Business Finance Lecture 10

Lecture 10: Short-term Þnancial planning and management (Chpt. 17) Managing cash Reasons for holding cash ! The speculative motive Ñ the need to hold cash to take advantage of additional investment opportunities, such as bargain purchases, attractive interest rates and favourable exchange rate ßuctuations. ! The precautionary motive Ñ the need to hold cash as a safety margin to act as a Þnancial reserve. ! The transaction motive Ñ the need to hold cash to satisfy normal disbursement (payment of wages and salaries, trade debts, taxes and dividends) and collection activities (from product sales, the selling of assets and new Þnancing) associated with a ÞrmÕs ongoing operations. ! Discussion point Is there a potential conßict of interest between managers, creditors and shareholders about how much cash a company should hold? ! • Managers: prefer large amounts of cash to give maximum ßexibility to take advantage of investment opportunities that might arise (speculative motive).! • Creditors: prefer large amounts of cash to give security (precautionary motive).! • Shareholders: prefer moderate amounts of cash as they want the cash back to invest a greater return elsewhere.! To determine the appropriate cash balance, the Þrm must weigh the beneÞts of holding cash against the costs of them. ! Float! Float Ñ the difference between book cash and bank cash, representing the net effect of cheques in the process of clearing. ! A ÞrmÕs cash balance as reported in its Þnancial statements (book cash or ledger cash) is not the same thing as the balance shown in its bank account (bank cash or collected bank cash). The difference between bank cash and book cash is called ßoat, and represents the net effect of cheques in the process of clearing (moving through the banking system). ! Cheques written by a Þrm generate disbursement ßoat, causing a decrease in the ÞrmÕs book balance but no change in its available balance. Cheques received by the Þrm create collection ßoat. Collection ßoat increases book balances but does not immediately change available balances. !   Float management Float management involves controlling the collection and disbursement of cash: ! • Cash collection Ñ the aim is to speed up collections and reduce the lag between the time customers pay their bills and the time the cash becomes available.! • Cash disbursement Ñ the aim is to control payments and minimise the ÞrmÕs costs associated with making payments.! The size of the ßoat depends on both the cash levels and the time delay involved. ! Lecture example 1: daily ßoat ! You make a bank transfer of $500 to another country each month. It takes two days for the order to go through clearing. What is your average daily disbursement ßoat?! Answer: ! You have a $500 ßoat for 2 days. So we say that the total ßoat is 2 x $500 = $1,000. Assuming 30 days in the month, the average daily ßoat is: $1,000/30 = $33.33.! Managing seasonal cash demands ! Firms have temporary cash surpluses for various reasons. Two of the most important are the Þnancing of seasonal or cyclical activities of the Þrm and the Þnancing of planned or possible expenditures. ! ! Some Þrms have a predictable cash ßow pattern. They have surplus cash ßows during part of the year and deÞcit cash ßows for the rest of the year. For example, Toys R Us has a seasonal cash ßow pattern inßuenced by the holiday season. A Þrm like this may buy marketable securities when surplus cash ßows occur, and sell marketable securities when deÞcits occur. Of course, bank loans are another shortterm Þnancing device. The use of bank loans and marketable securities to meet temporary Þnancing needs is illustrated below, where the Þrm is following a compromise working capital policy. ! Planned or possible expenditures Firms frequently accumulate temporary investments in marketable securities to provide the cash for a plant construction programme, dividend payment or other large expenditure. Thus Þrms may issue bonds and shares before the cash is needed, investing the proceeds in short-term marketable securities and then selling the securities to Þnance   the expenditures. Also, Þrms may face the possibility of having to make a large cash outlay. An obvious example would involve the possibility of losing a large lawsuit. Firms may build up cash surpluses against such a contingency. ! Discussion point: please list companies or industry sectors that are likely to have seasonal cash patterns. ! Managing a target cash balance ! Target cash balance Ñ a ÞrmÕs desired cash level as determined by the trade-off between carrying costs and shortage costs. ! Carrying (or opportunity) costs Ñ the interest that could be earned by investing the cash elsewhere. ! Shortage (or adjustment) costs Ñ the costs associated with holding too little cash. ! The basic idea: What is the optimum starting cash balance? ! The Þgure represents the cash management problem for a Þrm that has a ßexible capital policy. If a Þrm tries to keep its cash holdings too low, it will Þnd itself running out of cash more often than is desirable, and thus selling marketable securities (and perhaps later buying marketable securities to replace those sold) more frequently than would be the case if the cash balance were higher. Thus, trading costs will be high when the cash balance is small. These costs will fall as the cash balance becomes larger.! In contrast, the opportunity costs of holding cash are low if the Þrm holds little cash. These costs increase as the cash holdings rise, because the Þrm is giving up more interest that could have been earned. ! In the Þgure shown here, the sum of the costs is given by the total cost curve. As shown, the minimum total cost occurs where the two individual cost curves cross at point C*. At this point, the opportunity costs and trading costs are equal. This point represents the target cash balance, and it is the point the Þrm should try to Þnd. ! BAT model The Baumol-Allais-Tobin (BAT) model is a classic means of analysing cash management problems. It determines the (optimal) target cash balance (C*) by minimising total costs. It considers a company that requires regular net cash outßows to pay for operating expenses. Cash in the bank account is replenished by selling marketable securities. !   Opportunity costs ! Opportunity costs Ñ opportunity cost is interest missed by keeping cash on current account, earning zero interest, rather than investing in marketable securities. ! To determine the opportunity costs of holding cash, we have to Þnd out how much interest is foregone:! = average bank cash balance x interest rate on marketable securities! = initial cash balance x interest rate on marketable securities ! :. opportunity costs = (C/2) x R! Trading costs ! Trading costs Ñ trading costs is the cost of selling marketable securities to replenish bank balance, assumed to be a Þxed cost per trade. ! To determine the total trading costs for the year, we need to know how many times the Þrm will have to sell marketable securities during the year:! = number of times replenish cash x cost of sale ! = (amount of cash needed in planning period / initial cash balance needed) x cost of one trade ! :. trading costs = (T/C) x F! Total cost! Optimum starting cash position C* is where the two lines cross on the graph given earlier, where: opportunity costs = trading costs. That is: (C*/2) x R = (T/C*) x F ! That is: ! !∗ = $ (&' × )) ! + Where: F = the Þxed cost of selling securities to replenish cash! T = the total amount of new cash needed for transaction purposes over the relevant planning period Ñ usually, one year! R = the opportunity cost of holding cash; this is the interest rate on marketable securities! Lecture example 2: BAT ! Golden Socks begins week 0 with a cash balance in its bank account (non-interest bearing current account) of £1.2 million. Cash outßows exceed by £600,000 a week. Interest on marketable securities is 10% and each trade costs £1,000. ! (a) How long will it take to reduce the bank account to £0?! (b) How many times does the company need to sell marketable securities to replenish the cash in one year? ! (c) What is the optimum initial cash balance?!   ! Answer (a): 2 weeks (£1.2m / £600,000 per week) ! Answer (b): 52 weeks / 2 weeks = 26 times a year! ! Answer (c): T = total net cash outßows in one year ! = £1.2m x 26! = £31.2m ! F = cost per trade! = £1,000! R = interest rate on marketable securities ! = 10%! !∗ = $ ,,,,,,,= $ (&' × )) ! + (& × -., &00, 000 × ., 000) 0. .0 ! !!!!!!!=£!789,937! Final answer = £789,937! Assumptions:! • The model assumes that the Þrm has a constant disbursement rate ! • The model assumes that there are no cash receipts during the projected period ! • No safety stock is allowed ! Miller-Orr Model This model is a more sophisticated model because, unlike BAT, it allows: ! • Daily ßuctuation in net cash ßows, including net cash outßows ! • Includes a measure of uncertainty, σ2! To determine whether we need to use Miller Orr for the question (as opposed to using BAT), variance must be mentioned in the question.! The Þgure here shows how the system works. It operates in terms of an upper limit (U*) and a lower limit (L) to the amount of cash, as well as a target cash balance (C*). The Þrm allows its cash balance to wander around between the lower and upper limits. As long as the cash balance is somewhere between U* and L, nothing happens. !   When the cash balance reaches its upper limit (U*), as it does at point X, the Þrm moves U* Ñ C* cash out of the account and into marketable securities. This action moves the cash balance down to C*. In the same way, if the cash balance falls to the lower limit (L), as it does at point Y, the Þrm will sell C* Ñ L worth of securities and deposit the cash in the account. This action takes the cash balance up to C*. ! Upper%control%limit% – invest,%returning%balance%to%C* Lower%control%limit - Sell%marketable%securities%to% replenish%cash%to%C* Using the model ! To get started, management sets the lower limit (L). This limit essentially deÞnes a safety stock, so where it is set depends on how much risk of a cash shortfall the Þrm is willing to tolerate. Alternatively, the minimum might just equal a required compensating balance. ! As with the BAT model, the optimal cash balance depends on trading costs and opportunity costs. Once again, the cost per transaction of buying and selling marketable securities, F, is assumed to be Þxed. Also, the opportunity cost of holding cash is R, the interest rate period on marketable securities. The only extra piece of information that is needed is σ2, the variance of the net cash ßow per period. For our purposes the period can be anything Ñ a day, or a week for example Ñ as long as the interest rate and the variance are based on the same length of time. As a result, the formulas are as follows: ! Cash balance target: ! C* = L + (3/4 x F x σ2/R)(1/3) Upper limit:! U* = 3 x C* Ñ 2 x L Average cash balance:! A* = (4 x C* Ñ L)/3 Where: C* = target cash balance ! L = the lower limit (given in the question)! F = Þxed cost per transaction ! σ2 = variance of the periodÕs net cash ßows! R = interest rate on marketable securities! Lecture example 3: Miller-Orr! Short term securities yield is 0.02% per day. It costs the company £1 each time it buys or sells securities. The daily variance of cash ßows is £4. You require a £10 minimum checking (current) account balance. What is the target balance, upper limit and average cash balance according to the Miller-Orr model? ! All of the values are for one day/daily rate (as opposed to monthly): R = 0.0002! F = 1!   σ2 = 4! L = 10! ! So, the optimum target cash balance is: ! ' ' !" # $ % & ( ) * ) +, - ' ' # ./ % & ) . ) ( ( /0///, =£34.66' Upper cash limit: ! U* = (3 x C*) Ñ (2 x L)! = (3 x £34.66) Ñ (2 x £10) ! = £83.99 ! Average cash balance: ! A* = (4 x C* Ñ L)/3! = [(4 x £34.66) Ñ £10]/3! = £42.88! Comparison of the BAT and Miller-Orr models These two models differ in complexity, but they have some similar implications: ! • The greater the interest rate, the lower is the target cash balance ! • The greater the order cost, the higher is the target balance ! The advantage of the Miller-Orr model is that it improves our understanding of the problem of cash management by considering the effect of uncertainty, as measured by the variation in net cash inßows. ! Factors inßuencing the target cash balance The Þrm obtains cash by selling marketable securities. Another alternative would be to borrow cash. However, this introduces additional considerations for cash management: ! • Borrowing is likely to be more expensive than selling marketable securities, because the interest rate is likely to be higher ! • The need to borrow will depend on managementÕs desire to hold low cash balances Ñ a Þrm is more likely to borrow to cover an unexpected cash outßow with greater cash ßow variability and lower investment in marketable securities ! Secondly, for large Þrms, the trading costs of buying and selling securities are small when compared with the opportunity costs of holding cash (compensating balance). Suppose a Þrm has £1 million in cash that wont be needed for 24 hours. Should the Þrm invest the money or leave it sitting? ! Suppose the Þrm can invest the money at an annualised rate of 7.57% per year. The daily rate in the case is about two basis points (0.02% or 0.0002). The daily return earned on £1 million is thus 0.0002 x £1 million = £200. In many cases, the order cost will be much less than this; so a large Þrm will buy and sell securities very often before it will leave substantial amounts of cash idle. !   Managing credit When a Þrm sells goods and services, it can demand cash on or before the delivery date, or it can extend credit to customers and allow some delay in payment. Granting credit is making an investment in a customer Ñ an investment tied to the sale of a product or service. ! Why do Þrms grant credit? Not all do, but the practice is extremely common. The obvious reason is that offering credit is a way of stimulating sales. The costs associated with granting credit are not trivial. First, there is a chance that the customer will not pay. Second, the Þrm has to bear the costs of carrying the receivables. The credit policy decision thus involves a trade-off between the beneÞts of increased sales and the costs of granting credit. ! Key terms ! Terms of sale Ñ the conditions under which a Þrm sells its goods and services for cash or credit (e.g. credit period, cash discount and discount period, and the type of credit instrument) ! Credit analysis Ñ the process of determining the probability that customers will not pay. ! Collection policy Ñ the procedures followed by a Þrm in collecting trade receivables.! Credit period Ñ the period for which credit is granted. ! Cash discount Ñ Ô2/10, net 30Õ for example means: take a 2% discount from the full price if you pay within 10 days (i.e. the cash discount period), or else pay the full amount in 30 days (i.e. the net credit period). ! The credit policy ! If a Þrm decides to grant credit to its customers, then it must establish procedures for extending credit and collecting. In particular, the Þrm will have to deal with the terms of sale, credit analysis and collecting policy.! The cash ßows from granting credit ! The trade receivables period is the time it takes to collect on a sale. There are several events that occur during this period. These events are the cash ßows associated with granting credit, as seen in the diagram above. As our time line indicates, the typical sequence of events when a Þrm grants credit is as follows: !   1. 2. 3. 4. The credit sale is made ! The customer sends a cheque to the Þrm ! The Þrm deposits the cheque ! The ÞrmÕs account is credited for the amount of the cheque ! Terms of sale ! As mentioned earlier, the terms of sale are made up of three distinct elements: the credit period, the cash discount and the type of credit instrument. ! Credit' Period Cash' Discounts Credit' Instruments The credit period The credit period is the basic length of time for which credit is granted, which varies from industry to industry. However, it is almost always between 30 and 120 days. If a cash discount is offered, then the credit period has two components: the net credit period (the length of time the customer has to pay) and the cash discount period (the time during which the discount is available). ! The invoice date is the beginning of the credit period. With EOM dating, all sales made during a particular month are assumed to be made at the end of that month. MOM, for middle of month, is another variation. ! There are a number of factors that inßuence the credit period. Many of these also inßuence our customerÕs operating cycles; so, once again, these are related subjects. Among the most important are these: ! 1. Perishability and collateral value Ñ perishable items have relatively rapid turnover and relatively low collateral value. Credit periods are thus shorter for such goods. For example, a food wholesaler selling fresh fruit and produce might use net seven days. ! 2. Consumer demand Ñ products that are well established generally have more rapid turnover. Newer or slow-moving products will often have longer credit periods associated with them to entice buyers. Also, sellers may choose to extend much longer credit periods for off-season sales (when customer demand is low). ! 3. Cost, proÞtability and standardisation Ñ relatively inexpensive goods tend to have shorter credit periods. The same is true for relatively standardised goods and raw materials. These all tend to have lower mark-ups and higher turnover rates, both of which lead to shorter credit periods. However, there are exceptions: car dealers generally pay for the vehicles as they are received for example. ! 4. Credit risk Ñ the greater the credit risk of the buyer, the shorter the credit period is likely to be (if credit is granted at all).! 5. Size of the account Ñ if an account is small, the credit period may be shorter because small accounts cost more to manage, and the customers are less important. ! 6. Competition Ñ when the seller is in a highly competitive market, longer credit periods may be offered as a way of attracting customers. !   7. Customer type Ñ a single seller might offer different credit terms to different buyers. A food wholesaler, for example, might supply groceries, bakeries and restaurants. Each group would probably have different credit terms. More generally, sellers often have both wholesale and retail customers, and they frequently quote different terms to the two types. ! Cash discounts As we have seen, cash discounts are often part of the terms of sale. One reason why they are offered is to speed up the collection of receivables. This will have the effect of reducing the amount of credit being offered, and the Þrm must trade this off against the cost of the discount. ! Lecture example 4: cash discount ! A buyer is purchasing an item at a price of £1,000. The seller is considering offering a discount quoted as: Ô2/10, 30Õ. Interest rates are 10%. Should the seller offer the discount?! 2/10, 30 means that the buyer has a choice between:! • Paying the full price of £1,000 in 30 days ! • Taking a 2% discount and pay in 10 days, paying £980 now, 20 days earlier ! If the buyer takes the discount, the seller has effectively borrowed £980 from the buyer for 20 days and paid £20 interest. ! Is this a good rate of interest?! • You borrow 20/980 every 20 days (the interest rate for the period)! • For 365/20 periods in a year, so m = 365/20! So, EAR = (1 + 20/980)^(365/20) ! = 44.6%! Conclusion: This discount is really expensive for the seller as they are effectively borrowing at 44.6% from the buyer but can borrow at 10% from the bank. On the other hand, it is really attractive to the buyer as they are earning interest of 44.6% from the seller when market interest rates are 10%.! Credit instruments Credit instrument Ñ the evidence of indebtedness. ! Most trade credit is offered on open account Ñ this means that the only formal instrument of credit is the invoice, which is sent with the shipment of goods and which the customer signs as evidence that the goods have been received. Afterwards, the Þrm and its customers record the exchange on their books of account. ! Analysing credit policy: credit policy effects ! In evaluating credit policy, there are Þve basic factors to consider: !   1. Revenue effects Ñ if the Þrm grants credit, then there will be a delay in revenue collections as some customers take advantage of the credit offered and pay later. However, the Þrm may be able to charge a high price if it grants credit, and it may be able to increase the quantity sold. Total revenues may thus increase. ! 2. Cost effects Ñ although the Þrm may experience delayed revenues if it grants credit, it will still incur the costs of sales immediately. Whether the Þrm sells for cash or credit, it will still have to acquire or produce the merchandise (and pay for it). ! 3. Cost of debt Ñ when the Þrm grants credit, it must arrange to Þnance the resulting receivables. As a result, the ÞrÕs cost of short-term borrowing is a factor in the decision to grant credit. ! 4. Probability of non-payment Ñ if the Þrm grants credit, some percentage of the credit buyers will not pay. This canÕt happen, of course, if the Þrm sells for cash. ! 5. The cash discount Ñ when the Þrm offers a cash discount as part of its credit terms, some customers will choose to pay early to take advantage of the discount. ! Credit analysis: When should credit be granted?! Once a Þrm decides to grant credit to its customers, it must then establish guidelines for determining who will and who will not be allowed to buy on credit. Credit analysis refers to the process of deciding whether or not to extend credit to a particular customer. It usually involves tow steps: gathering relevant information, and determining creditworthiness. Firms will need to evaluate different scenarios, such as: ! • One time sale ! • Repeat business ! Collection policy ! Ageing schedule Ñ a compilation of trade receivables by the age of each account. ! Collection policy is the Þnal element in credit policy. Collection policy involves monitoring receivables to spot trouble, and obtaining payment on past-due accounts. ! Monitoring receivables To keep track of payments by customers, most Þrms will monitor outstanding accounts. First of all, a Þrm will normally keep track of its average collection period (ACP) through time. If a Þrm is in a seasonal business, the ACP will ßuctuate during the year; but unexpected increases in the ACP are a cause for concern. Either customers in general are taking longer to pay, or some percentage of trade receivables are seriously overdue. ! The ageing schedule is a second basic tool for monitoring receivables. To prepare one, the credit department classiÞes accounts by age. Suppose a Þrm has £100,000 in receivables. Some of these accounts are only a few days old, but others have been outstanding for quite some time. The following is an example of an ageing schedule: !   If the Þrm has a credit period of 60 days, then 25% of its accounts are late. Whether or not this is serious depends on the nature of the ÞrmÕs collections and customers. It is often the case that accounts beyond a certain age are almost never collected. Monitoring the age of accounts is very important in such cases. ! Collection effort A Þrm usually goes through the following sequence of procedures for customers whose payments are overdue: ! 1. Send out a delinquency letter informing the customer of the past-due status of the amount ! 2. Make a telephone call to the customer ! 3. Employ a collection agency ! 4. Take legal action against the customer ! At times, a Þrm may refuse to grant additional credit to customers until arrears are cleared up. This may antagonise a normally good customer, which points to a potential conßict between the collections department and the sales department. In probably the worst case, the customer Þles for bankruptcy. When this happens, the credit-granting Þrm is just another unsecured creditor. The Þrm can simply wait, or it can sell its receivable. ! Managing inventory Like receivables, inventories represent a signiÞcant investment for many Þrms.! Key elements ! • The%Financial%Manager%and% Inventory%Policy Inventory) Management • Inventory%Types • Inventory%Costs The Þnancial manager and inventory policy ! Despite the size of a typical ÞrmÕs investment in inventories, the Þnancial manager of a Þrm will not normally have primary control over inventory management. Instead, other functional areas such as purchasing, production and marketing will usually share decision-making authority regarding inventory. !   Inventory types ! For a manufacturer, inventory is normally classiÞed into one of three categories: raw materials, work in progress or Þnished goods. ! Inventory costs ! Two basic types of costs are associated with current assets in general, and with inventory in particular. The Þrst of these is carrying costs. Here, carrying costs represent all of the direct and opportunity costs of keeping inventory on hand, which include: ! • • • • Storage and tracking costs ! Insurance and taxes ! Losses due to obsolescence, deterioration, or theft ! The opportunity cost of capital on the invested amount ! The other type of costs associated with inventory is shortage costs. These are associated with having inadequate inventory on hand. The two components of shortage costs are restocking costs and costs related to safety reserves. Depending on the ÞrmÕs business, restocking or order costs are either the costs of placing an order with suppliers or the costs of setting up a production run. The costs related to safety reserves are opportunity losses such as lost sales and loss of customer goodwill that results from having inadequate inventory.! A basic trade-off exists in inventory management, because carrying costs increase with inventory levels, whereas shortage or restocking costs decline with inventory levels. The basic goal of inventory management is thus to minimise the sum of these two costs.! Inventory management techniques ! ABC approach The ABC approach is a simple approach in which the basic idea is to divide inventory into three (or more) groups. The underlying rationale is that a small portion of inventory in terms of quantity might represent a large portion in terms of inventory value. For example, this situation would exist for a manufacturer that uses some relatively expensive, hightech components and some relatively inexpensive basic materials in producing its products. This can be mapped out on a graph, where the percentage of inventory items vs. the percentage of inventory value are compared. ! The economic order quantity model (EOQ) The economic order quantity (EOQ) model is the best-known approach for explicitly establishing an optimal inventory level. The basic idea is illustrated below, which plots the various costs associated with holding inventory (vertical axis) against inventory levels (horizontal axis). As shown, inventory-carrying costs rise and restocking costs decrease as inventory levels increase. From seen earlier, the general shape of the total inventory cost curve is familiar. With the EOQ model, we can attempt to speciÞcally locate the minimum total cost point, Q*. !   An important point to keep in mind is that the actual cost of the inventory itself is not included. The reason is that the total amount of inventory the Þrm needs in a given year is dictated by ales. What we are analysing here is how much the Þrm should have on hand at any particular time. More precisely, we are trying to determine what order size the Þrm should use when it restocks its inventory. ! To develop the EOQ, we shall assume that the ÞrmÕs inventory is sold off at a steady rate until it hits zero. At that point, the Þrm restocks its inventory back to some optimal level. ! Optimum order quantity is where carrying costs = restocking costs. ! Total carrying cost ! = average inventory x 2 carrying costs per unit ! = (starting inventory / 2) x carrying costs per unit per period ! = (Q/2) x CC! Total restocking cost ! = Þxed cost per order x number of orders ! = Þxed cost per order x (total required per period/order quantity) ! = F x (T/Q)! Total costs ! = carrying costs x restocking costs ! = (Q/2) x CC + F x (T/Q) ! Finding the minimum point ! To Þnd the minimum point we have to set the two costs equal to each other and solve for optimum order quantity (EOQ)Q*:! !∗ = $ %& × ( ! )) Where: Q* = Economic Order Quantity (EOQ); ! Q = Quantity ordered each time or restocking quantity ! CC = Carrying cost per unit per year ! F = Fixed cost per order ! T = FirmÕs total unit of sales per year !   Lecture example 5: EOQ ! Black and White PLC: ! • Orders a total of 40,000 units of caps for the year ! • The restocking cost is £150 per order ! • The carrying cost is £12 per unit per year ! You may assume that the ÞrmÕs inventory is sold off at a steady rate until it hits zero. At that point, the Þrm restocks its inventory back to a given level. ! Calculate: (a) The restocking quantity that minimises the total inventory costs ! (b) The total restocking costs per year at the optimum order quantity ! (c) The total carrying costs per year at the optimum order quantity ! Answers: T = 40,000! F = £150 ! CC = £12! (a) Q* = (2T x F / CC)^0.5! = (2 x 40,000 x 150/12)^0.5 ! = 1,000 units ! (b) Total restocking costs = Þxed costs per order x number of orders at Q*! = F x (T/Q) ! = 150 x (40,000/1,000) ! = £6,000! (c) Total carrying costs = average inventory x carrying costs per unit at Q*! = (Q*/2) x CC! = (1,000/2) x 12 ! = £6,000! Note: as expected, at Q*, total restocking costs are the same as total carrying costs. ! Extensions to the EOQ model ! Thus far we have assumed that a company will let its inventory run down to zero and then reorder. In reality, a company will wish to reorder before its inventory goes to zero, for two reasons. First, by always having at least some inventory on hand, the Þrm minimises the risk of a stock-out and the resulting losses of sales and customers. Second, when a Þrm does reorder, there will be some time lag before the inventory arrives. Thus, we consider tow extensions to EOQ: ! • Safety stocks Ñ a safety stock is the minimum level of inventory that a Þrm keeps on hand. Inventories are reordered whenever the level of inventory falls to the safety stock level. Notice that adding a safety stock simply means that the Þrm does not run its inventory all the way down to zero. !  102 of 117  • Reorder points Ñ to allow for delivery time, a Þrm will place orders before inventories reach a critical level. The reorder points are the times at which the Þrm will actually place its inventory orders. The reorder points simply occur some Þxed number of days (or weeks or months) before inventories are projected to reach zero. !  