課程六 : Real Estate Financing

Flow of Real Estate Financial Capital

• The issues:• Real estate is capital intensive

• Typical capital structure is dominated by debt

• That is a major portion of the funds to purchase a home or construct an office building, etc must be borrowed

• The segment of the capital markets where these funds come from are called mortgage markets

• This sector of the debt market is by far the largest in the US and in some respect the world

Flow of Real Estate Financial Capital

• Potential developers, homeowners etc. must obtain financing in order to build, own and operate properties

• Funds are supplied by a variety of individuals, firms, institutions and government as shown in the figure

• Between the users and the sources of funds are a number of service organizations that make the raising of capital easier and more efficient

• Financial capital flows from suppliers to users in the form of debt (mortgage) and equity

• Providers of debt have priority claim on the revenue from operation• Equity holders have residual claim on cash flow

The Flow of Real Estate Financial Capital

ThriftsCommercial BanksInsurance companiesPension FundsREITsCredit UnionsGovernmentsNonfinancial businessHouseholdsForeign Investors

Mortgage BankersMortgage BrokersReal Estate BrokersInvestment BankersGovernment agenciesSyndicators

DevelopersOwners of HomesOwners of income PropertiesLand Owners

SUPPLIESOF CAPITAL

SERVICE GROUPS USERS OF CAPITAL

Equity

Debt

E

D

7.70%

8.11%6.09%

8.67%

9.34%

23.96% 36.12%

Mortgages

U.S. Government

Corporate Bonds

Consumer Credit

Bank Loans andCommercial Paper

Tax ExemptObligations

All Others3Q 1994

total: $12,309 Billion

Total Credit Outstanding in U.STotal Credit Outstanding in U.S

The Supply of Mortgage Debt • Types of lenders

– Portfolio lenders

– Non-portfolio lenders

– Depository institutions

– Contractual or non-depository institutions

– Specialized mortgage market intermediaries

• mortgage companies

• federally related agencies or GSEs

• real estate investment trusts

• Types of loans– Construction Loans

– Permanent loans

Total Mortgage Outstanding

1-4 family

Multifamily

Comm.

Farm

75.2%

16.1%

1.6%6.8%

Total $4,279 (billions, 3rd Q 1994)

Total Mortgage Debt Outstanding

• The total mortgage outstanding is around $4.3 trillion– single family mortgage debt accounts for the biggest share 75.2

% or $3.2 trillion ($3,217.5 billion)

– Commercial and multifamily accounts for roughly 23% or $1 trillion

• Residential Mortgages– Commercial banks and S&Ls are the major portfolio lenders of whole loans

– Roughly 49% or $1.6 trillion of the mortgages are securitized mainly by GNMA, FNMA FHLMC or GSEs

– GSEs hold 7.6% or $246.1 billion of whole loans

– GSEs account for roughly 57% or $1.75 trillion of 1-4 family residential mortgages

Mortgage Market Participants

Originations Servicing Holdings0

200

400

600

800

1000

Originations Servicing Holdingsthriftsmortgage CompaniesFederally Chartered CompaniesInsurance CompaniesCommercial BanksPension and Retirement FundsAll Others

In Billions of Dollars

Why Study Mortgage Market ?

• Shed light on how traditional method of financing assets by financial intermediaries is rapidly changing

• securitization is the new BIG BROTHER

• Demonstrates how financial engineering can redirect cash flows to create securities that more closely satisfy the asset/liability needs of investors

• Government agencies provide Credit guarantees for mortgage backed securities

• should government agencies continue to provide guarantee

Supply of loanable funds

• The amount of funds borrowed and lent depends on interest rates.– As rates rise many spending units save more and spend less

– Simultaneously when interest rates rise many spending units demand less credit

– The figure following illustrates the operation of supply and demand for loanable funds

– The demand schedule is downward sloping, reflecting greater willingness to borrow at lower rates.

– The supply schedule, s1, rise to the right, because people have more to lend at higher rates

– The intersection of the of the two schedules determines the amount of funds lent, f1, and the prevailing interest rate, i1

Supply and demand for loanable funds

d1

s2

s1

f1 f2

i1

i2

Amount of loanable funds

Interestrate

Real Estate Financial Instrument

• When ever real estate is financed, the property is pledged as collateral or security creating a financial instrument known either as MORTGAGE or DEED OF TRUST Power of secured debt: attempting to buy a $300 suit on credit versus obtaining $200,000 loan to build a house

– Mortgage : Two Parties– Deed of Trust : Three Parties– Promissory Note– Title Pledge

Note + Pledge

Funds

Pledge and lien are extinguished with performance of mortgage contract

MORTGAGE

Borrower(Mortgagor)

Lender(Mortgagee)

A bilateral financial contract

Note

Funds

pledgeof title

Titlegoesto borrowif nodefault

if defaultpropertyis soldand proceedsgoes tolender

DEED OF TRUST

Borrower(Trustor)

Lender(Beneficiary)

Trustee

A three-party financial contract

Important Contractual Provisions in Real Estate Financial Instruments

• Parties to the contract

• Loan amount

• Term of loan

• Interest rate

• Amortization period

• Property description

• Priority of loan

• Acceleration clause

• Escalation clause

• Prepayment clause

• callable mortgage

• non-callable mortgage

Important Contractual Provisions in real estate financial instrument

• Due-on-Sale Clause

• Default Clause (put option)

• Personal Liability Clause

• Deficiency Judgment

• Foreclosure

• Redemption Rights

– Equitable right

– Statutory right

• Escrow Provisions

Loan Termination• Termination by satisfying contract

• ending lien against pledged property• trustee provides deed of release• defeasance clause

• Termination by mutual agreement• Refinance• Recasting

• Deed in lieu of foreclosure• Termination by foreclosure

Redemption Rights

date ofdefault

Foreclosuresuite filed

Foreclosuresale

End ofStatutory period

Equitable Right of Redemption Period

Statutory Right of Redemption Period

FORECLOSURE PROCESS

Alternative mortgage contracts• Fixed Rate Mortgage (FRM)• Adjustable Rate Mortgage (ARM)• Graduated Payment Mortgage (GPM) • Shared Appreciation Mortgage (SAM)• Reverse Annuity Mortgage (RAM)• Growing Equity Mortgage (GEM)• Balloon Mortgage

Other Mortgages

• Junior Mortgage

• Purchase Money Mortgage

• Land Contract

• Wraparound Mortgage

Types of mortgage amortization

• Interest only mortgage (bullet loans)

• Partially amortizing or balloon mortgage

• Fully amortizing

Risks faced by mortgage finance intermediaries

• Credit risk:

• risk that money borrowed might not returned timely

• Default risk:

• risk that money lent might not be repaid

• Cash flow risk:

• risk that market conditions will alter scheduled cash flows

– prepayment risk

– inflation risk

– exchange risk

– interest rate risk

• Liquidity risk:

• risk that money will be needed before it is due

Mortgage Contract Rate

Generalized Mortgage Contract Rate

Rj = R* + (1-a)D + a E(P)

where:

Rj = contract interest rate on mortgage of type j.

R* = real rate of return

a = risk sharing parameter

D = risk loading

P = pure interest rate risk component

j = term of loan

a = 1

Rj = R* + E(P) Uncapped ARM or free floating rate.

0 < a < 1

Rj = R* + (1-a)D + aE(P) Capped ARM

a = 0

Rj = R* + D FRM

Contact rate = risk free rate + liquidity + default + prepayment + inflation + interest rate risk + origination and servicing cost

Mortgage Contract Rate

Mathematics of level-payment mortgages

• Mortgage investors must be able to calculate scheduled cash flows associated with mortgages.

• Servicers of mortgages must be able to calculate servicing fee

• We also need to know cash flow from mortgage pools to price MBS

Monthly Mortgage Payment• Mortgage payment requires the application of PVA

• PVA = A[1-(1+i)-n]/i– where:– A = amount of annuity– n = number of periods– PVA = present value of annuity – i = periodic interest rate

• The term in the outer bracket is called the present value of annuity factor (PVAF)

• Redefine terms for level pay mortgage

• MB0 = DS([1-(1+i)-n]/i)

– where:– DS = monthly mortgage payment– n = amortization period or term or mortgage

– MB0 = original mortgage amount

– i = simple monthly interest (annual/12)• Solving for DS gives

• DS = MB0{[i(1+i)n]/[(1+i)n -1 )]}

• The term in outer bracket is called mortgage constant or payment factor

• So what is a mortgage constant (MC)?

Illustration

• Original mortgage balance (MB0) = $100,000, term/amortization period (n) = 360 mons., interest rate (i) = 9.5 or .095/12 = .0079167

• DS = MB0{[i(1+i)n]/[(1+i)n -1 )]}• DS = $1,000,000{[.0079167(1.007967)360]/[(1.0079167)360 - 1]}

• = $100,000(.0084085) = $840.85

• Illustration using calculator:

-$100,000 = PV ; 9.5/12 = I; 30x12 = n; PMT = ?

Mortgage Balance• Mortgage Balance each period is given by the ff. formula

• MBt = MB0{[(1+i)n - (1+i)t]/[(1+i)n - 1]},

• where MB0 = mortgage balance after t months

• Example: Mortgage balance in 210th month is

• t = 210; n = 360; MB0 = $100,000; i = .095/12 = .0079167

• MB210 = 100,000{[(1.0079167)360 - (1.0079167)210]/[(1.0079167)360 - 1]} = $73,668

• Check (calculator): $840.85 = PMT 9.5/12 = i ; 150 = n PV =? $73,668

• Scheduled principal payment (Pt) is

• Pt = MB0{[i(1+i)t-1]/[(1+i)n - 1]

• Example: Scheduled principal payment for 210th month is

• P210 = {[.0079167(1.0079167)210 - 1]/[(1.0079167)360-1]}

• = 100,000{.0079167(5.19696) = $255.62

• CHECK:

• 840.85 = PMT ; 9.5/12 = i ; 13x12 = n ; PV = $75,171.72

• Balance at end of month 210 = $73,667.78

• Scheduled principal paid = $75,171.72 - $73,667.78 = $1503.94

Scheduled Principal Payment

Scheduled Interest• Scheduled interest is as follows:

• It = MB0{i[(1+i)n - (1+i)t-1]/[(1+i)n - 1]}

• where It = interest in month t

• Example: scheduled interest in month t is • I210 = 100,000{.0079167[(1.0079167)360 - (1.0079167)210 - 1]/

[(1.0079167)360 - 1]}

• = 100,000{.0079167[(17.095 - 5.19696)]/[17.095 - 1]} = $585.23

• CHECK

• Debt Service = 255. 62(p) + 585.23 (i) = $840.85

Monthly Mortgage Cash flow• If the mortgage investor services the mortgage the investor’s cash flo

w is principal, interest payment

• If the investor sells the right to service the mortgage the interest income is net of servicing fee

• Servicing fee = [MBt(servicing fee rate)]/12

• Example: assume servicing fee rate is .5%, then servicing fee for month 211 is = [(73,668)(.005)]/12 = 368.34/12 = $30.70

• Note the balance at end of month 210 ($73,668)is the beginning balance for month 211

• Net interest payment for month 211 = $583.21 - 30.70 = $552.51

Mortgage Amortization Schedule

Loan Amount = $100,000

Interest Rate = 10%

Term of Loan or amortization period = 30 yrs.

Mortgage Constant = .10608

Yearly payment

Debt Service = Loan Amount x Mortgage Constant

= 100,000 x .10608

Yearly Payment = $10,608

Amortization Schedule

A. INTEREST RATE METHOD

BOY1 principal balance = $100,000

EOY1 interest (100,000 x .1) = $10,000

EOY1 principal repaid = $608

(10,608 - 10,000)

EOY1 balance (100,000 - 608) = $99,392

BOY2 principal balance = $99,392

EOY2 interest (99,392 x .1) = $9,939.2

EOY2 principal repaid = $668.2

(10,608 - 9,939.2)

EOY2 balance (99,302 - 668.8) = $98,723.2

Amortization Schedule

Amount

Year Outstanding Payment Interest Principal

0 $100,000

1 99,392 $10,608 $10,000 $608

2 98,723.2 10,608 9,939.2 668.2

3 97,987.52 10,008 9,872.32 735.68

Amortization Schedule

B.PRESENT VALUE METHOD

Loan Amount = $100,000

Annual Interest Rate = 10%

Frequency of Payments = Monthly

Term of Loan = 30 yrs. (360 months)

Monthly Mortgage Constant = .00877572

Monthly Debt Service = 100,000 x .00877572 = $877.57

Annual Payment = 100,000 x .00877572 x 12 = $10,530.86

Amortization Schedule

BOY1 principal balance = $100,000

EOY1 balance = [PVAF 10/12, 348] x 877.57 = 113.3174 x 877.57 = $99,443.95

EOY1 prin. repaid = 100,000 - 99,443.95 = $556.05

EOY1 interest = 10,530.86 - 556.05 = $9,974.81

BOY2 principal balance = $99,443.95

EOY2 balance = [PVAF 10/12, 336] x 877.57 = 112.6176 x 877.57 = $98,829.83

EOY2 prin. repaid = 99,443.95 - 98,829.83 = $614.12

EOY2 interest = 10,530.86 - 614.12 = $9,916.74

Amortization Schedule

Amount

Year Outstanding Payment Interest Principal

0 $100,000

1 99,443.95 $10,530.86 $9,974.81 $556.05

2 98,829.83 10,530.86 9,916.74 614.12

3 98,151.47 10,530.86 9,852.50 678.36

Alternatives For Determining Mortgage Balance

1. Present value of annuity factor (PVAF)

PVAF i%, n - t

Proportion Outstanding = ---------------------------

PVAF i%, n

where

n = the period over which the loan is amortized

t = period in which balance is desired

n - t = remaining life of the loan

Alternative method of determining mortgage balance

2. Mortgage Constant (MC)

MC i%, n

Proportion Outstanding = ---------------------------

MC i%, n - t

Example

What is the proportion outstanding at the end of 10th year for a loan which is fully amortizing, with a term of 30 years, interest rate of 10%, monthly payments. The original loan amount is $100,000

PVAF 10/12%, 240 mon. 103.624619

PO = ------------------------------- = --------------- = .909380195

PVAF 10/12%, 360 mon 113.950820

Therefore balance outstanding = (.909380195)(100,000) = $90,938.02

Example

Mortgage Constant Approach

MC 10/12%, 360 mon .008776

PO = -------------------------- = ------------- = .909430051

MC 10/12%, 240 mon .009650

Proportion paid off = (1 - .909430051) = .0905699

Outstanding loan amount = 100,000x.909430051 = $90,943.0051

Alternatives for Determining %of Loan Outstanding

3. Future value of annuity factor (FVAF):

FVAF t , i

PO = 1 - ------------------------

FVAFn, i

204.844979

= 1 - --------------------- = .909380194

2260.487925

where:

FVAFt = future value of annuity factor in period t

FVAFn = future value of annuity factor in period n

t = year in which balance is desired

n = term or amortization period of loan