chap020 Working Capital Management.docx

1、chap020 Working Capital ManagementSolutions to Chapter 20Working Capital Management1. a. The discount is: 1% of $1,000 = $10 b. The customer gains an extra 40 days of credit.c. With the discount, the customer pays $990. Without the discount, the customer pays $1,000. The difference is: $10/$990 = 1.

2、01%A rate of 1.01% per 40 days of extra credit is equivalent to an annual rate of: (1.0101)365/40 1 = 0.0960 = 9.60%2. open account commercial draft trade acceptance the customers bankers acceptance3. a. Perishable goods (bread) call for a shorter credit period.b. Rapid inventory turnover (higher tu

3、rnover ratio) calls for a shorter credit period. c. The firm selling to customers with the more tangible and saleable assets will grant a longer credit period. This is the firm selling to electric utilities.4. a. The service charge discourages late payment. The due lag decreases and, therefore, pay

4、lag decreases.b. Companies might be forced to stretch payables. Due lag and, therefore, pay lag increase. c. Terms lag increases and, therefore, pay lag increases.5. The current terms allow a 3% discount if the customer gives up an extra 40 20 = 20 days of credit. The effective annual rate is: 1 + (

5、3/97) (365/20) 1 = 0.7435 = 74.35% a. The implicit rate increases because the discount is higher: 1 + (4/96) (365/20) 1 = 1.1064 = 110.64%b. The implicit rate increases because the extra days of credit bought by forfeiting the discount decrease to: 40 30 = 10 days 1 + (3/97) (365/10) 1 = 2.0397 = 20

6、3.97%c. The implicit rate increases because the extra days of credit bought by forfeiting the discount decreases to: 30 20 = 10 days 1 + (3/97) (365/10) 1 = 2.0397 = 203.97%6. Ledger balance = starting balance payments + deposits Ledger balance = $250,000 $20,000 $60,000 + $45,000 = $215,000 The pay

7、ment float is the outstanding total of not-yet-cleared checks written by the firm, which equals $60,000 in this case. The net float is: $60,000 $45,000 = $15,0007. If you pay your bill by writing a check in the traditional manner, there will be a delay of several days before the check is presented t

8、o your bank, and the bank debits your account. During this period, the money stays in your account and you may earn interest on the funds. In contrast, if you use the Internet to order your bank to send out a check on your behalf, the bank can debit your account immediately, at which point you will

9、stop earning interest on the funds. The bank, however, still has access to the funds until the check it sends out actually clears. Therefore, the bank is willing to provide you this service “for free.” In addition, it is cheaper for the bank to process electronic order payments than paper payments,

10、which is another source of savings that induce them to offer the service for no extra charge.8. a. Payment float = $20,000 6 = $120,000 Availability float = $22,000 3 = $ 66,000 Net float = $ 54,000b. If availability float were reduced by one day, then interest could be earned on $22,000. Annual int

11、erest earnings would be: 0.06 $22,000 = $1,3209. a. The lock-box reduces collection float by: 400 payments per day $2,000 per payment 2 days = $1,600,000 Daily interest saved = 0.00015 $1,600,000 = $240 The bank charge each day is: 400 payments per day $0.40 per payment = $160 The lock-box is worthw

12、hile; interest earnings exceed the bank charges. b. Break-even occurs when interest earned equals the bank fees: 0.00015 400 $2,000 Days saved = $160 Days saved = 1.3310. concentration bankingwire transfera lock-box system11. a. Two-thirds of customers pay within 15 days. The other one-third of cust

13、omers pay by day 30. Therefore, the accounts receivable period is: (2/3 15) + (1/3 30) = 20 days b. Investment in A/R = accounts receivable period daily sales c. With greater incentive to pay early, more customers will pay within 15 days instead of 30 days. Therefore, the accounts receivable period

14、is likely to decrease.12. a. PV of a cash-on-delivery sale = $50 $40 = $10 per carton Under the present cash-on-delivery policy, unit sales equal 1,000 cartons per month: $10 per carton 1,000 cartons = $10,000 If credit is extended, sales increase, but present value per carton decreases to: PV of re

15、venue Costper carton $9.505 per carton 1,060 cartons = $10,075 The higher sales more than make up for the time value cost of the credit extended. b. If the interest rate is 1.5%, PV per carton decreases to: PV of revenue Costper carton $9.261 per carton 1,060 cartons = $9,817 At the higher interest

16、rate, the higher sales no longer are enough to make up for the cost of the credit extended.c. The PV of the old customers remains unaffected. The PV of the new customers is positive: The additional sales gained by extending credit is 60 cartons. The profit margin (in present value terms) is: per car

17、ton13. PV(COST) = 96 PV(REV) = 101/1.01 = 100 a. The expected profit from a sale is: 0.93 ($100 $96) (0.07 $96) = $3 The firm should not extend credit. b. At the break-even probability, expected profit equals zero: p ($100 $96) (1 p) $96 = 0 p = 0.96 So if the firm is to break even, 96% of its custo

18、mers must pay their bills.c. A paying customer now represents a perpetuity of profits equal to:$100 $96 = $4 per monthThe present value is: $4/0.01 = $400So the present value of a sale, given a 7% default rate, is: (0.93 $400) (0.07 $96) = $365.28 It clearly pays to extend credit. d. (p $400) (1 p)

19、$96 = 0 p = 0.194 = 19.4% So the probability of payment must be greater than 19.4% to justify extending credit.14. a. The expected profit for a sale is: 0.95 ($1,200 $1,050) (0.05 $1,050) = $90 b. The break-even probability of collection is found by solving for p as follows: p ($1,200 $1,050) (1 p)

20、$1,050 = 0 p = 1,050/1,200 = 0.87515. From the discussion in the text regarding financial ratios (see Chapter 4), important ratios to consider are: Cash flow/Total debt Net income/Total assets Total debt/Total assets Working capital/Total assets Current assets/Current liabilities16. The cost is $50.

21、 PV (revenues) The expected profit for the order is therefore: 0.75 (57.74 50) (0.25 50) = $6.70 per iron You should reject the order.17. The more stringent policy should be adopted because profit will increase, as shown in the following table. For every $100 of current sales: Current Policy More St

22、ringent Policy Sales 100.0 95.0 Less bad debts* 6.0 3.8 Less cost of goods* 80.0 76.0 Profits 14.0 15.2 *6% of sales under current policy; 4% under proposed policy. *80% of sales18. a. Allowing for the possibility of default, the present value of a sale under current credit terms is: Under a cash-on

23、-delivery policy, sales would be 40% lower, but defaults and the time value cost of extended credit would be eliminated. Present value (assuming sales volume equal to 60% of current levels) would be: 0.6 (15 10) = 3 The switch to a COD policy seems to make sense.b. If customers who pay bills on time

24、 generate six additional repeat sales, then each successful sale is repeated an additional six times; in contrast, a defaulting sale occurs only once. The PV of a credit sale becomes (note that the 6-month annuity factor for 1% per month is 5.7955):annuity factor(1%, 6 months) (0.25 10) = $22.23 The

25、 present value of a cash-on-delivery policy given the lower sales volume is: 0.60 (15 10) + (15 10) Annuity factor(1%, 6 months) = $20.39 In this case, repeat sales make the extension of credit a preferable strategy.19. Profits from cash sales are currently: 100 ($101 $80) = $2,100a. If one month (3

26、0 days) free credit is granted, the present value of revenue per unit decreases to: $101/1.01 = $100Assuming that both old and new customers take advantage of the free credit, the present value of profits will increase to: 110 ($100 $80) = $2,200Allowing trade credit therefore is beneficial. b. Now

27、assume that 5% of all customers will default on their bills. The expected value of (discounted) profits becomes: Units sold p PV(REV COST) (1 p) PV(COST) = $110 0.95 ($100 $80) (0.05 $80) = $1,650 This is less than current profit of $2,100, which means that trade credit should not be allowed. c. If

28、only new customers pose default risk, you need to look at the incremental profit from the new customers the firm will attract by relaxing credit policy minus the value of the free credit that the firm extends to its current customers. The free credit costs the firm $1 per current customer, since the

29、 present value of a sale falls from $101 to $100. Value of new customers = 10 0.95 ($100 $80) (0.05 $80) = $150 Cost of free credit to current customers = 100 $1 = $100 Net benefit from advancing credit = $150 $100 = $50 Now it appears worthwhile to allow trade credit.20. a. Collection float decreas

30、es by: $15,000 per day 2 days saved = $30,000 b. Daily interest saving = 0.0002 $30,000 = $6c. Monthly savings = 30 $6 = $180This is the maximum fee Shermans should pay.21. a. The lock box will collect an average of: $300,000/30 = $10,000 per day The money will be available three days earlier; this

31、will increase the cash available to JAC by $30,000. Thus, JAC will be better off accepting the compensating balance offer: $25,000 is tied up in the compensating balance, but the lock-box frees up $30,000. b. Let x equal the average check size for break-even. Then the number of checks written per month is (300,000/x) and the monthly cost of the lockbox is: (300,000/x) 0.10The alternative is the compensating balance of $25,000; its monthly cost is th