GEK2013 Real Estate Finance

QUICK REFERENCE GUIDE GEK2013 – REAL ESTATE FINANCE

Chapter 1: Overview of Real Estate Finance

Definitions:

Real Estate Land and all natural part of the land and attachments to the land e.g. buildings, etc

Real Property All rights, interests and benefits related to ownership of real estate

Real Estate Finance

The study of the institutions, markets and instruments used to transfer money and credit for purpose of developing or acquiring real property

- Contract results in mutual benefits- Inherent risks to one/both parties

See Notes for Overview of Capital Market

1

Real Property

Real Estate (physical)

Land

Air Rights

Surface Rights

Mineral Rights

Fixtures

ImprovementsTo-the-land

On-the-land

Ownership rights (legal)

Right to Use

Right to Possess

Right to exclude ppl

Right to dispose

Characteristics (Read notes):- Physical- Institutional- Economic

Real Estate Market

Space Market (Tangible)Supply: Property OwnersDemand: Property Users

Asset Market (Intangible)Supply: Investors willing to sell

Demand: Investors willing to buy


Chapter 2: Institutions & Instruments of Financial Markets

Financial Assets Legal claim to future cash flow

Financial Market Forum for trading funds where suppliers and demanders of funds interact to transact business

Money Market Arena for trading short-term funds e.g. marketable securities

Capital Market Forum for trading in equity and long term debts e.g. long-term securities

Real Estate Financial Market

Forum for trading legal claims to future cash from real estate assets

Financial Assets

Properties of Financial Assets: See Notes for full explanation

- Moneyness - Divisibility - Reversibility - Term to maturity - Liquidity- Convertibility - Currency - Cash flow & Return

Predictability- Complexity - Tax Status

Role of Financial Assets

- Transfer funds from those with surplus to invest on those who needs funds.- Redistribute risk generated by tangible assets among seekers and providers of funds

Financial Markets

Major Institutions in financial markets

- Households - Governments - Nonfinancial Corporations- Depository institutions (banks) - Insurance companies - Asset management firms- Investment banks - Non-profit organizations - Foreign investors

Service Provided by Financial Institutions

- Transform financial assets into a different, and more widely preferable type of asset- Exchange financial assets both for customers and own account- Assist in creation of financial assets for customers and selling these assets - Provide investment advice and manage portfolio of other market participants

Instruments of Financial Markets (Asset Class)

- Common Stock - Bondso Residential MBSo Commercial MBSo CDOs

- Derivatives (Value depends on assets)

Financial Intermediaries

Role of Financial Intermediaries

- Flow of funds for Financial Institutions & Markets- Transform less desirable financial assets into other financial assets preferred by public by: (See Notes)

o Maturity Intermediationo Risk reduction via diversification (doesn’t work, only redistribute but not reduce risk)o Reducing costs of contracting the information processingo Providing payment mechanism

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Chapter 5: Mortgage Markets I

Mortgage Special form of debt that uses real estate as a security for the loanGives lender a lien on the property- If property is sold, owner not entitled to cash proceeds until loan amount and interest

accrued have been paid off- Owner’s interest subordinate to lender’s interest

Mortgage document

Pledges the property as collateral for the loan

Promissory Note Written document of agreement detailing financial and legal details of transactionSee Notes for its contents

Mortgage Loan A contractual document that protects mortgagee’s interest w.r.t. 3rd party claims on collateralClarify purposes and proof of borrower’s and lender’s intent

Mortgagor – Borrower Mortgagee – Lender

Default and Foreclosure

Lien A charge upon the property for the discharge of a debtLien status – Indicates loan’s seniority in the event of a foreclosure

Delinquency Non-payment of a mortgage payment due

Default - Occurs when borrower fails to perform one or more duties under terms of note- Occurs when borrower missed 90 days’ installment

Acceleration Clause

Provision that enables lender to demand payment of entire outstanding when first monthly payment is missed

Due-on-sale Clause Provision allowing lender to demand full repayment if borrower sells property

Foreclosure - Judicial foreclosure: Obtain court order to sell- Non-judicial foreclosure: trustee sale without court order- Notice of foreclosure- Public auction followed by private sale if property wasn’t sold

Loan Terminology

Loan-to-value ratioLTV= Loan

min (Market Value of Property , Selling Price of Property)Loan Principal - Amount actually borrowed

- Remaining Balance of loan

Debt Service Periodic payments for interest and principal

Interest Rate Rate charged for use of money

Market i/r Rate that clears the market for loanable funds

Contracted i/r Rate specified in contract for purpose of calculating interest charges

Nominal i/r Rate stated in a particular currency

Real i/r Rate in purchasing power

Loan Duration Time given to borrower to repay loan

Loan Amortization Regular, periodic repayment of principal

Mortgage Interest Rate (See Notes for Demand VS Supply)

it=r1+ p1+ f 1

3

r1, Real rate of Interest

f 1, Inflation Expectation

p1, Risk Premiums


Amortization Scheme

Constant Payment Mortgage: Loan is fully amortized with level paymentsGraduated Payment Mortgage: Loan is fully amortized with rising paymentsConstant Amortization Mortgage: Loan balance reduced by a constant amount each period

Borrower took on a $500,000 loan at 5% interest for 30yearsConstant Payment Mortgage Constant Amortization Mortgage1) Compute Monthly Debt Service

PV=500,000 ;n=360 ; i=5%12

; FV=0

PMT=$2,684.112) Compute Loan Outstanding End of Month1

PMT=2,684.11 ;n=359 ; i=5%12

; FV=0

PV=499,399.233) Difference between PV is the Principal Paid

Principal Paid=$ 600.774) Difference between principal payment and PMT

is Interest PaymentInterest Paid=$2,083.33

5) Repeat for all 360 months

1) Compute constant amortization amount

Amortization=500,000360

¿ $1,388.89

2) Compute monthly interest on loan balance

imonth1=500,000×5%12

¿ $2,083.33

imonth2=498,611.11×5%12

¿ $2,077.55

3) Compute Total Month’s PaymentM 1=1388.89+2083.33¿ $3,472.22

4) Repeat for all 360 months

$60,000 loan for 30years at 12% interest. 3% origination fee and 3% prepayment penalty on outstanding balance.

Loan Fees and Borrowing Costs

1) Compute monthly loan payments

PV=60,000 ;n=360 ; i=12%12

; FV=0PMT=$617.17

2) Calculate net cash disbursed (Loan amount – Origination fee / Discount points = Net disbursed)Net cash disbursed=60,000× (1−3%)¿58,200

3) Compute effective i/rPV=−58,200 ;n=360 ;PMT =617.17i=1.034%

Early repayments and Prepayment Penalty

- Loan Balance EOY5 = $58,597.93- Outstanding + Prepayment Penalty = 1.03% × $58,597.93 = $60,355.87- Monthly Debt Service = $617.17- Net Cash Disbursed = $58,200- Holding period = 5 years

PV=−58,200 ; FV=60,355.87 , PMT=617.17 ;n=60i=1.1043%

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Monthly

Simple


Chapter 6: Alternative Mortgage Instruments

Type Usage MathematicsAdjustable-Rate Mortgage See Notes for ARM Variables and Index

Allows lender to adjust contract i/r to reflect changes in market i/r. Change in rate reflected by change in monthly payment

in=min (Index+Margin , in−1+Cap)

Loan Amount = $100,000Index = 1 year Margin = 2.50Term = 30 years2/6 i/r capsTeaser Rate = 5%

See Notes for computation

Graduated-Payment Mortgage

Graduated Payment Mortgage designed to offset tilt effect by lowering payments on an FRM early on and increasing over time

Price-Level Adjusted Mortgage

Solves tilt problem and interest rate risk by separating real rate of return and inflation rate:

i=constant ror+inflationrate

$100,000 30years, 6% interest

PMT in Year 14% inflation PV=100,000 ;n=360 ; i=6%

12PMT=$599.55

Year 24% inflation PV=98,772×1.04 ;n=348 ; i=6%

12PMT=$625.53

Year 3-3% inflation PV=101,366×0.97 ;n=336 ; i=6%

12PMT=$604.83

Year 42% inflation PV=96,929×1.02;n=324 ; i=6%

12PMT=$616.92

Year 5-30 0% inflation PV=98,868 ;n=312 ; i=6%

12PMT=$612.92

Shared Appreciation Mortgage

Low initial contract rate with inflation collected in a lump sum based on house price appreciation

Appreciation amt. computed when house is sold or appraised in future

a=V−β1−t

, a : shareof appreciation ,V :LTV , β :reduction∈loan∫¿

t : lende r ' s tax rateReverse Annuity Mortgage

Borrower receives a series of payments and repays in a lump sum at some future time i.e. Reverse Mortgage

$200,000 at 9% for 5 years, annual paymentsn=5 ; i=9% ; FV=200,000PMT=$33,418.49

Pledged Account Combines a deposit with lender and fixed rate loan to form a graduated-payment structure

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Mortgage / Flexible Loan Insurance Program

Deposit in pledged as collateral

Type Advantages DisadvantagesFixed Rate Mortgage

- Future housing costs are known with relative certainty - Young households with lower incomes may not qualify for loans with the different ratios in play / Interest rates will be higher for those on mortgages with unstable payments

- Default rates are generally low, simplicity and standardization encourage securitization, easier to police

- Default rates are lower because payment shocks are avoided

- Exposes lenders with short-term liabilities to severe interest rate risk

Adjustable-Rate Mortgage

- If interest rates are expected to fall in the future, good for borrowers

- Provides lower initial rate and payment than FRMs

- Greater uncertainty about future mortgage payments- Difficult to understand. Subject to possible large increases in future

payment - Allows lenders with short-term liabilities to manage interest rate

risk- Default rates are higher than on FRMs. Diversity discourages

securitizationGraduated-Payment Mortgage

- Future housing costs are known with relative certainty - Easier to qualify for lower income households to take advantage of

future earning power- Lower monthly payments early in mortgage

- Interests larger than fixed rate mortgage to make up for the risk of rising mortgage outstanding

- Payments will be higher in later stages of the loan (must be confident that income will rise)

- Default rates are lower because payment shocks are avoided- Solves tilt effect

- Long duration makes management of interest rate risk difficult - Negative amortization

Price-Level Adjusted Mortgage

- While borrowers may face large payments at end of mortgage, its actual buying power is similar to initial payment if real income increases, then burden is reduced

- Interest rates changes doesn’t reflect changes in income levels- Mortgage balance increases faster than price appreciation-

- Lenders are protected against sudden inflation and enjoy relatively constant rates of returns

- Solves tilt effect and interest rate risks

- Sudden inflation would result in large payments, increasing default risk

Shared Appreciation Mortgage

- Relatively low interest rate and monthly payments - Not feasible in regions with declining home values- Buyer may not be able to buy out lender when specified payoff

time arrives; buyer would be forced to refinance or sell the house

Reverse Annuity Mortgage

- Way to access home equity without having burden of repayment- Creates income- Owners enjoy tax-free annuities- Continue to live in the house and benefit from appreciation and

property deductions

- Reduces value of estate (accumulating debt)- Home must be sold after death to repay mortgage if liquid assets

not sufficient- Annuities may place owners above certain welfare schemes

Flexible Loan Insurance Program

- May result in lower payments for borrower and thus greater affordability and lower risk for default

6


Flexible Maturity Adjustable Rate Mortgages

- Future payments are known in advance- Rate increases do not cause payment problems for borrowers

resulting in defaults

- Initial payment is higher. Payoff period is uncertain- Loan duration is not known in advance

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Chapter 7: Financing Decisions

House Value = $100,00080% LTV, 12% i/r, 25 years 90% LTV, 13% i/r, 25 years

Down payment¿20%×100,000=20,000PV=80,000 ;n=300 ; i=12%/12

PMT=$842.58

Down payment¿10%×100,000=10,000PV=90,000 ;n=300 ; i=13% /12

PMT=$1,015.05

Compute internal rate of return, irrBorrow $10,000 more but pay $172.47 more per month

PV=10,000 ;n=300 ;PMT=172.47i=1.7142×12=20.570%Evaluate this percentage. Would you pay 20.57% interest just to borrow an extra $10,000?

Assume borrower relocates after 5 yearsLoan Outstanding EOY5¿76,522.56 Loan Outstanding EOY5¿86,639.88Difference in loan outstanding¿86,639.88−76,522.56=10,117.32

PV=10,000 ; FV=10,117.32 ;i=1.73596×12=20.832%

With 2% origination feeLoan disbursement¿98%×80,000¿ $78,400 Loan disbursement¿98%×90,000¿ $88,200

Difference at time zero¿ $88,200−$78,400=$ 9,800Borrow $10,000 more but pay $172.47 more per month

PV=9,800 ;n=300 ; PMT=172.47i=1.750×12=21.00%

Assume Alternative #2 changed to 30 years80% LTV, 12% i/r, 25 years 90% LTV, 13% i/r, 30 years

Down payment¿20%×100,000=20,000PV=80,000 ;n=300 ; i=12%/12

PMT=$842.58

Down payment¿10%×100,000=10,000PV=90,000 ;n=360 ; i=13% /12

PMT=$995.58

Difference at time zero¿ $10,000Difference in monthly payment: First 300 months: $153.00; Final 60 months: $995.58

irr (−10,000 , {153 ,995.58 }, {300 ,60 } )=1.5720×12=18.864%

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n=60 ; PMT=172.47


Loan Refinancing

$80,000 loan at 15% for 30 years 5 years agoStick Switch

Refinance at 14% for 25 years, 2% prepayment penalty and upfront fee payable to $2,525

Year 0 – EOY5 PV=80,000 ;n=360 ; i=15% /12PMT=$1011.56

Loan outstanding EOY5¿ $78,976.50

PV=78,976.50 ;n=300 ; i=14% /12PMT=$950.69

∴newmonthly payment=$950.69

Returns from Refinancing Investment

Cost ¿ refinance=Prepayment Penalty+UpfrontCosts¿2%×$78,976.50+2,525=$4,104.53

Benefit ¿ refinancing=Initial Monthly Payment−NewMonthly Payment¿ $60.87

PV=4,104.53; n=300 ; PMT=60.87i=1.464×12=17.569%>14% cost of new borrowing

Effective Cost of RefinancingPV=78,976.50−4,105.53=$74,871 ;n=300 ; PMT=950.69

i=1.238×12=14.857%<15%cost of original loan

Buyer plans to relocate after 10 years of refinancing or not refinancingLoan Outstanding EOY10¿ $72,275.26 Loan Outstanding EOY10¿ $71,386.86

Difference in loan outstanding¿ $888.4PV=4,105; FV =888.4 ;n=120 ,PMT=60.87

i=1.1842×12=14.21%<17.569% irr if stay all theway

Two or more Loans

Financial Package Individual Loans Payment of individual loans$500,000: $100,000 at 7%, 30 years

$200,000 at 7.5%, 20 years$200,000 at 8%, 10 years

PMT=$665.30PMT=$1,611.19PMT=$2,426.55

irr (−500,000 , {4703.04 ,2276.49 ,665.30 } , {120 ,120 ,120 } )=0.6239×12=7.4873%

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Chapter 9: Controlling Default Risk

Loan Underwriting: Process of determining and controlling default risk, evaluate borrower’s loan request in terms of profitability and risk

See Notes for Underwriting Process

Type Formula Example

Loan-to-Value (LTV)

LTV= LoanProperty Value

Property Value=$500,000Loan=$ 400,000LTV=0.8

Payment to Income Ratio

-OR-Mortgage

Servicing Ratio

PIR /MSR=TotalMortgage ExpenseGross Monthly Income

Variation :CashTopup(¿CPF )

Debt Service

Jack’s gross income is $5,500Monthly loan payment is $4,540

PIR=45405500

=0.8255>TDSR

See Notes for variation in this ratio

Debt Coverage Ratio

DCR=Net Operating IncomeDebt Service

Breakeven Ratio

Debt Service+OperatingExpenseEffectiveGross Income

How much can a buyer finance?Gross household monthly income $7870

Car Loan $1500Car Insurance 250Credit Card 700Personal Loan 500Property tax & Insurance 300

Bank to grant 25-year 80% LTV at 3.5% p.a. with monthly payments subject to HEIR 30% and TDSR 60%

Housing-Expense to

Income Ratio

Gross Monthly Income $7,780Times: HEIR 0.30Max Permissible long term obligations $2,361Less: Property tax & insurance 300Max Principal & interest payment $2,061

PMT=2061 ;n=300 ; i=3.5% /12PV=$411,687

∴maxloan=$ 411,687

Total Debt Service Ratio

Gross Monthly Income $7,780Times: TDSR 0.60Max Permissible long term obligations $4,722Less: Property tax & insuranceLess: Payments on long-term debt

3002950

3,250Max Principal & interest payment $1,472

PMT=1472 ;n=300 ; i=3.5% /12PV=$294,033

∴maxloan=$294,033

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Chapter 11: Asset-Backed Securities

Securitization Process by which assets are packaged into securities sold on organized exchangesAsset-backed Security

A security created by pooling loans

Bankruptcy Remote

A bankruptcy remote company is a company within a corporate group whose bankruptcy has as little economic impact as possible on other entities within the group

Two types of assets used as collateral – existing and future

Securitization Structure

Amortizing Assets (Self-liquidating Structure) Non Amortizing Assets (Revolving Structure)Periodic payments consisting if principal & interestAmortization schedule on a pool/loan level

See Notes for further explanation

- No amortizing schedule- Lockout/revolving periodNo fixed period, only minimum payment, e.g. credit card

Fixed Rate Floating RatePossibility of mismatch between cash flow characteristics of underlying asset and liabilities. Interest rate

derivatives are used to mitigate the risk

Asset Classification

Credit RisksAsset Risk Structural Risk Third-Party Providers

- Underlying borrower’s ability to pay and service loans

- Experience of originators- Concentration of loans: a

single huge loan borrower?- Assessment of most likely

lost via weighted average loss & variability of loss

Can Cash Flow satisfy all obligations?- Loss allocation- Cash flow allocation- Interest rate spread- Potential of occurrence of trigger events- Changes in credit enhancement See Notes for Subordination Principle & Cash Flow Waterfall

- Credit guarantors (bond insurers)

- Servicer- Trustee- Lawyer

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Asset Backed Security

Others

- Customer loans- Credit Card Receivables- Leasing Receivables-Future cash flows

Mortgage Backed Security

- RMBS- CMBS (income producing)

Collateralized Debt Obligation

- Collateralized Loan Obligation- Collateralized Bond Obligation


Credit Enhancement (See Notes for Credit Enhancement)

*Monoline Insurance: An insurance company that provides guarantees to issuers to enhance the credit of the issuer. Issuers will often go to monoline insurance companies to either boost the rating of one of their debt issues or to ensure a debt issue does not become downgraded.

+Main motivation is to maintain ratio of senior-subordinate: Redirect prepayments disproportionately from subordinate to senior to ensure no deterioration of credit protection for senior bond class

Residential Mortgage Backed Securities

Prepayment Risk

Conditional Prepayment Rate – Single-Monthly Mortality rate (SMM)

SMM=1− (1−CPR )112

Monthly Prepayment=SMM ×(beginningbal formonth t−scheduled principal payment for month t)

Default Risk

1) Conditional Default Risk (CDR)Annualized value of unpaid principal balance of newly defaulted loans in a month as percentage of unpaid balance of pool

CDRM= defaulted loanbalancebeginningbal for month t−scheduled principal payment∈month t

CDRY=1−(1−CDRM )12

2) Cumulative Default Rate

Commercial Mortgage Backed Securities

- Prepayment terms- Role of servicer: transference of loan to special servicer when borrower is in default, imminent default,

or in violation of covenants- Role of buyers: junior bond buyers

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Credit Enhancement

Internal

Senior Subordinated

Structure+

Excess Spread

Overcollateralization

External Monoline Insurance*


Special Purpose VehicleA Special purpose vehicle is a legal entity created to fulfil a Specific or temporary objective. SPVs are typically used by companies to isolate the firm from financial risk. They are also commonly used to hide debt, hide ownership, and obscure relationships between different entities which are in fact related to each other

Some of the reasons for creating Special purpose entities are as follow:

- Securitization: SPVs are commonly used to securitise loans. For example, a bank may wish to issue a mortgage-backed security whose payments come from a pool of loans. However, to ensure that the holders of the mortgage-back securities have the first priority right to receive payments on the loans, these loans need to be legally separated from the other obligations of the bank. This is done by creating an SPV, and then transferring the loans from the bank to the SPV.

- Risk sharing: Corporates may use SPVs to legally isolate a high risk project/asset from the parent company and to allow other investors to take a share of the risk.

- Finance: Multi-tiered SPVs allow multiple tiers of investment and debt.- Asset transfer: Many permits required to operate certain assets (such as power plants) are either non-

transferable or difficult to transfer. By having an SPV own the asset and all the permits, the SPV can be sold as a self-contained package, rather than attempting to assign over numerous permits

Asset-Backed SecuritiesWhen a consumer takes out a loan, their debt becomes an asset on the balance sheet of the lender, collecting principal and interest payments from borrowers. The lender can then sell these assets to a trust or “special purpose vehicle,” which packages them into an asset backed security (ABS) that can be sold in the public market. The interest and principal payments made by consumers “pass through” to the investors that own the asset backed securities.

ABS benefit lenders because they can be removed from the balance sheet, allowing lenders to acquire additional funding as well as greater flexibility to pursue new business. 1) Investors of ABS and MBS are usually institutional investors and they use ABS to obtain higher yields than comparable-maturity U.S. Treasury securities among triple-A rated assets, as well as to provide a way to diversify their portfolios and augment their portfolio diversification. 2) ABS are one of the most secure investment vehicles from a credit standpoint. Predictable cash flow. The certainty and predictability of cash flow for many types and classes of ABS are well established. Investors can buy these securities with considerable confidence that the timing of payments will occur as expected. (Prepayment uncertainty). 3) Because ABS are secured by underlying assets, they offer significant protection against event-risk downgrades, particularly in contrast to corporate bonds. A major concern investors have about unsecured corporate bonds, no matter how highly rated, is that the rating agencies will downgrade them because of some disruptive event affecting the issuer. Such events include mergers, takeovers, restructurings and recapitalizations, which are often undertaken by corporate managers trying to boost shareholder value.

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QUICK REFERENCE GUIDE GEK2013 – REAL ESTATE FINANCEName Formula Usage Example

Simple Interest i=Principal ×i /r Interest earned on principal amount only

Total amount accumulated EOY2 if $1,000 invested at 10% simple interest:Total amount=1,000+2×10%×1,000=$1,200

Future Value FV=PV ∙θ Compute compound interest Total amount accumulated EOY2 if $1,000 invested at 7% interestFV=1,000 ∙ (1+0.07 )2=$1144.90

Present ValuePV=FV ∙

1θ

Value of an investment in today’s money

Present value of obtaining $105,000 EOY1 at 7% interest

PV=105,000 ∙ 1

(1+0.07 )1=$98,130.84

Future Value Annuity FVA=PMT ∙

θ−1i

Future value of a series of constant payments

Investor pays $200 per month for 5 years at 8% interest p.a.

FVA=100 ∙(1+ 8%12 )

5 ∙ 12

−1

8%12

=$14,695.37

Sinking Fund Factor (“PMT”) PMT=FVA∙

iθ−1

Amount set aside to be invested in order to accumulate desired future amount

Compute PMT to accumulate $33,100 EOY3 at 10% interest p.a.

PMT=33,100 ∙

10%12

(1+ 10%12 )3 ∙12

−1=$792.21

Present Value Annuity

Arrears

PVA=PMT ∙1−1

θi

=PMT ∙1−PV

i

How much to pay for an investment that hands out constant payments

Investment pays out $300 each month over 6 months at 8% interest p.a., how much to pay?

PVA=300 ∙

1− 1

(1+ 8%12 )6

8%12

¿ $1,758.74Advance

PVA=PMT ∙ (1+i ) ∙1−1

θi

Mortgage Constant PMT=PVA∙

i

1−1θ

Debt service necessary to amortize a present mortgage loan amount

You raised a mortgage of $100,000. Loan is for 15years, interest at 7% p.a.

14

n= years ¿


PMT=100,000 ∙ 7%

1−1

(1+7% )15¿ $10,979.46

Loan Outstanding EOY1

Outstandingmortgage Loan=10,979.46 ∙1− 1

(1+7% )14

7%=$96,020.52

Loan Outstanding

Effective RatesVS

Nominal RatesEAR=(1+ i

m )m

−1Convert nominal quotes to effective rates

Effective annual rate of 1% i/r per monthSimple interest rate of 1% per month=12% p.a.

EAR=(1+12%12 )12

−1=0.126825

FutureValue Factor ,θ=(1+i )n; Discount rate= 11+r

15

SamePMT

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GEK2013 Real Estate Finance