商业银行管理学课后习题答案及解析

《商业银行管理学》课后习题答案与解析

《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。

商业银行课后章节习题及参考答案

商业银行课后章节习题及参考答案第一章1．商业银行从传统业务发展到“金融百货公司”说明了什么问题？随着金融竞争的加剧，金融创新成为商业银行发展的关键和动力源。

这不仅表现在银行传统业务市场已被瓜分完毕，需要通过创新来挖掘新的市场和发展机会，而且对传统业务市场的竞争和重新分配也必须借助新的手段和方式。

各家商业银行纷纷利用新的科学技术、借鉴国外商业银行的先进经验，进行技术、制度和经营管理方式创新，全面拓展银行发展空间。

商业银行进行业务扩展可以分散经营风险，减少风险总量；多渠道获取利润；为社会提供全方位的金融服务；符合金融市场的运作要求内在统一性。

2．如何认识现代商业银行的作用？P5信用中介、支付中介、信用创造、金融服务3．银行组织形式有哪些？近年来，银行控股公司为什么发展迅速？P7银行的组织形式有：单一银行制、分行制和银行控股公司制（银行控股公司、非银行控股公司）金融控股公司的发展是随着全球金融自由化、市场竞争和现代信息技术在金融业广泛应用而日益兴隆的，它是现代经济发展的必然产物。

20世纪70年代中后期以来，全球范围内的放松市场监管、企业客户和个人客户的全球化发展，以及信息技术对金融业各个方面的战略性影响，使金融结构和客户结构发生了巨大变化。

各类金融机构开始向其他金融服务领域渗透，主要市场经济国家的金融业开始从分业经营体制向综合经营体制转型。

1.联合经营获得规模效应金融控股集团各子公司虽然是分业经营，但已经不是纯粹意义上的单一经营，而是互相联合起来，共同从事多种金融经营，保证集团整体效益的实现。

金融控股集团的基本作用是形成同一集团在品牌、经营战略、营销网络以及信息共享等方面的协同优势，降低集团整体的经营成本并从多元化经营中获取更多收益。

金融资产的强关联性和弱专用性，决定了其综合经营比其他行业更能形成规模经济和范围经济，而控股公司结构正是发挥这一优势的合适载体。

（产品创新、营销等）2.在当前监管体制下规避风险法人分业的作用是防止不同金融业务风险的相互传递，将风险控制在最小范围内，同时可对关联交易起到一定的遏制作用。

《商业银行管理》课后习题答案IMChap4

《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。

《商业银行管理学》课后习题答案之欧阳文创编

《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。

商业银行管理学课后题答案（第三版全）

商业银行管理学课后题答案（第三版全）商业银行：商业银行是以追求利润最大化为目标，以多种金融负债筹集资金，以多种金融资产为其经营对象，能利用负债进行信用创造，并向客户提供多功能、综合性服务的金融企业。

信用中介：是指商业银行通过负债业务，把社会上各种闲散货币资金集中到银行，通过资产业务，把它投向需要资金的各部门，充当有闲置资金者和资金短缺者之间的中介人，实现资金的融通。

作用：使闲散的货币转化为资本、使闲置资本得到充分利用、续短为长，满足这会对长期资本的需要。

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

CAMELS：美国联邦储备委员会对商业银行监管的分类检查制度，这类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）、资产（asset）、管理（management）、收益（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，可在本地或外地设有若干分支机构，并可以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大都市，下属所有分支行须由总行领导指挥。

优点：第一，有利于银行吸收存款，有利于银行扩大资本总额和经营规模，能取得规模经济效益。

第二，便于银行使用现代化管理手段和设备，提高服务质量，加快资金周转速度。

第三有利于银行调节资金、转移信用、分散和减轻多种风险。

第四，总行家数少，有利于国家控制和管理，其业务经营受地方政府干预小。

第五，由于资金来源广泛，有利于提高银行的竞争实力。

缺点：容易加速垄断的形成；并且由于其规模大，内部层次较多，使银行管理的难度增加等。

流动性：指资产变现的能力，商业银行保持随时能以适当的价格去的可用资金的能力，以便随时应付客户提存以及银行其他支付的需要。

其衡量指标有两个：一是资产变现的成本，二是资产变现的速度。

4.建立商业银行制度的基本原则有哪些？为什么要确立这些原则？答：（一）有利于银行业竞争。

《商业银行管理》课后习题答案IMChap6

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。

《商业银行管理》课后习题答案IMChap6

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。

《商业银行管理》课后习题答案IMChap21

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.。