Chapter 4

Chapter 4Chapter 4

History of Real History of Real Estate Finance Estate Finance and the Fixed-and the Fixed-Rate MortgageRate Mortgage

Chapter 4Chapter 4Learning ObjectivesLearning Objectives

Understand how residential lending Understand how residential lending evolved from the earliest of times evolved from the earliest of times through World War IIthrough World War II

Understand the mechanics of the Understand the mechanics of the standard fixed-rate mortgagestandard fixed-rate mortgage

History Of Real Estate History Of Real Estate FinanceFinance

ROMAN LAWROMAN LAW– Transfer of title and possession until Transfer of title and possession until

repaymentrepayment– No transfer of title or possession. No transfer of title or possession.

Lender could take title and possession Lender could take title and possession under suspicion of defaultunder suspicion of default

– No transfer of title or possession. No transfer of title or possession. Lender could take title under actual Lender could take title under actual defaultdefault

History Of Real Estate History Of Real Estate Finance Finance

GERMAN LAWGERMAN LAW– Gage is a deposit made to fulfill an Gage is a deposit made to fulfill an

agreementagreement– Mort is French for Dead. Real property Mort is French for Dead. Real property

(not transportable) was a dead gage(not transportable) was a dead gage– In default the lender could take title In default the lender could take title

but could not look further for reliefbut could not look further for relief


ENGLISH LAWENGLISH LAW– Concept of usury in that charging Concept of usury in that charging

interest was sinfulinterest was sinful– Equitable Right Of Redemption - Equitable Right Of Redemption -

Allowing borrower to redeem the Allowing borrower to redeem the property after defaultproperty after default


U.S. law is a mix of Roman, German, And U.S. law is a mix of Roman, German, And English lawEnglish law

EARLY EXPANSIONEARLY EXPANSION– Little need for lendingLittle need for lending– Some building societies formed to Some building societies formed to

consolidate funds for home buyingconsolidate funds for home buying POST-CIVIL WARPOST-CIVIL WAR

– Increased mortgage lending to finance Increased mortgage lending to finance westward expansionwestward expansion

– Typical loan was short-term, interest-onlyTypical loan was short-term, interest-only


Early 1900s through 1920sEarly 1900s through 1920s– Federal Reserve in 1913 allowed banks Federal Reserve in 1913 allowed banks

to write 5-year, 50% loan-to-value to write 5-year, 50% loan-to-value ratio, non-amortizing mortgagesratio, non-amortizing mortgages

– Building and Loan Associations Building and Loan Associations expanded rapidlyexpanded rapidly

– Real estate prices rose rapidlyReal estate prices rose rapidly– After 1929 market crash, real estate After 1929 market crash, real estate

prices dropped dramaticallyprices dropped dramatically


1930s1930s– Market crash in 1929 ushered in the Market crash in 1929 ushered in the

Great DepressionGreat Depression– Banking system collapsed, money Banking system collapsed, money

supply plummeted, unemployment supply plummeted, unemployment soaredsoared

– Refinancing short-term, non-Refinancing short-term, non-amortizing loans became a problemamortizing loans became a problem

– A number of federal agencies created A number of federal agencies created including FSLIC (1934), FHA (1934), including FSLIC (1934), FHA (1934), and Fannie Mae (1938)and Fannie Mae (1938)

Fixed-Rate MortgagesFixed-Rate Mortgages

PRESENT VALUE OF AN ANNUITYPRESENT VALUE OF AN ANNUITYPVPVANNANN = = (1+i)(1+i)nn – 1 – 1

(i) (1+i)(i) (1+i)nn

MORTGAGE CONSTANTMORTGAGE CONSTANTMCMCii = = (i) (1+i)(i) (1+i)nn

(1+i)(1+i)nn - 1 - 1


IMPORTANT VARIABLESIMPORTANT VARIABLES– Amount BorrowedAmount Borrowed– Contract Interest RateContract Interest Rate– Maturity (Term)Maturity (Term)– Outstanding BalanceOutstanding Balance– AmortizationAmortization– PaymentPayment– Financing Costs Including Discount PointsFinancing Costs Including Discount Points– Annual Percentage Rate (APR)Annual Percentage Rate (APR)


Suppose You Borrow $100,000 @ Suppose You Borrow $100,000 @ 7.50% For 30 Years, Monthly 7.50% For 30 Years, Monthly PaymentsPayments

– What Is Your Monthly Payment To What Is Your Monthly Payment To Fully Amortize The Loan Over Its Fully Amortize The Loan Over Its Term?Term?


PMT = AMT. BORROWED (MCPMT = AMT. BORROWED (MCi,ni,n))

PMT = $100,000 (MCPMT = $100,000 (MC7.5,307.5,30))

PMT = $100,000 x PMT = $100,000 x

(.075/12) (1+.075/12)(.075/12) (1+.075/12)360 360 (1+.075/12)(1+.075/12)360360 – 1 – 1

= $100,000 (.0069921)= $100,000 (.0069921)

= $699.21= $699.21

Fixed-Rate MortgagesFixed-Rate Mortgages KEYSTROKES FOR PAYMENT CALCULATIONKEYSTROKES FOR PAYMENT CALCULATION

– Enter amount borrowed as negative PVEnter amount borrowed as negative PV– Enter the contract rate (adjusted Enter the contract rate (adjusted

monthly)monthly)– Enter the number of paymentsEnter the number of payments– Solve for payment (PMT)Solve for payment (PMT)– Caution: If your calculator is set on one Caution: If your calculator is set on one

payment per year, you must divide the payment per year, you must divide the interest rate by 12 and multiply the interest rate by 12 and multiply the years by 12. years by 12.

Fixed-Rate MortgagesFixed-Rate Mortgages LOAN AMORTIZATIONLOAN AMORTIZATION

– Payment consists of interest and repayment Payment consists of interest and repayment of principalof principal

AMORTIZATION FOR MONTH ONEAMORTIZATION FOR MONTH ONE– Payment is $699.21Payment is $699.21– Interest portion is $100,000 (.075/12) = $625Interest portion is $100,000 (.075/12) = $625– Repayment of principal portion is remainder, Repayment of principal portion is remainder,

$699.21 - 625 = $74.21$699.21 - 625 = $74.21– Each month’s interest is calculated as the Each month’s interest is calculated as the

loan balance at the beginning of the month loan balance at the beginning of the month times the monthly interest ratetimes the monthly interest rate


OUTSTANDING BALANCEOUTSTANDING BALANCE– Present value of the remaining stream of Present value of the remaining stream of

payments discounted at the contract ratepayments discounted at the contract rate FOR OUR EXAMPLE AT THE EOY 5:FOR OUR EXAMPLE AT THE EOY 5:

– Enter the payment (699.21)Enter the payment (699.21)– Enter the contract rate (.075/12)Enter the contract rate (.075/12)– Enter the number of remaining payments Enter the number of remaining payments

(300)(300)– Solve for present value (PV) ($94,617)Solve for present value (PV) ($94,617)


Annual Percentage Rate (APR)Annual Percentage Rate (APR)– The effective cost of the loan assuming The effective cost of the loan assuming

it is held for its full termit is held for its full term– Some Items Included In APR Calculation:Some Items Included In APR Calculation:

Origination Fee, Lender Inspection Origination Fee, Lender Inspection Fee, Assumption Fee, Underwriting Fee, Assumption Fee, Underwriting Fee, Tax Service Fee, Document Prep Fee, Tax Service Fee, Document Prep Fee, Prepaid Interest, Mortgage Fee, Prepaid Interest, Mortgage Insurance Premium, Discount PointsInsurance Premium, Discount Points


ContractRate

Term Disc.Points

APR PMT @100,000

5.50% 30 yrs 0.00 5.56% $567.79

5.375% 30 yrs 1.00 5.705% $559.97

5.25% 30 yrs 2.00 5.534% $552.20

5.125% 30 yrs 2.50 5.42% $544.49


ContractRate

Term Disc.Points

APR Pmt @100,000

4.875% 15 yrs 0.00 5.09% $784.30

4.75% 15 yrs 1.00 5.302% $777.83

4.625% 15 yrs 1.25 4.787% $771.40

Trade Off Between Trade Off Between Contract Rate and Contract Rate and

Discount PointsDiscount Points

Contract RateContract Rate7%7%

6.75%6.75%

6.50%6.50%

6.25%6.25%

Discount PointsDiscount Points00

1.001.00

2.8752.875

3.003.00

Calculating The APRCalculating The APR

Assumption: Borrow $100,000 for 30 Assumption: Borrow $100,000 for 30 years, monthly paymentsyears, monthly payments

7% & O pts:7% & O pts:

100,000 - 0 = $665.30 (PVAF100,000 - 0 = $665.30 (PVAFi/12,360i/12,360) ) i =7%i =7%

6.75% & 1 pt:6.75% & 1 pt:

100,000 - 1,000 = $648.60 (PVAF100,000 - 1,000 = $648.60 (PVAFi/12,360i/12,360) )

i = 6.85%i = 6.85%

Calculating The APR Calculating The APR Cont.Cont.

6.50% & 2.875 pts:6.50% & 2.875 pts:

100,000-2,875= $632.07 100,000-2,875= $632.07 (PVAF(PVAFi/12,360i/12,360) ) i = 6.78%i = 6.78%

6.25% & 3 pts:6.25% & 3 pts:

100,000-3,000= 100,000-3,000= $615.72(PVAF$615.72(PVAFi/12,360i/12,360) ) i = 6.54%i = 6.54%

Calculating the Calculating the Effective Cost Under Effective Cost Under

Shortened Holding PeriodShortened Holding Period

Assumption: Borrow $100,000 for 30 years, Assumption: Borrow $100,000 for 30 years, monthly payments, hold for five yearsmonthly payments, hold for five years

7% & 0 pts:7% & 0 pts:

$100,000 - 0 = $665.30 (PVAF$100,000 - 0 = $665.30 (PVAF i/12,60i/12,60) + ) +

$94,132 (PVF$94,132 (PVFi/12,60i/12,60) ) i = 7%i = 7%

6.75% & 1 pt:6.75% & 1 pt:

$100,000 - $1,000 = $648.60 (PVAF$100,000 - $1,000 = $648.60 (PVAF i/12,60i/12,60) )

+ $93,876 (PVF+ $93,876 (PVFi/12,60i/12,60)) i = 6.99%i = 6.99%

Calculating the Effective Calculating the Effective Cost Under Shortened Cost Under Shortened

Holding PeriodHolding Period6.50% & 2.875 pts:6.50% & 2.875 pts:

$100,000 - 2,875 = $100,000 - 2,875 =

$632.07(PVAF$632.07(PVAFi/12,60i/12,60) + $93,611(PVF) + $93,611(PVFi/12,60i/12,60)) i = 7.2%i = 7.2%

6.25% & 3 pts:6.25% & 3 pts:

$100,000 - $3,000 = $615.72(PVAF$100,000 - $3,000 = $615.72(PVAF i/12,60i/12,60) ) + $93,337(PVF+ $93,337(PVFi/12,60i/12,60)) i = 6.98%i = 6.98%

Summary of Effective Summary of Effective CostsCosts

OptionOption APRAPR 5 5 YearsYears

7% & 0 pts7% & 0 pts 7%7% 7%7%

6.75% & 1 pt6.75% & 1 pt 6.85%6.85% 6.99%6.99%

6.50% &2.875 pts6.50% &2.875 pts 6.78%6.78%7.21%7.21%

6.25% & 3 pts6.25% & 3 pts 6.54%6.54% 6.98%6.98%

Prepayment PenaltyPrepayment Penalty

Assumptions: Assumptions: $100,000 at 7.5% for 30 $100,000 at 7.5% for 30 years, monthly payments. Five percent years, monthly payments. Five percent prepayment penalty over entire term. Repay prepayment penalty over entire term. Repay at the end of year 5 at the end of year 5

PMT = $699.21PMT = $699.21 BalanceBalanceEOY5 EOY5 == 94,61794,617 Effective cost with no pointsEffective cost with no points

$100,000 - 0 = $699.21(PVAF$100,000 - 0 = $699.21(PVAFi/12,60i/12,60)+)+$94,617(1.05)(PVF$94,617(1.05)(PVFi/12,60i/12,60))

i = 8.28%i = 8.28%

Fifteen Year MortgageFifteen Year Mortgage

Borrow $100,000 at 7.50% for 15 years, Borrow $100,000 at 7.50% for 15 years, monthly paymentsmonthly payments

PMTPMT15 15 == $100,000( MC$100,000( MC7.5,157.5,15) = $927.01) = $927.01

PMTPMT30 30 = $100,000 (MC= $100,000 (MC7.5,307.5,30) = $699.21) = $699.21

Total interest over 15 year termTotal interest over 15 year term $927.01(180) - $100,000 = $66,862$927.01(180) - $100,000 = $66,862

Total interest over 30 year termTotal interest over 30 year term $699.21(360) - $100,000=$151,716$699.21(360) - $100,000=$151,716

Difference in interest paidDifference in interest paid $151,716 - $66,862 = $151,716 - $66,862 = $84,854$84,854

Extra Payment MonthlyExtra Payment Monthly

PMT= $100,000 (MCPMT= $100,000 (MC7.5,307.5,30) = $699.21) = $699.21

$699.21/12= $58.27 Extra paid monthly$699.21/12= $58.27 Extra paid monthly New PMT= $699.21 + $58.27 = $757.48New PMT= $699.21 + $58.27 = $757.48 Number of payments at new payment Number of payments at new payment

amountamount$100,000 = $757.48 (PVAF$100,000 = $757.48 (PVAF7.5/12, n7.5/12, n))

n= 279.84, approximately 23 yearsn= 279.84, approximately 23 years

Amount savedAmount saved$699.21 ( 80.16) - $58.27 (279.84)$699.21 ( 80.16) - $58.27 (279.84)

$56,049 - $16,306 = $56,049 - $16,306 = $39, 743$39, 743

Calculating Discount Calculating Discount PointsPoints

Suppose you borrow $100,000 at 7% Suppose you borrow $100,000 at 7% for 30 years, monthly payments. The for 30 years, monthly payments. The APR on the loan is 7.25%. What APR on the loan is 7.25%. What amount of points were charged?amount of points were charged?

100,000 – pts = 665.30 (PVAF100,000 – pts = 665.30 (PVAF7.25/12, 3607.25/12, 360)) 100,000 – pts = 97526100,000 – pts = 97526 Pts = $2474Pts = $2474 2474/100,000 = 2.47 points2474/100,000 = 2.47 points

Extra Payment-Lump Extra Payment-Lump SumSum

PMT= $100,000 ( MCPMT= $100,000 ( MC7.5,307.5,30) = $699.21) = $699.21 $10,000 Extra paid at the end of year 3$10,000 Extra paid at the end of year 3 BALBALEOY3EOY3 : : $97,014 $97,014

Minus extra payment: Minus extra payment: $10,000$10,000

New balanceNew balanceEOY3 EOY3 : : $87,014$87,014 Number of payments remaining after extra Number of payments remaining after extra

paymentpayment$87,014= $699.21 ( PVAF$87,014= $699.21 ( PVAF7.5/12, n7.5/12, n))

n= 241.41n= 241.41

Amount saved: Amount saved: $699.21 (82.59) - $10,000= $699.21 (82.59) - $10,000= $47,748$47,748

Calculating Discount Calculating Discount Points w/ a Shortened Points w/ a Shortened

Holding PeriodHolding Period Suppose you take a FRM for $100,000 at Suppose you take a FRM for $100,000 at

7% for 30 years, monthly payments. The 7% for 30 years, monthly payments. The effective cost with a 5-year holding effective cost with a 5-year holding period is 7.375%. What amount of period is 7.375%. What amount of discount points were charged?discount points were charged?

100,000 – pts = 665.30 (PVAF100,000 – pts = 665.30 (PVAF7.375/12, 607.375/12, 60))

+ 94,132 (PVF+ 94,132 (PVF7.375/12, 607.375/12, 60))100,000 – pts = 98476100,000 – pts = 98476pts = $1524 or 1524/100,000 = pts = $1524 or 1524/100,000 = 1.524 1.524 ptspts

Equalizing APRsEqualizing APRs

Option 1: $100,000 at 6.5% for 30 Option 1: $100,000 at 6.5% for 30 years, monthly payments. APR = years, monthly payments. APR = 6.60%6.60%

Option 2: $100,000 at 6.25% for Option 2: $100,000 at 6.25% for 30 years, monthly payments. How 30 years, monthly payments. How many points must be charged to many points must be charged to equalize the APR on the two equalize the APR on the two options?options?

Equalizing APRs (con’t)Equalizing APRs (con’t)

100,000 – pts = 615.72 (PVAF100,000 – pts = 615.72 (PVAF6.60/12, 6.60/12,

360360))

100,000 – pts = 96,408100,000 – pts = 96,408

Pts = $3,592 Pts = $3,592

Pts = 3,592/100,000 = Pts = 3,592/100,000 = 3.592 pts3.592 pts

Calculating Financing Fees Calculating Financing Fees Other Than Discount Other Than Discount

PointsPoints

You borrow $100,000 at 6% for 30 You borrow $100,000 at 6% for 30 years, mthly pmts. You pay 2.50 years, mthly pmts. You pay 2.50 discount points. Your APR is 6.375%. discount points. Your APR is 6.375%. What is the amount of your other What is the amount of your other fees?fees?100,000 – 2,500 – fees = 100,000 – 2,500 – fees =

599.55 (PVAF599.55 (PVAF6.375/12, 3606.375/12, 360))100,000 – 2,500 – fees = 96,102100,000 – 2,500 – fees = 96,102Other Financing Fees = Other Financing Fees = $1,398$1,398

Interest-Only Fixed-Interest-Only Fixed-Rate MortgageRate Mortgage

Suppose you take a $140,000, 10/20 interest-only Suppose you take a $140,000, 10/20 interest-only FRM at 7%, monthly payments.FRM at 7%, monthly payments.

What is the interest-only payment?What is the interest-only payment?Pmt = 140,000 (.07/12) = $816.67Pmt = 140,000 (.07/12) = $816.67

What is the payment for the last 20 years to fully What is the payment for the last 20 years to fully amortize the loan?amortize the loan?

Pmt = 140,000 (MCPmt = 140,000 (MC7, 207, 20) = $1085.42) = $1085.42 What is the balance at the EOY20?What is the balance at the EOY20?

BalBalEOY20EOY20 = 1085.42 (PVAF = 1085.42 (PVAF7/12, 1207/12, 120) = $93,483) = $93,483

Chapter 4

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