycle.
5. a. A 45-day collection period implies all receivables outstanding from the previous quarter are collected in the current quarter, and:
(90 – 45)/90 = 1/2 of current sales are collected. So:
Q1 Q2 Q3 Q4
Beginning receivables $300 $400 $380 $470
Sales 800 760 940 870
Cash collections (700) (780) (850) (905)
Ending receivables $400 $380 $470 $435
b. A 60-day collection period implies all receivables outstanding from previous quarter are collected in the current quarter, and:
(90-60)/90 = 1/3 of current sales are collected. So:
Q1 Q2 Q3 Q4
Beginning receivables $300 $533 $507 $627
Sales 800 760 940 870
Cash collections (567) (787) (820) (917)
Ending receivables $533 $507 $627 $580
c. A 30-day collection period implies all receivables outstanding from previous quarter are collected in the current quarter, and:
(90-30)/90 = 2/3 of current sales are collected. So:
Q1 Q2 Q3 Q4
Beginning receivables $300 $267 $253 $313
Sales 800 760 940 870
Cash collections (833) (773) (880) (893)
Ending receivables $267 $253 $313 $290
6. The operating cycle is the inventory period plus the receivables period. The inventory turnover and inventory period are:
Inventory turnover = COGS/Average inventory
Inventory turnover = $52,827/{[$8,413 + 10,158]/2}
Inventory turnover = 5.6892 times
Inventory period = 365 days/Inventory turnover
Inventory period = 365 days/5.6892
Inventory period = 64.16 days
And the receivables turnover and receivables period are:
Receivables turnover = Credit sales/Average receivables
Receivables turnover = $67,312/{[$5,108 + 5,439]/2}
Receivables turnover = 12.7642 times
Receivables period = 365 days/Receivables turnover
Receivables period = 365 days/12.7642
Receivables period = 28.60 days
So, the operating cycle is:
Operating cycle = 64.16 days + 28.60 days
Operating cycle = 92.75 days
The cash cycle is the operating cycle minus the payables period. The payables turnover and payables period are:
Payables turnover = COGS/Average payables
Payables turnover = $52,827/{[$6,927 + 7,625]/2}
Payables turnover = 7.2604 times
Payables period = 365 days/Payables turnover
Payables period = 365 days/7.2604
Payables period = 50.27 days
So, the cash cycle is:
Cash cycle = 92.75days – 50.27 days
Cash cycle = 42.48 days
The firm is receiving cash on average 42.48 days after it pays its bills.
7. If we factor immediately, we receive cash on an average of 34 days sooner. The number of periods in a year are:
Number of periods = 365/34
Number of periods = 10.7353
The EAR of this arrangement is:
EAR = (1 + Periodic rate)m – 1
EAR = (1 + 2/98)10.7353 – 1
EAR = .2422 or 24.22%
8. a. The payables period is zero since the company pays immediately. The payment in each period is 30 percent of next period’s sales, so:
Q1 Q2 Q3 Q4
Payment of accounts $189.00 $213.00 $235.50 $186.30
b. Since the payables period is 90 days, the payment in each period is 30 percent of the current period sales, so:
Q1 Q2 Q3 Q4
Payment of accounts $162.00 $189.00 $213.00 $235.50
c. Since the payables period is 60 days, the payment in each period is 2/3 of last quarter’s orders, plus 1/3 of this quarter’s orders, or:
Quarterly payments = 2/3(.30) times current sales + 1/3(.30) next period sales.
Q1 Q2 Q3 Q4
Payment of accounts $171.00 $197.00 $220.50 $219.10
9. Since the payables period is 60 days, the payables in each period will be:
Payables each period = 2/3 of last quarter’s orders + 1/3 of this quarter’s orders
Payables each period = 2/3(.75) times current sales + 1/3(.75) next period sales
| Q1 | Q2 | Q3 | Q4 | ||
| Payment of accounts | $605.00 | $682.50 | $642.50 | $637.50 | |
| Wages, taxes, other expenses | 150.00 | 184.00 | 178.00 | 158.00 | |
| Long-term financing expenses | 60.00 | 60.00 | 60.00 | 60.00 | |
| Total | $815.00 | $926.50 | $880.50 | $855.50 |
10. a. The November sales must have been the total uncollected sales minus the uncollected sales from December, divided by the collection rate two months after the sale, so:
November sales = ($57,000 – 41,000)/0.15
November sales = $106,666.67
b. The December sales are the uncollected sales from December divided by the collection rate of the previous months’ sales, so:
December sales = $41,000/0.35
December sales = $117,142.86
c. The collections each month for this company are:
Collections = .15(Sales from 2 months ago) + .20(Last months sales) + .65 (Current sales)
January collections = .15($106,666.67) + .20($117,142.86) + .65($150,000)
January collections = $136,928.57
February collections = .15($117,142.86) + .20($150,000) + .65($173,000)
February collections = $160,021.43
March collections = .15($150,000) + .20($173,000) + .65($194,000)
March collections = $183,200.00
11. The sales collections each month will be:
Sales collections = .35(current month sales) + .60(previous month sales)
Given this collection, the cash budget will be:
| April | May | June | ||
| Beginning cash balance | $280,000 | $248,850 | $317,840 | |
| Cash receipts | ||||
| Cash collections from | ||||
| credit sales | 259,000 | 366,600 | 390,900 | |
| Total cash available | $539,000 | $615,450 | $708,740 | |
| Cash disbursements | ||||
| Purchases | 156,000 | 147,000 | 175,500 | |
| Wages, taxes, and expenses | 39,750 | 48,210 | 50,300 | |
| Interest | 11,400 | 11,400 | 11,400 | |
| Equipment purchases | 83,000 | 91,000 | 0 | |
| Total cash disbursements | 290,150 | 297,610 | 237,200 | |
| Ending cash balance | $248,850 | $317,840 | $471,540 |
Intermediate
12. a. If you borrow $60M for one month, you will pay interest of:
Interest = $60M(.0061)
Interest = $366,000
However, with the compensating balance, you will only get the use of:
Amount received = $60M – 60M(.04)
Amount received = $57.6M
This means the periodic interest rate is:
Periodic interest = $366,000/$57.6M
Periodic interest = .00635 or .635%
So, the EAR is:
EAR = [1 + ($366,000/$57.6M)]12 – 1
EAR = .0790 or 7.90%
b. To end up with $15M, you must borrow:
Amount to borrow = $15M/(1 – .04)
Amount to borrow = $15,625,000.00
The total interest you will pay on the loan is:
Total interest paid = $15,625,000(1.0061)6 – 15,625,000
Total interest paid = $580,667.35
13. a. The EAR of your investment account is:
EAR = 1.01404 – 1
EAR = 5.72%
b. To calculate the EAR of the loan, we can divide the interest on the loan by the amount of the loan. The interest on the loan includes the opportunity cost of the compensating balance. The opportunity cost is the amount of the compensating balance times the potential interest rate you could have earned. The compensating balance is only on the unused portion of the credit line, so:
Opportunity cost = .05($100M – 60M)(1.0140)4 – .05($100M – 60M)
Opportunity cost = $114,374.03
And the interest you will pay to the bank on the loan is:
Interest cost = $60M(1.022)4 – 60M
Interest cost = $5,456,809.58
So, the EAR of the loan in the amount of $60M is:
EAR = ($5,456,809.58 + 114,374.03)/$60M
EAR = .0929 = 9.29%
c. The compensating balance is only applied to the unused portion of the credit line, so the EAR of a loan on the full credit line is:
EAR = 1.0224 – 1
EAR = .0909 or 9.09%
14. a. A 45-day collection period means sales collections each quarter are:
Collections = 1/2 current sales + 1/2 old sales
A 36-day payables period means payables each quarter are:
Payables = 3/5 current orders + 2/5 old orders
So, the cash inflows each quarter are:
Q1 = $79 + 1/2($230) – 2/5(.45)($230) – 3/5(.45)($195) – .30($230) – $15
Q1 = $15.95
Q2 = 1/2($230) + 1/2($195) – 2/5(.45)($195) – 3/5(.45)($270) – .30($195) – $15 – 90
Q2 = –$59.00
Q3 = 1/2($195) + 1/2($270) – 2/5(.45)($270) – 3/5(.45)($290) – .30($270) – $15
Q3 = $9.60
Q4 = 1/2($270) + 1/2($290) – 2/5(.45)($290) – 3/5(.45)($250) – .30($290) – $15
Q4 = $58.30
The company’s cash budget will be:
WILDCAT, INC.
Cash Budget
(in millions)
| Q1 | Q2 | Q3 | Q4 | ||
| Beginning cash balance | $73.00 | $88.95 | $29.95 | $39.55 | |
| Net cash inflow | 15.95 | (59.00) | 9.60 | 58.30 | |
| Ending cash balance | $88.95 | $29.95 | $39.55 | $97.85 | |
| Minimum cash balance | (30.00) | (30.00) | (30.00) | (30.00) | |
| Cumulative surplus (deficit) | $58.95 | ($0.05) | $ 9.55 | $67.85 |
With a $30M minimum cash balance, the short-term financial plan will be:
WILDCAT, INC.
Short-Term Financial Plan
(in millions)
| b. | Q1 | Q2 | Q3 | Q4 | |
| Beginning cash balance | $30.00 | $30.00 | $30.00 | $30.00 | |
| Net cash inflow | 15.95 | (59.00) | 9.60 | 58.30 | |
| New short-term investments | (16.81) | 0 | (9.54) | (58.53) | |
| Income on short-term investments | 0.86 | 1.20 | 0 | 0.23 | |
| Short-term investments sold | 0 | 57.80 | 0 | 0 | |
| New short-term borrowing | 0 | 0 | 0 | 0 | |
| Interest on short-term borrowing | 0 | 0 | (0.06) | 0 | |
| Short-term borrowing repaid | 0 | 0 | 0 | 0 | |
| Ending cash balance | $30.00 | $30.00 | $30.00 | $30.00 | |
| Minimum cash balance | (30.00) | (30.00) | (30.00) | (30.00) | |
| Cumulative surplus (deficit) | 0 | 0 | 0 | 0 | |
| Beginning short-term investments | $43.00 | $59.81 | $2.01 | $11.55 | |
| Ending short-term investments | $59.81 | $2.01 | $11.55 | $70.08 | |
| Beginning short-term debt | 0 | 0 | 0 | 0 | |
| Ending short-term debt | 0 | 0 | 0 | 0 |
Below you will find the interest paid (or received) for each quarter:
Q1: excess funds at start of quarter of $43 invested for 1 quarter earns .02($43) = $0.86 income
Q2: excess funds of $59.81 invested for 1 quarter earns .02($59.81) = $1.20 in income
Q3: shortage funds of $2.01 borrowed for 1 quarter costs .03($2.01) = $0.06 in interest
Q4: excess funds of $11.55 invested for 1 quarter earns .02($11.55) = $0.23 in income
15. a. With a minimum cash balance of $45M, the short-term financial plan will be:
WILDCAT, INC.
Short-Term Financial Plan
(in millions)
| Q1 | Q2 | Q3 | Q4 | ||
| Beginning cash balance | $45.00 | $45.00 | $45.00 | $45.00 | |
| Net cash inflow | 15.95 | (59.00) | 9.60 | 58.30 | |
| New short-term investments | (16.51) | 0 | 0 | (53.76) | |
| Income on short-term investments | .56 | .89 | 0 | 0 | |
| Short-term investments sold | 0 | 44.51 | 0 | 0 | |
| New short-term borrowing | 0 | 13.60 | 0 | 0 | |
| Interest on short-term borrowing | 0 | 0 | (0.41) | (0.13) | |
| Short-term borrowing repaid | 0 | 0 | (9.19) | (4.41) | |
| Ending cash balance | $45.00 | $45.00 | $45.00 | $45.00 | |
| Minimum cash balance | (45.00) | (45.00) | 45.00) | (45.00) | |
| Cumulative surplus (deficit) | 0 | 0 | 0 | 0 | |
| Beginning short-term investments | $28.00 | $44.51 | 0 | 0 | |
| Ending short-term investments | $44.51 | 0 | 0 | $53.76 | |
| Beginning short-term debt | 0 | 0 | $13.60 | $4.41 | |
| Ending short-term debt | 0 | $13.60 | $4.41 | 0 |
b. And with a minimum cash balance of $15M, the short-term financial plan will be:
WILDCAT, INC.
Short-Term Financial Plan
(in millions)
| Q1 | Q2 | Q3 | Q4 | ||
| Beginning cash balance | $15.00 | $15.00 | $15.00 | $15.00 | |
| Net cash inflow | 15.95 | (59.00) | 9.60 | 58.30 | |
| New short-term investments | (17.11) | 0 | (9.95) | (58.85) | |
| Income on short-term investments | 1.16 | 1.50 | .35 | 0.55 | |
| Short-term investments sold | 0 | $57.50 | 0 | 0 | |
| New short-term borrowing | 0 | 0 | 0 | 0 | |
| Interest on short-term borrowing | 0 | 0 | 0 | 0 | |
| Short-term borrowing repaid | 0 | 0 | 0 | 0 | |
| Ending cash balance | $15.00 | $15.00 | $15.00 | $15.00 | |
| Minimum cash balance | (15.00) | (15.00) | (15.00) | (15.00) | |
| Cumulative surplus (deficit) | 0 | 0 | 0 | 0 | |
| Beginning short-term investments | $58.00 | $75.11 | $17.61 | $27.56 | |
| Ending short-term investments | $75.11 | $17.61 | $27.56 | $86.42 | |
| Beginning short-term debt | 0 | 0 | 0 | 0 | |
| Ending short-term debt | 0 | 0 | 0 | 0 |
Since cash has an opportunity cost, the firm can boost its profit if it keeps its minimum cash balance low and invests the cash instead. However, the tradeoff is that in the event of unforeseen circumstances, the firm may not be able to meet its short-run obligations if enough cash is not available.
Challenge
16. a. For every dollar borrowed, you pay interest of:
Interest = $1(.013) = $0.013
You also must maintain a compensating balance of 4 percent of the funds borrowed, so for each dollar borrowed, you will only receive:
Amount received = $1(1 – .04) = $0.96
We can adjust the EAR equation we have been using to account for the compensating balance by dividing the EAR by one minus the compensating balance, so:
EAR = [(1.013)4 – 1]/(1 – .04)
EAR = .05523 or 5.523%
Another way to calculate the EAR is using the FVIF (or PVIF). For each dollar borrowed, we must repay:
Amount owed = $1(1.013)4
Amount owed = $1.053
At the end of the year the compensating will be returned, so your net cash flow at the end of the year will be:
End of year cash flow = $1.053 – .04
End of year cash flow = $1.013
The present value of the end of year cash flow is the amount you receive at the beginning of the year, so the EAR is:
FV = PV(1 + R)
$1.013 = $0.96(1 + R)
R = $1.013/$0.96 – 1
EAR = .05523 or 5.523%
b. The EAR is the amount of interest paid on the loan divided by the amount received when the loan is originated. The amount of interest you will pay on the loan is the amount of the loan times the effective annual interest rate, so:
Interest = $210M[(1.013)4 – 1]
Interest = $11,134,791.48
For whatever loan amount you take, you will only receive 96 percent of that amount since you must maintain a 4 percent compensating balance on the portion of the credit line used. The credit line also has a fee of .105 percent, so you will only get to use:
Amount received = .96($210M) – .00105($500M)
Amount received = $201,075,000
So, the EAR of the loan is:
EAR = $11,134,791.48/$201,075,000
EAR = .05538 or 5.538%
17. You will pay interest of:
Interest = $8M(.08) = $640,000
Additionally, the compensating balance on the loan is:
Compensating balance = $8M(.06) = $480,000
Since this is a discount loan, you will receive the loan amount minus the interest payment. You will also not get to use the compensating balance. So, the amount of money you will actually receive on an $8M loan is:
Cash received = $8M – 640,000 – 480,000 = $6,880,000
The EAR is the interest amount divided by the loan amount, so:
EAR = $640,000/$6,880,000
EAR = .0930 or 9.30%
We can also use the FVIF (or PVIF) here to calculate the EAR. Your cash flow at the beginning of the year is $6,880,000. At the end of the year, your cash flow loan repayment, but you will also receive your compensating balance back, so:
End of year cash flow = $8,000,000 – 480,000
End of year cash flow = $7,520,000
So, using the time value of money, the EAR is:
$7,520,000 = $6,880,000(1 + R)
EAR = .0930 or 9.30%
R = $7,520,000/$6,880,000 – 1
1. Yes. Once a firm has more cash than it needs for operations and planned expenditures, the excess cash has an opportunity cost. It could be invested (by shareholders) in potentially more profitable ways. Question 10 discusses another reason.
2. If it has too much cash it can simply pay a dividend, or, more likely in the current financial environment, buy back stock. It can also reduce debt. If it has insufficient cash, then it must either borrow, sell stock, or improve profitability.
3. Probably not. Creditors would probably want substantially more.
4. In the case of Microsoft, the company’s reason given for holding cash was to pay for potential settlements in its monopoly cases brought by the U.S. government and the European Union. GM generally argued that it held cash to guard against future economic downturns.
5. Cash management is associated more with the collection and disbursement of cash. Liquidity management is broader and concerns the optimal level of liquid assets needed by a firm. Thus, for example, Ford and Chrysler’s stockpiling of cash was liquidity management; whereas, evaluating a lockbox system is cash management.
6. Such instruments go by a variety of names, but the key feature is that the dividend adjusts, keeping the price relatively stable. This price stability, along with the dividend tax exemption, makes so-called adjustable rate preferred stock very attractive relative to interest-bearing instruments.
7. 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. The firm has a net disbursement float of $500,000. If this is an ongoing situation, the firm may be tempted to write checks for more than it actually has in its account.
9. 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.
c. The primary disadvantage of NCDs is the normally large transactions sizes, which may not be feasible for the short-term investment plans of many smaller to medium-sized corporations.
d. The primary disadvantages of the commercial paper market are the higher default risk characteristics of the security and the lack of an active secondary market which may excessively restrict the flexibility of corporations to meet their liquidity adjustment needs.
e. The primary disadvantages of RANs is that some possess non-trivial levels of default risk, and also, corporations are somewhat restricted in the type and amount of these tax-exempts that they can hold in their portfolios.
f. The primary disadvantage of the repo market is the generally very short maturities available.
10. The concern is that excess cash on hand can lead to poorly thought-out investments. The thought is that keeping cash levels relatively low forces management to pay careful attention to cash flow and capital spending.
11. 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.
12. This is really a capital structure decision. If the firm has an optimal capital structure, paying off debt moves it to an under-leveraged position. However, a combination of debt reduction and stock buy-backs could be structured to leave capital structure unchanged.
13. 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.
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:
Average daily float = 6($85,000)/30
Average daily float = $17,000
2. a. The disbursement float is the average monthly checks written times the average number of days for the checks to clear, so:
Disbursement float = 4($25,000)
Disbursement float = $100,000
The collection float is the average monthly checks received times the average number of days for the checks to clear, so:
Collection float = 2(–$40,000)
Collection float = –$80,000
The net float is the disbursement float plus the collection float, so:
Net float = $100,000 – 80,000
Net float = $20,000
b. The new collection float will be:
Collection float = 1(–$40,000)
Collection float = –$40,000
And the new net float will be:
Net float = $100,000 – 40,000
Net float = $60,000
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 = 4($9,000)
Collection float = $36,000
b. The firm should pay no more than the amount of the float, or $36,000, 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:
Maximum daily charge = $36,000(.00025)
Maximum daily charge = $9.00
4. a. Total float = 4($16,000) + 5($3,000)
Total float = $79,000
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:
Average daily float = $79,000/30
Average daily float = $2,633.33
c. The average daily receipts are the average daily checks received divided by the number of days in a month. Assuming a 30 day month:
Average daily receipts = ($16,000 + 3,000)/30
Average daily receipts = $633.33
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:
Weighted average delay = 4($16,000/$19,000) + 5($3,000/$19,000)
Weighted average delay = 4.16 days
5. The average daily collections are the number of checks received times the average value of a check, so:
Average daily collections = $80(12,000)
Average daily collections = $960,000
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)($960,000)
PV = $1,920,000
The daily cost is a perpetuity. The present value of the cost is the daily cost divided by the daily interest rate. So:
PV of cost = $190/.00016
PV of cost = $1,187,500
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:
NPV = –$1,187,400 + 1,920,000
NPV = $732,500
The annual net savings excluding the cost would be the future value of the savings minus the savings, so:
Annual savings = $1,920,000(1.00016)365 – 1,920,000
Annual savings = $115,457.31
And the annual cost would be the future value of the daily cost, which is an annuity, so:
Annual cost = $190(FVIFA365,.016%)
Annual cost = $71,409.14
So, the annual net savings would be:
Annual net savings = $115,457.31 – 71,409.14
Annual net savings = $44,048.17
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 = [.65(5,000)($50)(2) + .35(5,000)($70)(3)]/30
Average daily float = $23,083
On average, there is $23,083 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:
Total collections = .65(5,000)($50) + .35(5,000)($70)
Total collections = $162,500 + 122,500
Total collections = $285,000
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($162,500/$285,000) + 3($122,500/$285,000)
Weighted average delay = 2.43 days
The average daily float is the weighted average delay times the average checks received per day. Assuming a 30 day month, we get:
Average daily float = 2.43($285,000/30 days)
Average daily float = $23,083
c. The most the firm should pay is the total amount of the average float, or $23,083.
d. The average daily interest rate is:
1.07 = (1 + R)365
R = .01854% per day
The daily cost of float is the average daily float times the daily interest rate, so:
Daily cost of the float = $23,083(.0001854)
Daily cost of the float = $4.28
e. The most the firm should pay is still the average daily float. Under the reduced collection time assumption, we get:
New average daily float = 1.5($285,000/30)
New average daily float = $14,250
7. a. The present value of adopting the system is the number of days collections are reduced times the average daily collections, so:
PV = 3(400)($1,400)
PV = $1,680,000
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:
NPV = $1.68M – [$0.75(400)/.0002]
NPV = $180,000
c. The net cash flows is the present value of the average daily collections times the daily interest rate, minus the transaction cost per day, so:
Net cash flow per day = $1.68M(.0002) – $0.75(400)
Net cash flow per day = $36
The net cash flow per check is the net cash flow per day divided by the number of checks received per day, or:
Net cash flow per check = $36/400
Net cash flow per check = $0.09
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:
Net cash flow per check = 3($1,400)(.0002) – $0.75
Net cash flow per check = $0.09 per check
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:
Cash balance reduction = 3($140,000)
Cash balance reduction = $420,000
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:
Average daily rate = 1.091/365 – 1
Average daily rate = .0236% per day
The daily return that can be earned from the reduction in days to clear the checks is:
Daily return = $420,000(.000236)
Daily return = $99.18
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:
Savings = $140,000 + $140,000(PVIFA.0236%,2)
Savings = $419,900.86
If the lockbox payments occur at the end of the month, we need the effective monthly interest rate, which is:
Monthly interest rate = 1.091/12 – 1
Monthly interest rate = 0.7207%
Assuming the lockbox payments occur at the end of the month, the lockbox payments, which are a perpetuity, will be:
PV = C/R
$419,900.86 = C / .007207
C = $3,026.36
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)
C = ($419,900.86 × .007207) / (1 + .007207)
C = $3,004.71
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:
Interest = $70,000(7)(52/2)(.0002)
Interest = $2,548
10. The benefit of the new arrangement is the $8 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:
NPV = $8,000,000 – ($600,000 – 500,000)
NPV = $7,900,000
The company should proceed with the new system. The savings are the NPV times the annual interest rate, so:
Net savings = $7,900,000(.05)
Net savings = $395,000
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:
PV = 2(600)($1,100)
PV = $1,320,000
And the daily interest rate is:
Daily interest rate = 1.0611/365 –1
Daily interest rate = .000160 or .0160% per day
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:
NPV = $1,320,000 – [$0.35(600)/.00016]
NPV = $4,652.17
Without the 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 addition cost. The annual fee is a perpetuity, so, with the fee, the NPV of taking the lockbox is:
NPV = $4,652.17 – [$1,000/.06]
NPV = –$12,014.50
With the fee, the lockbox system should not be accepted.
12. To find 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
Daily interest rate = .0134% per day
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:
NPV = 0 = ($5,500)(1)N – [$0.10(N)/.000134] – [$25,000/.05]
$500,000 = $5,500N – $748.05N
$4,751.95N = $500,000
N = 105.22 » 105 customers per day
Challenge
13. a. The amount the company will have available is the future value of the transfers, which are an annuity. The amount of each transfer is one minus the wire transfer cost, times the number of transfers, which is four since there are four banks, times the amount of each transfer. So, the total available in two weeks will be:
Amount available = (1 – .0015)(4)($130,000)(FVIFA.015%,14)
Amount available = $7,276,171.61
b. The bank will accept the ACH transfers from the four different banks, so the company incurs a transfer fee from each collection center. The future value of the deposits now will be:
Value of ACH = [4($130,000 – 700)(FVIFA.015%,14)]/1.00015
Value of ACH = $7,246,777.00
The company should not go ahead with the plan since the future value is lower.
c. To find the cost at which the company is indifferent, we set the amount available we found in part a equal to the cost equation we used in part b. Setting up this equation where X stands for the ACH transfer cost, we find:
[4($130,000 – $X)(FVIFA.015%,14)]/1.00015 = $7,276,171.61
X = $175.53
APPENDIX 20A
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 accounts, so they will have to raise the target cash balance to meet this requirement.
d. Decrease. If the credit rating improves, then the firm can borrow more easily, allowing it to lower the target cash balance and borrow if a cash shortfall occurs.
e. Increase. If the cost of borrowing increases, the firm will need to hold more cash to protect against cash shortfalls as its borrowing costs become more prohibitive.
f. Decrease. 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 other hand, fees are charged on the number of transactions, then the firm may wish to hold a higher cash balance so they are not transferring money into the account as often.
2. The target cash balance using the BAT model is:
C* = [(2T × F)/R]1/2
C* = [2($5,000)($10)/.07]1/2
C* = $1,195.23
The initial balance should be $1,195.23, and whenever the balance drops to $0, another $1,195.23 should be transferred in.
3. The holding cost is the average daily cash balance times the interest rate, so:
Holding cost = ($400)(.05)
Holding cost = $20.00
The trading costs are the total cash needed times the replenishing costs, divided by the average daily balance times two, so:
Trading cost = [($25,000)($6)]/[($400)(2)]
Trading cost = $187.50
The total cost is the sum of the holding cost and the trading cost, so:
Total cost = $20.00 + 187.50
Total cost = $207.50
The target cash balance using the BAT model is:
C* = [(2T × F)/R]1/2
C* = [2($25,000)($6)/.05]1/2
C* = $2,449.49
They should increase their average daily cash balance to:
New average cash balance = $2,449.49/2
New average cash balance = $1,224.74
This would minimize the costs. The new total cost would be:
New total cost = ($1,224.74)(.05) + [($25,000)($6)]/[2($1,224.74)]
New total cost = $122.47
4. a. The opportunity costs are the amount transferred times the interest rate, divided by two, so:
Opportunity cost = ($300)(.06)/2
Opportunity cost = $9.00
The trading costs are the total cash balance times the trading cost per transaction, divided by the amount transferred, so:
Trading cost = ($4,000)($25)/$300
Trading cost = $333.33
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
C* = [2($4,000)($25)/.06]1/2
C* = $1,825.74
5. The total cash needed is the cash shortage per month times twelve months, so:
Total cash = 12($360,000)
Total cash = $4,320,000
The target cash balance using the BAT model is:
C* = [(2T × F)/R]1/2
C* = [2($4.32M)($500)/.065]1/2
C* = $257,801.35
The company should invest:
Invest = $700,000 – 257,801.35
Invest = $442,198.65
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:
Sell securities = $4.32M/$257,801.35
Sell securities = 16.76 » 17 times.
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:
Lower limit = $60,000 – 40,000
Lower limit = $20,000
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:
Upper limit = $125,000 – 60,000
Upper limit = $65,000
of marketable securities will be purchased. This expenditure brings the cash level back down to the target balance of $60,000.
7. The target cash balance using the Miller-Orr model is:
C* = L + (3/4 × F × s2 / R]1/3
C* = $1,100 + [3/4($100)($75)2/.00021]1/3
C* = $2,361.79
The upper limit is:
U* = 3 × C* – 2 × L
U* = 3($2,361.79) – 2($1,100)
U* = $4,885.38
When the balance in the cash account drops to $1,100, the firm sells:
Sell = $2,361.79 – 1,100
Sell = $1,261.79
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:
Buy = $4,885.38 – 2,361.79
Buy = $2,523.59
of marketable securities. This expenditure lowers the cash level back down to the optimal level of $2,361.79.
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 target cash balance, and therefore the upper limit and the spread, will need to be higher. If the variance drops to zero, then the lower limit, the target balance, and the upper limit will all be the same.
9. The average daily interest rate is:
Daily rate = 1.071/365 – 1
Daily rate = .000185 or .0185% per day
The target cash balance using the Miller-Orr model is:
C* = L + (3/4 × F × s2 / R]1/3
C* = $150,000 + [3/4($960,000)($500)/.000185]1/3
C* = $162,476.05
The upper limit is:
U* = 3 × C* – 2 × L
U* = 3($162,476.05) – 2($150,000)
U* = $187,428.16
10. Using the BAT model and solving for R, we get:
C* = [(2T × F)/R]1/2
$2,200 = [2($21,000)($10)/R]1/2
R = [2($21,000)($10)]/$2,2002
R = .0868 or 8.68%
