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Chapter 5 Fixed-Rate Mortgage Mechanics © OnCourse Learning

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Chapter 5 Learning Objectives Understand the mechanics and terms of the standard fixed-rate mortgage (FRM) Understand the basic mortgage math and the process of calculating the effective cost of a mortgage 2 © OnCourse Learning

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Mechanics of the Fixed-Rate Mortgage The 30-year, fixed-rate mortgage (FRM) has dominated the mortgage market in the US since 1930s. Characteristics: Fixed-rate Fully amortizing Level payment 3 © OnCourse Learning

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The Mortgage Payment © OnCourse Learning 4

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Fixed-Rate Mortgages – Important Variables Amount Borrowed Contract Interest Rate Maturity (Term) Outstanding Balance Amortization Payment Financing Costs Including Discount Points Annual Percentage Rate (APR) © OnCourse Learning 5

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Fixed-Rate Mortgage Payment Calculation Example Suppose you borrow $100,000 @ 7.50% for 30 years, monthly payments. What is your monthly payment to fully amortize the loan over its term? © OnCourse Learning 6

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Fixed-Rate Mortgage Payment Calculation Example – Solution PMT = amount borrowed (MC i,n ) PMT = $100,000 (MC 7.5/12,360 ) PMT = $100,000 x (.075/12) (1+.075/12) 360 (1+.075/12) 360 – 1 = $100,000 (.0069921) = $699.21 © OnCourse Learning 7

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Fixed-Rate Mortgages: Keystrokes for Payment Calculation Enter amount borrowed as PV Enter the contract rate (adjusted monthly) in percentage Enter the number of payments Solve for payment (PMT) Caution: If your calculator is set on one payment per year, you must divide the interest rate by 12 and multiply the years by 12. 8 © OnCourse Learning

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Amortization of the Mortgage Payment consists of interest and repayment of principal Amortization in month 1 from the previous example: Payment is $699.21 Interest portion is $100,000 (.075/12) = $625 Repayment of principal portion is the remainder, $699.21 - 625 = $74.21 Each month’s interest is calculated as the loan balance at the beginning of the month times the monthly interest rate 9 © OnCourse Learning

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The Outstanding Balance of the Mortgage The outstanding balance is the present value of the remaining stream of payments discounted at the contract rate For our example at the EOY 5 using financial calculator: Enter the payment: (699.21) Enter the contract rate: 7.5/12 Enter the number of remaining payments: 300 Solve for present value (PV): ($94,617) 10 © OnCourse Learning

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Factors Affecting the Contract Interest Rate An increase in the loan amount Loan term Lock-in period Down payment Discount points Credit score 11 © OnCourse Learning

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The Effective Cost of the Mortgage The effective cost of the mortgage (EBC) is the borrower’s actual percentage cost of borrowing. Affected by the loan fees charged by the lender Loan fees include – origination fee; lender inspection fee, assumption fee, underwriting fee, VA funding fee FHA MIP, tax service fee, document preparation fee, flood certification fee, prepaid interest, MIP (first year). The lender may also charge the borrower discount points. 1 point = 1% of the loan amount and it is a cash charge paid by the borrower to the lender at time of origination The annual percentage rate (APR) is the effective borrowing cost of a loan, assuming it is held to maturity. 12 © OnCourse Learning

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Fixed-Rate Mortgages © OnCourse Learning 13

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Fixed-Rate Mortgages © OnCourse Learning 14

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Trade Off Between Contract Rate and Discount Points Contract RateDiscount Points 7.00%0.000 6.75%1.000 6.50%2.875 6.25%3.000 © OnCourse Learning 15

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Calculating the APR Solve for i: Contract amount of loan – point/fees = pmt (PVAIF i/12,n ) 16 © OnCourse Learning

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Calculating The APR Assumption: Borrow $100,000 for 30 years, monthly payments 7% & 0 pts: 100,000 - 0 = $665.30 (PVAIF i/12,360 ) i =7% 6.75% & 1 pt: 100,000 - 1,000 = $648.60 (PVAIF i/12,360 ) i = 6.85% 17 © OnCourse Learning

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Calculating The APR Cont. 6.50% & 2.875 pts: 100,000-2,875= $632.07 (PVAIF i/12,360 ) i = 6.78% 6.25% & 3 pts: 100,000-3,000= $615.72 (PVAIF i/12,360 ) i = 6.54% 18 © OnCourse Learning

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Calculating the Effective Cost Under Shortened Holding Period Assumption: Borrow $100,000 for 30 years, monthly payments, hold for five years 7% & 0 pts: $100,000 - 0 = $665.30 (PVAIF i/12,60 ) + $94,132 (PVIF i/12,60 ) i = 7% 6.75% & 1 pt: $100,000 - $1,000 = $648.60 (PVAIF i/12,60 ) + $93,876 (PVIF i/12,60 ) i = 6.99% 19 © OnCourse Learning

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Calculating the Effective Cost Under Shortened Holding Period 6.50% & 2.875 pts: $100,000 - 2,875 = $632.07(PVAIF i/12,60 ) + $93,611(PVIF i/12,60 ) i = 7.2% 6.25% & 3 pts: $100,000 - $3,000 = $615.72(PVAIF i/12,60 ) + $93,337(PVIF i/12,60 ) i = 6.98% 20 © OnCourse Learning

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Summary of Effective Costs OptionAPR5 Years 7% & 0 pts7%7% 6.75% & 1 pt6.85%6.99% 6.50% &2.875 pts6.78%7.21% 6.25% & 3 pts6.54%6.98% 21 © OnCourse Learning

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Prepayment Penalty Penalty to the borrow for repaying a mortgage before maturity Increases the cost of the loan Example: $100,000 at 7.5% for 30 years, monthly payments. Five percent prepayment penalty over entire term. Repay at the end of year 5. EBC=? PMT = $699.21 Balance EOY5 = 94,617 EBC with no points $100,000 - 0 = $699.21(PVAIF i/12,60 )+$94,617(1.05)(PVIF i/12,60 ) i = 8.28% 22 © OnCourse Learning

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Fifteen Year Fixed-Rate Mortgage Common alternative to the 30-year FRM Example: Borrow $100,000 at 7.50% for 15 years, monthly payments PMT15 = $100,000( MC 7.5/12,180 ) = $927.01 PMT30 = $100,000 (MC 7.5/12,360 ) = $699.21 Total interest over 15 year term $927.01(180) - $100,000 = $66,862 Total interest over 30 year term $699.21(360) - $100,000=$151,716 Difference in interest paid $151,716 - $66,862 = $84,854 23 © OnCourse Learning

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Interest-Only Fixed-Rate Mortgage Suppose you take a $140,000, 10/20 interest-only FRM at 7%, monthly payments. What is the interest-only payment? Pmt = 140,000 (.07/12) = $816.67 What is the payment for the last 20 years to fully amortize the loan? Pmt = 140,000 (MC 7/12,240 ) = $1085.42 What is the balance at the EOY20? BalEOY20 = 1085.42 (PVAIF 7/12, 120 ) = $93,483 24 © OnCourse Learning

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Balloon/Reset FRM 30 amortization, but becomes payable (“balloons”) over a shorter term Implies partial amortization over the stated term The remaining loan balance (balloon) must be repaid at maturity Typically balloon in 5 or 7 years 25 © OnCourse Learning

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Biweekly Mortgage Paying biweekly effectively reduces the payment period for the mortgage holding the amount and the interest rate constant Alternatively holding the maturity constant the total monthly payment is lower than with monthly payment mortgage Example: Borrow $100,000 at 10% for 30 years Pmt=$100,000(MC 10/26,780 )=$404.89 With monthly amortization pmt is $977,57 26 © OnCourse Learning

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Prepayment Protection Mortgage Popular in 1940s and again in late 1980s and 1990s The borrower gives up the right to prepay the mortgage without penalty in exchange for a lower interest rate Does not preclude prepayment, but rather imposes prepayment penalty Different cost structures Freddie Mac PPM structures: Initial restricted prepayment for the first 3 years followed by a penalty of 2% of the outstanding balance after year 3. 5-year restriction and penalty of 6 months’ interest on the remaining balance if prepaid after year 5. 27 © OnCourse Learning

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Extra Payment Monthly PMT= $100,000 (MC 7.5/12,360 ) = $699.21 $699.21/12= $58.27 Extra paid monthly New PMT= $699.21 + $58.27 = $757.48 Number of payments at new payment amount $100,000 = $757.48 (PVAIF 7.5/12, n ) n= 279.84, approximately 23 years Amount saved $699.21 ( 80.16) - $58.27 (279.84) $56,049 - $16,306 = $39,743 28 © OnCourse Learning

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Calculating Discount Points Suppose you borrow $100,000 at 7% for 30 years, monthly payments. The APR on the loan is 7.25%. What amount of points were charged? 100,000 – pts = 665.30 (PVAIF 7.25/12,360 ) 100,000 – pts = 97,526 Pts = $2,474 2,474/100,000 = 2.47 points 29 © OnCourse Learning

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Extra Payment-Lump Sum PMT= $100,000 ( MC 7.5/12,360 ) = $699.21 $10,000 Extra paid at the end of year 3 BAL EOY3 : $97,014 Minus extra payment: $10,000 New balance EOY3 :$87,014 Number of payments remaining after extra payment $87,014= $699.21 ( PVAIF 7.5/12, n ) n= 241.41 Amount saved: $699.21 (82.59) - $10,000= $47,748 30 © OnCourse Learning

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Calculating Discount Points with a Shortened Holding Period Suppose you take a FRM for $100,000 at 7% for 30 years, monthly payments. The effective cost with a 5- year holding period is 7.375%. What amount of discount points were charged? 100,000 – pts = 665.30 (PVAIF 7.375/12, 60 ) + 94,132 (PVIF 7.375/12, 60 ) 100,000 – pts = 98476 pts = $1524 or 1524/100,000 = 1.524 pts 31 © OnCourse Learning

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Equalizing APRs Option 1: $100,000 at 6.5% for 30 years, monthly payments. APR = 6.60% Option 2: $100,000 at 6.25% for 30 years, monthly payments. How many points must be charged to equalize the APR on the two options? 32 © OnCourse Learning

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Equalizing APRs (con’t) 100,000 – pts = 615.72 (PVAIF 6.60/12, 360 ) 100,000 – pts = 96,408 Pts = $3,592 Pts = 3,592/100,000 = 3.592 pts 33 © OnCourse Learning

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Calculating Financing Fees Other Than Discount Points You borrow $100,000 at 6% for 30 years, mthly pmts. You pay 2.50 discount points. Your APR is 6.375%. What is the amount of your other fees? 100,000 – 2,500 – fees = 599.55 (PVAIF 6.375/12, 360 ) 100,000 – 2,500 – fees = 96,102 Other Financing Fees = $1,398 34 © OnCourse Learning

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Negative Discount Points Cash rebate from the loan underwriter to either the mortgage broker or the borrower When paid to the mortgage broker, it is referred to as the yield spread premium When paid to the borrower, it is used to defray settlement costs May be referred to as a “no-cost mortgage” Contract interest rate would be above “par” Borrowers with shorter expected holding periods should be more attracted to this loan 35 © OnCourse Learning

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Negative Discount Points Example Loan: $100,000 at 6.5% for 30 years, monthly payments. Two discount point rebate to the borrower. Assume no financing fees. What is the monthly payment? $632.07 What is the APR? $102,000 = $632.07 (PVAIF i/12,360 ) APR = 6.31% What is effective cost with 5-year holding period? $102,000 = $632.07 (PVAIF i/12,60 ) +$93,611 (PVIF i/12,60 ) I = 6.022% If “par” is 6%, is this a good deal for the borrower? 36 © OnCourse Learning

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Fixed-Rate Mortgages and Interest Rate Risk Interest rate risk- risk of loss due to changes in market interest rates Market values of fixed payment mortgages change inversely with market rate changes. © OnCourse Learning 37

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Example: Understanding Interest Rate Risk Assume: $100,000 FRM @ 8% for 30 Years, Monthly Payments PMT = $100,000 ( MC 8/12,360 ) = $733.76 If the market rate immediately goes to 10%, the market value of this mortgage goes to: PV = $733.76 (PVAIF 10/12,360 ) = $83,613 Lender loses $16,387 © OnCourse Learning 38

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Example: Understanding Interest Rate Risk If the lender can adjust the contract rate to the market rate (10%), the payment increases and the market value of the loan stays constant Pmt = $100,000 (MC 10/12,360 ) = $877.57 PV = $877.57 (PVAIF 10/12,360 ) = $100,000 © OnCourse Learning 39

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