Chapter 19

(1) Explain the composition of a firm's working capital accounts and calculate the cash conversion cycle.

(5) Describe the mechanics of short-term borrowing through accounts payable, short-term bank loans, and commercial paper.

(1) Working capital management consists of managing a firm's current assets and current liabilities (where current refers to one year or less).

(2) Working capital management consists of choosing the levels of cash, marketable securities, receivables, and inventories, as well as the level and mix of types of short-term financing.

(a) It includes the sales impact. Granting easy credit and keeping high inventories may help boost sales and fill orders quickly, but these practices also raise costs.

(b) It includes liquidity. A firm must choose its levels of cash and marketable securities, taking into account needed liquidity and any required compensating balances.

(c) It includes relations with stakeholders since suppliers and customers are intimately affected by the management of working capital.

(d) It includes the short-term financing mix. A firm must choose its mix of types of short-term financing, as well as its proportions of short- and long-term financing.

(4) In the U.S. recent investment in short-term assets by manufacturing corporations represent 35% of total assets. Short-term debt accounts for roughly 25% of the total financing.

(5) We can characterize a firm's philosophy about how it finances working capital, in terms of the risk-return trade-off, as the maturity-matching approach, the conservative approach, or the aggressive approach.

(a) In the maturity-matching approach, the firm hedges its risk by matching the maturities of its assets and liabilities.

(b) The conservative approach uses more long-term and less short-term financing than the maturity-matching approach.

(c) An aggressive approach relies more upon short-term financing. While there is greater risk relying upon short-term financing to be renewed at the same rate, short-term financing is typically cheaper leading to higher profits.

(1) Disregarding the capacity to defer payables, the cash conversion cycle is the length of time between the payment of cash for inventory and receipt of cash from accounts receivable.

(a) If a firm holds its inventory 50 days and collects its accounts receivable in 30 days, then it would take 80 days for the original investment to be converted back into cash.

(b) However, if the firm has the option of creating an accounts payable for 20 days, the cash conversion cycle can be reduced from 80 days to 60 days.

(2) The cash conversion cycle is equal to the inventory conversion period, plus the receivables collection period, minus the payables deferral period.

(a) The inventory conversion period is the average time between buying inventory and selling the goods. We have: inventory conversion period = inventory/(cost of sales/365) = 365/(inventory turnover).

(b) The receivables collection period, or days' sales outstanding (DSO), is the average number of days that it takes to collect on accounts receivable. We have: receivables collection period = receivables/(sales/365) = 365/receivables turnover.

(c) The payables deferral period is (the accounts payable + wages, benefits, and payroll taxes payable) / ([the cost of sales + selling, general, and administrative expenses]/365).

(a) First, how much liquidity (cash plus marketable securities ) should the firm have?

(b) Second, what should be the relative proportions of cash and marketable securities in maintaining that liquidity?

(3) There are three basic motives for holding cash: transactions demand, the precautionary demand, and the speculative demand.

(a) The transactions demand is simply the need for cash to make everyday payments for such things as wages, raw materials, taxes, and interest.

(b) The precautionary demand is essentially the margin of safety required to meet unexpected needs.

(c) The speculative demand is based on the desire to take advantage of unexpected profitable opportunities that require cash.

(4) To help meet the three basic demands for cash, firms can hold cash in compensating balances.

(a) A compensating balance is an account balance that the firm agrees to maintain.

(c) Commercial banks may accept or require compensating balances in lieu of direct fees. The balance provides the bank with money for which it does not have to pay interest.

(a) U.S. Treasury securities such as T-bills, Treasury notes, and Treasury bonds can provide a short-term investment vehicle since firms can invest in these securities for very short periods by using repurchase agreements, or repos, with security dealers.

(b) U.S. federal agency securities are backed by U.S. government but give slightly higher rates than U.S. Treasury securities.

(c) Negotiable certificates of deposit (CD) are time deposits issues by domestic or foreign commercial banks that can be sold to a third party. Eurodollar CDs generally have higher risk and return than domestic CDs.

(d) Short-term tax-exempt municipal (munis) are short-term securities that are issued by state and local governments and are exempt from federal taxation.

(e) Bankers' acceptances are drafts that a commercial bank has "accepted." The value is based on the accepting bank's credit standing.

(f) Commercial paper are unsecured promissory notes that corporations issue. Commercial paper seldom has an original maturity of more than 270 days.

(g) Preferred stock and money market preferred stock pays dividends that qualify for the 70% dividends-received deduction. Money market preferred stock differs from other preferred stock. Its a short-term security that has a floating dividend rate that is reset frequently to reflect current interest rates.

(d) The firm will pay a fixed transactions cost each time it converts securities to cash.

(7) For the Baumol model, the annual cost of meeting the transactions demand is the transactions cost plus the opportunity (time value) cost: Cost = b(T/C) + i(C/2) where T = annual transactions volume in dollars (uniform through time); b = fixed cost per transaction; i = annual interest rate; and C = size of each deposit.

(b) Increasing C increases the average cash balance and the opportunity cost as well.

(8) The Miller-Orr cash management model is more realistic than the Baumol model.

(b) It uses two control limits and a return point (which is the target the firm returns to whenever it hits a control limit).

(9) Float is the difference between the available or collected balance at the bank and the firm's book or ledger balance.

(a) When you write a check, your book or ledger balance is reduced by the amount of the check, but your available or collected balance at the bank is not reduced until the check finally clears. This difference is disbursement float.

(b) Suppose you receive a check and deposit it in your bank. Until the funds are credited to your account, your book balance will be higher than your actual balance. In this case, you are experiencing collection float.

(a) Large payments can be made with wire transfers instead of paper checks. This reduces the (disbursement) float and is more costly for the firm to pay this way.

(b) Zero balance accounts (ZBAs) are special disbursement accounts that have a zero balance. They are funded out of a master account. Funds are automatically transferred into the ZBAs when checks are presented on them.

(c) Controlled disbursing is a technique that uses disbursing accounts at several banks in addition to the master account at the firm's lead bank. They work like ZBA.

(d) By centralizing payables, a cash manager knows when all bills must be paid and can make sure that funds are available and bills are paid on time.

(e) Lockboxes are post office boxes to which a firm directs its incoming checks. A bank is engaged to open the lockbox several times per day, process the checks, and collect them. This speed up the collection process (and shortens the collection float).

(1) There are three main sources of short-term funds: trade credit (borrowing from suppliers), bank loans, and commercial paper (selling short-term debt securities in the open market).

(2) Trade credit is the largest single source of short-term funds for businesses, presenting approximately one-third of the current liabilities of nonfinancial corporations.

(a) The terms "2/10, net 30" mean the buyer can take a 2% cash discount if payment is made within 10 days (the discount period); otherwise, the full amount is due within 30 days (the net period).

(b) The APR for trade credit is: APR = (Discount%/[100% - Discount%]) * (365/[Total period - Discount period]) where total period can be greater than net period if payables stretched.

(c) The APY for trade credit is: APY = (1 + [Discount%/{100% - Discount%}])^{(365/[Total period - Discount period])} - 1.

(d) Trade credit (assuming you can get it) is more flexible than other means of short-term financing. The firm does not have to negotiate a loan agreement, pledge collateral, or adhere to a rigid repayment schedule.

(3) Firms can stretch accounts payable by postponing payment beyond the end of the net period.

(4) Commercial bank lending is second to trade credit as a source of short-term financing.

(a) Commercial banks also provide intermediate-term financing (maturity between 1 and 10 years).

(b) Short-term unsecured bank loans take one of three basic forms: a specific transaction loan, a line of credit, or a revolving credit.

(ii) A line of credit is an arrangement between a bank and a customer concerning the maximum loan balance the bank will permit the borrower at any one time.

(iii) A revolving credit agreement represents a legal commitment to lend up to a specified maximum amount any time during a specified period.

(5) Bank term loans represent intermediate-term debt. It is a loan for a specified amount that requires the borrower to repay it according to a specified schedule.

(6) Despite the many differences in bank loan contracts, calculating the cost of a loan is not difficult.

(a) As with trade credit, we can compute the APR. It is: APR = (net cost of loan / cash advance)(1/f) where f is the fraction of a year that the loan is outstanding.

(b) The APY is: APY = (1 + [net cost of loan / cash advance])^(1/f) - 1 = (Net repayment / cash advance)^(1/f) - 1.

(7) The compensating balance reduces the effective loan proceeds, raising the cost of the usable funds.

(a) The nominal cost of borrowing with a compensating balance is: APR = (net cost of loan / cash advance)(1/f) = (interest charges / [loan amount - compensating balance])(1/f) = (rP / [P-B])(1/f) where P = amount of the loan; B = increase in the firm's average cash balances as a result of the compensating balance requirement; f = fraction of a year the loan is outstanding; r = interest rate on the loan amount; and, rP = interest charges.

(b) The foregoing equation assumes the compensating balances do not earn interest, but if the compensating balances earn some yield, y, the earned interest, yB, reduces the cost of the loan. In that case, the cost of the loan is: APR = (interest charges - interest received) / (loan amount - compensating balance)(1/f) = ([rP-yB] / [P-B])(1/f).

(8) Many loans are discount loans, which require the borrower to pay the interest in advance

(b) The stated loan amount is P, but the borrower gets only P - rPf, where f is the borrowing period expressed as a fraction of a year.

(d) With an interest expense of rPf, with a "true" loan amount of P - rPf, or P*(1-rf), and adjusting for a loan period of f, the APR is: APR = [rPf / (P-rPf)](1/f). Canceling out the P's, we get: APR = (rf / (1-rf)]/f = rf / (1-rf)*f. Canceling the f's, we get APR = r/(1-rf).

(9) Firms that borrow by pledging receivables, inventories, or marketable securities can borrow more.

(10) Interest on commercial paper is paid on a discount basis. For example, if 120-day prime commercial paper carries a 12% interest rate, then the APR interest cost (based on a 360-day year) is: APR = r / [1-rf]) = 0.12 / [1 - 0.12(120/360)] = 0.125 or about 12.5%.

(1) Electronic data interchange (EDI) is the exchange of information electronically, directly from one computer to another.

(a) By moving the information in this way, firms save time, personnel costs, material costs, and costs due to errors.

(b) In North America, the American National Standards Institute sets EDI standards for such things as invoices, shipping information, purchase orders, customer account information, requests for quotations, and many others.

(2) By simplifying the process and sending information almost instantaneously, EDI reduces labor costs, substantially reduces errors, and makes possible a much higher degree of control over the firm's resources.

(A3) The Mennen Corporation is interested in examining its cash conversion cycle. Suppose a Mennen manager has assembled the following data for your use: $1M in inventory (M=millions); $0.8M in A/R; $0.4M in A/P; $0.15M in wages, benefits, and payroll taxes payable; $25M in sales; $10M in cost of sales; and, $1.5M in selling, general, and administrative expenses. Estimate each of the below.

The inventory conversion period is the average time between buying inventory and selling the goods. We have: inventory conversion period = inventory/(cost of sales/[365 days]) = (365 days)/(inventory turnover) where inventory turnover is cost of goods sold divided by inventory = $10M / $1M = 10. We have: inventory conversion period = (365 days)/10 = 36.5 days.

The receivables collection period, or days' sales outstanding (DSO), is the average number of days that it takes to collect on accounts receivable. We have: receivables collection period = receivables / (sales/[365 days]) = (365 days) / receivables turnover where receivables turnover = sales / receivables = $25M / $0.8M = 31.25. We have: receivables collection period = (365 days) / 31.25 = 11.68 days.

The payables deferral period is (the accounts payable + wages, benefits, and payroll taxes payable) / ([the cost of sales + selling, general, and administrative expenses] / [365 days]) = (365 days) / (payables turnover) where payable turnover = (the cost of sales + selling, general, and administrative expenses) / (the accounts payable + wages, benefits, and payroll taxes payable) = ($10M + $1.5M) / ($0.4M + $0.15M) = ($11.5M) = ($0.55M) = 20.909091. We have: payables deferral period = (365 day) / 20.909091 = 17.46 days. [NOTE: Taking the first equation, we can multiply both the numerator and denominator by 365 and then insert the given values. This gives: payables deferral period = ($0.4M + $0.15M)(365 days) / ($10M + $1.5M) = 17.5 days.]

The cash conversion cycle is equal to the inventory conversion period, plus the receivables collection period, minus the payables deferral period. We have: cash conversion cycle = 36.5 days + 11.7 days - 17.5 days = 30.7 days.

(A8) You need to transfer $250,000 from Houston to Chicago. If you mail a check, it will cost $1.00 for postage and clearing the check, and it will take a total of five days for the funds to be transferred. During the money's 5-day travel, you will suffer an opportunity cost, because the $250,000 is not earning 3% APY interest. Alternatively, you can avoid the opportunity cost by sending a wire transfer costing $12.00, which instantaneously transfers the funds with no float. Calculate the cost of each alternative. Which is cheaper?

The wire transfer is the cheapest. The major reason is that its float costs are zero.

(A10) Suppose you are offered trade credit terms of 1.5/15, net 50. Answer the below questions.

(a) What is the APR cost of this trade credit if you skip the discount and pay at the end of the net period?

The APR for trade credit is: APR = (Discount% / [100% - Discount%])(365/[Total period - Discount period]) = (1.5% / [100% - 1.5%])(365/[50 days - 15 days]) = 0.1588 or about 15.88%.

(b) What would be the APR cost if you "stretched" the payables and paid after 75 days?

The APR for trade credit is: APR = (Discount% / [100% - Discount%])(365/[Total period - Discount period]) = (1.5% / [100% - 1.5%])(365/[75 days - 15 days]) = 0.0.9264 or about 9.26%.

(B1) Auburn Hair Products has an inventory turnover of six times per year, a receivables turnover of ten times, and a payables turnover of twelve times. What is Auburn Hair's inventory conversion period, the receivables collection period, and the payables deferral period? What is the cash conversion cycle?

(B5) Calculate the cost of skipping the discount and paying at the end of the net period for each of the following credit terms. Calculate the APR and APY cost of each.

The APR for trade credit is: APR = (Discount% / [100% - Discount%]) * (365 / [Total period - Discount period]) = (1% / [100% - 1%]) * (365 / [30 days - 10 days]) = 0.184343 or about 18.43%.

The APY for trade credit is: APY = (1 + [Discount% / {100% - Discount%}])^{(365/[Total period - Discount period])} - 1 =(1 + [1% / {100% - 1%}])^{(365/[30 days - 10 days])} - 1 = 0.2013 or about 20.13%.

The APR for trade credit is: APR = (Discount% / [100% - Discount%]) * (365 / [Total period - Discount period]) = (6% / [100% - 6%])(365/[70 days - 10 days]) = 0.3883 or about 38.83%.

The APY for trade credit is: APY = -1 + (1 + [Discount% / {100% - Discount%}])^{(365/[Total period - Discount period])} = -1 + (1 + [6% / {100% - 6%}])^{(365/[70 days - 10 days])} = 0.4570 or about 45.70%.

The APR for trade credit is: APR = (Discount% / [100% - Discount%]) * (365 / [Total period - Discount period]) = (2% / [100% - 2%]) * (365 / [45 days - 15 days]) = 0.2483 or about 24.83%.

The APY for trade credit is: APY = (1 + [Discount% / {100% - Discount%}])^{(365/[Total period - Discount period])} -1 = (1 + [2% / {100% - 2%}])^{(365/[45 days - 15 days])} - 1 = 0.2786 or about 27.86%.

(B12) Ray Brooks has discussed a $250,000 1-year loan with several different banks. Alternatives a, b, and c are described here. What are the APR and the APY of each alternative? Which alternative is the cheapest?

(a) A 15% annual rate on a simple interest loan (interest in arrears), with no compensating balance.

[NOTE. Interest in arrears means that the interest is paid at the end of the year.]

We can use the following general formula: APR = [interest charges / (loan amount - compensating balance)] * (1/f) = [rP / (P - B)] * (1/f) where r = interest rate on the loan amount = 0.15; P = amount of loan = $250,000; rP = interest charges = 0.15*$250,000 = $37,500; B = increase in the firm's average cash balances as a result of the compensating balance requirement (or the decrease in the amount of the loan as the result of paying interest at the beginning of the period) = 0; and, f = fraction of a year the loan is outstanding = 1. Inserting our values for rP, P, B, and f into our equation, we have: APR = [rP / (P - B)] * (1/f)= [$37,500 / ($250,000 - 0)] * (1/1) = (0.15) * 1 = 0.15 or 15%.

The APY is: APY = {(1 + [net cost of loan / (cash advance)])^(1/f)} - 1 = {(1 + [rP / (P - B)])^(1/f)} - 1. Expressing 1 as (P - B) / (P - B), inserting the latter term for 1 in our equation, performing algebraic manipulations, and recognizing the net repayment is P - B + rP, it can be shown that APY = {(net repayment / cash advance)^(1/f)} - 1 = {([(P - B) + rP] / (P - B))^(1/f)} - 1. Inserting our values, we have APY = {([($250,000 - 0) + $37,500] / ($250,000 - $0))^(1/1)} - 1 = ($287,500 / $250,000)¹ - 1 = 1.15 - 1.00 = 0.15 or 15%.

NOTE. We just saw (and will also see in parts b and c) that when f = 1, APR is the same as APY. This is because 1*(1/f) = 1^(1/f) when f = 1. Inserting in the latter expression, we have: 1*(1/1) = 1 and 1^(1/f) = 1. It can also be seen since both APR and APY equal [rP / (P - B)] when f = 1. We have:

APY = {(1 + [rP / (P - B)])^(1/f)} - 1 = {(1 + [rP / (P - B)])^(1/1)} - 1 = {(1 + [rP / (P - B)])¹} - 1 = 1 + [rP / (P - B)] - 1 = [rP / (P - B)].

(b) An 11% annual rate on a simple interest loan (interest in arrears), with a 20% compensating balance requirement and interest due at the end of the year.

APR = [interest charges / (loan amount - compensating balance)] * (1/f) = [rP / (P - B)] * (1/f) where r = interest rate on the loan amount = 0.11; P = amount of loan = $250,000; rP = interest charges = 0.11*$250,000 = $27,500; B = increase in the firm's average cash balances as a result of the compensating balance requirement = (0.2)*($250,000) = $50,000; and, f = fraction of a year the loan is outstanding = 1. Inserting our values, we have: APR = [$27,500 / ($250,000 - $50,000)] * (1/1) = [$27,500/$200,000] * 1 = 0.1375 or 13.75%.

The APY is: APY = {(1 + [net cost of loan / (cash advance)])^(1/f)} - 1 = {(1 + [rP / (P - B)])^(1/f)} - 1. Expressing 1 as (P - B) / (P - B) and performing algebraic manipulations as suggested previously, it can be shown that APY = {(net repayment / cash advance)^(1/f)} - 1 = {([(P - B) + rP] / (P - B))^(1/f)} - 1. Inserting our values, we have APY = {([($250,000 - $50,000) + $27,500] / ($250,000 - $50,000))^(1/1)} - 1 = ($227,500 / $200,000)¹ - 1 = 1.1375 - 1.00 = 0.1375 or 13.75%.

The interest paid at the beginning of the year is 0.14*$250,000 = $35,000. This serves to lower the cash advance by $35,000. In essence, it functions like a compensating balance.

APR = [interest charges / (loan amount - compensating balance)] * (1/f) = [rP / (P - B)] * (1/f) where r = interest rate on the loan amount = 0.14; P = amount of loan = $250,000; rP = interest charges = 0.14*$250,000 = $35,000; B = the decrease in the amount of the loan as a result of paying interest at the beginning of the year = (0.14)*($250,000) = $35,000; and, f = fraction of a year the loan is outstanding = 1. Inserting our values, we have: APR = [$35,000 / ($250,000 - $35,000)] * (1/1) = [$35,000 / $215,000] * 1 = 0.1627907 or about 16.28%.

The APY is: APY = {(1 + [net cost of loan / (cash advance)])^(1/f)} - 1 = {(1 + [rP / (P - B)])^(1/f)} - 1. Expressing 1 as (P - B) / (P - B) and performing algebraic manipulations as suggested in part a, it can be shown that APY = {(net repayment / cash advance)^(1/f)} - 1 = {([(P - B) + rP] / (P - B))^(1/f)} - 1. Inserting our values, we have APY = {([($250,000 - $35,000) + $35,000] / ($250,000 - $35,000))^(1/1)} - 1 = ($250,000 / $215,000)¹ - 1 = 1.1627907 - 1.00 = 0.1627907 or about 16.28%.

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