《商业银行管理学》课后习题及答案

CHAPTER 23BANK MERGERS AND ACQUISITIONSGoal of This Chapter: To understand why the banking industry undertakes so many mergers each year, to discover the steps necessary to evaluate and complete a bank merger or acquisition and explore the research evidence concerning the impact of mergers on the banks involved and on service to the public.Key Terms Presented in This ChapterProfit Potential Purchase-of-Assets MethodsCash Flow Risk Purchase-of-Stock MethodEarnings Risk Wholesale BanksTax Benefits Retail BanksMarket-Positioning Benefits Bank Merger Act of 1960Cost Savings (Efficiency) Competitive EffectsMerger Premium Public BenefitsExchange Ratio Justice Department Merger GuidelinesDilution of Ownership Herfindahl-Hirschman IndexChapter OutlineI. Introduction: Merger Trends in BankingII. Mergers on the RiseIII. Motives for the Rapid Growth of Bank Mergers (Merger Motivations)A. Profit PotentialB. Risk ReductionC. Rescue of Failing BanksD. Tax and Market-Positioning MotivesE. Cost Savings or Efficiency MotiveF. Mergers as a Device for Reducing CompetitionG. Other Merger MotivesH. Merger Motives that Banking Executives IdentifyIII. Selecting a Suitable Merger PartnerA. Stock Price EffectsB. Opportunities for Improving Operating EfficiencyC. Diversification Effects and OpportunitiesD. Merger Premiums, P-E Ratios, and Exchange RatiosIV. The Merger and Acquisition Route to Future GrowthV. Methods of Consummating Merger TransactionsA. Purchase-of-Assets MethodB. Purchase-of-Stock MethodVI. Regulatory Rules Applying to Bank Mergers in the United StatesA. Bank Merger Act of 1960285B. Competitive Effects of MergerC. The Public Benefits TestD. Department of Justice Merger Guidelines and the Herfindahl - Hirschman Index VII. The Merger Decision-Making Process by U.S. Federal RegulatorsVIII. New Merger Rules in EuropeIX. Making a Success of MergersX. Research Studies of MergersA. The Financial Impact on BanksB. The Public BenefitsXI. Summary of the ChapterConcept Checks23-1. Exactly what is a bank merger?Mergers between banks result in the combining of the assets and liabilities of two or more banks. To effect a merger the shareholders of all the banks involved must approve the merger transaction once it is negotiated among the management of the various banks that are parties to the merger. Once the shareholders of each bank involved give approval to the merger, approval must then be sought from the Department of Justice and the principal federal regulatory agency of each bank in the merger.23-2. Why are there so many mergers each year in the banking industry?Many (if not most) mergers occur because the shareholders of the banks involved expect increased profit potential once the merger is consummated. Alternatively, many partners to mergers anticipate reduced cash-flow risk and possibly reduced earnings risk as well.23-3. What factors seem to motivate most bank mergers?Among the most powerful merger motivations are the belief in greater profit potential if a bank merger is consummated, the expectation of a possible reduction of cash flow risk or earnings risk, the possible rescue of failing banks, the gaining of a tax advantage where profits of one merger partner may be offset by the losses of another merger partner, the search for market-positioning benefits in new markets or in superior locations in existing markets, and the pursuit of lower cost and greater efficiency so that the merged institution achieves a greater margin of revenues over operating expense.23-4. What factors should a bank consider when choosing a good merger partner?The following items are the principal factors usually reviewed by the acquiring banking organization:∙Age and history of the bank.∙Background of management.∙Comparative management styles of the merging organizations.286∙Types of services offered.∙Recent history of changes in deposits, loans, and market shares.∙Principal customers served. Geographic fit.∙Internal control procedures.∙Personnel situation.∙Compatibility of accounting and management information systems.∙Condition/depreciation schedule for offices and other physical assets.∙Adequacy of capital, earnings per share, and ownership dilution before and following the proposed merger.∙Growth of expenses.∙Before-tax and after-tax income and rate of return.23-5. What factors must the regulatory authorities consider when deciding whether to approve or deny a bank merger?Mergers that would significantly damage competition cannot be approved unless there are mitigating instigating circumstances (e.g., one of the banks involved is failing). Public convenience must also be weighed by the banking agencies to determine if the merger would improve the supply of needed services that are perhaps currently not being conveniently and efficiently provided to the public.23-6. When is a banking market too concentrated to allow a merger to proceed? What could happen if a bank merger were approved in an excessively concentrated market area?The Department of Justice guidelines state that the banking market area is too concentrated if the postmerger Herfindahl index is greater than 1800 or if the Herfindahl index changes by more than 200 points. If the Justice Department decides that the resultant merger will make the banking market too concentrated they are likely to challenge the merger in federal court.23-7. What steps that management can take appear to contribute to the chances for success in a bank merger? Why do you think many bank mergers produce disappointing results?There are several steps management can take to improve their chances of success after a merger. First they can know themselves, their strengths and weaknesses and the goals they want to pursue. They can also get a team together before any merger to do a detailed analysis of the potential merger and new market area. They can be careful to establish a realistic price for the target firm. Once the merger has taken place they should form a combined management team from both firms to direct the consolidation of the two firms. They should also establish lines of communication between senior management and branch and line management as well as communication channels for other employees and customers. Finally they should set up customer advisory panels to comment on the new bank’s community image, availabil ity of services and helpfulness. Mergers sometimes produce disappointing results because of ill-prepared management, a mismatch of corporate cultures, excess prices paid by the acquirer, inattention to customers feelings and concerns and a general lack of fit between the two firms.23-8. What does recent research tell us about the impact of most bank mergers?287A recent study, which looked at the earnings impact of approximately 600 national bank mergers, found no significant differences in profitability between merging and comparably sized nonmerging banks serving the same local markets. However, CEOs at a substantial majority of the nearly 600 U.S. bank mergers occurring from 1970-1985 believed their capital base improved and they were now a more efficient banking organization. However, as a study by Rose found there is no guarantee of success in a merger. This study of 572 banks which purchased nearly 650 other banks found a symmetric distribution of earnings outcomes for these mergers – nearly half displaying negative earnings results.23-9. Does it appear that most bank mergers among banking firms serve the public interest?Most studies that have looked at this issue find few real public benefits. However, there is also no convincing evidence that the public has suffered a decline in service quality or availability following most bank mergers. On the positive side, mergers may significantly lower the bank failure rate.Problems23-1. Evaluate the impact of the following proposed mergers upon post-merger earnings per share (EPS) if:A. The acquiring bank has a stock price of $18 per share on 200,000 shares of commonoutstanding with an EPS of $6 due to total net earnings of $1,200,000. The acquiredbank is earning $5 per share on 100,000 shares outstanding and reports total netearnings of $300,000 and its stock sells for $15 per share. If earnings total$1,600,000 after the merger occurs, the acquired bank's shareholders will receive$15 / $18 or 0.833 of a share of stock in the acquiring bank for each share they heldin the acquired institution. This means 0.833 x 100,000 or 83,300 additional sharesof the acquiring bank will be issued for a post-merger total of 283,300 sharesoutstanding. Therefore, the post-merger EPS will be $1,600,000 / 283,300sharesor $5.65 per share.B. The acquiring bank is reporting an EPS of $12 and its stock (with 80,000 sharesoutstanding) is selling for $20 per share. The acquired institution has EPS of $14and its stock (with 75,000 shares outstanding) is presently trading at $24 per share.If the two banks agree to exchange stock at current market values, the acquiredbank's stockholders will receive $24 / $20 or 1.2 shares in the acquiring bank foreach share they hold or 90,000 (1.2 x 75,000) additional shares. After the mergerthere will be 170,000 shares outstanding. With $900,000 in post-merger earnings,the combined banking organization's EPS will be $900,000 / 170,000 shares or$5.29 per share.23-2. The merger premiums and exchange ratios for the mergers described are calculated as follows:288A. The acquired bank is selling at $8 per share with 30,000 shares outstanding, whilethe acquiring bank's stock is selling for $12 per share with 50,000 common equity shares outstanding. The acquiring bank will pay a $4 bonus per share to effect the merger. Therefore, a merger premium will be paid amounting to:Merger Premium (in Percent) = [($8 + $4) / $8] x 100 = 150 percent.With an additional $4 per-share bonus the acquired bank's stock will be valued at $12, exactly the same as the acquiring bank's stock for a $12 / $12 or 1:1 exchange ratio. Earnings per share from the merger will be:EPS = $1,250,000 / 80,000 shares = $15.63.Before the merger, the acquiring bank had an EPS of $20, while the acquired bank reported an EPS of $8.33. This suggests there will be some earnings dilution for the shareholders of the acquiring bank (from $20 to $15.63 per share) as well as some ownership dilution.B. If the acquiring bank's stock is currently selling for $30 per share and the acquiredinstitution's shares are trading at $24 per share and the acquired firm's shareholders are offered a $2 per-share bonus to merge, the merger premium will be:Merger Premium (in Percent) = [($24 + $2) / $24] x 100 = 108.33 percent.Thus, the acquired bank's stock will exchange in a ratio of $26 to $30 for theacquiring bank's stock or 0.867 to 1. Thus, the acquired bank's shareholders willreceive 0.867 x 40,000 or 34,667 shares in the merged institution which will then have a total of 154,667 shares outstanding.Post-merger EPS should be: $900,000 / 154,667 shares = $ 5.82.Before the merger, the acquiring institution reported an EPS of $7.08 and theacquired institution had an EPS of $3.75. Again, the acquiring institution'sshareholders will experience some earnings dilution as well as some decline in their ownership share.28929023-3. The Herfindahl-Hirschman Index for the Silverton Metropolitan Area is calculated as follows:Bank Current Deposits Current Deposit Market Share Current DepositMarket Share Squared Silverton National Bank $ 854 million 39.54 % 1563.41 Commerce National Bank 383 million 17.73 314.35 Rocky Mountain Trust Company211 million 9.77 95.45Security National Bank 107 million 4.95 24.50Total $2160 million 100.0 % 2782.27The Silverton market has an HHI above 1800 and is, therefore, highly concentrated. If Rocky Mountain Trust Co. and Security National Bank merge, their combined market share is 14.72 percent and the HHI climbs to 2879.0, a change of only 96.7 points which may be acceptable to the regulatory authorities. However, if Silverton County Merchants Bank and Rocky Mountain Trust Company plan to merge, the combined market share of these two banks is 37.78 percent and the HHI rises to 3329.59, a change of 547 points which will, in all probability, be challenged by the regulatory authorities.23-4. Langley Bank and Trust has just received an offer to merge from Courthouse County National Bank. Langley's stock is currently selling for $40 per share. Moreover, the shareholders of Courthouse County Bank agree to pay Langley's stockholders a bonus of $10 per share. What is the merger premium in this case? If Courthouse County's shares are currently trading for $65 per share, what is the exchange ratio between the equity shares of the two banks? Suppose that Langley has 10,000 shares and Courthouse County has 30,000 shares outstanding. How many shares will Langley’s shareholders wind up with after the merger? How many total shares will the merged bank have outstanding?The merger premium must be:percent 125x100$40$10+ $40The exchange ratio between the respective banks' shares is:($40 + $10) / $65 = 0.77 to 1.If Langley has 10,000 shares outstanding and Courthouse County has 30,000 shares, Langley's shareholders will receive 0.77 x 10,000 or 7,700 shares in the consolidated banking company. The merged firm will have 37,700 shares of stock outstanding.23-5. The community of Wanslow is served by three banks which recently reported total deposits of $234 million, $182 million, and $67 million, respectively. Please calculate the Herfindahl index for the Wanslow market area. Suppose that the second and third largest banks merge, what wouldthe post-merger Herfindahl index be? Under the most recent Department of Justice guidelines discussed in the chapter, would the U.S. Department of Justice be likely to challenge this merger?The banking market in Wanslow has the following structure:Deposits Market Share Square of EachMarket Share Bank A $234 million 48.4% 2342.6 Bank B 182 million 37.7% 1421.3 Bank C 67 million 13.9% 193.2 Totals $483 million 100.0% 3957.1 Thus, the Herfindahl-Hirschmann index is 3957.1 in the Wanslow market area. This is a relatively concentrated market to begin with. If the second and third largest banks merge, the post-merger Herfindahl index climbs to 5,005.2 because the combined share of banks B and C jumps to over 50 percent. Clearly, the Herfindahl index rises by more than 200 points and far exceeds 1800 in total. This merger would be challenged by the Department of Justice in the absence of mitigating factors.23-6. In which of the situations described below do the stockholders of both acquiring and acquired banks experience a gain in earnings per share of stock as a result of a merger:P/E Ratio of AcquiringBank P/E Ratio ofAcquiredBankPre-MergerEarnings ofAcquiring BankPre-MergerEarnings ofAcquired BankCombinedEarningsAfter MergerA. 5 3 $750,000 $425,000 $1,200,000B. 4 6 470,000 490,000 850,000C. 8 7 890,000 650,000 1,540,000D. 12 12 1,615,000 422,000 2,035,000The rule is that the stockholders of both acquiring and acquired banks will experience a gain in earnings per share of stock if a bank with a higher P/E ratio acquired a bank with a lower P/E ratio and combined earnings do not fall after the merger. Only cases A and C meet these criteria and the shareholders in these two cases should experience an earnings-per-share gain.23-7. Please list the steps that you believe should contribute positively to success in a bank merger transaction. What management decisions or actions could cause trouble and not contribute to a bank’s merger goals? On average what proportion of bank mergers would you expect would be likely to achieve the goals of management and/or the owners and what proportion would likely fall short of the mergers’ objectives?The steps a bank can take that will contribute positively to the success in a bank merger include the following:291A.The bank must first evaluate its own financial condition, understand its ownstrengths and weaknesses and its own goals. Mergers can then magnify strengthsand minimize weaknesses.B.The bank should form a team to perform a detailed analysis of all potential newmarkets and acquisitions.C.The bank must establish a realistic price for the acquisitionD.After the merger, a combined management team should be formed to continuallywork towards and assess the progress towards the consolidation of the two firms.E. A communication system needs to be formed between senior management andother managers so everyone feels involved in the merger.munication channels need to be formed so customers and employeesunderstand why the merger took place and what the consequences of the merger arelikely to be.G.Customer advisory panels need to be formed to evaluate and comment on thebank’s image in the community, marketing effectiveness and general helpfulness tocustomers.Management decisions and actions which could cause problems for the merger include managers that are ill-prepared, mergers where there is a poor understanding of each other’s culture, mergers where an excessive price is paid for the merger, mergers where customers feelings and concerns are ignored and mergers where the new firm cannot move forward in a cohesive manner.According to some research, it appears that only half of all mergers achieve the goal of an increase in earnings (or profitability). The other half of mergers see a decrease in earnings for the new firm.Web Site Problems1. How are mergers and acquisitions reshaping the banking industry today at the local, national and international levels? Where on the web can you go to get some idea about how to answer this question?A search on the web for how mergers and acquisitions are shaping the banking industry can lead to answers at all levels. First as a n example of the trends at the local and national level, one good source appears to be a speech by William Poole, President of the St. Louis Federal Reserve (/general/speeches/990112.html). He does not foresee the decline of the community bank because they still retain some advantages including the personal touch. However, I believe he sees continued consolidation among the largest banks. In Europe the outlook is similar. In a speech by Dr. A.H.E.M. Wellink, President of De Nederlandsche Bank(http://www.dnb.nl/english/e_speeches/1999/we991006.htm), he states that changes in technology and the Euro as well as other changes will the structure of the European banking industry by continuing the drive toward consolidation in the industry.2. What appears to be the ingredients of a successful bank merger or acquisition? How can the web help you approach this important issue?292A search on successful bank mergers and acquisition may produce some results from the web. There are several merger and acquisition consultants on the web that can help banks as well as other types of firms. One place (/integrate-intl-mergers.html) suggests that the key ingredient of a successful merger is to make sure the merger partner is suitable (that there are similar cultures,etc.) and that a good due diligence is completed before the merger or acquisition.3. In what parts of the world are most bank mergers occurring today? What does the evidence from the web suggest?I believe that there is considerable activity in cross border mergers in recent years. If a search is done on bank mergers across the world this may lead to several sources of information. One source that has been cited here before is one of the publications of the European Central Bank which states that there are many cross-border mergers taking place, often between European Community member banks and outsiders. There is also information out on the web that suggests that cross-border mergers are taking place in Asia(/external/pubs/ft/fandd/2001/03/mody.htm). This suggests that bank mergers are growing at a considerable rate in many places in the world.293294。

《商业银行管理》课后习题答案IMChap4在学习商业银行管理的过程中，课后习题是巩固知识、检验理解的重要环节。

以下是对《商业银行管理》第四章课后习题的详细答案。

一、选择题1、商业银行的核心资本包括（）A 股本和公开储备B 股本和未公开储备C 债务资本和附属资本D 债务资本和公开储备答案：A解析：核心资本又称一级资本，包括股本（普通股和永久非累积优先股）和公开储备（股票发行溢价、未分配利润等）。

2、下列属于商业银行附属资本的是（）A 重估储备B 普通股C 未分配利润D 公开储备答案：A解析：附属资本包括未公开储备、重估储备、普通准备金、混合资本工具和长期次级债务等。

3、商业银行资本充足率的计算公式是（）A 资本/风险加权资产B 资本/总资产C （核心资本+附属资本）／风险加权资产D （核心资本+附属资本）／总资产答案：C解析：资本充足率＝（核心资本＋附属资本）／风险加权资产。

4、按照《巴塞尔协议》的要求，商业银行的资本充足率不得低于（）A 4%B 8%C 10%D 12%答案：B解析：《巴塞尔协议》规定商业银行的资本充足率不得低于 8%。

二、简答题1、简述商业银行资本的作用。

答：商业银行资本具有以下重要作用：首先，资本为银行的开业、正常经营和持续增长提供了资金基础。

它是银行设立和注册的必要条件，为银行的初期运营提供启动资金。

其次，资本是银行抵御风险的重要防线。

在面临各种风险如信用风险、市场风险、操作风险等时，资本可以吸收损失，保护存款人和其他债权人的利益，维持银行的信誉和稳定。

再者，资本有助于树立公众对银行的信心。

充足的资本向外界传递了银行稳健经营、有能力应对潜在风险的信号，增强了客户、投资者和监管机构对银行的信任。

此外，资本还为银行的扩张和业务发展提供了支持。

银行可以利用资本进行新业务的开拓、分支机构的设立以及技术设备的更新等。

2、简述《巴塞尔协议》对商业银行资本构成的规定。

答：《巴塞尔协议》将商业银行的资本分为核心资本和附属资本两大部分。

第一章商业银行：商业银行是以追求利润最大化为目标，以多种金融欠债筹集资本，以多种金融财富为其经营对象，能利用欠债进行信用创建，并向客户供应多功能、综合性服务的金融公司。

信用中介：是指商业银行经过欠债业务，把社会上各样闲散钱币资本集中到银行，经过财富业务，把它投向需要资本的各部门，充任有闲置资本者和资本欠缺者之间的中介人，实现资本的融通。

作用：使闲散的钱币转变为资本、使闲置资本获取充分利用、续短为长，知足这会对长久资本的需要。

支付中介：是指商业银行利用活期存款账户，为客户办理各样钱币结算、钱币收付、钱币兑换和转移存款等业务活动。

CAMELS：美国联邦贮备委员会对商业银行看管的分类检查制度，这种分类检查制度的主要内容是把商业银行接受检查的范围分为六大类：资本（ capital）、财富（ asset ）、管理（ management）、利润（ earning ）、流动性（ liquidity）和对市场风险的敏感性（ sensitivity）。

分行制：分行制银行是指那些在总行之下，可在当地或外处设有若干分支机构，并能够从事银行业务的商业银行。

这种商业银行的总部一般都设在多半市，部下所有分支行须由总行领导指挥。

长处：第一，有益于银行汲取存款，有益于银行扩大资本总数和经营规模，能获得规模经济效益。

第二，便于银履行用现代化管理手段和设施，提升服务质量，加快资本周转速度。

第三有益于银行调理资本、转移信用、分别和减少多种风险。

第四，总专家数少，有益于国家控制和管理，其业务经营受地方政府干涉小。

第五，因为资本根源宽泛，有益于提升银行的竞争实力。

弊端：简单加快垄断的形成；并且因为其规模大，内部层次许多，使银行管理的难度增添等。

流动性：指财富变现的能力，商业银行保持随时能以适合的价钱去的可用资本的能力，以便随时对付客户提存以及银行其余支付的需要。

其权衡指标有两个：一是财富变现的成本，二是财富变现的速度。

4.成立商业银行制度的基根源则有哪些？为何要确定这些原则？答：（一）有益于银行业竞争。

《商业银行管理学》课后习题及题解第一章商业银行管理学导论习题一、判断题1. 《金融服务现代化法案》的核心内容之一就是废除《格拉斯－斯蒂格尔法》。

2. 政府放松金融管制与加强金融监管是相互矛盾的。

3. 商业银行管理的最终目标是追求利润最大化。

4. 在金融市场上，商业银行等金融中介起着类似于中介经纪人的角色。

5. 商业银行具有明显的企业性质，所以常用于企业管理的最优化原理如边际分享原理、投入要素最优组合原理、规模经济原理也适用于商业银行。

6. 金融市场的交易成本和信息不对称决定了商业银行在金融市场中的主体地位。

7. 企业价值最大化是商业银行管理的基本目标。

8. 商业银行管理学研究的主要对象是围绕稀缺资源信用资金的优化配置所展开的各种业务及相关的组织管理问题。

9. 商业银行资金的安全性指的是银行投入的信用资金在不受损失的情况下能如期收回。

二、简答题1. 试述商业银行的性质与功能。

2. 如何理解商业银行管理的目标？3. 现代商业银行经营的特点有哪些？4. 商业银行管理学的研究对象和内容是什么？5. 如何看待“三性”平衡之间的关系？三、论述题1. 论述商业银行的三性目标是什么，如何处理三者之间的关系。

2. 试结合我国实际论述商业银行在金融体系中的作用。

第一章习题参考答案一、判断题1.√2.×3.×4.√5.×6.√7.×8.√9.√二、略；三、略。

第二章商业银行资本金管理习题一、判断题1. 新巴塞尔资本协议规定，商业银行的核心资本充足率仍为4％。

2. 巴塞尔协议规定，银行附属资本的合计金额不得超过其核心资本的50%。

3. 新巴塞尔资本协议对银行信用风险提供了两种方法：标准法和内部模型法。

4. 资本充足率反映了商业银行抵御风险的能力。

5. 我国国有商业银行目前只能通过财政增资的方式增加资本金。

6. 商业银行计算信用风险加权资产的标准法中的风险权重由监管机关规定。

二、单选题1. 我国《商业银行资本充足率管理办法》规定，计入附属资本的长期次级债务不得超过核心资本的。

第一章商业银行：商业银行是以追求利润最大化为目标，以多种金融欠债筹集资本，以多种金融财富为其经营对象，能利用欠债进行信用创建，并向客户供应多功能、综合性服务的金融公司。

信用中介：是指商业银行经过欠债业务，把社会上各样闲散钱币资本集中到银行，经过财富业务，把它投向需要资本的各部门，充任有闲置资本者和资本欠缺者之间的中介人，实现资本的融通。

作用：使闲散的钱币转变为资本、使闲置资本获取充分利用、续短为长，知足这会对长久资本的需要。

支付中介：是指商业银行利用活期存款账户，为客户办理各样钱币结算、钱币收付、钱币兑换和转移存款等业务活动。

CAMELS：美国联邦贮备委员会对商业银行看管的分类检查制度，这种分类检查制度的主要内容是把商业银行接受检查的范围分为六大类：资本（ capital）、财富（ asset ）、管理（ management）、利润（ earning ）、流动性（ liquidity）和对市场风险的敏感性（ sensitivity）。

分行制：分行制银行是指那些在总行之下，可在当地或外处设有若干分支机构，并能够从事银行业务的商业银行。

这种商业银行的总部一般都设在多半市，部下所有分支行须由总行领导指挥。

长处：第一，有益于银行汲取存款，有益于银行扩大资本总数和经营规模，能获得规模经济效益。

第二，便于银履行用现代化管理手段和设施，提升服务质量，加快资本周转速度。

第三有益于银行调理资本、转移信用、分别和减少多种风险。

第四，总专家数少，有益于国家控制和管理，其业务经营受地方政府干涉小。

第五，因为资本根源宽泛，有益于提升银行的竞争实力。

弊端：简单加快垄断的形成；并且因为其规模大，内部层次许多，使银行管理的难度增添等。

流动性：指财富变现的能力，商业银行保持随时能以适合的价钱去的可用资本的能力，以便随时对付客户提存以及银行其余支付的需要。

其权衡指标有两个：一是财富变现的成本，二是财富变现的速度。

4.成立商业银行制度的基根源则有哪些？为何要确定这些原则？答：（一）有益于银行业竞争。

CHAPTER 6ASSET/LIABILITY MANAGEMENT: DETERMINING AND MEASURING INTEREST RATES AND CONTROLLING A BANK’S INTEREST-SENSITIVE GAP Goals of This Chapter: To learn how to measure a bank's exposure to interest-rate risk and how to reduce that risk exposure through coordinated management of bank assets and liabilities.Key Terms Presented In This ChapterAsset-liability Management Yield to Maturity (YTM)Asset Management Bank Discount RateLiability Management Net Interest MarginFunds Management Interest-Sensitive Gap ManagementInterest Rate RiskChapter OutlineI. Introduction: The Necessity for Coordinating Bank Asset and Liability ManagementDecisionsII. Asset/Liability Management StrategiesA. Asset Management StrategyB. Liability Management StrategyC. Funds Management StrategyIll. Interest Rate Risk: One of the Banker's Greatest ChallengesA. Nature of Interest-Rate RiskB. Forces Determining Interest RatesC. The Measurement of Interest Rates1. Yield to Maturity2. Bank Discount RateD. The Components of Interest RatesE. Bankers' Response to Interest Rate RiskIV. One of the Goals of Interest-Rate HedgingA. The Net Interest MarginB. Interest-Sensitive Gap Management1. Asset-Sensitive Position2. Liability-Sensitive Position3. Calculation of a Bank's Interest-Sensitive Gap4. Impact of Changing Interest Rates on the Gap5. Decisions that need to be Made Concerning Gap Management6. Computer Techniques for Managing Gap7. Cumulative Gap8. Strategies in Gap Management9. Limitations of Interest-Sensitive Gap Management10. Weighted Interest-Sensitive GapV. Summary of the ChapterConcept Checks6-1. What do the following terms mean: Asset management? Liability management? Funds management?Asset management refers to a banking strategy where management has control over the allocation of bank assets but believes the bank's sources of funds (principally deposits) are outside its control. Liability management is a strategy of control over bank liabilities by varying interest rates offered on borrowed funds. Funds management combines both asset and liability management approaches into a balanced liquidity management strategy.6-2. What factors have motivated banks to develop funds management techniques in recent years?The necessity to find new sources of funds in the 1970s and the risk management problems encountered with troubled loans and volatile interest rates in the 1970s and 1980s led to the concept of planning and control over both sides of a bank's balance sheet -- the essence of funds management.6-3. What forces cause interest rates to change? What kinds of risk do bankers face when interest rates change?Interest rates are determined, not by individual banks, but by the collective borrowing and lending decisions of thousands of participants in the money and capital markets. They are also impacted by changing perceptions of risk by participants in the money and capital markets, especially the risk of borrower default, liquidity risk, price risk, reinvestment risk, inflation risk, term or maturity risk, marketability risk, and call risk.Bankers can lose income or value no matter which way interest rates go. Rising interest rates can lead to losses on bank security instruments and on fixed-rate loans as the market values of these instruments fall. Falling interest rates will usually result in capital gains on fixed-rate securities and loans but a bank will lose income if it has more rate-sensitive assets than liabilities. Rising interest rates will also cause a loss to bank income if a bank has more rate-sensitive liabilities than rate-sensitive assets.6-4. What makes it so difficult for banks to forecast interest rate changes?Interest rates cannot be set by an individual bank or even by a group of banks; they are determined by thousands of investors trading in the credit markets. Moreover, each market rate of interest has multiple components--the risk-free interest rate plus various risk premia. A change in any of these rate components can cause interest rates to change. To consistently forecast market interest rates correctly would require bankers to correctly anticipate changes in the risk-free interest rate and in all rate components. Another important factor is the timing of the changes. To be able to take full advantage of their predictions, they also need to know when the changes will take place.6-5. What is the yield curve and why is it important for bankers to know about its shape or slope?The yield curve is a graphical description of the distribution of market interest rates by maturity of financial instrument. The slope of the yield curve determines the spread between long-term and short-term interest rates. In banking most of the long-term rates apply to loans and securities (i.e., bank assets) and most of the short-term interest rates are attached to bank deposits and money market borrowings. Thus, the shape or slope of the yield curve has a profound influence on a bank's net interest margin or spread between asset revenues and liability costs.6-6. What is it that a bank wishes to protect from adverse movements in interest rates?A bank wishes to protect both the value of bank assets and liabilities and the revenues and costs generated by both assets and liabilities from adverse movements in interest rates.6-7. What is the goal of hedging in banking?The goal of hedging in banking is to freeze the spread between asset returns and liability costs and to offset declining values on certain assets by profitable transactions so that a target rate of return is assured.6-8. First National Bank of Bannerville has posted the following financial statement entries: Interest revenues $63 millionInterest costs $42 millionTotal earning assets $700 millionThe bank's net interest margin must be:Net Interest = $63 mill. - $42 mill. = 0.03 or 3 percentMargin $700 mill.If interest revenues and interest costs double while earning assets grow by 50 percent, the net interest margin will change as follows:($63 mill. - $42 mill.) * 2 = 0.04 or 4 percent$700 mill. * (1.50)Clearly the net interest margin increases--in this case by one third.6-9. Can you explain the concept of gap management?Gap management involves determining the maturity distribution and the repricing schedule for a bank's assets and liabilities. When more assets are subject to repricing or will reach maturity in a given period than liabilities or vice versa, the bank has a GAP and is exposed to loss from adverse interest-rate movements based on the gap's size.6-10 When is a bank asset sensitive? Liability sensitive?A bank is asset sensitive when it has more interest-rate sensitive assets maturing or subject to repricing during a specific time period than rate-sensitive liabilities. A liability sensitive position, in contrast, would find the bank having more interest-rate sensitive deposits and other liabilities than rate-sensitive assets for a particular planning period.6-11. Commerce National Bank reports interest-sensitive assets of $870 million andinterest-sensitive liabilities of $625 million. Because interest-sensitive assets are larger than liabilities by $245 million the bank is asset sensitive.If interest rates rise, the bank's net interest margin should rise as asset revenues increase by more than the resulting increase in liability costs. On the other hand, if interest rates fall, the bank's net interest margin will fall as asset revenues decline faster than liability costs.6-12. First National Bank has a cumulative gap for the coming year of + $135 million and interest rates are expected to fall by two and a half percentage points. What is the expected change in First National's net interest income?ExpectedChange in = $135 million * (-0.025) = -$3.38 millionNet Interest IncomeWhat change will occur in net interest income if interest rates rise by one and a quarter percentage points?Expected Changein Net Interest = $135 million * (+0.0125) = +$1.69 millionIncome6-13 How do you measure a bank’s dollar interest-sensitive gap? Its relative interest-sensitive gap? What is the interest-sensitivity ratio?The dollar interest-sensitive gap is measured by taking the repriceable (interest-sensitive) assets minus the repriceable (interest-sensitive) liabilitiies over some set planning period. Common planning periods include 3 months, 6 months and 1 year. The relative interest-sensitive gap is the dollar interest-sensitive gap divided by some measure of bank size (often total assets). The interest-sensitivity ratio is just the ratio of interest-sensitive assets to interest sensitive liabilities. Regardless of which measure you use, the results should be consistent. If you find a positive (negative) gap for dollar interest-sensitive gap, you should also find a positive (negative) relative interest-sensitive gap and a interest sensitivity ratio greater (less) than one.6-14 Suppose Carroll Bank and Trust reports interest-sensitive assets of $570 million and interest-sensitive liabilities of $685 million. What is the bank’s dollar interest-sensitive gap? Its relative interest-sensitive gap and interest-sensitivity ratio?Dollar Interest-Sensitive Gap = Interest-Sensitive Assets – Interest Sensitive Liabilities= $570 - $685 = -$115Relative Gap = $ IS Gap = -$115 = -0.2018 or -20.18 percent Bank Size $570Interest-Sensitivity = Interest-Sensitive Assets =$570 = .8321 Ratio Interest-Sensitive Liabilities $6856-15 Explain the concept of weighted interest-sensitive gap. How can this concept aid bank’s real interest-sensitive gap risk exposure?Weighted interest-sensitive gap is based on the idea that not all interest rates change at the same speed. Some are more sensitive than others. Interest rates on bank assets may change more slowly than interest rates on liabilities and both of these may change at a different speed than thoseinterest rates determined in the open market. In, the weighted interest-sensitive gap methodology all interest-sensitive assets and liabilities are given a weight based on their speed (sensitivity) relative to some market interest rate. Fed Funds loans, for example, have an interest rate which is determined in the market and which would have a weight of 1. All other loans, investments and deposits would have a weight based on their speed relative to the Fed Funds rate. To determine the interest-sensitive gap, the dollar amount of each type of asset or liability would be multiplied by its weight and added to the rest of the interest-sensitive assets or liabilities. Once the weighted total of the assets and liabilities is determined, a weighted interest-sensitive gap can be determined by subtracting the interest-sensitive liabilities from the interest-sensitive assets. This weighted interest-sensitive gap should be more accurate than the unweighted interest-sensitive gap. The interest-sensitive gap may change from negative to positive or vice versa and may change significantly the interest rate strategy pursued by the bank.Problems6-1. A government bond is currently selling for $900 and pays $80 per year in interest for 5 years when it matures. If the redemption value of this bond is $1,000, what is its yield to maturity if purchased today for $900. The yield to maturity equation for this bond would be:$900 = $80(1YTM)1+ + $80(1YTM)2+ + $80(1YTM)3+ + $80(1YTM)4++ $80(1YTM)5+ + $1,000(1YTM)5+At an YTM of 10 percent the bond's price is $924.28, while at 12 percent its price becomes $864.40. Thus, the true YTM lies between 10% and 12%. To find the true YTM we use: 10% + 40.864$28.924$900$28.924$-- * 2% ≈ 10.81%6-2. Suppose the government bond described in problem #1 is held for 3 years and then the bank acquiring the bond decides to sell it at a price of $950. Can you figure out the average annual yield the bank will have earned for its 3-year investment in the bond?In this instance the yield-to-maturity equation can be modified slightly to find the correct holding-period yield that the bank would earn. Specifically,$900 = $80(1HPY)1+ + $80(1HPY)2++ $80(1HPY)3+ + $950(1HPY)3+At an HPY of 10% the bond's price becomes $912.31, while at 12% the bond's price is $868.56.The true holding period yield must be:10% + 912.31900912.31868.56--⎡⎣⎢⎤⎦⎥ x 2% ≈10.56%.6-3. U.S. Treasury bills are available for purchase this week at the following prices (based upon $100 par value) and with the indicated maturities:a. $97.25, 182 days.b. $96.50, 270 days.c. $98.75, 91 days.The discount rates and equivalent yields to maturity (bond-equivalent or coupon-equivalent yields) on each of these Treasury bills are:Discount Rates Equivalent Yields to Maturitya.(10097.25)100- * 360182 = 5.44% (365x.0544)[360(0.0544x182)]- = 19.856350.1 = 5.67% b.(10096.50)100- * 360270 = 4.67% (365x.0467)[360(.0467x270)]- = 17.046347.39 = 4.91% c. (10098.75)100- * 36091 = 4.95% (365x.0495)[360(.0495x91)]- = 18.07355.5 = 5.08%6-4. The First State Bank of Ashfork reports a net interest margin of 3.25 percent in its most recent financial report with total interest revenues of $88 million and total interest costs of $72 million. What volume of earning assets must the bank hold?The relevant formula is:Net Interest Margin = .0325 = AssetsEarning mil. $72mill. $88-Then Earning Assets = $492.31 million.Suppose the bank's interest revenues rise by 8 percent and its interest costs and earning assets increase 10 percent. What will happen to Ash Fork's net interest margin?Substituting in the correct formula we have:New Net Interest Margin = .10)million(1 $492.3.10)million(1 $72.08)(1 million $88++-+= million$541.53million $79.20million $95.04-= 0.0293 or 2.93 percent.6-5. If a bank's net interest margin, which was 2.85 percent, doubles and its total assets, which stood originally at $545 million, rise by 40 percent, what change will occur in the bank's net interest income?The correct formula is:.0285 * 2 = .4)(1*million 545$Income Interest Net +or Net Interest Income = 0.057 * $763 million= $43.49 million.6-6. The cumulative interest-rate gap of Snidal State Bank and Trust Company doubles from an initial figure of -$35 million. If market interest rates fall by 25 percent from an initial level of 6 percent, what change will occur in Snidal Bank's net interest income?The key formula here is:Change in the Bank's = Change in interest rates (in percentage points) * cumulative gap Net Interest = 0.06 * -.25 x (-$35 mill.) * 2Income = 1.05Thus, the bank's net interest income will rise by 5 percent.6-7. Given: Merchants State Bank has recorded the following financial data for the past three years (dollars in millions):Current Year Previous Year Two Years Ago Interest revenues $57 $56 $55 Interest expenses 49 42 34 Loans (Excluding nonperforming) 411 408 406 Investments 239 197 174 Total deposits 487 472 467 Money market borrowings 143 118 96 Solution:Net interest margin (NIM) = Net Interest Income/Earning Assets, whereNet Interest Income = Net Interest Revenues - Net Interest ExpensesEarning Assets = Loans + InvestmentsNIM(Current) = ($57-49)/(411 + 239) = 8/650 = 0.0123 or 1.23%NIM(previous) = ($56-42)/(408 + 197) = 14/605 = 0.0231 or 2.31%NIM(Two years ago) = ($55-34)/(406 + 174) = 21/580 = 0.0362 or 3.62%The net interest margin has been declining steadily and significantly. Probable causes include greater increases in interest expenses relative to interest income due to shifts in funding mix with greater dependence on borrowed funds (more expensive sources) relative to deposits (less expensive sources). Additionally, the mix in earning assets, with greater growth in lower yielding investment securities than in higher yielding loans, is another contributor to the steadily declining net interest margin.Management needs to reevaluate its funding strategies and its loan and investment strategies. If slower loan growth is related to external forces -- for example, a weaker economy -- then less borrowing should be considered. If the slower loan growth is more internal, then more aggressive loan management would be appropriate.6-8 The First National Bank of Wedora, California has the following interest-sensitive gaps:Coming WeekNext30 DaysNext31-90 DaysMore Than90 DaysInterest - $144 $110 $164 $184 Sensitive +29 +19 29 8 Assets = $173 $129 $193 $192 Interest - $232 $ --- $ --- $ --- Sensitive 98 84 196 35 Liabilities = 36 6 --- ---$366 $90 $196 $35 GAP - $193 + $39 - $3 + $157 Cumulative GAP - $193 - $154 - $157 $0First National has a cumulative zero gap and therefore is not vulnerable to loss if interest rates rise. It does have a positive gap in two periods--the next 30 days and more than 90 days. During these particular periods a rise in interest rates would produce a short-run gain.6-9 First National Bank of Barnett currently has the following interest-sensitive assets and liabilities on its balance sheet:Interest-Sensitive Assets Interest-Sensitive LiabilitiesFederal fund loans $65Security holdings $42 Interest-bearing deposits $185Loans and leases $230 Money-market borrowings $78What is the bank’s current interest-sensitive gap? Suppose its Federal funds loans carry an interest-rate sensitivity weight of 1.0 while its investments have a rate-sensitivity weight of 1.15 and its loans and leases display a rate-sensitivity weight of 1.35. On the liability side First National’s rate-sensitivity weight is 0.79 for interest-bearing deposits and 0.98 for itsmoney-market borrowings. Adjusted for these various interest-rate sensitivity weights, what is the bank’s weighted interest-sensitive gap? Suppose the Federal funds interest rate increases or decreases one percentage point. How will the bank’s net interest income be affecte d (a) given its current balance sheet make up and (b) reflecting its weighted balance sheet adjusted for the foregoing rate-sensitivity weights?Solution:Dollar IS Gap = ISA - ISL = ($65 + $42 + $230) - ($185 + $78) = $337 - $263 = $74 Weighted IS Gap = [(1)($65) + (1.15)(42) + (1.35)(230)] - [(.79)($185) + (.98)($78)] = $65 + $48.3 + $310.5 - $146.15 + $76.44= $423.8 - $222.59= $201.21a.) Change in Bank’s Income = IS Gap * Change in interest rates= ($74)(.01) = $.74 millionUsing the regular IS Gap, net income will change by plus or minus $740,000b.) Change in Bank’s Income = Weighted IS Gap * Change in interest rates= ($201.21)(.01) = $2.012Using the weighted IS Gap, net income will change by plus or minus $2,012,0006-10 McGraw Bank and Trust has interest-sensitive assets of $225 million and interest-sensitive liabilities of $168 million. What is the bank’s dollar interest-sensitive gap? What is McGraw’srelative interest-sensitive gap? What is the value of its interest-sensitivity ratio? Is the bank asset sensitive or liability sensitive? Under what scenario for market interest rates will the bank experience a gain in net interest income? A loss in net interest income?Dollar Interest-Sensitive Gap = ISA – ISL = $225 - $168 = $57Relative Interest-Sensitive Gap = ISA – ISL = $57 = 0.2533Bank Size $225Interest-Sensitivity Ratio = ISA = $225 = 1.3393ISL $168This bank is asset sensitive. More assets will be repriced during this time period than liabilities. This means that if interest rates rise, the interest earned on assets will rise relative to the interest paid on liabilities and net interest margin will rise. However, if interest rates fall, interest earned on assets will fall more than interest paid on liabilities and net interest margin will fall.Web Site Problems1. Suppose you want to know what types of banks make the greatest use of asset-liability management tools and what their biggest ALM problems are? Where would you go on the web to try to get answers to these questions?Almost all banks are required by regulators to have some kind of ALM management in place. These techniques can be as simple as the interest sensitive gap discussion in this chapter or the duration gap management in the next chapter. However, there are many consulting firms out there that have developed specific models for managing ALM. One way to see what is out there is to do a search on bank ALM management and see some of the sites that are out there. These sites range from sites for the consulting firms to more general sites that provide a good definition and description of ALM management. Two sources that are available at this time for general information on asset-liability management are/glossaryassetliabilitymanagement.htm and/Products/nccb_asset.htm. However if you want a good discussion of specific models and the problems people are having with ALM management, one good source appears to be /. This site has several discussion groups on various ALM topics.2. If a new web model to apply ALM techniques to a bank’s risk exposure is developed, at what web site are you most likely to find a discussion of that new ALM model?The best place to get information about a new ALM model would be the/ site mentioned above. If a promising new model were developed it would be sure to show up in the discussion groups mentioned above.3. If you need guidance on how to prepare bank forecasts and measure risk as part of a bank’s ALM activities which web site could be most helpful to you?If you are not willing to go to a consultant about how to develop bank forecasts and measure risk, the / web site would probably be the most helpful site. There are many discussions there about how to deal with specific measurement issues and how to find information to determine the risk of your bank compared to peer institutions.85。

CHAPTER 6ASSET/LIABILITY MANAGEMENT: DETERMINING AND MEASURING INTEREST RATES AND CONTROLLING A BANK’S INTEREST-SENSITIVE GAP Goals of This Chapter: To learn how to measure a bank's exposure to interest-rate risk and how to reduce that risk exposure through coordinated management of bank assets and liabilities.Key Terms Presented In This ChapterAsset-liability Management Yield to Maturity (YTM)Asset Management Bank Discount RateLiability Management Net Interest MarginFunds Management Interest-Sensitive Gap ManagementInterest Rate RiskChapter OutlineI. Introduction: The Necessity for Coordinating Bank Asset and Liability ManagementDecisionsII. Asset/Liability Management StrategiesA. Asset Management StrategyB. Liability Management StrategyC. Funds Management StrategyIll. Interest Rate Risk: One of the Banker's Greatest ChallengesA. Nature of Interest-Rate RiskB. Forces Determining Interest RatesC. The Measurement of Interest Rates1. Yield to Maturity2. Bank Discount RateD. The Components of Interest RatesE. Bankers' Response to Interest Rate RiskIV. One of the Goals of Interest-Rate HedgingA. The Net Interest MarginB. Interest-Sensitive Gap Management1. Asset-Sensitive Position2. Liability-Sensitive Position3. Calculation of a Bank's Interest-Sensitive Gap4. Impact of Changing Interest Rates on the Gap5. Decisions that need to be Made Concerning Gap Management6. Computer Techniques for Managing Gap7. Cumulative Gap8. Strategies in Gap Management9. Limitations of Interest-Sensitive Gap Management10. Weighted Interest-Sensitive GapV. Summary of the ChapterConcept Checks6-1. What do the following terms mean: Asset management? Liability management? Funds management?Asset management refers to a banking strategy where management has control over the allocation of bank assets but believes the bank's sources of funds (principally deposits) are outside its control. Liability management is a strategy of control over bank liabilities by varying interest rates offered on borrowed funds. Funds management combines both asset and liability management approaches into a balanced liquidity management strategy.6-2. What factors have motivated banks to develop funds management techniques in recent years?The necessity to find new sources of funds in the 1970s and the risk management problems encountered with troubled loans and volatile interest rates in the 1970s and 1980s led to the concept of planning and control over both sides of a bank's balance sheet -- the essence of funds management.6-3. What forces cause interest rates to change? What kinds of risk do bankers face when interest rates change?Interest rates are determined, not by individual banks, but by the collective borrowing and lending decisions of thousands of participants in the money and capital markets. They are also impacted by changing perceptions of risk by participants in the money and capital markets, especially the risk of borrower default, liquidity risk, price risk, reinvestment risk, inflation risk, term or maturity risk, marketability risk, and call risk.Bankers can lose income or value no matter which way interest rates go. Rising interest rates can lead to losses on bank security instruments and on fixed-rate loans as the market values of these instruments fall. Falling interest rates will usually result in capital gains on fixed-rate securities and loans but a bank will lose income if it has more rate-sensitive assets than liabilities. Rising interest rates will also cause a loss to bank income if a bank has more rate-sensitive liabilities than rate-sensitive assets.6-4. What makes it so difficult for banks to forecast interest rate changes?Interest rates cannot be set by an individual bank or even by a group of banks; they are determined by thousands of investors trading in the credit markets. Moreover, each market rate of interest has multiple components--the risk-free interest rate plus various risk premia. A change in any of these rate components can cause interest rates to change. To consistently forecast market interest rates correctly would require bankers to correctly anticipate changes in the risk-free interest rate and in all rate components. Another important factor is the timing of the changes. To be able to take full advantage of their predictions, they also need to know when the changes will take place.6-5. What is the yield curve and why is it important for bankers to know about its shape or slope?The yield curve is a graphical description of the distribution of market interest rates by maturity of financial instrument. The slope of the yield curve determines the spread between long-term and short-term interest rates. In banking most of the long-term rates apply to loans and securities (i.e., bank assets) and most of the short-term interest rates are attached to bank deposits and money market borrowings. Thus, the shape or slope of the yield curve has a profound influence on a bank's net interest margin or spread between asset revenues and liability costs.6-6. What is it that a bank wishes to protect from adverse movements in interest rates?A bank wishes to protect both the value of bank assets and liabilities and the revenues and costs generated by both assets and liabilities from adverse movements in interest rates.6-7. What is the goal of hedging in banking?The goal of hedging in banking is to freeze the spread between asset returns and liability costs and to offset declining values on certain assets by profitable transactions so that a target rate of return is assured.6-8. First National Bank of Bannerville has posted the following financial statement entries: Interest revenues $63 millionInterest costs $42 millionTotal earning assets $700 millionThe bank's net interest margin must be:Net Interest = $63 mill. - $42 mill. = 0.03 or 3 percentMargin $700 mill.If interest revenues and interest costs double while earning assets grow by 50 percent, the net interest margin will change as follows:($63 mill. - $42 mill.) * 2 = 0.04 or 4 percent$700 mill. * (1.50)Clearly the net interest margin increases--in this case by one third.6-9. Can you explain the concept of gap management?Gap management involves determining the maturity distribution and the repricing schedule for a bank's assets and liabilities. When more assets are subject to repricing or will reach maturity in a given period than liabilities or vice versa, the bank has a GAP and is exposed to loss from adverse interest-rate movements based on the gap's size.6-10 When is a bank asset sensitive? Liability sensitive?A bank is asset sensitive when it has more interest-rate sensitive assets maturing or subject to repricing during a specific time period than rate-sensitive liabilities. A liability sensitive position, in contrast, would find the bank having more interest-rate sensitive deposits and other liabilities than rate-sensitive assets for a particular planning period.6-11. Commerce National Bank reports interest-sensitive assets of $870 million andinterest-sensitive liabilities of $625 million. Because interest-sensitive assets are larger than liabilities by $245 million the bank is asset sensitive.If interest rates rise, the bank's net interest margin should rise as asset revenues increase by more than the resulting increase in liability costs. On the other hand, if interest rates fall, the bank's net interest margin will fall as asset revenues decline faster than liability costs.6-12. First National Bank has a cumulative gap for the coming year of + $135 million and interest rates are expected to fall by two and a half percentage points. What is the expected change in First National's net interest income?ExpectedChange in = $135 million * (-0.025) = -$3.38 millionNet Interest IncomeWhat change will occur in net interest income if interest rates rise by one and a quarter percentage points?Expected Changein Net Interest = $135 million * (+0.0125) = +$1.69 millionIncome6-13 How do you measure a bank’s dollar interest-sensitive gap? Its relative interest-sensitive gap? What is the interest-sensitivity ratio?The dollar interest-sensitive gap is measured by taking the repriceable (interest-sensitive) assets minus the repriceable (interest-sensitive) liabilitiies over some set planning period. Common planning periods include 3 months, 6 months and 1 year. The relative interest-sensitive gap is the dollar interest-sensitive gap divided by some measure of bank size (often total assets). The interest-sensitivity ratio is just the ratio of interest-sensitive assets to interest sensitive liabilities. Regardless of which measure you use, the results should be consistent. If you find a positive (negative) gap for dollar interest-sensitive gap, you should also find a positive (negative) relative interest-sensitive gap and a interest sensitivity ratio greater (less) than one.6-14 Suppose Carroll Bank and Trust reports interest-sensitive assets of $570 million and interest-sensitive liabilities of $685 million. What is the bank’s dollar interest-sensitive gap? Its relative interest-sensitive gap and interest-sensitivity ratio?Dollar Interest-Sensitive Gap = Interest-Sensitive Assets – Interest Sensitive Liabilities= $570 - $685 = -$115Relative Gap = $ IS Gap = -$115 = -0.2018 or -20.18 percent Bank Size $570Interest-Sensitivity = Interest-Sensitive Assets =$570 = .8321 Ratio Interest-Sensitive Liabilities $6856-15 Explain the concept of weighted interest-sensitive gap. How can this concept aid bank’s real interest-sensitive gap risk exposure?Weighted interest-sensitive gap is based on the idea that not all interest rates change at the same speed. Some are more sensitive than others. Interest rates on bank assets may change more slowly than interest rates on liabilities and both of these may change at a different speed than thoseinterest rates determined in the open market. In, the weighted interest-sensitive gap methodology all interest-sensitive assets and liabilities are given a weight based on their speed (sensitivity) relative to some market interest rate. Fed Funds loans, for example, have an interest rate which is determined in the market and which would have a weight of 1. All other loans, investments and deposits would have a weight based on their speed relative to the Fed Funds rate. To determine the interest-sensitive gap, the dollar amount of each type of asset or liability would be multiplied by its weight and added to the rest of the interest-sensitive assets or liabilities. Once the weighted total of the assets and liabilities is determined, a weighted interest-sensitive gap can be determined by subtracting the interest-sensitive liabilities from the interest-sensitive assets. This weighted interest-sensitive gap should be more accurate than the unweighted interest-sensitive gap. The interest-sensitive gap may change from negative to positive or vice versa and may change significantly the interest rate strategy pursued by the bank.Problems6-1. A government bond is currently selling for $900 and pays $80 per year in interest for 5 years when it matures. If the redemption value of this bond is $1,000, what is its yield to maturity if purchased today for $900. The yield to maturity equation for this bond would be:$900 = $80(1YTM)1+ + $80(1YTM)2+ + $80(1YTM)3+ + $80(1YTM)4++ $80(1YTM)5+ + $1,000(1YTM)5+At an YTM of 10 percent the bond's price is $924.28, while at 12 percent its price becomes $864.40. Thus, the true YTM lies between 10% and 12%. To find the true YTM we use: 10% + 40.864$28.924$900$28.924$-- * 2% ≈ 10.81%6-2. Suppose the government bond described in problem #1 is held for 3 years and then the bank acquiring the bond decides to sell it at a price of $950. Can you figure out the average annual yield the bank will have earned for its 3-year investment in the bond?In this instance the yield-to-maturity equation can be modified slightly to find the correct holding-period yield that the bank would earn. Specifically,$900 = $80(1HPY)1+ + $80(1HPY)2++ $80(1HPY)3+ + $950(1HPY)3+At an HPY of 10% the bond's price becomes $912.31, while at 12% the bond's price is $868.56.The true holding period yield must be:10% + 912.31900912.31868.56--⎡⎣⎢⎤⎦⎥ x 2% ≈10.56%.6-3. U.S. Treasury bills are available for purchase this week at the following prices (based upon $100 par value) and with the indicated maturities:a. $97.25, 182 days.b. $96.50, 270 days.c. $98.75, 91 days.The discount rates and equivalent yields to maturity (bond-equivalent or coupon-equivalent yields) on each of these Treasury bills are:Discount Rates Equivalent Yields to Maturitya.(10097.25)100- * 360182 = 5.44% (365x.0544)[360(0.0544x182)]- = 19.856350.1 = 5.67% b.(10096.50)100- * 360270 = 4.67% (365x.0467)[360(.0467x270)]- = 17.046347.39 = 4.91% c. (10098.75)100- * 36091 = 4.95% (365x.0495)[360(.0495x91)]- = 18.07355.5 = 5.08%6-4. The First State Bank of Ashfork reports a net interest margin of 3.25 percent in its most recent financial report with total interest revenues of $88 million and total interest costs of $72 million. What volume of earning assets must the bank hold?The relevant formula is:Net Interest Margin = .0325 = AssetsEarning mil. $72mill. $88-Then Earning Assets = $492.31 million.Suppose the bank's interest revenues rise by 8 percent and its interest costs and earning assets increase 10 percent. What will happen to Ash Fork's net interest margin?Substituting in the correct formula we have:New Net Interest Margin = .10)million(1 $492.3.10)million(1 $72.08)(1 million $88++-+= million$541.53million $79.20million $95.04-= 0.0293 or 2.93 percent.6-5. If a bank's net interest margin, which was 2.85 percent, doubles and its total assets, which stood originally at $545 million, rise by 40 percent, what change will occur in the bank's net interest income?The correct formula is:.0285 * 2 = .4)(1*million 545$Income Interest Net +or Net Interest Income = 0.057 * $763 million= $43.49 million.6-6. The cumulative interest-rate gap of Snidal State Bank and Trust Company doubles from an initial figure of -$35 million. If market interest rates fall by 25 percent from an initial level of 6 percent, what change will occur in Snidal Bank's net interest income?The key formula here is:Change in the Bank's = Change in interest rates (in percentage points) * cumulative gap Net Interest = 0.06 * -.25 x (-$35 mill.) * 2Income = 1.05Thus, the bank's net interest income will rise by 5 percent.6-7. Given: Merchants State Bank has recorded the following financial data for the past three years (dollars in millions):Current Year Previous Year Two Years Ago Interest revenues $57 $56 $55 Interest expenses 49 42 34 Loans (Excluding nonperforming) 411 408 406 Investments 239 197 174 Total deposits 487 472 467 Money market borrowings 143 118 96 Solution:Net interest margin (NIM) = Net Interest Income/Earning Assets, whereNet Interest Income = Net Interest Revenues - Net Interest ExpensesEarning Assets = Loans + InvestmentsNIM(Current) = ($57-49)/(411 + 239) = 8/650 = 0.0123 or 1.23%NIM(previous) = ($56-42)/(408 + 197) = 14/605 = 0.0231 or 2.31%NIM(Two years ago) = ($55-34)/(406 + 174) = 21/580 = 0.0362 or 3.62%The net interest margin has been declining steadily and significantly. Probable causes include greater increases in interest expenses relative to interest income due to shifts in funding mix with greater dependence on borrowed funds (more expensive sources) relative to deposits (less expensive sources). Additionally, the mix in earning assets, with greater growth in lower yielding investment securities than in higher yielding loans, is another contributor to the steadily declining net interest margin.Management needs to reevaluate its funding strategies and its loan and investment strategies. If slower loan growth is related to external forces -- for example, a weaker economy -- then less borrowing should be considered. If the slower loan growth is more internal, then more aggressive loan management would be appropriate.6-8 The First National Bank of Wedora, California has the following interest-sensitive gaps:Coming WeekNext30 DaysNext31-90 DaysMore Than90 DaysInterest - $144 $110 $164 $184 Sensitive +29 +19 29 8 Assets = $173 $129 $193 $192 Interest - $232 $ --- $ --- $ --- Sensitive 98 84 196 35 Liabilities = 36 6 --- ---$366 $90 $196 $35 GAP - $193 + $39 - $3 + $157 Cumulative GAP - $193 - $154 - $157 $0First National has a cumulative zero gap and therefore is not vulnerable to loss if interest rates rise. It does have a positive gap in two periods--the next 30 days and more than 90 days. During these particular periods a rise in interest rates would produce a short-run gain.6-9 First National Bank of Barnett currently has the following interest-sensitive assets and liabilities on its balance sheet:Interest-Sensitive Assets Interest-Sensitive LiabilitiesFederal fund loans $65Security holdings $42 Interest-bearing deposits $185Loans and leases $230 Money-market borrowings $78What is the bank’s current interest-sensitive gap? Suppose its Federal funds loans carry an interest-rate sensitivity weight of 1.0 while its investments have a rate-sensitivity weight of 1.15 and its loans and leases display a rate-sensitivity weight of 1.35. On the liability side First National’s rate-sensitivity weight is 0.79 for interest-bearing deposits and 0.98 for itsmoney-market borrowings. Adjusted for these various interest-rate sensitivity weights, what is the bank’s weighted interest-sensitive gap? Suppose the Federal funds interest rate increases or decreases one percentage point. How will the bank’s net interest income be affecte d (a) given its current balance sheet make up and (b) reflecting its weighted balance sheet adjusted for the foregoing rate-sensitivity weights?Solution:Dollar IS Gap = ISA - ISL = ($65 + $42 + $230) - ($185 + $78) = $337 - $263 = $74 Weighted IS Gap = [(1)($65) + (1.15)(42) + (1.35)(230)] - [(.79)($185) + (.98)($78)] = $65 + $48.3 + $310.5 - $146.15 + $76.44= $423.8 - $222.59= $201.21a.) Change in Bank’s Income = IS Gap * Change in interest rates= ($74)(.01) = $.74 millionUsing the regular IS Gap, net income will change by plus or minus $740,000b.) Change in Bank’s Income = Weighted IS Gap * Change in interest rates= ($201.21)(.01) = $2.012Using the weighted IS Gap, net income will change by plus or minus $2,012,0006-10 McGraw Bank and Trust has interest-sensitive assets of $225 million and interest-sensitive liabilities of $168 million. What is the bank’s dollar interest-sensitive gap? What is McGraw’srelative interest-sensitive gap? What is the value of its interest-sensitivity ratio? Is the bank asset sensitive or liability sensitive? Under what scenario for market interest rates will the bank experience a gain in net interest income? A loss in net interest income?Dollar Interest-Sensitive Gap = ISA – ISL = $225 - $168 = $57Relative Interest-Sensitive Gap = ISA – ISL = $57 = 0.2533Bank Size $225Interest-Sensitivity Ratio = ISA = $225 = 1.3393ISL $168This bank is asset sensitive. More assets will be repriced during this time period than liabilities. This means that if interest rates rise, the interest earned on assets will rise relative to the interest paid on liabilities and net interest margin will rise. However, if interest rates fall, interest earned on assets will fall more than interest paid on liabilities and net interest margin will fall.Web Site Problems1. Suppose you want to know what types of banks make the greatest use of asset-liability management tools and what their biggest ALM problems are? Where would you go on the web to try to get answers to these questions?Almost all banks are required by regulators to have some kind of ALM management in place. These techniques can be as simple as the interest sensitive gap discussion in this chapter or the duration gap management in the next chapter. However, there are many consulting firms out there that have developed specific models for managing ALM. One way to see what is out there is to do a search on bank ALM management and see some of the sites that are out there. These sites range from sites for the consulting firms to more general sites that provide a good definition and description of ALM management. Two sources that are available at this time for general information on asset-liability management are/glossaryassetliabilitymanagement.htm and/Products/nccb_asset.htm. However if you want a good discussion of specific models and the problems people are having with ALM management, one good source appears to be /. This site has several discussion groups on various ALM topics.2. If a new web model to apply ALM techniques to a bank’s risk exposure is developed, at what web site are you most likely to find a discussion of that new ALM model?The best place to get information about a new ALM model would be the/ site mentioned above. If a promising new model were developed it would be sure to show up in the discussion groups mentioned above.3. If you need guidance on how to prepare bank forecasts and measure risk as part of a bank’s ALM activities which web site could be most helpful to you?If you are not willing to go to a consultant about how to develop bank forecasts and measure risk, the / web site would probably be the most helpful site. There are many discussions there about how to deal with specific measurement issues and how to find information to determine the risk of your bank compared to peer institutions.85。

CHAPTER 21PRICING CONSUMER AND REAL ESTATE LOANSGoal of the Chapter: To learn how consumer and real estate loan rates may be determined and to see the options a bank loan officer has today in pricing loans to individuals and families.Key Terms Presented in This ChapterAnnual percentage rate (APR) Compensating deposit balanceSimple interest Fixed rate mortgages (FRMs)Discount rate method Adjustable-rate mortgages (ARMs)Add-on method PointsRule of 78sChapter OutlineI. Introduction: The Challenge of Pricing Consumer and Real Estate LoansII. The Interest Rate Attached to Nonresidential Consumer LoansA. Cost-Plus Loan Rate ModelB. Annual Percentage RateC. Simple InterestD. The Discount Rate MethodE. The Add-On Loan Rate MethodF. Rule of 78sG. Compensating Balance RequirementsIII. Use of Variable Rates on Consumer LoansIV.Interest Rates on Home Mortgage LoansA.Fixed Rated MortgagesB.Variable Rate MortgagesC.Charging the Customer Mortgage PointsV Summary of the ChapterConcept Checks21-1. What options does a bank loan officer have in pricing consumer loansMost consumer loans, like most business loans, are priced off some base or cost rate, with a profit margin and compensation for risk added on. The rate on a consumer loan may be figured from the cost-plus model or the base-rate model. Most installment and lump-sum payment loans are made with fixed interest rates. However, due to the volatility of interest rates in the 1 970’s and 1980's, a greater number of floating rate consumer loans have appeared.21-2. Suppose a customer is offered a loan at a discount rate of 8 percent and pays $75 in interest at the beginning of the term of the loan. What net amount of credit did this customer receive?The relevant formula is:Then the net amount of credit received must be $75/.08 or $937.50.Suppose you are told that the effective rate on this loan is 12 percent. What is the average loan amount the customer had available during the year?In this instance:Interest Owed $75Effective loan ratio = Average Loan Amount During the Year= x = 0.12Then the average loan amount during the year must be:x = $75 = $625.0.1221-3. See if you can determine what APR you are charging a consumer loan customer using the tables inside the back cover of this text if you grant the customer a loan for 5 (payable in monthly installments) years which carries a finance charge per $100 of $42.74.The terms quoted mean that the customer must pay an APR of 15 percent according to the Annual Percentage Rate Table in the tables inside the text's back cover.21-4. A customer is quoted an APR of 16 percent on a loan of $10,000, lasting for 4 and payable in monthly installments years.According to the Table in Appendix B the Finance charge per $100 of amount financed must be $36.03 or $36.03 *100 = $3603 in total finance charges.Problems21-1. William Crenshaw, who owns a small retail business, has requested a personal loan of $4500 for one year. He asks for a lump-sum loan with no installment payments; the loan, as requested, will be repaid at the end of the year plus interest. However, the bank wants monthly payments at an annual interest rate of 13 percent.If Crenshaw had received the loan under his preferred terms he would pay:Discount Interest Owed $75 loan rate = Net Amount = x = 0.08 of Credit ReceivedInterest Owed = Principal *Rate * Time = $4500 * 0.13 * 1 = $585.On the other hand, if the loan is repaid in 12 equal monthly installments (of $375 apiece) theinterest owed would be:First Month: $4500 x 0.13 x 1/12 = $48.75Second Month: $4125 x 0.13 x 1/12 = $44.69Third Month: $3750 x 0.13 x 1/12 = $40.62Fourth Month: $3375 x 0.13 x 1/12 = $36.56Fifth Month: $3000 x 0.13 x 1/12 = $32.50Sixth Month: $2625 x 0.13 x 1/12 = $28.44Seventh Month: $2250 x 0.13 x 1/12 =$24.37Eighth Month: $1875 x 0.13 x 1/12 = $20.31Ninth Month: $1500 x 0.13 x 1/12 = $16.25Tenth Month: $1125 x O.13 x 1/12 = $12.19Eleventh Month: $750 x 0.13 x 1/12 = $ 8.12Twelfth Month: $375 x 0.13 x 1/12 = $ 4.06Total Interest Paid $316.86In straight dollar terms it appears that Crenshaw pays less interest ($316.86 versus $585) with the loan paid back in monthly installments rather than repayment of a lump sum at the end. However, because Crenshaw has use of only about half the loan's balance (or $2250) on average over the year when repayment is in 12 equal installments he pays an approximate effective interest rate of $316.86/$2250 or 14.08% with the installment loan which significantly exceeds the loan contract rate of 13% under the lump-sum loan contract. (Note: We emphasize the word approximate.)As an alternative solution to this problem, we could prepare an amortization schedule for this loan, which would look like the following:For a $4,500 loan with a 13% annual interest rate and repayment on a monthly basis, the payment each month would be $401.85.Interest PrincipalBeginning Balance Payment Portion Portion Ending Balance$4,500.00 $401.85 $48.75 $351.10 $4,148.90$4,148.90 $401.85 $44.95 $356.90 $3,792.00$3,792.00 $401.85 $41.08 $360.77 $3,431.23$3,431.23 $401.85 $37.17 $364.68 $3,066.55$3,066.55 $401.85 $33.22 $368.63 $2,697.92$2,697.92 $401.85 $29.23 $372.62 $2,523.30$2,523.30 $401.85 $25.19 $376.66 $2,146.64$2,146.64 $401.85 $23.26 $378.59 $1,768.05$1,768.05 $401.85 $19.15 $382.70 $1,385.35$1,385.35 $401.85 $15.01 $386.84 $ 998.51$ 998.51 $401.85 $10.82 $391.03 $ 607.48$ 607.48 $401.85 $ 6.58 $395.27 $ 212.21$ 212.21 $214.51* $ 2.30 $212.21 $ 0.00Total Interest Paid $336.71* The final payment will equal the balance remaining before the last payment plus the interest on that balance. In most, if not all cases, this payment will be different from the regular payment.21-2. Frank Petrel plans to start an auto repair shop and has requested a $10,000 new-venture loan. The bank wishes to make a discount-rate loan at prime plus 2 percentage points or 14.5 percent.This means Petrel will receive net loan proceeds of $10,000 - $10,000 * 0.145 = $8550.Using this net figure as a base, Petrel will pay an effective interest rate of$1450 / $8550 or 16.96%.Alternative Scenario 1:Would Mr. Petrel be better off if he were able to get a $10,000 personal loan with a 12.5% add-on rate for one year? Why or why not?Solution:In this instance, Petrel would have to repay the $10,000 plus $10,000 x 0.125 in interest or $1250. He would be asked to make monthly installment payments of ($10,000 + $1250) / 12or $937.50 per month for 12 months. Because Petrel would have only $5,000 in borrowed funds on average to use over a 12-month period, the approximate effective interest rate he would pay under the add-on rate method would be $1250 / $5000 or about 25 percent. (A financial calculator solution gives us an effective rate of 22.32%.) Clearly this effective rate would be much higher than the interest rate on the discount business loan.Alternative Scenario 2:What happens to the effective rate on Mr. Petrel's loan if the prime rate changes to 10 percent?Solution:The rate on Mr. Petrel's discounted loan would be 12 percent (10% + 2%).The net proceeds from the loan would, therefore, be$10,000 - ($10,000 * .12) = $10,000 - $1,200 = $8,800.The effective cost of the loan would then be$1,200 / $8,800 = .1364 or 13.64%. (Declines from 16.96%)Alternative Scenario 3:How does the effective rate on this loan change if the prime rate increases to 13 percent?Solution:The rate on Mr. Petrel's discounted loan would be 15 percent (13% + 2%).The net proceeds from the loan would be$10,000 - ($10,000 *.15) = $10,000 - $1,500 = $8,500.The effective cost of the loan would then be$1,500 / $8,500 = .1765 or 17.65%. (Increases from 16.96%)Alternative Scenario 4:Suppose Mr. Petrel is able to raise personal equity to put into the new business in the amount of $2,500 from his accumulated savings and from a small loan extended by a close friend. The bank will then lend him just $7,500 at a discount rate of prime plus one-and-one-half percentage points (currently prime is 12 percent). What is the effective interest rate on the loan in this case?Solution:The rate on Mr. Petrel's discounted loan would be 13.5 percent (12% + 1.5%).The net proceeds from the loan would be$7,500 - ($7,500 *.135) = $7,500- $1,012.50 = $6,487.50.The effective cost of the loan would then be$1,012.50 / $6,487.50 = .1561 or 15.61%.21-3. The Robbins family has asked for a 20-year mortgage in the amount of $60,000 to purchase a home. At a 10 percent loan rate, what is the required monthly payment?Solution:$579.01 1- 0.10/12) 1(0.10/12) (1 * 0.10/12 * 60,000$12*2012*20=++Because of the computational problems in the above formula, an easier approach is to use the tables inside the text's back cover to find the:Total Finance Charge Per $100 Financed = $131.61Total Finance Charge on the Loan Amount Requested =($60,000 / $100) x $131.61 = $78,966Required Monthly Payment = Total Finance Charge + Loan AmountNumber of Payments= [$78,966 + $60,000] / 240 = $ 579.03Alternative Scenario 1:If the Robbinses' home mortgage loan rate is adjustable and rises to 11 percent at the beginning of the second year of the loan, what will the required monthly payment be?Solution:$628.48 1- 0.11/12) 1(0.11/12) (1 * 0.11/12 * 000,60$12*1912*19=++Note that we assume the first-year loan rate is 10 percent and then rises to 11 percent for theremaining 19 years (or 228 months) of the 20 year loan. Also, for ease of calculations, we assume that there has been no significant reduction in the principal amount of the loan. In reality, the Robbins will have reduced the principal to approximately $59,000 at the end of the first year. Interpolation in the tables inside the text's back cover for an 11percent loan for 228 remaining monthly payments gives:Total Finance Usage Per $100 Financed = $104.59) - ($147.73 * 180- 240180-228 104.59$+= $104.59 + $34.51 = $139.10Total Finance Charge on Remainder of Loan = ($60,000/$100) * $139.10 = $83,460Required Monthly Payment = $59,000)on ($618 $629.21 228$60,000 $83,460=+Alternative Scenario 2:Suppose the rate on the Robbinses' home mortgage declines to 9 percent at the beginning of the loan's second year. What happens to the required monthly payment?Solution:Note: Since Table 3 in the Appendix does not have 9 percent, we will calculate the required monthly payment using a financial calculator.Required Monthly Payment for $60,000 at 9 percent (.75% per month) for 19 years/(228 months)= $550.14 ($540.97 for $59,000)Alternative Scenario 3:Would the Robbins family be better off under all of the above scenarios if they took out a 15-year mortgage instead of a 20-year mortgage? What would they gain and what would they give up with this mortgage loan of a shorter maturity?Solution:The answer to this question depends upon the Robbinses' ability to make the higher payments that would be required on a shorter term mortgage.In each case, the Robbinses would have a higher monthly payment; however, their total payments would be less, their home would be paid for in less time, and they would accumulate equity in the home more quickly.21-4. James Alters received a $1500 loan last month with the intention of repaying the loan in 12 months. However, Alters now discovers he has the cash to repay the loan right now after making just one payment. What percentage of the total finance charge is Alters entitled toreceive as a rebate and what percentage of the loan's finance charge is the bank entitled to keep?The Rule of 78s applies here. James Alters is entitled to receive back as an interest rebate:percent 63.33 = 100x 78671211...2111 + . . . + 2 + 1=++++of the total finance charges on the loan: the lender is entitled to keep 36.67 percent of the finance charges associated with this loan.21-5. Constance Homer asks for a $10,000 loan. Slidell Corners State Bank agrees to give her immediate use of $9400 and to deduct $600 in interest up front. The effective discount rate on this loan is:6.38% $9400$600 Received Credit of Amount Net Owed Interest ==21-6. The Lindal family wants to borrow $2500 for a year to finance a European vacation. If the family must pay a 12 percent add-on loan rate, how much in interest will they pay?Interest Paid = Loan principal * Loan Rate = $2500 * 0.12 = $300What is the amount of each required monthly payment?Amount of Monthly Payment = $233.33 12$300 $2500=+What is the effective loan rate in this case?Effective Loan Rate = 24%or 0.24 $1250$300 Year the During Amount Average Owed Interest ==21-7. The APR for Joseph Nework's $10,000, 3-year automobile loan can be determined from the annual percentage rate table for monthly payment plans inside the back cover of the text.If Joseph must pay $2217 in total finance charges over 36 months, the table tells us he is paying100$2217$ or $22.17 per $100 or an APR of 13.50 percent.21-8. If Kyle Ellisor is to receive a 30-year mortgage loan in the amount of $225,000 at an APR of 14%, he will pay finance charges of $326.55 per $100 borrowed over the life of this loan (see the annual percentage rate tables inside the back cover of the text). Therefore, he will pay in total finance charges$100$225,00* $326.55 = $734,737.50.21-9. The Quisling family asks to borrow $1800 at 11 percent simple interest for one year. It will pay the following interest bill:I = P * r * t = $1800 * 0.11 * l = $198Therefore, they must pay back a total of $1998 in principal and interest.21-10. Mary Perland will pay the following in interest on her $1200 loan for one year at 8 percent simple interest:First Quarter: I = $1200 x 0.08 x 1/4 = $24Second Quarter: I = $900 x 0.08 x 1/4 = $18Third Quarter: I = $600 x 0.08 x 1/4 = $12Fourth Quarter: I = $300 x 0.08 x 1/4 = $6Total Interest owed = $24 + $18 + $12 + $6 = $60.If Mary were offered the $1200 loan at a 6 percent simple interest rate and the loan is paid in lump sum at maturity, she will pay total interest of:$1200 * 0.06 x 1 = $72.She clearly would pay more in interest but would have the full $1200 available for her use for one year.21-11. The Tielman family has asked for a $2500 loan for one year to complete home repairs. First National Bank assesses an 8 percent rate of interest and requires a $500 minimum compensating balance left in a deposit. The effective interest rate on this loan must be:10%or 0.10 $2000$200 $500 - $25000.08 * $2500 Amount Loan Net Owed Interest ===Actually 10 percent is the minimum loan rate. If the Tielman's keep a deposit balance larger than the minimum $500 required the effective loan rate will climb higher.21-12. Bill and Sue Rogers are negotiating with their local bank for a home mortgage loan in the amount of $80,000. The bank levies an up-front fee of 1.5 points on this loan. The dollar amount of points they must pay upfront is:Dollar Value of Points = $80,000 * 0.015 = $1200.The Rogers will have available for their use only $78,800 or $80,000 less $1200.21-13 As a loan officer you quote Mr. and Mrs. Coldner an APR of 14 percent on a two year loan to remodel their kitchen. The loan amount is $6000. Using the APR tables inside the back cover of the text determine the total finance charge on this loan.$913.80 15.23 x $100$6000= is the total amount in finance charges the Coldner’s wi ll pay.If they insist on a 12 percent loan$778.80 12.98 x $100$6000= is the total amount in finance charges the Coldner’s will payThe bank will lose $13521-14. Dresden bank’s personal loan department quotes Mr. Angelo a finance charge of $6.06 for each $100 in credit the bank is willing to extend to him for a year (assuming the balance of the loan will be paid off in 12 equal installments). What APR is Mr. Angelo being quoted by the bank? How much would he save per $100 borrowed if he could retire the loan in 6 months?The APR on this loan is 11 percent. If he could retire the loan in 6 months the finance charges per $100 would be $3.23. He would save $2.83 per $100 borrowed.21-15. Would you expect loan interest rates on new cars to be higher than on used cars? Why or why not? Would you expect a personal loan to carry a higher interest rate than an automobile loan? Why or why not?I would expect the interest rate on the new car loan to less than the interest rate on a used car loan. In general, newer cars are easier to sell than used cars and the bank would stand a better chance of getting their money back in the event of default on the loan. However, this may depend on the make and model of the car and the market for used cars.I would expect the interest rate on the personal loan to be higher than the interest rate on the automobile loan. In the personal loan there may not be any specific and identifiable assets pledged as collateral on the loan. In the case of the automobile loan the car purchased is generally used as collateral. In the event of default it may be more difficult for the bank to get their funds back on the personal loan.Web Site Problems1. What methods are in greatest demand today to aid in the pricing of consumer loans and real estate (particularly housing) credit? How can the world wide web be of help in this area? What web sites look especially good?I believe that the most common method for calculating consumer loan interest rates and payments is the APR. Since this is the method that banks must report by law, it is now the most often used method for calculating payments on consumer loans. The web can help because there are a number of places on the web where can find information about prevailing interest rates on consumer loans and a number of places that will calculate your payments based on a particular APR and amount borrowed. For examplehttp://moneysense.quicken.ca/eng/auto/calculators/payments/index.phtml is a place to calculate automobile loans. There are many other places on the web where you can make the same calculation.2. Why is credit scoring useful in helping to price consumer and home mortgage loans? Where can you go to get good credit-scoring information?The demand for consumer loans has expanded exponentially in recent years. As a result the need for a quick and reliable way to determine whether an individual will pay back a loan was needed. This led to the development of credit scoring. There are many web sites that discuss credit scoring and the advantages and disadvantages of these models. One web site that I found is/article1.htm. This web site is good because it does give a history of why credit scoring models have developed and a very basic description of how it works and the advantages and disadvantages. In addition there are several web sites where you can get an estimate of your credit score.3. Why is regulation so important in the personal loan area? How can you use the web to stay abreast of rule changes in the consumer loan field?Regulations are needed in this important field because it is very easy to take advantage ofill-informed individuals by charging them excessive interest rates and fees. Because of the changing technology and increased consumer demand for loans there have been a number of changes in regulations for consumer lending in recent years and changes will continue to be made in the future. There are a number of sites out on the web to help individuals keep up with these changes. One place to check is with the regulatory agencies overseeing banks (OCC, FDIC, FRS) as these agencies regularly post updates to the laws. In addition, as a banker there are several web sites that advertise seminars and classes on consumer lending which would include a discussion of the latest laws and regulations in this important area. One web site that lists several classes in this area is the web site of the American Bankers Association (ABA) at/Conferences+and+Education/onlinecourse8.htm.。

CHAPTER 19PRICING BUSINESS LOANSGoal of This Chapter: To explore different methods used by bankers today to price business loans and to evaluate the strengths and weaknesses of these pricing methods for achieving a bank's goals.Key Terms Presented in This ChapterCost-plus loan pricing Below-prime pricingPrice leadership Cap ratesPrime rate Customer profitability analysisLIBORChapter OutlineI. Introduction: The Challenge of Trying to Correctly Price Business Loans in a HighlyCompetitive MarketII. The Cost-Plus Loan Pricing MethodIll. The Price Leadership ModelA. Prime or Base Rate PricingB. Loan Risk and the MarkupC. Prime-Plus versus Times Prime PricingD. LIBOR-based Loan PricingE. Below-Prime Market Pricing (The Markup Model)F. Loans Bearing Maximum Interest Rates (Caps)IV. Customer Profitability AnalysisA. The Basic FormulaB. A Numerical ExampleC. Earnings Credit for Customer DepositsD. The Future of Customer Profitability AnalysisVI. Summary of the ChapterConcept Checks19-1. What methods are in use today to price business loans?The following methods are in use today to price business loans:a. Cost-plus pricing d. CAP rateb. Price leadership pricing model e. Customer Profitability Analysisc. Markup market-pricing modelCost-plus-profit pricing requires the bank to estimate the total cost involved in making aloan and then adds to that cost estimate a small margin for profit. The price-leadership model, on the other hand, bases the loan rate upon a national or international rate (such as prime or LIBOR) posted by major banks and then adds a small increment on top for profit or risk. The markup model prices a loan on the basis of cost plus a risk premium added to those loans with greater credit risk and/or longer term loans that have greater term risk.CAP rates specify a maximum rate that a borrower can be assessed, thus limiting a borrower's interest-rate risk. Customer profitability analysis looks at all the revenues and costs involved in serving a customer and then requires the bank to calculate the net rate of return from this particular customer.19-2. The loan rate quoted for this $10 million corporate loan would be:Loan Rate = 4 percent Loan Funds Cost + .5 percent Non-funds Operating Cost+ .375 percent default risk premium+ .625 percent term risk premium+ .25 percent profit margin= 5.75 percentBased on a $10 million loan this customer will pay in interest each year:$10,000,000*.0575 = $575,000.19-3. What are the principal strengths and weaknesses of the loan-pricing methods in use today?a. Cost-plus pricingStrength: considers the cost of raising loanable funds and operating costs of running the bank.Weaknesses: banks must know what their costs are in order to consistently makeprofitable, correctly priced loans; gives little regard to competition from other lenders.b. Price leadership pricing modelStrength: considers competition from other lenders, allows for a risk premium to be added to the base or prime rate.Weakness: does not consider the marginal cost of raising loanable funds.c. Markup market-pricing modelStrength: allows banks to compete more aggressively with the commercial paper market.Weakness: narrow margins (markups) on loans.d. CAP rateStrength: is another service option that a bank may offer its customers for a specific fee.Weakness: a prolonged period of high interest rates will effectively transfer the risk offluctuating interest rates from borrower to lender.e. Customer profitability analysisStrength: takes the whole customer relationship into account when pricing each loan request.Weakness: must consider revenues and expenses from all of the bank's dealings with the customer.19-4. What is customer profitability analysis?Customer profitability analysis looks at all the revenues and costs involved in serving a customer and then requires the bank to calculate the net rate of return from all the services the bank sells to this particular customer.Problems19-1. The expected revenues and costs from continuing the present relationship between Enterprise National Bank and USF Corporation were given in this problem and the reader is asked to estimate the expected net rate of return if the bank renews its loan to USF.The total of expected revenues and expected costs is:Expected Revenues Expected CostsInterest Revenue $ 1,100,000 Deposit Interest $ 25,000 Commitment Fees 100,000 Cost of Other Funds Raised 975,000 Deposit Service 4,500 Wire Transfer Costs 1,300 (Maintenance) Fees Loan Processing Costs 12,400 Wire Transfer Fees 3,500 Record keeping Expenses 4,500 Agency Fees 8,800 Account Activity Cost 19,000 Total Expected $1 216,800 Total Expected Costs $ 1,037,200 RevenuesGiven: Total Expected Revenues = $1,216,800Total Expected Costs = $1,037,200Net Revenue = $1,216,800 - $1,037,200 = $179,600Net Funds Loaned = $10,000,000 - $2,125,000 = $7,875,000Expected Net Rate of Return = $179,600/ $7,875,000 = .0228 or 2.28%Because the estimated net rate of return is positive, the bank should strongly consider approving the loan as requested because the bank can earn a premium over its costs.If you decide to turn down this request, under what assumptions regarding revenues, expenses, and customer-maintained deposit balances would you make this loan?An initial reaction might be to increase loan revenues by raising the interest rate on the loan or increasing the loan commitment fee. Depending on the customer's relationship with the bank and with other banks, this may prove to be extremely difficult. Initially, it was assumed that the customer would draw down the entire line of credit, that is, borrow the full $10,000,000. If the customer were to borrow less than the full amount, the cost of funds raised to support this loan could be reduced, increasing the net revenue from the loan. Relative to expenses, it would be more likely that some adjustment in the expenses associated with the relationship would be more appropriate. For example, a careful examination of the relationship activities could allow for a revision of estimated costs incurred by the bank to manage the various aspects of the relationship. As far as the customer-maintained balances are concerned, there could be an opportunity to revise these estimates upward, making the net funds loaned smaller and the expected net rate of return greater.Alternative Scenario 1:Given: Prime rate drops from 10% to 8%. No change in interest costs.Solution:Interest Revenue = 9% x $10,000,000 = $900,000Change in Interest Revenue = $900,000 - $1,100,000 = -$200,000Net Revenue = [$1,216,800 - $200,000] - $1,037,200 = -$20,400Since the expected net revenues are now negative, the estimated net rate of return will be negative (-$20,400 / 7,875,000 = - 0.26%). With this negative expected net rate of return, the bank should carefully review the relationship. If this is a long, very good relationship, the bank should consider making the loan; however, there should be further negotiations to insure the profitability of the relationship. This might include restructuring the deposit relationship.Alternative Scenario 2:Given: Required Rate on Time Deposit = 9.25% (up from 9%)Cost of Other Funds Raised = $1,065,000 (up from $975,000)Prime Rate = 9.5% (down from 10%)Solution:Interest revenue = 10.5% x $ 10,000,000 = $1,050,000Change in Interest Revenue = $1,050,000 - $1,100,000 = -$50,000Add'I Interest Expense (Time Deposit) = $25,695 - $25,000 = $695Add'I Cost of Other Funds = $1,065,000 - $975,000 = $90,000 Additional Funding Costs $90,695Net Revenue = [$1,216,800 - $50,000] - [$1,037,200 + $90,695]= $1,166,800- $1,127,895 = $38,905Since the net revenue under these conditions is positive ($ 38,905), the bank should make the loan. Alternative Scenario 3:Given: All revenues, except interest revenue, and costs held constant.Solution:Break Even Revenues = $1,037,200Break Even Interest Revenue = $1,037,200 - [$100,000 + $4,500+ $3,500 + $ 8,800]= $1,037,200 - $116,800 = $920,400Break Even * $10,000,000 = $920,400Break Even = $920,400 / $10,000,000 = .092 or 9.2%Break Even = Prime Break Even + 1 = 9.2%Prime Break Even = 9.2% - 1 = 8.2%Alternative Scenario 4:Given: All costs, except interest costs, and revenues held constant.Solution: Break Even Revenues = $1,216,800Break Even Interest Costs = $1,216,800 - [$1,300 + $12,400+ 4,500 + $19,000]= $1,216,800 - $ 37,200 = $1,179,60019-2 Chilton Westover Bank has sold negotiable CDs in the amount of $6 million at a yield of 8.75% and purchased $4 million in federal funds at a rate of 8.40%. The weighted average cost of bank funds in this case would be:$ 6,000,000 * .0875 = $525,000$ 4,000,000 * .0840 = $336,000Total Interest Cost = $861,000On a $10 million loan this is an average annual interest cost of $861,000/$10,000,000 or 0.0861 which is 8.61 %. There were also $25,000 in noninterest costs or 0.25% of the loan total of $10million. With a one percent risk premium and a 0.25% minimal profit margin, the loan rate on a cost-plus basis would be:Interest Cost + Non-interest Cost + Risk Premium + Profit Margin =8.61% + 0.25% + 1.00% + 0.25% = 10.11%.Alternative Scenario 1:Given: Funding entire loan with federal funds at 8.4%.Solution:Loan rate on a cost-plus basis would be:Interest Cost + Non-interest Cost + Risk Premium + Profit Margin =8.40% + 0.25% + 1.00% + 0.25% = 9.90%The bank faces the risk that its interest cost component, the federal funds rate, which can change daily, could increase quickly and take up the "slack" in the loan rate, thereby reducing the profit margin on the loan.Alternative Scenario 2:Given: Noninterest costs unexpectedly rise to $38,000 and the customer insists on a cap of 10 percent on the rate.Solution:Profit Margin = Loan Rate – [Interest Cost + Noninterest Cost + Risk Premium]= 10.00% - [8.61% + 0.38% +1.00%]= 10.00%-9.99% = .01%The profit margin, for all intents and purposes, disappears.19-3. Englewood Bank is confronted with a $15 million loan request to fund accounts receivable and inventory for APEX Exports. The bank would prefer a floating-rate loan for 90 days at a rate of LIBOR + 0.25%. Most recently LIBOR was at 9.25%. APEX, however, wants the loan rate set1at 1.014 * LIBOR.At today’s prevailing LIBOR rate the customer's requested loan-rate formula would generate a loan interest rate of 1.014 * 9.25% = 9.38%. The bank wanted to charge a rate of 9.25% + 0.25% = 9.50%. Loan rates tend to move up and down faster with the customer's loan-rate formula than with the bank's LIBOR-plus formula. This customer appears to believe interest rates will soon decline, pulling its loan rate lower.Alternative Scenario:Given: The bank's counterproposal to Apex is LIBOR plus 0.125% with a compensating balance of $250,000.Solution:At the prevailing LIBOR rate of 9.25%, the effective rate of the counter proposal is:[9.25% + 0.125%]/[($15,000,000 - $ 250,000)/$15,000,000]= 9.375%/.9833 = 9.53%On an effective cost basis, Apex is not likely to agree to this request. However, if Apex looks only at the 9.375% rate, they might accept the request. Apex's opportunity cost of the minimum balance would come into play in accepting or rejecting the counter proposal.19-4. RJK Corporation was quoted a loan rate equal to the prevailing federal funds interest rate plus 3/8 of a percentage point (or 0.375%) . RJK wanted the loan renewed at money-market borrowing cost plus 0.25%. If the base rate is set at the federal funds rate the loan rate as requested by RJK would be:Week 1 Week 2 Week 3 Week 4 Week 5 Fed Funds 8.72% 8.80% 8.69% 8.46% 8.46% Margin 0.25% 0.25% 0.25% 0.25% 0.25% Loan Rate 8.97% 9.05% 8.94% 8.71% 8.71% Clearly the other money-market interest rates would have generated somewhat lower loan rates, especially the CD and Treasury bill rates. However, interest rates fell over the period examined, resulting in lower loan revenues for the bank. The bank would have been better off to offer its customer a fixed interest rate over the next five weeks.Alternative Scenario:Given: Bank desires to set a floor of 8%. Borrower agrees with the proposal if bank agrees to a loan rate of base rate plus 0.125%.Solution:The major risk faced by the bank is the risk that interest rates will rise along with other costs. If this occurs, increased fixed costs could erode the profit margin. Although this borrower would appear to be an excellent credit risk, increasing interest rates and inflation could result in increased default risk for the borrower over an extended period of time.Both the one-month commercial paper rate and the one-month CD rate have less volatility. Additionally, both maturities (i.e., one month) are closer to the five-week maturity of the requested loan. One might argue that either of these would be preferable, since they would maintain a higher rate in a declining interest rate environment. The one-month commercial paper rate had the lowestdecline during the five-week period, less than 2%, whereas the federal funds rate declined by approximately 3% and the CD rate declined by over 2%. If this trend were to continue over the next five-week period, the commercial paper rate would appear to be a better alternative.Web Site Problems1. What market interest rates are most widely used as base rates to price commercial loans? Where on the world wide web can you go to observe current and past levels of and changes in these market rates?After doing a search on the web, the Bloomberg site gave me the national averages for business loan rates. Their web site is /markets/rates.html. There are many other web sites out there that would also give this information or similar information. The table below lists key interest rates for business loans at the current time.Rate Current %Federal Funds 3.693 month LIBOR 3.71Prime Rate 7.002 Year AAA Industrial 4.5410 year .AAA Industrial 6.11From this information it appears that banks are most likely using the below prime market pricing (the markup) model to price their loans. These loan rates are close to the Federal Funds and LIBOR rates and are below the bank’s prime rate. Other loans to more risky customers may be priced differently.2. If you wanted to know more about the principles and procedures of business loan pricing where on the web would you go?One web site that has basic definitions for loans and may be a good place to start is/index.asp. This is the web site for Direct Loans. There are links to other sites from this one as well as frequently asked questions. A search of the web for business loan procedures may lead to other important web sites and information.。

《商业银行管理学》课后习题及题解第一章商业银行管理学导论习题一、判断题1. 《金融服务现代化法案》的核心内容之一就是废除《格拉斯－斯蒂格尔法》。

2. 政府放松金融管制与加强金融监管是相互矛盾的。

3. 商业银行管理的最终目标是追求利润最大化。

4. 在金融市场上，商业银行等金融中介起着类似于中介经纪人的角色。

5. 商业银行具有明显的企业性质，所以常用于企业管理的最优化原理如边际分享原理、投入要素最优组合原理、规模经济原理也适用于商业银行。

6. 金融市场的交易成本和信息不对称决定了商业银行在金融市场中的主体地位。

7. 企业价值最大化是商业银行管理的基本目标。

8. 商业银行管理学研究的主要对象是围绕稀缺资源信用资金的优化配置所展开的各种业务及相关的组织管理问题。

9. 商业银行资金的安全性指的是银行投入的信用资金在不受损失的情况下能如期收回。

二、简答题1. 试述商业银行的性质与功能。

2. 如何理解商业银行管理的目标？3. 现代商业银行经营的特点有哪些？4. 商业银行管理学的研究对象和内容是什么？5. 如何看待“三性”平衡之间的关系？三、论述题1. 论述商业银行的三性目标是什么，如何处理三者之间的关系。

2. 试结合我国实际论述商业银行在金融体系中的作用。

第一章习题参考答案一、判断题1.√2.×3.×4.√5.×6.√7.×8.√9.√二、略；三、略。

第二章商业银行资本金管理习题一、判断题1. 新巴塞尔资本协议规定，商业银行的核心资本充足率仍为4％。

2. 巴塞尔协议规定，银行附属资本的合计金额不得超过其核心资本的50%。

3. 新巴塞尔资本协议对银行信用风险提供了两种方法：标准法和内部模型法。

4. 资本充足率反映了商业银行抵御风险的能力。

5. 我国国有商业银行目前只能通过财政增资的方式增加资本金。

6. 商业银行计算信用风险加权资产的标准法中的风险权重由监管机关规定。

二、单选题1. 我国《商业银行资本充足率管理办法》规定，计入附属资本的长期次级债务不得超过核心资本的。