# Chapter 5 Fixed-Rate Mortgage Mechanics © OnCourse Learning.

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Chapter 5 Fixed-Rate Mortgage Mechanics © OnCourse Learning

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

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

The Mortgage Payment © OnCourse Learning 4

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

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

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

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

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

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

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

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

Fixed-Rate Mortgages © OnCourse Learning 13

Fixed-Rate Mortgages © OnCourse Learning 14

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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