Chapter 4

Managing Non-Interest Income & Non-Interest Expense1Issues in Interest Income & Interest ExpenseDeregulation in the 1990s lead to an increase in competition and a decrease in NIM.NIM is inversely related to bank size.

22Issues in Interest Income and Interest ExpenseCore deposit growth has slowedDisintermediationRelative loan yields have fallen dueIncreased competition for loansRefinance optionResult is lower NIM Banks must increase non-interest income (relative to non-interest expense) to grow profits

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Non-Interest IncomeSources of Non-Interest IncomeFiduciary ActivitiesDeposit Service ChargesTrading RevenueInvestment Banking/Brokerage ActivitiesInsurance CommissionsNet Servicing FeesNet Gains/Losses on Loan SalesOther Net Gains/Losses and Other Non-Interest Income

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Non-Interest IncomeAll fees are NOT created equalSome fees are stable and predictable over time, while others are highly volatile because they are cyclical Non-Interest Income has increased as a proportion of net operating revenueLargest contributors are deposit service charges and other non-interest incomeLarger banks rely more on non-interest income than their smaller counterparts

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Non-Interest IncomeDeposit Service FeesStable source of revenueRelatively price inelasticLarge banks tend to charge more for these services than small banks99NSF and Overdraft fees are relatively inelastic10

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Non-Interest ExpensePersonnel ExpenseOccupancy ExpenseGoodwill ImpairmentOther Intangible AmortizationOther Operating Expense

1212Non-Interest ExpenseKey RatiosBurden (Net Overhead Expense)Burden = Non-Interest Expense Non-Interest IncomeLower is betterNet Non-Interest MarginNet Non-Interest Margin = Burden/Average Total AssetsLower is better

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Non-Interest ExpenseKey RatiosEfficiency Ratio

Larger banks tend to have lower (better) efficiency ratios because they generate more non-interest incomeLow efficiency ratios do not always lead to higher ROEs

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Non-Interest ExpenseKey RatiosEfficiency Ratio15

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Non-Interest ExpenseKey RatiosOperating Risk Ratio

Lower is better because proportionally more income comes from fees

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Non-Interest ExpenseKey RatiosOperating Risk Ratio

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Non-Interest ExpenseKey RatiosProductivity RatiosAssets per Employee

Average Personnel Expense

Can be biased on the high side due to senior management compensation19

Non-Interest ExpenseKey RatiosProductivity RatiosDollar Amount of Loans Per Employee

Net Income Per Employee

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Non-Interest ExpenseKey RatiosProductivity Ratios21

Which Lines of Business and Customers are Profitable?Line-of-Business Profitability AnalysisRisk-Adjusted Return on Capital

Return on Risk-Adjusted Capital22

22Which Lines of Business and Customers are Profitable?Customer Profitability AnalysisAnalyses of customer profitability profiles suggest that banks make most of their profit from a relatively small fraction of customersView is that 20% of a banks customers account for 80% of profits232324

24Which Lines of Business and Customers are Profitable?Customer Profitability AnalysisExpense ComponentsNon-Credit ServicesCheck-processing expenses are the major non-credit cost item for commercial customersCredit ServicesCost of FundsLoan Administration Expense2525Which Lines of Business and Customers are Profitable?Customer Profitability AnalysisExpense ComponentsTransaction RiskRisk of fraud, theft, error, and delays in processing, clearing, and settling paymentsDefault RiskSingle largest riskBusiness Risk ExpenseLosses and allocations for potential losses

2626Which Lines of Business and Customers are Profitable?Customer Profitability AnalysisRevenue ComponentsInvestment Income from Deposit BalancesEarnings CreditNon-Interest IncomeFee IncomeLoan Interest2727Which Lines of Business and Customers are Profitable?Aggregate Profitability Results From Customer Profitability AnalysisProfitable customers maintain multiple relationships with the bankUnprofitable customers tend to shop for the lowest price and do not use multiple products

2828Which Lines of Business and Customers are Profitable?What Is The Appropriate Business Mix?Some fee income comes from relatively stable services and lines of business, while other fees are highly volatile. One problem is that some managers view these volatile fees as permanent sources of income.Community banks do not have the same opportunities to enter investment banking and specialty intermediation.

2929Which Lines of Business and Customers are Profitable?What Is The Appropriate Business Mix?

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31Which Lines of Business and Customers are Profitable?Cost Management StrategiesExpense ReductionOutsourcingOperating EfficienciesReduce costs but maintaining the existing level of products and servicesIncrease the level of output but maintaining the level of current expensesImprove workflow

3232Which Lines of Business and Customers are Profitable?Cost Management StrategiesOperating EfficienciesEconomies of ScaleEconomies of Scope

3333Which Lines of Business and Customers are Profitable?Revenue EnhancementContribution GrowthAllocates resources to best improve overall long-term profitabilityIncreases in expenses are acceptable and expected, but must coincide with greater anticipated increases in associated revenues.

3434Managing Non-Interest Income & Non-Interest Expense35The Performance of Nontraditional Banking Companies36The Performance of Nontraditional Banking CompaniesExamine:Goldman SachsInvestment bank converted to financial holding company in 2008Mutual of Omaha BankSubsidiary of Mutual of OmahaBMW Bank of North AmericaAn industrial loan corporation (ILC) owned by BMW Financial Services, a division of BMW North America37The Performance of Nontraditional Banking CompaniesFinancial Services Modernization Act (1999)Effectively allowed commercial and investment banks to merge.Investment Banking ActivitiesSecurities underwritingAdvisory servicesMarket makingPropriety trading and investing38The Performance of Nontraditional Banking Companies39

The Financial Performance of Goldman SachsSecurities UnderwritingInvestment banks assist in raising funds through the issuance of bonds or stocks. If the security offering is a first-time placementInitial Public Offering (IPO)First-time placement40The Financial Performance of Goldman SachsAdvisory ServicesInvestment banks offer numerous fee-based services that assist in managing risksPrimary services are:Providing advice concerning mergers and acquisitions and spin-offs of lines of businessManaging investable assetsMaking risk management decisions involving the uses of foreign currencies, commodities, and derivatives

41The Financial Performance of Goldman SachsMarket MakingInvestment banks may stand willing to buy securities from participants who want to sell and to sell securities to participants who want to buyProfit from the bid-ask spread. May also make a profit from the difference between the yield on the securities owned and the interest paid on debtActs as a broker and does not take ownership of the underlying security.

42The Financial Performance of Goldman SachsProprietary Trading and Principal InvestingPrincipal InvestingWhen an investment bank takes a position in a security, derivative or stock of a company with the expectation that it will hold the position for some time, possibly even years, before trading out of it43The Financial Performance of Goldman SachsProprietary Trading and Principal InvestingPrincipal InvestingHedge FundAn investment fund that is limited to a small number of sophisticated investors. The funds managers take positions that are of any type and not subject to regulation. Managers generally charge a 2 percent fee applied to the amount of assets under management plus a 20 percent performance fee equal to 20 percent of the profit generated during a year. This 2 + 20 fee structure generates an extraordinary profit for the managers with limited downside risk.44The Financial Performance of Goldman SachsProprietary Trading and Principal InvestingPrincipal InvestingPrivate Equity FundAccept investments from institutional investors in the form of limited partnership investmentsThe funds use the proceeds to buy companies and make other investments, but usually have a longer investment horizon than hedge funds when entering transactions. Fund managers earn a management fee plus a percentage (usually 20 percent) of profits in excess of some minimum rate of return.45The Financial Performance of Goldman SachsHow Did Goldman Sachs Perform in 2007?Goldman Sachs Income StatementRecord profitsEPS over $26ROE of nearly 33%4647

The Financial Performance of Goldman Sachs48

The Financial Performance of Goldman SachsHow Did Goldman Sachs Perform in 2007?Goldman Sachs Balance SheetFinancial Instruments Owned Cash and derivative securitiesCollateralized AgreementsBorrowed securities and other financial instruments purchased under an agreement to resell at a later date.Receivables Amounts owed to Goldman Sachs by brokers, the firms customers, and counterparties to derivative and other contracts. PayablesAmounts owed by Goldman Sachs4950

The Financial Performance of Goldman SachsHow Did Goldman Sachs Perform in 2007?Key Performance RatiosAlthough Goldman Sachs did well in 2007, events in 2008 demonstrated that Goldmans business model was not sustainableGoldman Sachs faced a severe liquidity crisis in 2008 due to the collapse of the housing market and declines in the values of assets that Goldman ownedIts stock price fell from over $240 per share in 2007 to under $70 in 2008In its fourth quarter of 2008, Goldman reported its first quarterly loss since it began trading as a public company51The Financial Performance of Goldman Sachs52

The Financial Performance of Goldman SachsHow Did Goldman Sachs Perform in 2007?Risk Faced by Goldman Sachs With the credit crisis of 20072009, the money and capital markets stopped functioning in any normal senseThe commercial paper market froze and large institutions were hesitant to lend to each otherLenders were hesitant to roll over their debts and Goldman was unable to sell a sufficient volume of assets to readily access cashManagement thus decided to convert to a FHC, which would allow it to access more stable, core deposits for its fundingOn the negative side, Goldman agreed to be regulated by the Federal Reserve as a bank53The Financial Performance of Goldman SachsHow Did Goldman Sachs Perform in 2007?Goldmans Risk Profile in 2007Increasing and/or high rates and widening credit spreadsMarket fluctuations that may adversely affect the value of large trading and investment positionsDeclines in the number and size of securities underwritings and mergers and acquisitions that may lower revenuesDeclines in equity values that may lower asset management feesPossible decline in the volume of transactions executed by the firm as a specialist or market makerAn increase in market volatility that may cause the firm to reduce its proprietary trading54The Financial Performance of Goldman SachsHow Did Goldman Sachs Perform in 2007?Goldmans Risk ProfileEach of the above factors appeared to be to the detriment of Goldman Sachs in 2008Goldman holds in its portfolio many different types of securities, some of which are difficult to value. Under FASB 157, Goldman Sachs is required to classify assets as Level 1, Level 2, or Level 355The Financial Performance of Goldman SachsHow Did Goldman Sachs Perform in 2007?Goldmans Risk Profile56

The Financial Performance of Mutual of Omaha BankMutual of Omaha (MO)An insurance company that offers a wide range of life, disability, long-term care, and medical supplement insurance along with annuities and mutual fundsIn 2007, the company opened Mutual of Omaha Bank (MOB), a thrift with 13 locations in Nebraska and Colorado through the acquisition and merger of three existing banksMOBs strategic objective is to acquire community banks in fast-growing cities with a high density of Mutual of Omaha insurance customers57The Financial Performance of Mutual of Omaha BankMutual of OmahaIn 2007, Mutual of Omaha had almost $20 billion in assets.Business model is to combine insurance and banking activities under the holding company5859

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The Financial Performance of Mutual of Omaha BankMutual of Omaha Banks Risk ProfileMOB faces the same types of risk that other commercial banks faceIts primary exposure is to credit riskThe principal benefit from operating as part of MO is the diversification benefit and access to capital61The Financial Performance of BMW Financial Services and BMW Bank of North AmericaIndustrial Loan Companies (ILCs)Originated in the early 1900s to make loans to borrowers who could not get loans at commercial banksOver time, ILCs were granted the right to issue deposits that were insured by the FDICToday, the majority of ILCs are based in Utah, California, Colorado, and Nevada

62Industrial Loan CompaniesHistorically, most ILCs operated to assist their parent organization in some facet of the firms core businessILCs gained notoriety when Wal-Mart applied for an ILC charter in 2005Many community banks argued against granting Wal-Mart a charter because they were concerned that Wal-Mart would offer traditional banking services in all stores and potentially drive them out of business63The Financial Performance of BMW Financial Services and BMW Bank of North AmericaIndustrial Loan CompaniesThe primary criticisms against granting commerce companies ILC charters are:There should be a separation between commerce and banking to protect customers from potential conflicts of interestFirms like Wal-Mart could become so large and powerful that they might dominant business in many communitiesILCs are not subject to the same regulation as commercial bankswhich may create safety and soundness problems64The Financial Performance of BMW Financial Services and BMW Bank of North AmericaBMW Bank of North America is an ILC owned by BMW Financial ServicesBMW Financial Services offers loans, leases, and credit cards via BMW BankAlthough BMW Bank operates from a single office in Utah, it collects deposits and uses borrowed funds to underwrite loans and leases for the purchase of automobiles at BMW dealers65The Financial Performance of BMW Financial Services and BMW Bank of North AmericaBMW Bank is chartered by the state of Utah and is also regulated by the FDIC because its deposits are FDIC insuredBMW Bank makes loans to individuals either in the form of credit card loans or loans for automobilesThe bank obtains most of it financing in the form of small time deposits and federal funds purchased66The Financial Performance of BMW Financial Services and BMW Bank of North America67

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BMW Banks Risk ProfileReported higher ROE then peersInvested proportionately more in loans than peersGets no funding from demand deposits, raising its cost of fundsEfficiency ratio is significantly lower than peersHigher charge-offs than peers69The Financial Performance of BMW Financial Services and BMW Bank of North America70

The Performance of Nontraditional Banking Companies71Pricing Fixed-Income Securities72The Mathematics of Interest RatesTermsPresent Value = PVThe value today of a single future cash flow or series of cash flowsFuture Value = FVThe amount to which a single cash flow or series of cash flows will grow over a given period of time when compounded at a given interest rate73The Mathematics of Interest RatesTermsInterest Rate Per Year = iNumber of Periods = n74Future Value and Present Value: Single PaymentSuppose you invest $1,000 for one year at 5% per year. What is the future value in one year?PV(1+i) = FV1$1,000(1.05) = $1,050

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Future Value and Present Value: Single PaymentSuppose you leave the money in for another year. How much will you have two years from now?PV(1+i)2 = FV2$1,000(1.05)2 = $1,102.50

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The Mathematics of Interest RatesFinancial Calculators can solve the equation:FV = PV(1 + i)nThere are 4 variables. If 3 are known, the calculator will solve for the 4thPMT represents multiple payments

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The Mathematics of Interest RatesHP 10BIIFuture Value

Present Value

I/YR Interest Rate per YearInterest is entered as a percent, not a decimalFor 10%, enter 10, NOT .10

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The Mathematics of Interest Rates

79HP 10BIINumber of Periods

Periods per Year

Gold C All

Clears out all TVM registersShould do between all problems

79I am providing information on the Texas Instruments BA-II Plus other calculators are similar. If you recommend or require a specific calculator other than this one, you may want to make the appropriate changes.

Note: the more information students have to remember to enter the more likely they are to make a mistake. For this reason, I normally tell my students to set P/Y = 1 and leave it that way. Then I teach them to work on a period basis, which is consistent with using the formulas. If you want them to use the P/Y function, remind them that they will need to set it every time they work a new problem and that CLR TVM does not affect P/Y.

If students are having difficulty getting the correct answer, make sure they have done the following:Set decimal places to floating point (2nd Format, Dec = 9 enter)Double check and make sure P/Y = 1Make sure to clear the TVM registers after finishing a problem (or before starting a problem) It is important to point out that CLR TVM clears the FV, PV, N, I/Y and PMT registers. C/CE and CLR Work DO NOT affect the TVM keys

The remaining slides will work the problems using the notation provided above for calculator keys. The formulas are presented in the notes section.The Mathematics of Interest Rates

80HP 10BIIGold C All (Hold down [C] button)Check P/YR

# Gold P/YRSets Periods per Year to #

Gold DISP #Gold and [=] buttonSets display to # decimal places

80I am providing information on the Texas Instruments BA-II Plus other calculators are similar. If you recommend or require a specific calculator other than this one, you may want to make the appropriate changes.

Note: the more information students have to remember to enter the more likely they are to make a mistake. For this reason, I normally tell my students to set P/Y = 1 and leave it that way. Then I teach them to work on a period basis, which is consistent with using the formulas. If you want them to use the P/Y function, remind them that they will need to set it every time they work a new problem and that CLR TVM does not affect P/Y.

If students are having difficulty getting the correct answer, make sure they have done the following:Set decimal places to floating point (2nd Format, Dec = 9 enter)Double check and make sure P/Y = 1Make sure to clear the TVM registers after finishing a problem (or before starting a problem) It is important to point out that CLR TVM clears the FV, PV, N, I/Y and PMT registers. C/CE and CLR Work DO NOT affect the TVM keys

The remaining slides will work the problems using the notation provided above for calculator keys. The formulas are presented in the notes section.The Mathematics of Interest RatesHP 10BIICash flows moving in opposite directions must have opposite signs.8181I am providing information on the Texas Instruments BA-II Plus other calculators are similar. If you recommend or require a specific calculator other than this one, you may want to make the appropriate changes.

Note: the more information students have to remember to enter the more likely they are to make a mistake. For this reason, I normally tell my students to set P/Y = 1 and leave it that way. Then I teach them to work on a period basis, which is consistent with using the formulas. If you want them to use the P/Y function, remind them that they will need to set it every time they work a new problem and that CLR TVM does not affect P/Y.

If students are having difficulty getting the correct answer, make sure they have done the following:Set decimal places to floating point (2nd Format, Dec = 9 enter)Double check and make sure P/Y = 1Make sure to clear the TVM registers after finishing a problem (or before starting a problem) It is important to point out that CLR TVM clears the FV, PV, N, I/Y and PMT registers. C/CE and CLR Work DO NOT affect the TVM keys

The remaining slides will work the problems using the notation provided above for calculator keys. The formulas are presented in the notes section.The Mathematics of Interest RatesWhat is the future value of $1000 at 5% interest per year for two years?Inputs: N = 2i = 5PV = 1000Output: FV = -1102.50

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Future Value and Present Value: Single PaymentSolving for the Rate of InterestPV(1+i)n = FVn

i = (FVn/PV)1/n -1

83Future Value and Present Value: Single PaymentSolving for the Rate of InterestSuppose we invest in a CD that promises to double our money in 8 years. What is the annual interest rate?i = ($1,800/$1,000)1/8 -1 = .0762 = 7.62%

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Future Value and Present Value: Single PaymentSolving for Present ValuePV(1+i)n = FVn

PV = FVn/(1+i)n

85Future Value and Present Value: Single PaymentSolving for Present ValueSuppose you have a choice between receiving a cash payment of $50,000 today or $60,000 in three years. If you could earn 7% on your investments, which would you choose?PV = $60,000/(1+.07)3 = $48,978

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Future Value and Present Value: Single PaymentSolving for Present ValueSince $48,978 is less than $50,000, you would prefer the $50,000 today

87Future Value and Present Value: Multiple PaymentsFuture ValueWhat is the future value of the following cash flow stream at the end of year 3?88

Future Value and Present Value: Multiple PaymentsFuture ValueWhat is the future value of the following cash flow stream at the end of year 3?

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Future Value and Present Value: Multiple PaymentsFuture ValueFind the value of each cash flow at the end of Year 3 and add them togetherCash Flow 0: FV = 7,000(1.08)3 = 8,817.98Cash Flow 1: FV = 4,000(1.08)2 = 4,665.60Cash Flow 2: FV = 4,000(1.08) = 4,320Cash Flow 3: FV = 4,000Total value in 3 years8,817.98 + 4,665.60 + 4,320 + 4,000 = 21,803.5890Future Value and Present Value: Multiple PaymentsFuture ValueFinancial Calculator SolutionStep 1: Find the PV of the cash flows

91Future Value and Present Value: Multiple PaymentsFuture ValueFinancial Calculator SolutionStep 2: Find the FV of the NPVNote: 1 difference due to rounding

92Future Value and Present Value: Multiple PaymentsPresent ValueWhat is the present value of the following cash flow stream?93

Future Value and Present Value: Multiple PaymentsPresent ValueWhat is the present value of the following cash flow stream?94

Future Value and Present Value: Multiple PaymentsPresent ValueFind the value of each cash flow today and add them together.Cash Flow 1: FV = 200/(1.12) = 178.57Cash Flow 2: FV = 400/(1.12)2 = 318.88Cash Flow 3: FV = 600(1.12)3 = 427.07Cash Flow 4: FV = 800/(1.12)4 = 508.41Total value178.57 + 318.88 + 427.07 + 508.41 = 1,432.9395Future Value and Present Value: Multiple PaymentsPresent ValueFinancial Calculator Solution

96Simple versus Compound InterestCompound InterestInterest on InterestSimple Interest No Interest on Interest97Simple versus Compound InterestSuppose is $1,000 deposited today at 5% for 2 yearsFV with Simple Interest$1,000 + $50 + $50 = $1,100FV with Compound Interest$1000(1.05)2 = $1,102.50The extra $2.50 comes from the extra interest earned on the first $50 interest payment5%* $50 = $2.50.

98Simple versus Compound InterestCompounding FrequencyCompounding Frequencyi = Nominal Interest Ratei* = Effective Annual Interest Ratem = Number of Compounding Periods in a Year

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Simple versus Compound InterestCompounding FrequencySuppose you can earn 1% per month on $100 invested today. How much are you effectively earning?i* = (1 + .12/12)12 1 i* = (1.01)12 1 = .1268 = 12.68%

100Simple versus Compound InterestCompounding FrequencyFinancial Calculator Solution

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The Relationship Between Interest Rates and Option-Free Bond PricesBond PricesA bonds price is the present value of the future coupon payments (CPN) plus the present value of the face (par) value (FV)

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The Relationship Between Interest Rates and Option-Free Bond PricesBond Prices and Interest Rates are Inversely RelatedConsider a bond which pays semi-annual interest payments of $375 with a maturity of 3 yearsIf the market rate of interest is 7.50%, the price of the bond is:

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The Relationship Between Interest Rates and Option-Free Bond PricesBond Prices and Interest Rates are Inversely RelatedFinancial Calculator Solution

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105Point out that the APR is the same in either case, but your effective rate is different. Ask them which account they should use.The Relationship Between Interest Rates and Option-Free Bond PricesBond Prices and Interest Rates are Inversely RelatedIf the market rates of interest increases to 10%, the price of the bond falls to:

106

The Relationship Between Interest Rates and Option-Free Bond PricesBond Prices and Interest Rates are Inversely RelatedFinancial Calculator Solution

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107Point out that the APR is the same in either case, but your effective rate is different. Ask them which account they should use.The Relationship Between Interest Rates and Option-Free Bond PricesBond Prices and Interest Rates are Inversely RelatedIf the market rates of interest decreases to 5%, the price of the bond rises to:

108

The Relationship Between Interest Rates and Option-Free Bond PricesBond Prices and Interest Rates are Inversely RelatedFinancial Calculator Solution

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109Point out that the APR is the same in either case, but your effective rate is different. Ask them which account they should use.The Relationship Between Interest Rates and Option-Free Bond PricesBond Prices and Interest Rates are Inversely RelatedPar BondYield to maturity = coupon rateDiscount BondYield to maturity > coupon ratePremium BondYield to maturity < coupon rate110110Point out that the APR is the same in either case, but your effective rate is different. Ask them which account they should use.The Relationship Between Interest Rates and Option-Free Bond Prices111

111Point out that the APR is the same in either case, but your effective rate is different. Ask them which account they should use.The Relationship Between Interest Rates and Option-Free Bond PricesBond Prices Change Asymmetrically to Rising and Falling RatesFor a given absolute change in interest rates, the percentage increase in an option-free bonds price will exceed the percentage decrease112112Point out that the APR is the same in either case, but your effective rate is different. Ask them which account they should use.113

The Relationship Between Interest Rates and Option-Free Bond PricesMaturity Influences Bond Price SensitivityFor bonds that pay the same coupon rate, long-term bonds change proportionally more in price than do short-term bonds for a given rate change114114Point out that the APR is the same in either case, but your effective rate is different. Ask them which account they should use.115

The Relationship Between Interest Rates and Option-Free Bond PricesThe Size of the Coupon Influences Bond Price SensitivityFor bonds that have the same maturity, long-term bonds will change proportionally more in price than short-term bonds for a given change in the rate change

116116Point out that the APR is the same in either case, but your effective rate is different. Ask them which account they should use.

117Duration and Price VolatilityDuration as an Elasticity MeasureMaturity simply identifies how much time elapses until final paymentIt ignores all information about the timing and magnitude of interim payments118118Duration and Price VolatilityDuration as an Elasticity MeasureDuration is a measure of the effective maturity of a securityDuration incorporates the timing and size of a securitys cash flowsDuration measures how price sensitive a security is to changes in interest ratesThe greater (shorter) the duration, the greater (lesser) the price sensitivity119119Duration and Price VolatilityDuration as an Elasticity MeasureDuration versus MaturityConsider the cash flows for these two securities

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120Duration and Price VolatilityDuration as an Elasticity MeasureDuration versus MaturityThe maturity of both is 20 yearsMaturity does not account for the differences in the timing of the cash flows121121Duration and Price VolatilityDuration as an Elasticity MeasureDuration versus MaturityWhat is the effective maturity of both?The effective maturity of the first security is: (1,000/1,000) x 1 = 20 yearsThe effective maturity of the second security is: [(900/1,000) x 1]+[(100/1,000) x 20] = 2.9 yearsDuration is similar, however, it uses a weighted average of the present values of the cash flows122122Duration and Price VolatilityDuration as an Elasticity MeasureDuration is an approximate measure of the price elasticity of demand

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Duration and Price VolatilityDuration as an Elasticity MeasureThe longer the duration, the larger the change in price for a given change in interest rates

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Duration and Price VolatilityMeasuring DurationDuration is a weighted average of the time until the expected cash flows from a security will be received, relative to the securitys priceMacaulays Duration

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Duration and Price VolatilityMeasuring DurationExampleWhat is the duration of a bond with a $1,000 face value, 10% coupon, 3 years to maturity and a 12% YTM?

126

Duration and Price VolatilityMeasuring DurationExampleWhat is the duration of a bond with a $1,000 face value, 10% coupon, 3 years to maturity but the YTM is 5%?

127

Duration and Price VolatilityMeasuring DurationExampleWhat is the duration of a bond with a $1,000 face value, 10% coupon, 3 years to maturity but the YTM is 20%?

128

Duration and Price Volatility129

Duration and Price VolatilityDuration of a Zero Coupon BondWhat is the duration of a zero coupon bond with a $1,000 face value, 3 years to maturity but the YTM is 12%?

By definition, the duration of a zero coupon bond is equal to its maturity

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Duration and Price VolatilityComparing Price SensitivityThe greater the duration, the greater the price sensitivity

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Duration and Price VolatilityComparing Price SensitivityWith Modified Duration, we have an estimate of price volatility:132

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Recent Innovations in the Valuation of Fixed-Income SecuritiesTraditional fixed-income valuation methods are too simplistic because:Investors often do not hold securities until maturityPresent value calculations assume all coupon payments are reinvested at the calculated Yield to MaturityMany securities carry embedded options, such as a call or put, which complicates valuation since it is unknown if the option will be exercised and at what price 134134Recent Innovations in the Valuation of Fixed-Income SecuritiesFixed-Income securities should be priced as a package of cash flows with each cash flow discounted at the appropriate zero coupon rate135135Recent Innovations in the Valuation of Fixed-Income SecuritiesTotal Return AnalysisSources of ReturnCoupon InterestReinvestment IncomeInterest-on-interestCapital Gains or Losses136136Recent Innovations in the Valuation of Fixed-Income SecuritiesTotal Return AnalysisExampleWhat is the total return for a 9-year, 7.3% coupon bond purchased at $99.62 per $100 par value and held for 5-years?Assume the semi-annual reinvestment rate is 3% and after five years a comparable 4-year maturity bond will be priced to yield 7% (3.5% semi-annually) to maturity137137Recent Innovations in the Valuation of Fixed-Income SecuritiesTotal Return Analysis138

138Money Market YieldsInterest-Bearing Loans with Maturities of One Year or LessThe effective annual yield for a loan less than one year is:

139

Money Market YieldsInterest rates on different money market instruments are measured and quoted in different termsSome money market instruments are quoted on a discount basis, while others bear interestSome yields are quoted on a 360-day year rather than a 365 or 366 day year

140140Money Market YieldsInterest-Bearing Loans with Maturities of One Year or LessAssume a 180 day loan is made at an annualized rate of 10%. What is the effective annual yield?

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Money Market Yields360-Day versus 365-Day YieldsSome securities are reported using a 360 year rather than a full 365 day yearThis will mean that the rate quoted will be 5 days too small on a standard annualized basis of 365 days142142Money Market Yields360-Day versus 365-Day YieldsTo convert from a 360-day year to a 365-day year:i365 = i360 (365/360)ExampleOne year instrument at an 8% nominal rate on a 360-day year is actually an 8.11% rate on a 365-day year:i365 = 0.08 (365/360) = 0.0811143143Money Market YieldsDiscount YieldsSome money market instruments, such as Treasury Bills, are quoted on a discount basisThis means that the purchase price is always below the par value at maturityThe difference between the purchase price and par value at maturity represents interest144144Money Market YieldsDiscount YieldsThe pricing equation for a discount instrument is:

where: idr= discount rate Po= initial price of the instrument Pf = final price at maturity or sale h= number of days in holding period

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145Money Market YieldsTwo Problems with the Discount RateThe return is based on the final price of the asset, rather than on the purchase priceIt assumes a 360-day yearOne solution is the Bond Equivalent Rate: ibe

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146Money Market YieldsA problem with the Bond Equivalent Rate is that it does not incorporate compounding. The Effective Annual Rate addresses this issue.

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147Money Market YieldsExample:Consider a $1 million T-bill with 182 days to maturity and a price of $964,500

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148Money Market YieldsYields on Single-Payment, Interest-Bearing SecuritiesSome money market instruments, such as large negotiable CDs, Eurodollars, and federal funds, pay interest calculated against the par value of the security and make a single payment of interest and principal at maturity149149Money Market YieldsYields on Single-Payment, Interest-Bearing SecuritiesExample: consider a 182-day CD with a par value of $1,000,000 and a quoted rate of 7.02%.Actual interest paid at maturity is:(0.0702)(182 / 360) $1,000,000 = $35,490The 365 day yield is:i365 = 0.0702(365 / 360) = 0.0712The effective annual rate is:

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Pricing Fixed-Income Securities152Funding the Bank153The Relationship Between Liquidity Requirements, Cash, and Funding SourcesThe amount of cash that a bank holds is influenced by the banks liquidity requirementsThe size and volatility of cash requirements affect the liquidity position of the bankDeposits, withdrawals, loan disbursements, and loan payments affect the banks cash balance and liquidity position154154155

The Relationship Between Liquidity Requirements, Cash, and Funding SourcesRecent Trends in Bank Funding SourcesBank customers have become more rate consciousMany customers have demonstrated a a strong preference for shorter-term depositsCore deposits are viewed as increasingly valuableBank often issue hybrid CDs to appeal to rate sensitive depositors156156The Relationship Between Liquidity Requirements, Cash, and Funding SourcesRecent Trends in Bank Funding SourcesRetail FundingDeposit AccountsTransaction accountsMoney market deposit accountsSavings accountsSmall time deposits157The Relationship Between Liquidity Requirements, Cash, and Funding SourcesRecent Trends in Bank Funding SourcesBorrowed FundingFederal Funds purchasedRepurchase agreementsFederal Home Loan Bank borrowings

158The Relationship Between Liquidity Requirements, Cash, and Funding SourcesRecent Trends in Bank Funding SourcesWholesale FundingIncludes borrowed funds plus large CDsEquity FundingCommon stockPreferred stockRetained earnings

159159The Relationship Between Liquidity Requirements, Cash, and Funding SourcesRecent Trends in Bank Funding SourcesVolatile (Managed) LiabilitiesFunds purchased from rate-sensitive investorsFederal Funds purchasedRepurchase agreementsJumbo CDsEurodollar time depositsForeign DepositsInvestors will move their funds if other institutions are paying higher rates160160The Relationship Between Liquidity Requirements, Cash, and Funding SourcesRecent Trends in Bank Funding SourcesCore DepositsStable deposits that customers are less likely to withdraw when interest rates on competing investments riseIncludes:Transactions accountsMMDAsSavings accountsSmall CDs161161162

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164

Characteristics of Retail-Type DepositsRetail DepositsSmall denomination (under $100,000) liabilitiesNormally held by individual investorsNot actively traded in the secondary market165Characteristics of Retail-Type DepositsTransaction AccountsMost banks offer three different transaction accountsDemand DepositsDDAsNegotiable Order of Withdrawal NOWsAutomatic Transfers from SavingsATS

166Characteristics of Retail-Type DepositsTransaction AccountsDemand DepositsChecking accounts that do not pay interestHeld by individuals, business, and governmental unitsMost are held by businesses since Regulation Q prohibits banks from paying explicit interest on for-profit corporate checking accounts

167Characteristics of Retail-Type DepositsTransaction AccountsNOW AccountsChecking accounts that pay interestATS AccountsCustomer has both a DDA and savings accountThe bank transfers enough from savings to DDA each day to force a zero balance in the DDA accountFor-profit corporations are prohibited from owning NOW and ATS accounts

168Characteristics of Retail-Type DepositsTransaction AccountsAlthough the interest cost of transaction accounts is very low, the non-interest costs can be quite highGenerally, low balance checking accounts are not profitable for banks due to the high cost of processing checks

169Characteristics of Retail-Type DepositsNontransactional AccountsNon-transaction accounts are interest-bearing with limited or no check-writing privileges

170Characteristics of Retail-Type DepositsNontransactional AccountsMoney Market Deposit AccountsPay interest but holders are limited to 6 transactions per month, of which only three can be checksAttractive to banks because they are not required to hold reserves against MMDAs

171Characteristics of Retail-Type DepositsNontransactional AccountsSavings AccountsHave no fixed maturitySmall Time Deposits (Retail CDs)Have a specified maturity ranging from 7 days on upLarge Time Deposits (Jumbo CDs)Negotiable CDs of $100,000 or moreTypically can be traded in the secondary market

172Characteristics of Retail-Type DepositsEstimating the Cost of Deposit AccountsInterest CostsLegal Reserve RequirementsCheck Processing CostsAccount ChargesNSF feesMonthly feesPer check fees

173Characteristics of Retail-Type DepositsEstimating the Cost of Deposit AccountsTransaction Account Cost AnalysisClassifies check-processing as:DepositsElectronicNon-ElectronicWithdrawalsElectronicNon-Electronic

174Characteristics of Retail-Type DepositsEstimating the Cost of Deposit AccountsTransaction Account Cost AnalysisClassifies check-processing as:Transit ChecksDepositedCashedAccount Opened or ClosedOn-Us checks cashedGeneral account maintenanceTruncatedNon-Truncated

175Characteristics of Retail-Type DepositsEstimating the Cost of Deposit AccountsTransaction Account Cost AnalysisElectronic TransactionsConducted through automatic deposits, Internet, and telephone bill paymentNon-Electronic TransactionsConducted in person or by mailTransit ChecksChecks drawn on any bank other than the bank it was deposited into176Characteristics of Retail-Type DepositsEstimating the Cost of Deposit AccountsTransaction Account Cost AnalysisOn-Us Checks CashedChecks drawn on the banks own customers accountsDepositsChecks or currency directly deposited in the customer's account Account MaintenanceGeneral record maintenance and preparing & mailing a periodic statement 177Characteristics of Retail-Type DepositsEstimating the Cost of Deposit AccountsTransaction Account Cost AnalysisTruncated AccountA checking account in which the physical check is truncated at the bank and the checks are not returned to the customerOfficial Check IssuedA check for certified funds. Net Indirect CostsThose costs not directly related to the product such as management salaries or general overhead costs178179

Characteristics of Retail-Type DepositsCalculating the Average Net Cost of Deposit AccountsAverage Historical Cost of FundsMeasure of average unit borrowing costs for existing fundsAverage Interest CostCalculated by dividing total interest expense by the average dollar amount of liabilities outstanding180Characteristics of Retail-Type DepositsCalculating the Average Net Cost of Deposit Accounts181

Characteristics of Retail-Type DepositsCalculating the Average Net Cost of Deposit AccountsExample:If a demand deposit account does not pay interest, has $20.69 in transaction costs charges, $7.75 in fees, an average balance of $5,515, and 5% float, what is the net cost of the deposit?

182

183

Characteristics of Large Wholesale DepositsWholesale LiabilitiesCustomers move these investments on the basis of small rate differentials, so these funds are labeled:Hot MoneyVolatile LiabilitiesShort-Term Non-Core funding184Characteristics of Large Wholesale DepositsWholesale LiabilitiesJumbo CDs$100,000 or moreNegotiableCan be traded on the secondary marketMinimum maturity of 7 daysInterest rates quoted on a 360-day year basisInsured up to $100,000 per investor per institutionIssued directly or indirectly through a dealer or broker (Brokered Deposits)185Characteristics of Large Wholesale DepositsWholesale LiabilitiesJumbo CDsFixed-RateVariable-RateJump Rate (Bump-up) CDDepositor has a one-time option until maturity to change the rate to the prevailing market rate

186Characteristics of Large Wholesale DepositsWholesale LiabilitiesJumbo CDsCallableZero CouponStock Market IndexedRate tied to stock market index performanceRate BoardsRepresent venues for selling non-brokered CDs via the Internet to institutional investorsRate boards help raise funds quickly and represent a virtual branch for a bank187Characteristics of Large Wholesale DepositsIndividual Retirement AccountsEach year, a wage earner can make a tax-deferred investment up to $8,000 of earned incomeFunds withdrawn before age 59 are subject to a 10% IRS penaltyThis makes IRAs an attractive source of long-term funding for banks188Characteristics of Large Wholesale DepositsForeign Office DepositsEurocurrencyFinancial claim denominated in a currency other than that of the country where the issuing bank is locatedEurodollarDollar-denominated financial claim at a bank outside the U.S. Eurodollar depositsDollar-denominated depots in banks outside the U.S.189190

Characteristics of Large Wholesale DepositsBorrowing Immediately Available FundsFederal Funds PurchasedThe term Fed Funds is often used to refer to excess reserve balances traded between banksThis is grossly inaccurate, given reserves averaging as a method of computing reserves, different non-bank players in the market, and the motivation behind many tradesMost transactions are overnight loans, although maturities are negotiated and can extend up to several weeksInterest rates are negotiated between trading partners and are quoted on a 360-day basis191Characteristics of Large Wholesale DepositsBorrowing Immediately Available FundsSecurity Repurchase Agreements (RPs or Repos)Short-term loans secured by government securities that are settled in immediately available fundsIdentical to Fed Funds except they are collateralizedTechnically, the RPs entail the sale of securities with a simultaneous agreement to buy them back later at a fixed price plus accrued interest192Characteristics of Large Wholesale DepositsBorrowing Immediately Available FundsSecurity Repurchase Agreements (RPs or Repos)Most transactions are overnightIn most cases, the market value of the collateral is set above the loan amount when the contract is negotiated. This difference is labeled the marginThe lenders transaction is referred to as a Reverse Repo193Characteristics of Large Wholesale DepositsBorrowing Immediately Available FundsStructured Repurchase AgreementsEmbeds an option (call, put, swap, cap, floor, etc.) in the instrument to either lower its initial cost to the borrower or better help the borrower match the risk and return profile of an investmentFlipper RepoCarries a floating rate that will convert, or flip, to a fixed rate after some lock-out period194Characteristics of Large Wholesale DepositsBorrowing From the Federal ReserveDiscount WindowDiscount RatePolicy is to set discount rate 1% (1.5%) over the Fed Funds target for primary (secondary) credit loansTo borrow from the Federal Reserve, banks must apply and provide acceptable collateral before the loan is grantedEligible collateral includes U.S. government securities, bankers acceptances, and qualifying short-term commercial or government paper195Characteristics of Large Wholesale DepositsBorrowing From the Federal ReserveDiscount Rate

196Current Interest Rates 9/09/2009Primary Credit0.50%Secondary Credit1.00%Seasonal Credit0.25%Fed Funds Target0 - 0.25%Characteristics of Large Wholesale DepositsBorrowing From the Federal ReservePrimary CreditAvailable to sound depository institutions on a short-term basis to meet short-term funding needs197Characteristics of Large Wholesale DepositsBorrowing From the Federal ReserveSecondary CreditAvailable to depository institutions that are not eligible for primary creditAvailable to meet backup liquidity needs when its use is consistent with a timely return to a reliance on market sources of funding or the orderly resolution of a troubled institution198Characteristics of Large Wholesale DepositsBorrowing From the Federal ReserveSeasonal CreditDesigned to assist small depository institutions in managing significant seasonal swings in their loans and deposits199Characteristics of Large Wholesale DepositsBorrowing From the Federal ReserveEmergency CreditMay be authorized in unusual and exigent circumstances by the Board of Governors to individuals, partnerships, and corporations that are not depository institutions200Characteristics of Large Wholesale DepositsOther Borrowing from the Federal ReserveTerm Auction FacilityAllows banks to bid for an advance that will generally have a 28-day maturityBanks must post collateral against the borrowings and cannot prepay the loan201201Characteristics of Large Wholesale DepositsOther Borrowing from the Federal ReserveTerm Securities Lending FacilityA facility in which the Open Market Trading Desk of the Federal Reserve Bank of New York makes loans to primary securities dealers202Characteristics of Large Wholesale DepositsFederal Home Loan Bank AdvancesThe FHLB system is a government-sponsored enterprise created to assist in home buyingThe FHLB system is one of the largest U.S. financial institutions, rated AAA because of the government sponsorshipAny bank can become a member of the FHLB system by buying FHLB stockIf it has the available collateral, primarily real estate related loans, it can borrow from the FHLBFHLB advances have maturities from 1 day to as long as 20 years

203204

Electronic MoneyIntelligent CardContains a microchip with the ability to store and secure informationMemory CardSimply store information

205Electronic MoneyDebit CardOnlinePIN basedTransaction goes through the ATM systemOfflineSignature based transactionsTransaction goes through the credit card system

206Electronic MoneyElectronic Funds Transfer (EFT)An electronic movement of financial data, designed to eliminate the paper instruments normally associated with such funds movementTypes of EFTACH: Automated Clearing HousePOS: Point of SaleATMDirect DepositTelephone Bill PayingAutomated Merchant Authorization SystemsPreauthorized Payments

207208

Check 21Check Clearing for the 21st Century Act Facilitates check truncation by reducing some of the legal impedimentsFoster innovation in the payments and check collection system without mandating receipt of check in electronic formImprove the overall efficiency of the nations payment system

209Check 21Check TruncationConversion of a paper check into an electronic debit or image of the check by a third party in the payment system other than the paying bankFacilitates check truncation by creating a new negotiable instrument called a substitute check

210Check 21Substitute CheckThe legal equivalent of the original check and includes all the information contained on the originalCheck 21 does NOT require banks to accept checks in electronic form nor does it require banks to create substitute checksIt does allow banks to handle checks electronically instead of physically moving paper checks

211212

Check 21Check Clearing ProcessBanks typically place a hold on a check until it verifies that the check is goodExpedited Funds Availability ActUnder Reg CC, it states that:Local check must clear in no more than two business daysNon-local checks must clear in no more than five business daysGovernment, certified, and cashiers checks must be available by 9 a.m. the next business day

213214

Measuring the Cost of FundsAverage Historical Cost of FundsMany banks incorrectly use the average historical costs in their pricing decisionsThe primary problem with historical costs is that they provide no information as to whether future interest costs will rise or fall.Pricing decisions should be based on marginal costs compared with marginal revenues

215Measuring the Cost of FundsThe Marginal Cost of FundsMarginal Cost of DebtMeasure of the borrowing cost paid to acquire one additional unit of investable fundsMarginal Cost of EquityMeasure of the minimum acceptable rate of return required by shareholdersMarginal Cost of FundsThe marginal costs of debt and equity

216Measuring the Cost of FundsThe Marginal Cost of FundsCosts of Independent Sources of FundsIt is difficult to measure marginal costs preciselyManagement must include both the interest and noninterest costs it expects to pay and identify which portion of the acquired funds can be invested in earning assets

217Measuring the Cost of FundsThe Marginal Cost of FundsCosts of Independent Sources of FundsMarginal costs may be defined as :

218

Measuring the Cost of FundsThe Marginal Cost of FundsCosts of Independent Sources of FundsExample:Market interest rate is 2.5%Servicing costs are 4.1% of balancesAcquisition costs are 1.0% of balancesDeposit insurance costs are 0.25% of balancesNet investable balance is 85% of the balance (10% required reserves and 5% float)

219Measuring the Cost of FundsThe Marginal Cost of FundsCosts of Independent Sources of FundsExample:

220

Measuring the Cost of FundsThe Marginal Cost of FundsCosts of Independent Sources of FundsCost of DebtEquals the effective cost of borrowing from each source, including interest expense and transactions costsThis cost is the discount rate, which equates the present value of expected interest and principal payments with the net proceeds to the bank from the issue

221Measuring the Cost of FundsThe Marginal Cost of FundsCosts of Independent Sources of FundsCost of DebtExample:Assume the bank will issue:$10 million in par value subordinated notes paying $700,000 in annual interest and a 7-year maturityIt must pay $100,000 in flotation costs to an underwriterThe effective cost of borrowing (kd) is 7.19%

222Measuring the Cost of FundsThe Marginal Cost of FundsCosts of Independent Sources of FundsCost of DebtExample:

223

Measuring the Cost of FundsThe Marginal Cost of FundsCosts of Independent Sources of FundsCost of EquityThe marginal cost of equity equals the required return to shareholdersIt is not directly measurable because dividend payments are not mandatory224Measuring the Cost of FundsThe Marginal Cost of FundsCosts of Independent Sources of FundsCost of EquitySeveral methods are commonly used to approximate this required return:Dividend Valuation ModelCapital Asset Pricing Model (CAPM)Targeted Return on Equity ModelCost of Debt + Risk Premium

225Measuring the Cost of FundsThe Marginal Cost of FundsCosts of Independent Sources of FundsCost of Preferred StockPreferred stock acts as a hybrid of debt and common equityClaims are superior to those of common stockholders but subordinated to those of debt holdersPreferred stock pays dividends that may be deferred when management determines that earnings are too low. The marginal cost of preferred stock can be approximated in the same manner as the Dividend Valuation Model however, dividend growth is zero

226Measuring the Cost of FundsThe Marginal Cost of FundsCosts of Independent Sources of FundsTrust Preferred StockTrust preferred stock is attractive because it effectively pays dividends that are tax deductibleThis loan interest is tax deductible such that the bank effectively gets to deduct dividend payments as the preferred stock

227Measuring the Cost of FundsWeighted Marginal Cost of Total FundsThis is the best cost measure for asset-pricing purposesIt recognizes both explicit and implicit costs associated with any single source of funds

228Measuring the Cost of FundsWeighted Marginal Cost of Total FundsIt assumes that all assets are financed from a pool of funds and that specific sources of funds are not tied directly to specific uses of funds

229

230

Funding Sources and Banking RisksBanks face two fundamental problems in managing liabilities. Uncertainty over:What rates they must pay to retain and attract fundsThe likelihood that customers will withdraw their money regardless of rates

231Funding Sources and Banking RisksFunding Sources: Liquidity RiskThe liquidity risk associated with a banks deposit base is a function of:The competitive environmentNumber of depositorsAverage size of accountsLocation of the depositorSpecific maturity and rate characteristics of each account232Funding Sources and Banking RisksFunding Sources: Liquidity RiskInterest ElasticityHow much can market interest rates change before the bank experiences deposit outflows?If a bank raises its rates, how many new funds will it attract?Depositors often compare rates and move their funds between investment vehicles to earn the highest yields It is important to note the liquidity advantage that stable core deposits provide a bank233Funding Sources and Banking RisksFunding Sources: Interest Rate RiskMany depositors and investors prefer short-term instruments that can be rolled over quickly as interest rates changeBanks must offer a substantial premium to induce depositors to lengthen maturitiesThose banks that choose not to pay this premium will typically have a negative one-year GAP 234Funding Sources and Banking RisksFunding Sources: Interest Rate RiskOne strategy is to aggressively compete for retail core depositsIndividual are not as rate sensitive as corporate depositors and will often maintain their balances through rate cycles as long as the bank provides good service

235Funding Sources and Banking RisksFunding Sources: Credit and Capital RiskChanges in the composition and cost of bank funds can indirectly affect a banks credit risk by forcing it to reduce asset quality For example, banks that substitute purchased funds for lost demand deposits will often see their cost of funds rise Rather than let their interest margins deteriorate, many banks make riskier loans at higher promised yields While they might maintain their margins in the near-term, later loan losses typically rise with the decline in asset quality236Funding the Bank237PV

FV

5%

0

1

$1,000

$1,050

0

2

$1,000

$1,102.50

PV

FV

5%

1

N

I/YR

PV

PMT

FV

FV

PV

I/YR

N

P/YR

C

Gold

C

Gold

Gold

#

P/YR

Gold

#

DISP

N

I/YR

PV

PMT

FV

2

5

100

-1102.50

N

I/YR

PV

PMT

FV

8

7.62

-1,000

1,800

N

I/YR

PV

PMT

FV

3

7

60,000

-48,978

8%

0

1

2

3

4,000

4,000

4,000

7,000

0

1

2

3

4,000

4,000

4,000

7,000

8%

?

?

?

?

FV =

CFj

7,000

CFj

4,000

CFj

4,000

CFj

4,000

I/YR

8

NPV

Gold

17,308.39

N

I/YR

PV

PMT

FV

3

8

17,308.39

-21,803.59

1

2

200

12%

PV = ?

400

3

4

800

600

1

2

200

12%

400

3

4

800

600

?

?

?

?

?

0

CFj

0

CFj

200

CFj

400

CFj

600

I/YR

12

NPV

Gold

1,432.93

CFj

800

Gold

P/YR

12

Gold

NOM%

12

EFF%

Gold

12.6825

N

I/YR

PV

PMT

FV

6

?

350

10,000

7.5

Gold

P/YR

2

N

I/YR

PV

PMT

FV

6

-9,365.54

375

10,000

10

Gold

P/YR

2

N

I/YR

PV

PMT

FV

6

-10,688.52

375

10,000

5

Gold

P/YR

2

0

5

10

15

20

$1,000

0

5

900

10

15

20

1

$100