CHAPTER 20 Accounts Receivable and Inventory Management CHAPTER ORIENTATION The investment of funds in accounts receivable inventory involves a trade-off between profitability and risk For accounts receivable, this trade-off occurs as less creditworthy customers with a higher probability of bad debts are taken on to increase sales With respect to inventory management, a larger investment in inventory leads to more efficient production and speedier delivery, hence, increased sales However, additional financing to support the increase in inventory and increased handling and carrying costs is required In addition, the concept of total quality management and single-sourcing have had a major impact on inventory purchasing CHAPTER OUTLINE I Accounts receivable A Typically, accounts receivable account for just over 20 percent of a firm's assets B The size of the investment in accounts receivable varies from industry to industry and is affected by several factors including the percentage of credit sales to total sales, the level of sales and the credit and collection policies, more specifically the terms of sale, the quality of customers and collection efforts C Although all these factors affect the size of the investment, only the credit and collection policies are decision variables under the control of the financial manager D The terms of sale are generally stated in the form a/b net c, indicating that the customer can deduct a percentage if the account is paid within b days; otherwise, the account must be paid within c days 240 E If the customer decides to forgo the discount and not pay until the final payment date, the annualized opportunity cost of passing up this a% discount and withholding payment until the cth day is determined as follows: annualized opportunity cost of forgoing the discount = a 1 a x 360 c b Example: Given the trade credit terms of 2/10, net 30, what is the annualized opportunity cost of passing up the percent discount and withholding payment until the 30th day? Solution: Substituting the values from the example, we get 36.73% = F A second decision variable in determining the size of the investment in accounts receivable in addition to the trade credit terms is the type of customer G H 0.02 360 x  0.02 30  10 The costs associated with extending credit to lower-quality customers include: a Increased costs of credit investigation b Increased probability of customer default c Increased collection costs Analyzing the credit application is a major part of accounts receivable management Several avenues are open to the firm in considering the credit rating of an applicant Among these are financial statements, independent credit ratings and reports, bank references, information from other companies, and past experiences One commonly used method for credit evaluation is called credit scoring and involves the numerical evaluation of each applicant in which an applicant receives a score based upon the answers to a simple set of questions The score is then evaluated relative to a predetermined standard, its level relative to that standard determining whether or not credit scoring should be extended to the applicant The major advantage of credit scoring is that it is inexpensive and easy to perform The key to maintaining control over the collection of accounts receivable is the fact that the probability of default increases with the age of the account One common way of evaluating the current situation is ratio analysis a examining the average collection period b ratio of receivables to assets 241 c d e II ratio of credit sales to receivables (accounts receivable turnover ratio) amount of bad debts relative to sales over time aging of accounts receivable schedule I Once delinquent accounts have been identified, the third and final variable is determined by the firm’s collection policies A direct trade-off does exist between collection expenses and lost goodwill on one hand and noncollection of accounts on the other, and this trade-off is always part of making the decision J Credit should be extended to the point that marginal profitability on additional sales equals the required rate of return on the additional costs we have to consider investment in inventories + receivables + change in cost of cash discount to generate those sales Inventory A Typically, inventory accounts for about four to five percent of a firm's assets B The purpose of carrying inventories is to uncouple the operations of the firm; that is, to make each function of the business independent of each other function C As such, the decision with respect to the size of the investment in inventory involves a basic trade-off between risk and return D The risk comes from the possibility of running out of inventory if too little inventory is held, while the return aspect of this trade-off results because increased inventory investment costs money E There are several general types of inventory Raw materials inventory consists of the basic materials that have been purchased from other firms to be used in the firm's production operations This type of inventory uncouples the production function from the purchasing function Work in process inventory consists of partially finished goods that require additional work before they become finished goods This type of inventory uncouples the various production operations Finished goods inventory consists of goods on which the production has been completed but the goods are not yet sold This type of inventory uncouples the production and sales function Stock of cash inventory, already discussed in some detail in preceding chapters, serves to make the payment of bills independent of the collection of accounts due F In order to effectively manage the investment in inventory, two problems must be dealt with: the order quantity problem and the order point problem G The order quantity problem involves the determination of the optimal order size for an inventory item given its expected usage, carrying, and ordering costs 242 H The economic order quantity (EOQ) model attempts to determine the order size that will minimize total inventory costs The EOQ is given as Q* = where C = carrying cost per unit O = ordering cost per order S = total demand in units over the planning period Q* = the optimal order quantity in units I The order point problem attempts to answer the following question: How low should inventory be depleted before it is reordered? J In answering this question two factors become important: What is the usual procurement or delivery time and how much stock is needed to accommodate this time period? How much safety stock does the management desire? K Modification for safety stocks is necessary since the usage rate of inventory is seldom stable over a given timetable L This safety stock is used to safeguard the firm against changes in order time and receipt of shipped goods M The greater the uncertainty associated with forecasted demand or order time, the larger the safety stock The costs associated with running out of inventory will also determine the safety stock levels N A point is reached where it is too costly to carry a larger safety stock given the associated risk Inflation can also have an impact on the level of inventory carried Goods may be purchased in large quantities in anticipation of price rises O The cost of carrying goods may increase, causing a decline in Q*, the optimal order quantity The just-in-time inventory control system is more than just an inventory control system; it is a production and management system Under this system, inventory is cut down to a minimum, and the time and physical distance between the various production operations is also minimized 243 III Actually the just-in-time inventory control system is just a new approach to the EOQ model which tries to produce the lowest average level of inventory possible Average inventory is reduced by locating inventory supplies in convenient locations and setting up restocking strategies that cut time and thereby reduce the needed level of safety stock TQM and Inventory Purchasing management A The concept of total quality management has led to strong customer-supplier relationships in an effort to increase quality B In many cases firms that only a few years ago placed an upper limit of 10 or 20 percent on the purchases of any part from a single supplier now rely on a single supplier using the single-sourcing relationship C Single sourcing ties the interests of the supplier to the firm to which it supplies and allows the supplier to provide input on production techniques that might improve quality D Financially, the TQM view argues that higher quality will result in increased sales and market share and as a result the traditional economic analysis of inventory management is flawed ANSWERS TO END-OF-CHAPTER QUESTIONS 20-1 The size of the investment in accounts receivable is determined primarily by these factors: (1) The percentage of credit sales to total sales While this factor plays a major role in determining the investment in accounts receivable, it is generally not within the control of the financial manager In essence, the nature of the business tends to determine the blend between credit sales and cash sales (2) The level of sales As sales increase, so will accounts receivable Again, this is not an effective decision tool (3) Credit and collection policies Specifically the terms of sale, the quality of customer, and collection efforts are determinants of the level of investment in receivables that are under the control of the financial manager 20-2 (a) 1/20 net 50 means a percent discount can be taken if the account is paid within 20 days; otherwise, it can be paid within 50 days (b) 2/30 net 60 means a percent discount can be taken if the account is paid within 30 days; otherwise, it must be paid within 60 days (c) Net 30 means there are no discounts offered and the account must be paid within 30 days 244 (d) 2/10, 1/30 net 60 means a two percent discount can be taken if the account is paid within 10 days, and if paid after 10 days but before and up to 30 days, a one percent discount can be taken; otherwise, the account must be paid within 60 days 20-3 The purpose of an aging account is to provide a breakdown both in dollars and percentage terms of the proportion of receivables that are past due The same function could essentially be handled through ratio analysis, provided accounts receivable were broken down according to when they were due However, an aging account provides control over past due accounts in an extremely efficient manner 20-4 If a credit manager experienced no bad debt losses over the past year, then credit was probably not extended to enough customers Ideally credit should be extended to the point where marginal revenue from added sales due to increased credit is equal to the marginal costs associated with increased bad debts, costs of investigation, costs of collection, and increased required rate of return Obviously the credit manager was nowhere near this level if no bad debts were incurred 20-5 Credit scoring involves the numerical evaluation of credit applicants based upon their answers to simple questions This score is then evaluated relative to a predetermined standard, many times generated through the use of multiple discriminant analysis; its level relative to the standard determining whether or not credit should be extended to the applicant The major advantage of credit scoring is that it is inexpensive and easy to perform Once standards are set, a computer or clerical worker without specialized training can easily evaluate applicants 20-6 The returns associated with a more liberal credit policy come from the fact that extending credit to weaker customers or liberalizing the trade credit terms will probably increase sales, resulting in a larger profit level The risks involved largely result from the increased possibility of extending credit that will eventually become bad debts 20-7 The logic behind marginal analysis is to examine the incremental or marginal benefits, and incremental costs associated with any change in the credit policy; and if this change produces more benefits than costs, the change should be made If, however, the incremental costs are greater than the incremental benefits, the proposed change should be dropped 20-8 The purpose of carrying inventories is to uncouple the operations of the firm; that is, to make each function of the business independent of each other's function By uncoupling the various operations of the firm, delays or shutdowns in one area no longer affect the production and sale of the final product Raw materials inventory, for example, uncouples the production function from the purchasing function Work in process inventory uncouples the various production operations 20-9 Yes The stock of cash carried by a firm is simply a special type of inventory In terms of uncoupling the various operations of the firm, the purpose of holding cash is to make the payment of bills independent of the collection of accounts due 245 20-10 In order to effectively control the investment in inventory, the firm must: (1) determine the optimal order size for the inventory item, given its expected usage, carrying, and ordering costs; (2) determine how low inventory should be allowed to deplete before it is reordered 20-11 The major assumptions of the EOQ model include: (1) Constant or uniform demand (2) Constant unit price regardless of amount ordered (3) Constant carrying costs per unit (4) Constant ordering costs per order regardless of the size of the order (5) Instantaneous delivery (6) Independent orders 20.12 The risk associated with the inventory investment is that if the level of inventory is too low, the various functions of business will not be effectively uncoupled, and delays in production and customer delivery will result The return aspects of this trade-off result because increased inventory investment costs money As the size of the inventory increases, the storage and handling cost, in addition to the required rate of return on capital invested in inventory, will rise Thus, the more inventory the firm holds, the less risk they run of stocking out of inventory and the greater are their inventory expenses 20.13 Inflation affects the EOQ model by increasing carrying costs (C) which results in a small EOQ level In addition, if inflation is accompanied by major periodic price increases, this may cause the EOQ model to lose its applicability and be replaced by a policy of anticipatory buying; that is, buying in anticipation of a price increase in order to secure the goods at a lower cost 20-14 With single-sourcing, a company uses very few suppliers or, in many cases, a single supplier as a source for a particular part or material In this way the company has a more direct influence and control over the quality performance of a supplier, since the company accounts for a larger proportion of the supplier's volume The company and supplier can then enter into a partnership where the supplier agrees to meet the quality standards of the customer In this way the supplier can be brought into the TQM program of the customer 20-15 The TQM view argues that the traditional analysis is flawed in that it ignores the fact that increased sales and market share result from better quality products and that this increase in sales will more than offset the higher costs associated with increased quality In effect, it is argued that the benefits from quality improvement are underestimated 246 SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A a 360 x 1 a c b 20-1A where a b c = = = amount of the discount the discount period the net period 0.02 360 x  0.02 50  10 = 18.37% a 360 x 1 a c b 20-2A where a b c = = = amount of the discount the discount period the net period 0.02 360 x  0.02 30  20 = 73.47% 20-3A a 360 x 1 a c b where a b c = = = (a) 0.01 x  0.01 360 20  10 = 36.36% (b) 0.02  0.02 360 30  10 = 36.73% (c) 0.03 360 x  0.03 30  10 = 55.67% (d) 0.03 360 x  0.03 60  10 = 22.27% x amount of the discount the discount period the net period 247 (e) 0.03 360 x  0.03 90  10 = 13.92% (f) 0.05 360 x  0.05 60  10 = 37.89% 20-4A Applicant #1 Z = Z = Z = 3.3(0.2) + 1.0(0.2) + 0.6(1.2) + 1.4(0.3) + 1.2(0.5) 0.66 + 0.2 + 0.72 + 0.42 + 0.6 2.6 < 2.7 thus, reject Applicant #2 Z = Z = Z = 3.3(0.2) + 1.0(0.8) + 0.6(1.0) + 1.4(0.3) + 1.2(0.8) 0.66 + 0.8 + 0.6 + 0.42 + 0.96 3.44 > 2.7 thus, accept Applicant #3 Z = Z = Z = 3.3(0.2) + 1.0(0.7) + 0.6(0.6) + 1.4(0.3) + 1.2(0.4) 0.66 + 0.7 + 0.36 + 0.42 + 0.48 2.62 < 2.7 thus, reject Applicant #4 Z = Z = Z = 3.3(0.1) + 1.0(0.4) + 0.6(1.2) + 1.4(0.4) + 1.2(0.4) 0.33 + 0.4 + 0.72 + 0.56 + 0.48 2.49 < 2.7 thus, reject Applicant #5 Z = Z = Z = 3.3(0.3) + 1.0(0.7) + 0.6(0.5) + 1.4(0.4) + 1.2(0.7) 0.99 + 0.7 + 0.30 + 0.56 + 0.84 3.39 > 2.7 thus, accept Applicant #6 Z = Z = Z = 3.3(0.2) + 1.0(0.5) + 0.6(0.5) + 1.4(0.4) + 1.2(0.4) 0.66 + 0.5 + 0.30 + 0.56 + 0.48 2.5 < 2.7 thus, reject 20-5A (a) Sales  cost of goods sold Sales = Gross Profit Margin $600,000  Cost of goods sold $600,000 = 0.10 Cost of goods sold = $540,000 248 (b) (c) (d) Cost of goods sold Average inventory = Inventory turnover ratio $540,000 Average inventory = Average inventory = $90,000 Inventory turnover ratio = 360 Average Collection Period Inventory turnover = Inventory turnover ratio = times Cost of goods sold Average inventory = times $480,000 Average inventory = times Average inventory = $53,333 Cost of goods sold Average inventory = Inventory turnover ratio $1,150,000 Average inventory = Average inventory = $230,000 (1 - Gross profit margin) (Sales) = (0.86)($25,000,000) Cost of Goods Sold = $21,500,000 cost of goods = times $21,500,000 Average inventory = times Average inventory = $ 2,687,500 Inventory turnover ratio = 20-6A Step 1: 360 45 Estimate the Change in Profit 249  600   3000    $.10 +   $10    600  Order five times: = = $30.00 + $50.00 = $80  300   3000    $0.10 +   $10    300  Order ten times: = Order 15 times: (c) (1) (2) (3) (4) (5) (6) (a) Q* = $15.00 + $100 = $115 =  200   3000    $0.10 +   $10    200  = $10 + $150 = $160 constant or uniform demand constant unit price constant carrying costs constant ordering costs instantaneous delivery independent orders 20-9A = 2SO C = 2(20,000)50 0.25 = (b) 2828 boxes It assumes among other things that the rolls are not perishable assumptions include: (1) constant or uniform demand (2) constant unit price (3) constant carrying costs (4) constant ordering costs (5) instantaneous delivery (6) independent orders 252 Other 20-10A (a) Q* = 2SO C 2(50,000)500 75 = = (b) 816.4967 units or 816 units Total costs = S Q   C +   O 2 Q =  816   50,000    $75 +   $500    816  = $30,600 + $30,637 = $61,237 Note that carrying cost ($30,600) differs from ordering cost ($30,637) due to a $37 rounding error Recall that Q* was rounded down by 4967 units 20-11A (a) Q* = 2SO C = 2(500,000)90 40 = 15,000 Units (b) 500,000 15,000 (c) Inventory order point = delivery time stock + safety stock (d) = Average inventory 33 1/3 orders per year = x 500,000 + 15,000 50 = 10,000 + 15,000 = 25,000 units = EOQ + safety time stock = 15,000 + 15,000 = 7,500 + 15,000 = 22,500 units 253 20-12A (a) EOQ = 2SO C = 2(500,000)(100) 50 = 14,142 units: but since orders must be placed in 200unit lots, the effective EOQ becomes 14,200 units = 35.2 orders per year (b) 500,000 14,200 (c) Inventory order point = Delivery time stock + safety stock (d-a) EOQ = = 50 = 40,000 + 5,000 = 45,000 units x 500,000 + 5,000 2(500,000)(100) 2.5 = 6,324.5 = = 6,325 units, but since orders must be placed in 200 unit lots the effective EOQ becomes 6,400 = 78.1 orders per year (d-b) 500,000 6,400 (d-c) x 500,000 + 5,000 50 = 40,000 + 5,000 = 45,000 units 6,325 (d-d) Yes, as carrying costs rise the EOQ level drops and the number of orders per year rises which means that on average less inventory will be kept on hand 254 SOLUTION TO INTEGRATIVE PROBLEM Accounts Receivable The size of the investment in accounts receivable is determined primarily by these factors: (a) The percentage of credit sales to total sales While this factor plays a major role in determining the investment in accounts receivable, it is generally not within the control of the financial manager In essence, the nature of the business tends to determine the blend between credit sales and cash sales (b) The level of sales As sales increase, so will accounts receivable Again, this is not an effective decision tool (c) Credit and collection policies Specifically the terms of sale, the quality of customer, and collection efforts are determinants of the level of investment in receivables that are under the control of the financial manager (a) a 360 x 1 a c b where a b c x (a) = = = = 18.18% a 360 x 1 a c b where a b c x Step 1: Step 2: = = = amount of the discount the discount period the net period = 24.49% Estimate the Change in Profit = = = amount of the discount the discount period the net period ($1,000,000 x 25) - ($1,000,000 x 08) $250,000 - $80,000 $170,000 Estimate the cost of additional investment in account receivable and inventory Estimate the additional investment in accounts receivable: = = = ($8,000,000 / 360) x 75 - ($7,000,000 / 360) x 60 $1,666,667 - $1,166,667 $500,000 255 Additional accounts receivable and inventory times the required rate of return: = = Step 3: Estimate the change in the cost of the cash discount = = = Step 4: ($500,000 + $50,000) 15 $82,500 ($8,000,000 x 02 x 50) - ($7,000,000 x 01 x 50) $80,000 - $35,000 $45,000 Compare the incremental revenues with the incremental costs = = = Step - (Step + Step 3) $170,000 - ($82,500 + $45,000) $42,500 The policy should be adopted Inventory Management EOQ = 2SO C = 2(250,000)100 = 7,071 units or 7,100 units = 35.2 orders per year 250,000 7,100 Inventory order point = Delivery time stock + safety stock Average inventory = x 250,000 + 5,000 50 = 5,000 + 5,000 = 10,000 units = EOQ = 7,100 + 5,000 = 8,550 units + Safety stock 256 EOQ Elasticity of EOQ with respect to a double in sales EOQ Elasticity of EOQ with respect to a double in carrying costs EOQ Elasticity of EOQ with respect to a double in ordering costs = 2(500,000)100 = 10,000 units = % Δ EOQ % Δ Sales = Δ EOQ EOQ Δ Sales Sales =  10,000  7,100   500,000  250,000    /   7,100 250,000     = 4085 1.0 = = 4085 or 40.85% 2( 250,000)100 = 5,000 = %  EOQ %  Carrying Costs = 5,000  7,100 7,100 = -29.58% 2 1 = 2(250,000)200 = 10,000 = %  EOQ %  Ordering Costs 257 = 10,000  7,100 7,100 = 40.85% 200  100 100 The selling price of the item does not enter the EOQ equation and does not affect the level of EOQ The EOQ equation attempts to minimize costs and as such the selling price does not enter into its calculation; thus the elasticity of EOQ with respect to the selling price is The major assumptions of the EOQ model include: (1) (2) (3) (4) (5) (6) Constant or uniform demand Constant unit price regardless of amount ordered Constant carrying costs per unit Constant ordering costs per order regardless of the size of the order Instantaneous delivery Independent orders 10 Inflation affects the EOQ model by increasing carrying costs (C) which results in a small EOQ level In addition if inflation is accompanied by major periodic price increases this may cause the EOQ model to lose its applicability and be replaced by a policy of anticipatory buying, that is, buying in anticipation of a price increase in order to secure the goods at a lower cost 11 A decrease in the average delivery time decreases the inventory order point Inventory can be ordered when there is a lower level of inventory Safety stock may also be reduced The total level of inventory held will decrease in this situation 12 If ordering costs decrease, then it is more economical to order more often and the EOQ decreases This in turn means that less inventory on average will be held Solutions to Problem Set B 20-1B a 360 x 1 a c b where a b c = = = 0.02 360 x  0.02 60  10 amount of the discount the discount period the net period = 14.69% 258 a 360 x 1 a c b 20-2B where a b c x = = = amount of the discount the discount period the net period = 36.73% a 360 x 1 a c b 20-3B where a = amount of the discount b = the discount period c = the net period (a) 0.01 360 x = 24.24%  0.01 20  (b) 0.02 360 x = 10.50%  0.02 90  20 (c) 0.01 360 x = 4.55%  0.01 100  20 (d) 0.04 360 x = 37.50%  0.04 50  10 (e) 0.05 360 x = 23.68%  0.05 100  20 (f) 0.05 360 x = 94.74%  0.05 50  30 259 20-4B Applicant #1 Z = 3.3(0.3) + 1.0(0.4) + 0.6(1.2) + 1.4(0.3) + 1.2(0.5) Z = 0.99 + 0.4 + 0.72 + 0.42 + 0.6 Z = 3.13 > 2.7 thus, accept Z = 3.3(0.2) + 1.0(0.6) + 0.6(1.3) + 1.4(0.4) + 1.2(0.3) Z = 0.66 + 0.6 + 0.78 + 0.56 + 0.36 Z = 2.96 > 2.7 thus, accept Z = 3.3(0.2) + 1.0(0.7) + 0.6(0.6) + 1.4(0.3) + 1.2(0.2) Z = 0.66 + 0.7 + 0.36 + 0.42 + 0.24 Z = 2.38 < 2.7 thus, reject Z = 3.3(0.1) + 1.0(0.5) + 0.6(1.8) + 1.4(0.5) + 1.2(0.4) Z = 0.33 + 0.5 + 1.08 + 0.7 + 0.48 Z = 3.09 > 2.7 thus, accept Z = 3.3(0.5) + 1.0(0.7) + 0.6(0.5) + 1.4(0.4) + 1.2(0.6) Z = 1.65 + 0.7 + 0.30 + 0.56 + 0.72 Z = 3.93 > 2.7 thus, accept Z = 3.3(0.2) + 1.0(0.4) + 0.6(0.2) + 1.4(0.4) + 1.2(0.4) Z = 0.66 + 0.4 + 0.12 + 0.56 + 0.48 Z = 2.22 < 2.7 thus, reject Applicant #2 Applicant #3 Applicant #4 Applicant #5 Applicant #6 260 20-5B (a) (b) Sales  cost of goods sold Sales = Gross Profit Margin $550,000  Cost of goods sold $550,000 = 0.10 Cost of goods sold = $495,000 Cost of goods sold Average inventory = Inventory turnover ratio $495,000 Average inventory = Average inventory = $99,000 Inventory turnover ratio = 360 Average Collection Period Inventory turnover = 360 35 Inventory turnover ratio = 10.286 times Cost of goods sold Average inventory = 10.286 times $480,000 Average inventory = 10.286 times Average inventory = $46,665.37 = Inventory turnover ratio $1,250,000 Average inventory = Average inventory = $208,333 (c) 261 (d) 20-6B Step 1: Step 2: (1 - Gross profit margin) (Sales) = cost of goods (0.85)($25,000,000) = $21,250,000 Inventory turnover ratio = = 7.2 times $21,250,000 Average inventory = 7.2 times Average inventory = $ 2,951,389 Estimate the Change in Profit = ($1,000,000 x 20) - ($1,000,000 x 08) = $200,000 - $80,000 = $120,000 Estimate the cost of additional investment in accounts receivable and inventory Estimate the additional investment in accounts receivable: = ($7,000,000 / 360) x 90 - ($6,000,000 / 360) x 40 = $1,750,000 - $666,667 = $1,083,333 Additional accounts receivable and inventory times the required rate of return: Step 3: = ($1,083,333 + $40,000) 15 = $168,500 Estimate the change in the cost of the cash discount = Step 4: $0 (no change) Compare the incremental revenues with the incremental costs = Step - (Step + Step 3) = $120,000 - $168,500 = - $48,500 The policy should not be adopted 262 20-7B Step 1: Estimate the Change in Profit Step 2: = ($1,000,000 x 20) - ($1,000,000 x 08) = $200,000 - $80,000 = $120,000 Estimate the cost of additional investment in accounts receivable and inventory Estimate the additional investment in accounts receivable: = ($18,000,000 / 360) x 50 - ($17,000,000 / 360) x 30 = $2,500,000 - $1,416,667 = $1,083,333 Additional accounts receivable and inventory times the required rate of return: Step 3: = ($1,083,333 + $60,000) 15 = $171,500 Estimate the change in the cost of the cash discount = Step 4: $0 (no change) Compare the incremental revenues with the incremental costs = Step - (Step + Step 3) = $120,000 - $171,500 = - $51,500 The change should not be made 20-8B (a) Q* = 2SO C = 2(3500)9 = 315,000 = 561.2 units 263 (b) Total costs S Q =   C +   O 2 Q Order one time: =  3500   3500    $.20 +   $9    3500  = $350 + $9 = $359 =  875   3500    $.20 +   $9    875  = $87.50 + $36 = $123.50 =  700   3500    $.20 +   $9    700  = $70.00 + $45.00 = $115 =  350   3500    $0.20 +   $9    350  = $35.00 + $90 = $125 =  234   3500    $0.20 +   $9    234  = $23.40 + $134.62 = $158.02 Order four times: Order five times: Order ten times: Order 15 times: (c) 20-9B (1) (2) (3) (4) (5) (6) constant or uniform demand constant unit price constant carrying costs constant ordering costs instantaneous delivery independent orders (a) Q* = 2(21,000)55 0.20 = 3,398.5 boxes 264 = 2SO C (b) It assumes among other things that the rolls are not perishable assumptions include: (1) (2) (3) (4) (5) (6) Other constant or uniform demand constant unit price constant carrying costs constant ordering costs instantaneous delivery independent orders 20-10B (a) (b) Q* Total costs = 2SO C = 2(55,000)500 70 = 886.40 units or 886 units = S Q   C +   O 2 Q =  886   55,000    $70 +   $500    886  = $31,010 + $31,038.37 = $62,048.37 Note that carrying cost ($31,010) differs from ordering cost ($31,038.37) due to a $37 rounding error 20-11B (a) Q* = 2SO C = 2(600,000)90 45 = 15,492 units or 15,400 units = 38.96 orders per year (or about 39 orders) (b) 600,000 15,400 (c) Inventory order point = delivery time stock + safety stock = x 600,000 + 15,000 = 12,000 + 15,000 = 27,000 units 265 (d) Average inventory EOQ + safety time stock = = 15,400 + 15,000 = 7,700 + 15,000 = 22,700 units 20-12B (a) EOQ = 2SO C = 2(500,000)(75) 45 = 12,909.90 units: but since orders must be placed in 200 unit lots, the effective EOQ becomes 13,000 units (b) 500,000 13,000 = 38.5 orders per year (c) Inventory order point = Delivery time stock + safety stock = x 500,000 + 5,000 50 = 40,000 + 5,000 = 45,000 units (d-a) EOQ = 2(500,000)(75) 2.5 = 5,477 units, but since orders must be placed in 200 unit lots the effective EOQ becomes 5,400 = 93 orders per year (d-b) 500,000 5,400 (d-c) x 500,000 + 5,000 50 = 40,000 + 5,000 = 45,000 units (d-d) Yes As carrying costs rise the EOQ level drops and the number of orders per year rises which means that on average less inventory will be kept on hand 266 ... = $ 120, 000 - $168,500 = - $48,500 The policy should not be adopted 262 20- 7B Step 1: Estimate the Change in Profit Step 2: = ($1,000,000 x 20) - ($1,000,000 x 08) = $200 ,000 - $80,000 = $ 120, 000... benefits from quality improvement are underestimated 246 SOLUTIONS TO END-OF -CHAPTER PROBLEMS Solutions to Problem Set A a 360 x 1 a c b 20- 1A where a b c = = = amount of the discount the discount... c b 20- 2A where a b c = = = amount of the discount the discount period the net period 0.02 360 x  0.02 30  20 = 73.47% 20- 3A a 360 x 1 a c b where a b c = = = (a) 0.01 x  0.01 360 20 