Chapter-4-Fixed-Rate-Mortgage-Loans(内含中文笔记)

1、Chapter 4 Fixed Rate Mortgage Loans Contents Determinants of Mortgage Interest Rate Development of Mortgage Loan Payment Patterns CPM vs. CAM Determining a Loan Balance Lenders Yield & Borrowers Borrowing Costs Other Loan PatternsObjectives of this chapter Pricing and structuring FIR mortgage lo

2、ans Rate of interest, fees, and other terms Techniques for determining the lenders yield and the borrowers cost Loan discounts, origination fees, prepayment penalties, prepaid interest 1. Determinants of Mortgage Interest Rates Sources of funds, economic growth, inflation, etc. Market rate of intere

3、st What will borrowers pay for the use of funds? What are lenders willing to accept for lending the funds? Derived demand: Demand for mortgage loans derived from demand for housing按揭贷款需求源自对房屋按揭贷款需求源自对房屋的需求的需求 Demand & supply of mortgage funds Housing Demand Factors: Number of households desiring

4、 housing Income Demographics (size, age, tastes, preference)人口统计数据人口统计数据 Mortgage Funds Supply Factors Cost of attracting funds from savers 吸引资金的成本吸引资金的成本 Cost of managing and originating loans 管理组织成本管理组织成本 Risk of potential losses 潜在损失风险潜在损失风险 Return and risk on alternative investment opportunities

5、: stock, bonds, etc. 别的机会更好别的机会更好Components of the Mortgage Interest Rate A one-year mortgage loan r = Real Rate of interestf = Inflation Ratep = Risk Premiums抵押贷款利率抵押贷款利率=通胀利率通胀利率+风险溢价风险溢价+利率利率pfrit2.Mortgage Payment Patterns Early loan payment (1930s-1940s) Large proportion of down payment require

6、ment e.g. maximum loan: 50% of housing price Short term: maximum 5 yrs “Interest only”: with full loan balance due after 5 yrs, so another loan of lesser amount would be made 5年后可以收回贷款年后可以收回贷款CAM vs. CPM Constant Amortization Mortgage (CAM) 等额等额本本金金还贷还贷 loan amortization (principal amortization) rem

7、ains the same 每期偿还的本金一样每期偿还的本金一样 monthly payment changes Constant Payment Mortgage (CPM) 等额等额本息本息还还贷贷 loan amortization changes monthly payment remains the same 每期偿还的金每期偿还的金额一样额一样 mortgage loan constant 抵押贷款常数抵押贷款常数 monthly payment/ loan amount Mortgage Payment Patterns Example 4-1 Calculating the P

8、ayment for a CPM等额等额本本息息还贷还贷 $60,000 Mortgage Loan 12% Interest 30 Years Monthly Payments=?CPMPV= $60,000 , n=30 yrs，i=0.12, PMT=? PMT=60,000.010286 =$617.17mi)mi(111PAVPMTmn12.12)12.12(111000,60PMT1230CPM （PMT不变）不变） Monthly payment PMT=$617.17 Interest paid in the first month 先求利息先求利息 (.12/12) x $6

9、0,000 = $600.00 利率利率*LB=利息利息 LB=现值现值-偿还的本金部分偿还的本金部分 Principal paid in the first month $617.17 - $600.00 = $17.17 PMT-利息利息=偿还的本金偿还的本金 LB=60000-17.17=59982.83 Every month, interest portion declines LB下降，利息下降下降，利息下降 Every month, principal portion increases. 随之偿还的本金增加随之偿还的本金增加 Exhibit 4-5, p.81CAM 等额等额本

10、金本金还贷还贷 Example 4-2 Calculating the Payment for a CAM $60,000 Mortgage Loan 12% Interest 30 Years Monthly Payments=?CAM in the 1st month （偿还本金不变）（偿还本金不变）1. Principal of the loan $60,000 will be amortized equally in 30 years. $60,000/360=$166.67 2. Interest paid in the first month $60,0001$600.00 利率利

11、率*LB=利息利息3. the first month payment: Monthly principal payment+ monthly interest $166.67+$600= $766.67CAM in the 2nd month1.Principal of the loan $60,000 will be amortized equally in 30 years. $60,000/360=$166.672.Interest paid in the second month ($60,000-$166.67)1$598.33 LB=现值-偿还的本金部分3.the second

12、month payment:Monthly principal repayment+ monthly interest $166.67+ $598.33 =$765.00 Exhibit 4-1, p.77Total interest payment in CPM & CAM1. CPM:Interest: $617.17360$60,000= $162,181.22. CAM:Interest:$600+($600-$1.67)+($600-$1.672)+($600-$1.673)+($600-$1.67359)=$600360$1.67（1+2+3+359)=$216000-$1

13、.67 (359+1) 359/2=$108,084.6Interest of CPMInterest of CAMComparing the CAM & CPM CAMHigher initial monthly paymentsMore difficult for a borrower to qualify for a loanMonthly payment declines over timeLess total interest paymentMortgage Payment PatternsCPMLower initial monthly paymentMonthly pay

14、ment remains the sameLoan balance reduced more slowly than CAMMore total interest payment than CAM PMT不变，但低，不变，但低，总利息高总利息高3. Determining a Loan Balance, p.84 Most loans are repaid before maturity Mortgage Balance (MB): Essentially “removing” the interest that was built into the payment by discountin

15、g 通过贴现剥离利息之后通过贴现剥离利息之后 Method: Compute the present value of the remaining payments (mortgage balance)Example 4-3: p.84From Example 4-1, what is the future expected loan balance at the end of 10 years? Calculating the Payment for a CPM $60,000 Mortgage Loan 12% Interest 30 Years Monthly Payments Loan

16、 will be paid off at the end of 10 yearsSolution: PMT=$617.17, i=12%, n=20mimiPMTmn)1 (11PAV1212.)1212.1 (1117.617PAV2012MBPAV= $56,051.21 Monthly loan balance factor 贷款余额系数贷款余额系数 p.85 a percentage of loan balance to the original amount MLBF=MB/ original amount =$56,051.21/$60,000 =93.42%4. Loan Clo

17、sing Costs 抵押贷款手续费抵押贷款手续费Statutory costs: government agencies for the borrowers Title closing 法定费用法定费用Recording fees, etc.Third Party Charges: 第三方费用第三方费用appraisals, surveys, inspections, title insurance, etc.Additional Finance Charges: loan origination fees 附加筹资费用附加筹资费用Expenses incurred for possessi

18、ng loan applications, loan documentation and amortization schedules, obtaining credit records 贷款费用用于补偿贷款人为受理贷款申请，准备贷款文件贷款费用用于补偿贷款人为受理贷款申请，准备贷款文件和摊销程序表，获得信用报告所带来的支出，认为应该得到补偿和摊销程序表，获得信用报告所带来的支出，认为应该得到补偿Loan Closing Costs Additional Finance Charges: fixed cost Lenders yield, i.e. borrowers costLoan ori

19、gination fees: cover origination expensesLoan discount fees 贷款贴现费贷款贴现费 termed as “Discount Points (贴现点数贴现点数)”, raise the yield on a mortgage loan1 Point = 1% of the loan amountUsed to raise the yield on the loanBorrower tradeoff : points vs. contract rate Why charge loan discount Points? “Sticky” mo

20、rtgage rates (upward and downward) Interest rates increase after lender and investor agree on the yield on mortgages to be sold yet before the loan is originated 贷款利率具有粘性贷款利率具有粘性 合同已订，利率增加合同已订，利率增加 Price the risk taken by the lenders 贷款由贷款者促贷款由贷款者促成成 Early repayment of a loan does not allow recovery

21、 of origination costs Loan Fees & Borrowing Costs Calculating the effective interest cost Example 4-4: p.87-88 Contract loan amount: $60,000 Discount Points: 3% Loan actually disbursed:$60,000(1-3%)= =$58,200 Interest rate: 12% 30 YearsContract loan amount: $60,000 Less: Origination fee: $1,800N

22、et cash disbursed by lender $58,200Monthly repayment (PMT): $617.17 Effective borrowing cost: EBC=?算算PMT的时候还是正常算，只有算到实际的时候还是正常算，只有算到实际利率的时候才是减去点数利率的时候才是减去点数mi)mi(111PAVPMTmn12i)12i(111200,58617.171230i=12.41% Rule of thumb (经验之谈经验之谈) in real estate finance: For every 2 points in the origination fee

23、charged the borrower, the effective cost to the borrower, or the yield earned by the lender, increase by approximately of a percent above the contract rate 每收两个点数就相当于在合同的利率上加上每收两个点数就相当于在合同的利率上加上0.25Truth-in-lending Act 诚实贷款法案诚实贷款法案 Lender must disclose to the borrower the annual percentage rate (APR

24、, 年比分率年比分率) )不能掩饰实际不能掩饰实际利率利率 Calculation of APR: Rounding the effective interest cost up or down to 1/8 of a percent, e.g. 12.41% APR=12.375% APR does reflect origination fees, discount points and treat them as additional income or yield to the lender 实际利率折射里费用，点数实际利率折射里费用，点数Loan cost in the case o

25、f Prepayment Example 4-5: p.89Contract loan amount: $60,000 Discount Points 3%Less: Origination fee: $1,800Net cash disbursed by lender $58,200NAR=12% Monthly repayment: $617.17 Prepaid in 5 yrsEffective interest cost of the borrower: EIC =?Relationship between yield and time Effective interest cost

26、 will equal to the contract rate when no finance charges are made 无需支付费用的时候，有效利息成本无需支付费用的时候，有效利息成本=合约利率合约利率 If finance fees are charged: 存在费用的时候存在费用的时候 effective interest cost will be higher than the contract rate 有效利息成本大于合约利率有效利息成本大于合约利率 effective interest cost (lenders yield) will increase as earl

27、y repayment occurs 越早偿还，收益率越高越早偿还，收益率越高Prepayment penaltiesPrepayment penalties提前清偿罚息提前清偿罚息 A technique to raise lenders yield Lender may be trying to recover a proportion of loan origination cost not charged to the borrower at closing (lower initial closing cost) ？ Early repayment may disturb the l

28、enders investment plan when interest rates are stable or expected to decline 扰乱贷款者的投资计划扰乱贷款者的投资计划 Prepayment penalties not included in the annual percentage rate (APR)不被包括在不被包括在APR中中Yield included Prepayment penaltiesExample 4-6: p.92Contract loan amount: $60,000 Less: Origination fee: $1,800Net cas

29、h disbursed by lender $58,200Loan balance (MB) $58,598.16 Prepayment penalties points 3%Prepayment penalties charge $1,758 (Loan balance3%) Total (FV) $60,356 Monthly repayment: $617.17 Prepaid in 5 yrsEffective interest cost: EIC=?Charging fees to achieve yield How the lenders “price” a loan? Examp

30、le 4-7, p.93 For a lender, a desired yield is 13% (EAY) n=30 yrs, NAR=12%, expected repayment at the end of 10 yrs 预期预期10年提前清偿年提前清偿 PV=-1 unit (in the view of lender, cash outflow) How much the origination fee (points) should the lender charge? PV= -0.9453 net disbursement: 94.53% of the contract lo

31、an amount Points: 5.47%4. Other Loan PatternsAssumption: all loans have been fully amortizing, i.e. loan balance is zero at maturity (FV=0)common for most single family residential loan situations 完全摊销完全摊销For income-producing property: When loan payments must be structured to fit a specific requirem

32、ent of real estate transaction, loan may call for a partial, zero, or even negative amortization pattern.4. Other Loan Patterns Partially Amortizing ( Balloon Loan ) Interest Only Loans Negative Amortization “Interest Only” Option Loans Reverse Annuity MortgagesBalloon Loan 气球贷款、期末整还式贷款气球贷款、期末整还式贷款

33、The final payment on a loan, when that payment is greater than the preceding installment payments and pays the loan in full. Balloon loans are applicable to individuals who expect a financial windfall at some point in the future. This might be due to an inheritance, a large tax refund, or an expecte

34、d dividend. (1) Partially Amortizing, Balloon Loan Example 4-8, p.93-94 PV=$60,000, n=30, i=12%, LB/FV=$40,000 (Balloon Payment) PMT=?(1) Partially Amortizing PMT=$605.72 (partially amortizing) PV Under negative amortization pattern: payments are not large enough to meet monthly interest requirement

35、s in the mortgage note. 1. Example 4-10 (a), p.95 PV=$60,000, n=30, i=12%, FV=$80,000PMT=?2. Set for desired monthly payment, then to solve the loan balance at the maturityExample 4-10 (b), p.95PV=$60,000, n=5, i=12%, PMT =$400FV=?(4)“Interest Only” Option Loans An innovation of mortgage loan which

36、gives the borrower the option of making monthly payments at interest only plus the option of making full or partial principal payments during the “interest only” period A more complicated case: Example 4-11, p.96Example 4-11, p.96 PV=$100,000, n=30 yrs, i=6% Payment scheme:First 1-2 yrs: “interest o

37、nly”; Year 3, PMT increased by $200Year 4-10, resumption of “interest only”; Year 11-30, full amortizing, loan balance (FV)=0 The payment pattern ?Loan structuring Loans can be structured to achieve many results. A process of adjusting loan terms to calibrate loan payments, loan balances, amortizati

38、on rates, etc.(5) Reverse Annuity Mortgages 反向年金抵押反向年金抵押 An innovative financial instrument designed for the retired home-owners who seek ways to supplement their retirement income. Post-war “baby boomers”: home-owners, approaching retirement 。 RAM: An arrangement in which a homeowner borrows agains

39、t the equity in his/her home and receives regular monthly payments from the lender. also called “reverse mortgage” or “home equity conversion mortgage” (房屋价值转换抵押贷款房屋价值转换抵押贷款) FRM vs. RAM In a typical FRM, you make monthly principal and interest payments. Over time, the loan balance decreases as you

40、build up equity in your home, until at the loans term you own the home. 贷款减少，抵押资产的贷款减少，抵押资产的净值增加净值增加 With a RAM, the borrower receives money for the equity in their home. As they receive money, the equity in their home declines and their loan balance increases. 抵押资产抵押资产的净值减少，贷款增加的净值减少，贷款增加Applicant

41、of RAMTo qualify for a reverse annuity mortgage the borrower or borrowers must: Own their own home with no existing mortgages or liens. Be at least 62 years of age or older.相当于把房子卖给银行，抵押的房子需要是没有贷款和留置权的，业相当于把房子卖给银行，抵押的房子需要是没有贷款和留置权的，业主至少主至少62岁。岁。The amount of money received under a RAM The specific r

42、everse annuity mortgage program that the borrower selects The type of cash advances received (for example, lump sum distribution, or monthly payments)； The borrowers age (in general, the older an individual is, the more cash they may receive) Age 62, 50% of value Age 72, 60% of value Age 82, 70% of

43、value The value of the borrowers home (the more valuable the home, the more cash the borrower will receive)RAM RAMs also require up-front costs, including origination fees (points), mortgage insurance, loan servicing fees, and other closing costs. The house remains in the elderly home owners name, s

44、o the borrowers (elderly home owners) continue to maintain the residence, pay property taxes and hazard insurance. 业业主需要继续付税务和保险主需要继续付税务和保险 Reverse mortgages will use up some or all of the equity in the elderly home owners home. This will leave less assets for a borrowers heirs to inherit. Repayment

45、 of a RAM At some point in time, a reverse mortgage must be paid off the mortgage balance and accrued interest is paid back. Repayment of a reverse mortgage typically happens when: The last owner of the property named on the loan dies The home owner(s) sell the home The home owner(s) permanently mov

46、e out of the homeExample 4-12 (a) Value of a real property $500,000 FV= -$250,000, n=10 yrs, i=10% PMT=? In Year 10, the lender will be owed $250,000; the borrower will have $250,000 ($500,000-$250,000) left in equity of the house. Example 4-12 (b) To compute loan balance of RAM, we reverse the procedure To find the loan balance at the end of Year 3, n=3 yrs, i=10%, PMT=$1220.44,