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 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 ( ) = $ © 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 © OnCourse Learning

Amortization of the Mortgage  Payment consists of interest and repayment of principal  Amortization in month 1 from the previous example:  Payment is $  Interest portion is $100,000 (.075/12) = $625  Repayment of principal portion is the remainder, $ = $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% % % %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, = $ (PVAIF i/12,360 ) i =7% 6.75% & 1 pt: 100, ,000 = $ (PVAIF i/12,360 ) i = 6.85% 17 © OnCourse Learning

Calculating The APR Cont. 6.50% & pts: 100,000-2,875= $ (PVAIF i/12,360 ) i = 6.78% 6.25% & 3 pts: 100,000-3,000= $ (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, = $ (PVAIF i/12,60 ) + $94,132 (PVIF i/12,60 ) i = 7% 6.75% & 1 pt: $100,000 - $1,000 = $ (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% & pts: $100, ,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 = $  Balance EOY5 = 94,617  EBC with no points $100, = $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 ) = $  PMT30 = $100,000 (MC 7.5/12,360 ) = $  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, © 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) = $  What is the payment for the last 20 years to fully amortize the loan? Pmt = 140,000 (MC 7/12,240 ) = $  What is the balance at the EOY20? BalEOY20 = (PVAIF 7/12, 120 ) = $93, © 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=$100,000(MC 10/26,780 )=$  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 © OnCourse Learning

Extra Payment Monthly  PMT= $100,000 (MC 7.5/12,360 ) = $  $699.21/12= $58.27 Extra paid monthly  New PMT= $ $58.27 = $  Number of payments at new payment amount  $100,000 = $ (PVAIF 7.5/12, n ) n= , approximately 23 years  Amount saved  $ ( 80.16) - $58.27 (279.84)  $56,049 - $16,306 = $39, © 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 = (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 ) = $  $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= $ ( PVAIF 7.5/12, n ) n=  Amount saved: $ (82.59) - $10,000= $47, © 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 = (PVAIF 7.375/12, 60 ) + 94,132 (PVIF 7.375/12, 60 ) 100,000 – pts = pts = $1524 or 1524/100,000 = 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 = (PVAIF 6.60/12, 360 )  100,000 – pts = 96,408  Pts = $3,592  Pts = 3,592/100,000 = 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 = (PVAIF 6.375/12, 360 ) 100,000 – 2,500 – fees = 96,102 Other Financing Fees = $1, © 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? $  What is the APR? $102,000 = $ (PVAIF i/12,360 ) APR = 6.31%  What is effective cost with 5-year holding period? $102,000 = $ (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 8% for 30 Years, Monthly Payments PMT = $100,000 ( MC 8/12,360 ) = $  If the market rate immediately goes to 10%, the market value of this mortgage goes to: PV = $ (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 ) = $ PV = $ (PVAIF 10/12,360 ) = $100,000 © OnCourse Learning 39