Chapter-4-Fixed-Rate-Mortgage-Loans(內含中文筆記)

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按揭貸款需求源自對房屋按揭貸款需求源自對房屋的需求的需求 Demand & supply of mortgage funds Housing Demand Factors: Number of households desiring

4、 housing Income Demographics (size, age, tastes, preference)人口統(tǒng)計數據人口統(tǒng)計數據 Mortgage Funds Supply Factors Cost of attracting funds from savers 吸引資金的成本吸引資金的成本 Cost of managing and originating loans 管理組織成本管理組織成本 Risk of potential losses 潛在損失風險潛在損失風險 Return and risk on alternative investment opportunities

5、: stock, bonds, etc. 別的機會更好別的機會更好Components of the Mortgage Interest Rate A one-year mortgage loan r = Real Rate of interestf = Inflation Ratep = Risk Premiums抵押貸款利率抵押貸款利率=通脹利率通脹利率+風險溢價風險溢價+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年后可以收回貸款年后可以收回貸款CAM vs. CPM Constant Amortization Mortgage (CAM) 等額等額本本金金還貸還貸 loan amortization (principal amortization) rem

7、ains the same 每期償還的本金一樣每期償還的本金一樣 monthly payment changes Constant Payment Mortgage (CPM) 等額等額本息本息還還貸貸 loan amortization changes monthly payment remains the same 每期償還的金每期償還的金額一樣額一樣 mortgage loan constant 抵押貸款常數抵押貸款常數 monthly payment/ loan amount Mortgage Payment Patterns Example 4-1 Calculating the P

8、ayment for a CPM等額等額本本息息還貸還貸 $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不變）不變） 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=現值現值-償還的本金部分償還的本金部分 Principal paid in the first month $617.17 - $600.00 = $17.17 PMT-利息利息=償還的本金償還的本金 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. 隨之償還的本金增加隨之償還的本金增加 Exhibit 4-5, p.81CAM 等額等額本

10、金本金還貸還貸 Example 4-2 Calculating the Payment for a CAM $60,000 Mortgage Loan 12% Interest 30 Years Monthly Payments=?CAM in the 1st month （償還本金不變）（償還本金不變）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=現值-償還的本金部分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不變，但低，不變，但低，總利息高總利息高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 通過貼現剝離利息之后通過貼現剝離利息之后 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 貸款余額系數貸款余額系數 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 抵押貸款手續(xù)費抵押貸款手續(xù)費Statutory costs: government agencies for the borrowers Title closing 法定費用法定費用Recording fees, etc.Third Party Charges: 第三方費用第三方費用appraisals, surveys, inspections, title insurance, etc.Additional Finance Charges: loan origination fees 附加籌資費用附加籌資費用Expenses incurred for possessi

18、ng loan applications, loan documentation and amortization schedules, obtaining credit records 貸款費用用于補償貸款人為受理貸款申請，準備貸款文件貸款費用用于補償貸款人為受理貸款申請，準備貸款文件和攤銷程序表，獲得信用報告所帶來的支出，認為應該得到補償和攤銷程序表，獲得信用報告所帶來的支出，認為應該得到補償Loan Closing Costs Additional Finance Charges: fixed cost Lenders yield, i.e. borrowers costLoan ori

19、gination fees: cover origination expensesLoan discount fees 貸款貼現費貸款貼現費 termed as “Discount Points (貼現點數貼現點數)”, 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 貸款利率具有粘性貸款利率具有粘性 合同已訂，利率增加合同已訂，利率增加 Price the risk taken by the lenders 貸款由貸款者促貸款由貸款者促成成 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的時候還是正常算，只有算到實際的時候還是正常算，只有算到實際利率的時候才是減去點數利率的時候才是減去點數mi)mi(111PAVPMTmn12i)12i(111200,58617.171230i=12.41% Rule of thumb (經驗之談經驗之談) 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 每收兩個點數就相當于在合同的利率上加上每收兩個點數就相當于在合同的利率上加上0.25Truth-in-lending Act 誠實貸款法案誠實貸款法案 Lender must disclose to the borrower the annual percentage rate (APR

24、, 年比分率年比分率) )不能掩飾實際不能掩飾實際利率利率 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 實際利率折射里費用，點數實際利率折射里費用，點數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 無需支付費用的時候，有效利息成本無需支付費用的時候，有效利息成本=合約利率合約利率 If finance fees are charged: 存在費用的時候存在費用的時候 effective interest cost will be higher than the contract rate 有效利息成本大于合約利率有效利息成本大于合約利率 effective interest cost (lenders yield) will increase as earl

27、y repayment occurs 越早償還，收益率越高越早償還，收益率越高Prepayment penaltiesPrepayment penalties提前清償罰息提前清償罰息 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 擾亂貸款者的投資計劃擾亂貸款者的投資計劃 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 預期預期10年提前清償年提前清償 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 完全攤銷完全攤銷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 氣球貸款、期末整還式貸款氣球貸款、期末整還式貸款

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” (房屋價值轉換抵押貸款房屋價值轉換抵押貸款) 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. 貸款減少，抵押資產的貸款減少，抵押資產的凈值增加凈值增加 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. 抵押資產抵押資產的凈值減少，貸款增加的凈值減少，貸款增加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.相當于把房子賣給銀行，抵押的房子需要是沒有貸款和留置權的，業(yè)相當于把房子賣給銀行，抵押的房子需要是沒有貸款和留置權的，業(yè)主至少主至少62歲。歲。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. 業(yè)業(yè)主需要繼續(xù)付稅務和保險主需要繼續(xù)付稅務和保險 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,