1 Mortgage Basics. 2 Types of Mortgages Types of Collateral: –Residential 1 to 4 family homes (up...

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Mortgage Basics

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Types of Mortgages

• Types of Collateral:– Residential

• 1 to 4 family homes (up to 4 units)

– Commercial • Larger apartments & non-residential

• Permanent vs. Construction– Perm on completed existing buildings– Construction loans finance development projects

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Government Involvement

• Government-Insured (FHA, VA)– Include “mortgage insurance”, allows higher L/V

ratio– More “red tape”, longer approval process– No “due-on-sale” clause, may be assumable

• Conventional– Normally max L/V=80%, unless private mortgage

insurance (PMI)– Majority of all loans

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Terminology

• Owner begins with "O", so: "...or" ===> Owner

• "Lessor" is Owner (Landlord), "Lessee" is Renter.

• "Mortgagor" is Owner (Borrower), "Mortgagee" is Lender.

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Legal Structure of Mortgages

• Mortgages have 2 parts (documents):– Promissory Note: Contract establishing debt.– Mortgage Deed: Secures debt with real property

collateral (potentially conveys title).

• Two legal bases of mortgages:– "Lien Theory" (most states): borrower holds title,

lender gets lien.– "Title Theory" (a few states): Lender holds title.

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TYPICAL COVENANTS & CLAUSES

1) Promise to PaySpecifies principal, interest, penalties, etc.,

along with date, names, etc.

2) Covenant to Avoid Liens w Priority over the MortgageFor example, if borrower fails to pay property

tax, she is in default of mortgage too, because property tax lien has priority over mortgage lien.

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3) Hazard InsuranceBorrower must insure value of the property (at least

up to mortgage amount) against fire, storm, etc.

*4) Mortgage InsuranceBorrower must hold mortgage insurance (usually

only if loan is not Govt insured and Loan/Value ratio > 80%). In essence, mortgage insurance will pay lender the difference between foreclosure sale proceeds and the debt owed to lender, if any. In effect, Govt (FHA, VA) loans automatically have mortgage insurance from the Govt.

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5) EscrowBorrower required to pay insurance and property tax

installments to lender in advance, who holds funds in escrow until due to insurer and property tax authority, when lender pays these bills for the borrower.

*6) Order of Application of PaymentsFirst to penalties and expenses, then to interest, then to

principal balance. (This implements the “4 Rules”.)

7) Good Repair ClauseBorrower must maintain property in good repair.

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8) Lender's Right to InspectLender has right to enter property, with prior

notice and at the owner’s convenience, to verify that borrower is keeping property in good repair.

9) Joint & Several LiabilityEach party signing the mortgage is

individually completely liable for the entire mortgage debt.

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*10) Acceleration ClausesAllow lender to make the entire outstanding

loan balance due immediately under certain conditions. Normally applied to default (to enable lender to sue for entire loan balance in foreclosure) and to implement a “due-on-sale” clause.

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*11) "Due-on-Sale" ClauseLender may accelerate loan when/if borrower

transfers a substantial beneficial interest in the property to another party. This normally prevents mortgage from being “assumed” by a buyer of the property. Govt insured loans (FHA, VA) usually do not have this clause, but most conventional residential mortgages do. Results in “demographic prepayment” (as distinguished from “financial prepayment”) of residential mortgages.

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*12) Borrower's Right to ReinstateAllows borrower to stop the “acceleration” of the loan

under default, up to time of court decree, upon curing of the default (payment of all back payments and penalties and expenses required under the loan terms).

13) Lender in PossessionProvision giving lender automatic right of possession

of the property in the event of default on the loan. Enables lender to control leasing and care & maintenance of the building prior to completion of the foreclosure process.

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*14) Release ClausesStates the conditions for freeing the real

property collateral from the loan security (e.g., when debt is paid off the lender must release the property by returning the mortgage deed and extinguishing the lien or returning the title to the borrower). More complicated release provisions are involved in loans in which the collateral will be sold of gradually in parts or parcels.

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15) Estoppel ClauseRequires borrower to provide lender with a

statement of the remaining outstanding balance on the loan. This provision is necessary to enable loan to be sold in the secondary market, as the identity of the “lender” (that is, the current owner or holder of the mortgage asset) will change as the mortgage is sold in the secondary market.

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*16) Prepayment ClauseProvision giving the borrower the right (without

obligation) to pay the loan off prior to maturity, like “callable” bonds. This effectively gives the borrower a call option on a bond, where the bond has cash flows equivalent to the remaining cash flows on the mortgage, and the exercise price of the option is the outstanding loan balance (plus prepayment penalties) on the mortgage (i.e., what one would have to pay to retire the debt).

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*17) Lender's Right to Notice (Jr Loans)A provision in junior loans requiring the borrower to

notify the lender if a foreclosure action is being brought against the borrower by any other lien-holder. Junior lien-holders may wish to help to cure the default or help work out a solution short of foreclosure, because junior lien-holders will stand to lose much more in the foreclosure process than the senior lien-holder.

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*18) Subordination ClauseA provision making the loan subordinate to

(that is, lower in claim priority in the event of foreclosure than) other loans which the borrower obtains subsequent to the loan in question. Often used in seller loans and subsidized financing, to enable the recipient of such financing to still obtain a regular first mortgage from normal commercial sources.

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*19) Future AdvancesProvision for some or all of the contracted principal

of the loan to be disbursed to the borrower at future points in time subsequent to the establishment (and recording) of the loan. This is common in construction loans, where the cash is disbursed as the project is built.

20) Covenant against RemovalBorrower (property owner) is not permitted to

remove from the property any part of the collateral, such as fixtures attached to the building.

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21) Personal Property ClausesProvisions including in the collateral specified items

of personal property (as opposed to the real property that is automatically included in the mortgage deed). “Real property” includes land and any structures and fixtures attached to the land. “Personal property” includes movable, non-fixed items such as furniture, most appliances, cars, boats, etc.

22) Owner Occupancy ClauseRequires borrower to live in the house.

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23) Sale in One Parcel ClausePrevents the collateral property from being broken

up into parcels sold separately.

*24) Exculpatory ClauseRemoves the borrower from responsibility for the

debt, giving the lender “no recourse” beyond taking possession of the collateral which secures the loan. Without an exculpatory clause, the lender can obtain a “deficiency judgment” and sue the borrower for any remaining debt owed after the foreclosure sale.

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etc., etc. . . .Anything the borrower and lender mutually agree on to include in the contract.

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More Terminology

“Purchase Money Mortgage" vs Refinancing

"Land Contract" Title does not pass until contract paid off

"Wraparound Mortgage" ("wrap") 2nd Mortgage issued by seller to buyer, seller

keeps 1st Mortgage alive, using wrap pmts to cover (smaller) 1st Mortgage pmts.

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Priority of Claims in Foreclosure

Lien Priority established by Date of Recording, except:Property Tax Lien comes first

Sometimes Mechanics LiensExplicit Subordination ClauseBankruptcy Proceedings may modify debtholder rights

"First Mortgage" (earlier recording) = "Senior Debt“

"2nd (etc) Mortgage" = "Junior Debt“

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Example:1st Mortgage = $90,0002nd Mortgage= $20,0003rd Mortgage = $10,000Property sells in foreclosure for $100,000:

1st Mortgagee gets $90,0002nd Mortgagee gets $10,0003rd Mortgagee gets 0.

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"Redeem up, Foreclose down"

Senior Lien Holders obtain their claim (to the extent foreclosure sale proceeds and their priority allows), even if they did not bring the suit.

Junior Lien Holders lose claims after foreclosure, provided they are included in the foreclosure suit.

Lien Holder bringing foreclosure suit normally buys the property in the foreclosure sale, for amount sufficient to cover its claim.

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Mortgage Math

What is PV of $1000 per month for 15 months plus $10,000 paid 15 months from now at 10% nominal annual interest?

= (14.045)1000 + (0.8830)10000

= $14,045 + $8,830

= (PVIFA.00833,15)*PMT + (PVIF.00833,15)*FV

1515 1210.1

000,10$

1210.1

000,1$

1210.1

000,1$875,22$

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(With calculator set to pmts at “END” of periods, and P/YR=12…)

Mortgage Math Keys: DCF Keys:15----> N key 10----> I/YR key10----> I/YR key 0 ----> CFj key1000 ----> PMT key 1000----> CFj key10000----> FV key 14 ----> Nj keyPV ----> -22,875 11000---->CFj key

NPV ----> 22,875

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How the Calculator "Mortgage Math" Keys Work. . .

The five "mortgage math" keys on your calculator (N,I,PV,PMT,FV) solve:

NN r

FV

r

PMT

r

PMT

r

PMTPV

11110

2

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or:0 = -PV + (PVIFAr,N)*PMT +

(PVIFr,N)*FV

where:r = i / m,

where: i = Nominal annual interest rate

m = Number of payment periods per year (mP/YR).

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Example: 10%, 20-yr fully-amortizing mortgage with payments

of $1000/month.

The calculator solves the following equation for PV:

The result is: PV = 103625.

2402402 00833.1

0

00833.1

1000

00833.1

1000

00833.1

10000 PV

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THE BASIC RULES OF CALCULATING LOAN

PAYMENTS & BALANCESLet:

P = Initial Contract Principal (Loan Balance at time zero, when money is borrowed)

rt = Contract Interest rate (per payment period, e.g., =i/m) applicable for payment in Period "t“

IEt = Interest portion of payment in Period "t“

PPt = Principal paid down ("amortized") in the Period "t" payment

OLBt = Outstanding loan balance after the Period "t" payment has been made

PMTt = Amount of the loan payment in Period "t“

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THE FOUR BASIC RULES:

1) IEt = rt(OLBt-1)

2) PPt = PMTt – IEt

3) OLBt = OLBt-1 - PPt

Equivalent to PV of remaining loan payments

4) OLB0 = PKnow how to set up these rules in a spreadsheet, so you

can calculate payment schedule, interest, principal, and outstanding balance after each payment, for any type of loan that can be dreamed up! (See “schedpmt.xls”, downloadable from course web site.)

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APPLICATION OF THE FOUR RULES TO SPECIFIC

LOAN TYPES1) Fixed-Rate loans (FRMs):

The contract interest rate is constant throughout the life of the loan: rt=r, all t.

2) Constant-Payment loans (CPMs):The payment is constant throughout the life

of the loan:PMTt=PMT, all t.

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3) Constant-Amortization loans (CAMs):The principal amortization is constant throughout the life

of the loan: PPt=PP, all t.

4) Fully-Amortizing loans:Initial contract principal is fully paid off by maturity of

loan:PPt=P over all t=1,…,N.

5) Partially-Amortizing loans:Loan principal not fully paid down by due date of loan:

PPt<P, so OLBN must be paid as “balloon” at maturity.

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6) Interest-Only loans:The principal is not paid down until the end:

PMTt=IEt, all t

(equivalently: OLBt=P, all t, and in calculator equation: FV

= -PV).

7) Graduated Payment loans (GPMs):The initial payment is low, usually initial PMT1 < IE1,

so OLB at first grows over time (“negative amortization”), followed by higher payments scheduled later in the life of the loan.

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8) Adjustable-Rate loans (ARMs):The contract interest rate varies over time (rt

not constant, not known for certain in advance, loan payment schedules & expected yields must be based on assumptions about future interest rates).

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Classical Fixed-Rate Mortgage

The “classical” mortgage is both FRM & CPM:PMT = P/(PVIFAr,N) = P / [(1 – 1/(1+r)N )/r]

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$60,000, 12%, 30-year CPM...

MONTH BEG. BAL.

INTEREST PMT PRIN END BAL.

1 $60,000.00

$600.00 $617.17 $17.17 $59,982.83

2 $59,982.83

$599.83 $617.17 $17.34 $59,965.49

3 $59,965.49

$599.65 $617.17 $17.51 $59,947.98

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You should know what formulas you would place in each cell of a spreadsheet (e.g., Excel) to produce such a table. (See “schedpmt.xls”, downloadable from course web site.)

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Using Your Calculator

1) Calculate Loan Payments:Example: $100,000 30-year 10% mortgage

with monthly payments:360----> N

10----> I/YR

100000 ----> PV

0 ----> FV

PMT----> - 877.57

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2) Calculate Loan Amount (Affordability): Example: You can afford $500/month

payments on 30-year, 10% mortgage:360----> N10----> I/YR500----> PMT0----> FVPV----> - 56,975.41 = Amt you can borrow.

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3) Calculate Outstanding Loan Balance:Example: What is the remaining balance on $100,000,

10%, 30-year, monthly-payment loan after 5 years (after 60 payments have been made)?First get loan terms in the registers:

360----> N10----> I/YR100000----> PV0----> FVPMT----> - 877.57

Then calculate remaining balance either way below:N ----> 60 N----> 300FV ----> - 96,574.32 PV----> 96,574.32

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4) Calculate payments & balloon on partially amortizing loan:Same as (3) above.

5) Calculate the payments on an interest-only loan:Example: A $100,000 interest-only 10% loan with

monthly payments: N can be anything,10 ---> I/YR, 100000 ---> PV, -100000---> FV,PMT ---> -833.33

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6) Meet affordability constraint by trading off payment amount with amortization rate:Example: Go back to example #2 on the previous

page. The affordability constraint was a $500/mo payment limit. Suppose the $56,975 which can be borrowed at 10% with a 30-year amortization schedule falls short of what the borrower needs.

How much slower amortization rate would enable the borrower to obtain $58,000?

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Enter: I/YR = 10, PV = -58000, PMT = 500, FV = 0,

Compute: N = 410.

Thus, the amortization rate would have to be 410 months, or 34 years.

Note: This does not mean loan would have to have a 34-year maturity, it could still be a 30-year partially-amortizing loan, with balloon of $20,325 due after 30 years.

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7) Determining principal & interest components of payments:Example: For the $100,000, 30-year, 10% mortgage in

problem #1 on the previous page, break out the components of the 12 payments numbering 50 through 61.

In the HP-10B, after entering the loan as in problem #1, enter:50, INPUT, 61, AMORT, = $9,696.06 int, = $834.80 prin, =$96,501

OLB61.

To get the corresponding values for the subsequent calendar year, press AMORT again, to get: = $9,608.65 int, = $922.21 prin, =$95,579 OLB73.

(Other business calculators can do this too.)

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Loan Yields and Mortgage Valuation

Loan Yield = Effective Interest RateYield = IRR of loan

Recall: IRR based on cash flows.

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Using calculator equation:

NN r

FV

r

PMT

r

PMT

r

PMTPV

11110

2

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Let:PV= CF0

PMT= CFt , t=1,2,...,N-1

PMT + FV = CFN

N= Holding Period

where: CFj represents actual cash flow at

end of period "j".

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Then, by the definition of "r" in the equation above, we have:

NN

r

CF

r

CF

r

CFCFNPV

1110

221

0

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(bearing in mind that:

Expressed in nominal per annum terms (i=mr, where m=P/YR), we can thus find the yield by computing the I/YR, provided the values in the N, PV, PMT, and FV registers equal the appropriate actual cash flow and holding period values.

NN

NNN r

CF

r

FVPMT

r

FV

r

PMT

1111

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In 2ndary mkt, loans are priced so their yields equal the “mkt’s required yield” (like expected total return, E(r)=rf+RP, from before).

At the time when a loan is originated (primary market), the loan yield is usually approximately equal to its contract interest rate. (But not exactly…)

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The tricky part in loan yield calculation: (a) The holding period over which we wish to calculate

the yield may not equal the maturity of the loan (e.g., if the loan will be paid off early, so N may not be the original maturity of the loan): N maturity ;

(b) The actual time-zero present cash flow of the loan may not equal the initial contract principal on the loan (e.g., if there are "points" or other closing costs that cause the cash flow disbursed by the lender and/or the cash flow received by the borrower to not equal the contract principal on the loan, P): CF0 P ;

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(c)The actual liquidating payment that pays off the loan at the end of the presumed holding period may not exactly equal the outstanding loan balance at that time (e.g., if there is a "prepayment penalty" for paying off the loan early, then the borrower must pay more than the loan balance, so FV is then different from OLB): CFN PMT+OLBN

So we must make sure that the amounts in the N, PV, and FV registers reflect the actual cash flows…

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Example

• $200,000 mortgage, 30-year maturity, monthly payments

• 10% annual interest• The loan has “2 points”

– (‘discount points’ or prepaid interest)

• Also a 3 point prepayment penalty through end of 5th year.

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• What is yield (“effective interest rate”) assuming holding period of 4 years (i.e., borrower will pay loan off after 48 months)?

• Break this problem into 3 steps: (1)Compute the loan cash flows using the contract

values of the parameters(N=360, I=10%, PV=200000, FV=0, Compute PMT=$1755.14);

(2)Alter the amounts in the registers to reflect the actual cash flows;

(3)Compute yield.

• (You must do these steps in this order.)

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Step 1)360----> N10----> I/YR200000 ----> PV0 ----> FVPMT----> - 1755.14

Step 2)48----> NFV----> - 194804 X 1.03 = - 200,649 ----> FV196000 ----> PV

Step 3)I/YR----> 11.22%

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Expected yield (like E(r) or “going-in IRR”) is 11.22%, even though “contractual interest rate” on the loan is only 10%. (When closing costs and prepayment

penalties are quoted in "points", you do not need to know the amount of the loan to find its yield.)

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General rule to calculate yield:

Change the amount in the PV Register last,

(just prior to computing the yield).

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Equivalent solution to previous problem:

Use CF keys instead of mortgage math keys…

196000 ----> CFj key

- 1755.14 ----> CFj key

47 ----> Nj key

- 202404 ----> CFj key

IRR ----> 11.22%

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Using Market Yields to Value Mortgages

(Note: This is performing a DCF NPV analysis of the loan as an investment, finding what price can be paid for the loan so the deal is NPV=0. Market’s required yield is “r”, the opportunity cost of capital for the loan.)

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Example

• $100,000 mortgage, 30-year, 10%, 3 points prepayment penalty before 5 years.

• Expected time until borrower prepays loan = 4 years.

• How much is the loan worth today if the market yield is 11.00%?

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Step 1) 360--->N,

10--->I/YR,

100000--->PV,

0--->FV,

Compute PMT---> -877.57.

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Step 2) 48--->N, FV---> -97,402 * 1.03 = -100,324 --->FV.

 Step 3) I/YR---->11.00%.

Step 4) PV----> 98,697.

The loan is worth $98,697. (Watch out for order of steps. Cash flows first, then input

the market yield, then compute the loan value as the PV.)

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Determining required “discount points” (or “origination fee”):To avoid lender doing NPV < 0 deal in

making loan, we need:(100,000 - 98,697) / 100,000 = 1.30% =

1.30 points

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Yield-Maintenance Prepayment Penalty

Suppose previously described 30-year, $100,000, 10% loan is issued with one discount point up front, but a prepayment penalty is also specified calling for a penalty amount such that if the loan is paid off early the lender must receive a yield of 12% instead of the 10% contract interest rate.

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If the borrower wants to pay the loan off after the fourth year (48 months), what will the prepayment penalty be?

Answer: Original loan in registers, then:48=N, FV=97402, 99000=PV, 12=I/YR, FV=105883,

so in this case: Penalty = 105883 – 97402 = $8,481.

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Valuing a "seller loan" or subsidized loan:(Been there, done that.)

Example: $100,000, 10%, 30-yr amort loan, no points or ppmt

penalty, maturing in 48 months with a balloon:360N, 10I/YR, 100000PV, 0FV, Compute

PMT=877.57

Next change: 48N, Compute FV=97402

Next change: 11I/YR, Compute PV=96811

So NPV = $100,000 - $96,811 = +$3189.

This is before-tax market value based NPV.

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Determining Market Yields

Market yields come from market prices in the bond market.

Quoted in "bond-equivalent" (BEY) or "coupon-equivalent" (CEY) terms,

Based on the classical bond format which is 2 pmts/yr (m=2P/YR)

Mortgages typically have monthly pmts: 12 pmts/yr (m=12P/YR).

“Apples vs oranges” in comparing yields between mortgages & bonds.

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e.g., “10% yield”:For a bond, for each $1 you invest at the beginning

of the year you would have:(1.05)(1.05)= (1.05)2= $1.1025

For a mortgage, you would have:(1.00833)(1.00833)...(1.00833)=(1.00833)12= $1.1047

To make “apples vs apples” comparisons, define:Effective Annual Yield

EAY = (1 + ENAR/m)m -1

Equivalent Nominal Annual Rate ENAR = [(1 + EAY)1/m - 1]m

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For bonds m=2;

For mortgages m=12.

Thus, BEY = ENAR with m=2. "Mortgage Equivalent Yield" (MEY) = ENAR

with m=12.

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Example: What is MEY equivalent to 10% BEY?

2----> P/YR │

10----> I/YR │

EFF%----> 10.25 │(1 + .10/2)2 -1 = .1025

12----> P/YR │

NOM%----> 9.80 │[(1 + .1025)1/12 - 1]12 = .0980

 Thus, 9.80% monthly MEY = 10.00% BEY

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Refinancing

This is essentially a comparison of two loans.

NPV is the evaluation (decision) framework.OCC (disc.rate, “r”) = Eff. int. rate in current loan

market (“mkt yield”).

Basic principles (“apples vs apples”):

1) Compare over same time horizon;

2) Compare over the same debt amount.

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Overview of solution steps:1. Compute NPV of incremental CFs of having New

Loan instead of Old Loan (keeping in mind the “apples vs apples” principles).

2. Subtract from this the transaction cost of obtaining the New Loan (e.g., title insurance, appraisal fees, etc). This gives the NPV of refinancing, except for:

3. Subtract the value of the refinancing option in the Old Loan, which you are giving up when you refinance. (This is the “prepayment option”, the call option on a bond.)

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Steps (1) & (2) are all that is presented in typical R.E. finance textbooks. Unfortunately, the option value can often swamp the NPV result from the first two steps.

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Step 1) The NPV of the incremental cash flows. Compare the two loans: Old vs New.Note: In principle, this analysis should be based on

“investment value” on an after-tax basis. Requires use of computer spreadsheet. (See

“frmrefin.xls”, downloadable from course web site.) The after-tax NPV will be less than the before-tax

NPV, but generally it will be quite a bit greater than (1-taxrate)*BTNPV, the more so the longer the holding period (approaching BTNPV in the limit).

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Most convenient way to do Step 1...NPV = PV(Benefit) - PV(Cost)Benefit = Remaining cash flows on old loan you

save by paying off old loan.Cost = Amount you must pay to pay off old loan

today.Discount rate = Market rate today = Yield (over

expected holding period) on new loan.Analysis horizon = Expected holding period (same

under either loan, also applies to calculate market opportunity cost of capital as yield on new loan).

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(Note: With this procedure, you do not need to calculate how much you will borrow under the new loan in order to determine the NPV of refinancing.)

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Example of Step 1

Loan refinancing NPV calculation:– Old loan was $100,000 30-year mortgage taken

out 5 years ago at 10%.– Currently int rates on new 30-year loans are down

to 8%, with 2 points.– You expect to be in your house 7 years more

(Exptd holding per.=y yrs).– Old loan has 1 point prepayment penalty.– New loan has no prepayment penalty.– What is NPV of refinancing before considering

transaction costs and option value?

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1st) Compute yield on new loan over expected holding period (current OCC):

360 = N, 8 = I/YR, 1 = PV, 0 = FV,

Compute PMT = - .0073376.

Now change to: 84 = N, and compute FV = - .9247743.

Now change to: .98 = PV, and compute I/YR = 8.3905%

Write down this yield (or store in calc memory).

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2nd) Get remaining CFs of Old loan, and its current payoff amount:

360 = N, 10 = I/YR, 100000 = PV, 0 = FV, and compute PMT = - 877.57.Now change to: 60 = N, and compute FV = 96,574X 1.01 = 97,540Write this number down (or store). It is what you have to

pay to get rid of the old loan.Now change to: 144 = N, and compute FV = 87,771 X 1.01 = 88,649 FVNow change to: 84 = N.

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3rd) Find PV of those CFs at new market yield:8.3905 I/YRCompute: PV = 104,980.This is market value of pmts you will save by getting rid of

the old loan.

4th) From this "Benefit" of getting rid of the old loan, subtract the "Cost", that is, what you must pay to get rid of old loan:

104980 - 97540 = + $7,440 = "NPV of refinancing"

(after Step 1 only)(After-tax NPV = +$5,668, =76% of BTNPV.)

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Step 2, including transaction costs

Suppose there will be $1500 of transaction costs associated with finding and obtaining the new mortgage.

(This might include title insurance, appraisal, etc.)

The NPV of refinancing after considering these transaction costs is:$7,440 - $1,500 = $5,940 = NPV of refinancing

(after Step 2) (This still lacks consideration of opportunity

cost of giving up refinancing option value.)

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Step 3: Incorporating option value

The old loan not only contains a negative value to the borrower represented by the PV of the future cash outflow liabilities.

It also contains a positive value in the refinancing option.

(This is a “call option” on a bond, from the prepayment clause in the loan, making it like a “callable” bond.)

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This can be seen in the previous calculations. We found that by exercising that option today, the borrower of the old loan could obtain a positive NPV of $5,940.

Options always have positive value, because they give the holder a right without an obligation.

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The borrower does not have to refinance today (or ever) if she does not want to. A “right without obligation” enables the holder to take advantage of the “upside” of risk without being fully exposed to the “downside” of risk.

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When you pay off the old loan before its maturity, exercising the prepayment option, you then no longer have that option (in the old loan).

Thus, part of the cost of refinancing is the value of the prepayment option in the old loan that is given up by its exercise.

 How much is this option worth? . . .

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To rigorously value the refinancing option in a loan requires very advanced technical analysis. However, you can get a basic idea why (and how) this option value can make it worthwhile to wait and not refinance by considering the following simple numerical example.

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Note: Fundamentally, we are still applying the "NPV decision rule", which, if you recall, says that we should always maximize the NPV across all mutually exclusive alternatives.

Clearly, refinancing the old mortgage today is mutually exclusive with refinancing it a year from now instead.

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Thus, if these are our only two alternatives (refinancing today versus possibly refinancing in one year if interest rates are still low enough then), then we must pick the one that has the highest NPV.

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Step 3 example: Refinancing

Suppose we believe the following subjective probability distribution describes what interest rates (on the new loan) will be like in one year:6% with 50% chance;10% with 50% chance.

Now recalculate Steps 1 & 2 NPV under each of these scenarios, one year from now (6 years gone by on the old loan, 6 more years to go in the holding horizon).

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Using the same procedures as indicated before, we get the following expected NPVs (after subtracting $1500 transaction costs) as of one year from now, under each interest rate scenario:NPV1 = +$17,774, if interest rates are 6%;

NPV1 = -$ 3,232, if interest rates are 10%.

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Thus, if the 10% interest rate scenario transpires, you would not refinance, but simply keep the old loan. In that case you would face a NPV=0 effect (from doing nothing). This reflects the fact that options are rights without obligation. As a result, as of today the expected NPV next year due to the refinancing option in the old loan is:E0[refin1] = (50%)*(17774) + (50%)*(0) = +$8,887.

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What is the present value of this expected value one year from now?

Option values are risky, so they should be discounted at a high discount rate reflecting a large risk premium in the opportunity cost of capital. Suppose we require a 25% per annum return on holding the option. Then the PV today of the refinancing option in the old loan is:PV[refin1] = 8887 / 1.25 = +$7,110.

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Thus, under the above assumptions, the refinancing option in the old loan is worth $7,110. This value would be given up if we refinance today. In return, we would obtain the +$5,940 NPV from the exercise of the refinancing option today. Thus, step 3 of our refinancing calculation reveals that it does not make sense to refinance today:

NPV[refin0] = NPV0 - PV[refin1] = 5940 - 7110 = -$1,170

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Summary of Step 3 example

Although refinancing today is a positive-NPV action in a sense, it does not maximize the NPV across all the available alternative decisions.

Furthermore (though not shown in this example), the refinancing option value in the old loan would normally be reflected in the market value of the old loan, so that if we computed the NPV of refinancing based on market value, we would not get a positive NPV even just from examining the present possibility.

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In other words, given the refinancing option, the old loan would not really be worth $104,980 in the market today. Only a fool would pay that much to buy the old loan, given that there is a good chance the borrower will pay it off early with a liquidating payment of only $97,540. Indeed, the market value of the old loan today is probably only a little more than $97,540.

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Suppose the MV of the Old Loan today is $98,000. This means that the market value based NPV of the refinancing transaction today would be:98000 - 97540 - 1500 = -$1,040

(similar to the NPV we got by our explicit option valuation exercise above).

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Conventional wisdom "rule of thumb":Considering refinancing option value, it

usually does not make sense to refinance unless there is at least about 2 points spread in the interest rate between the old and new loans.

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However, if you are quite sure that interest rates are at their low point and will only be heading up, then you might refinance with less than a 2 point spread. (If you could really be sure interest rates would never be lower than today, then you can ignore step 3 and make your decision just on the basis of steps 1 & 2. But of course, nobody has a "crystal ball" for seeing future interest rates.)

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Additional Points

What about the prepayment option value in the new loan?

The prepayment option value is actually already included in the NPV evaluation we did in Step 3, at least in an approximate way. Recall that the NPV in Step 3 is based on the NPV without the option calculated in Step 1 (the +$7,440). Now recall that we used the new loan yield as the opportunity cost of capital applied to discount the old loan cash flows to arrive at that Step 1 NPV. In fact, in the mortgage market the new loan interest rate is set high enough to fully price the new loan prepayment option which the lender is giving the borrower in the new mortgage, so as to make the new loan a NPV=0 transaction from the lender’s perspective at the time of refinancing. That is, if the new loan did not have a prepayment option, it would have a lower interest rate. By applying this callable bond yield rate in Step 1, we arrive at a lower present value for the remaining old loan cash flows, and hence a lower NPV from refinancing in Step 1, than we otherwise would if we were using a non-callable bond yield rate as the opportunity cost of capital. This difference (very closely) incorporates the value of the new loan prepayment option, that is, gives us a Step 1 NPV which is already net of the new loan prepayment option value.

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How will it ever be optimal to refinance, considering the lost option value?

If you are familiar with basic option theory, it may help to understand that the prepayment option is a call option on a bond. The underlying asset is the old mortgage (excluding its prepayment option, otherwise we would be going around in circles). The exercise price is what one must pay to be released from the old mortgage. (Note that this exercise price changes over time as the remaining balance on the loan changes.) The prepayment option is normally an “American” option, in the sense that it may be exercised at any time. Basic option value theory tells us that it is optimal to exercise an American call option prior to the maturity (expiration date) of the option provided that: (1) the option is sufficiently “in the money” (underlying asset value sufficiently higher than the exercise price), and (2) that the underlying asset pays cash dividends that are large enough to provide a sufficient opportunity cost to holding the option (considering that the option holder does not receive dividends from the underlying asset until the option is exercised). In the case of the mortgage prepayment option the dividends are the monthly mortgage payments that the borrower must pay each month, which will be saved by exercising the option. Thus, by analogy to American call options, it is clear that there will be some level of current market interest rates below which the value of the underlying asset (the old mortgage without its prepayment option) will be high enough to place the prepayment option sufficiently in-the-money to make its immediate exercise optimal, in order to obtain the “dividends” of the loan payment savings. In principle, this option exercise decision is independent of how the borrower will be obtaining the capital to pay off the old loan, that is, whether the borrower is “refinancing” in the sense of using new debt capital, or “recapitalizing” by replacing debt with new equity capital.

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Can we use the Black-Scholes Model to value the prepayment option?

No, for several reasons. The prepayment option is normally an American option, not a European option, so the B-S model does not apply (given that the underlying asset pays dividends, so early exercise may be optimal). Second, the exercise price is not constant through time. Third, the underlying asset is a bond, not a stock, so the stochastic process that governs the underlying asset value is different from the random walk process assumed by the B-S model. For these reasons there is no closed-form analytical model of the mortgage prepayment option value. One must apply numerical methods to solve for the prepayment option value.

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Residential mortgage qualification & home

affordability

Definition: Process by which lenders (loan originators) determine which loans should be made (to whom), and the terms and conditions of those loans.

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Purpose: 1) To make default very rare

(bond investors are conservative)

2) To minimize losses in foreclosure

3) More generally: To make sure expected return to lender is sufficient, including consideration of default risk (so lender avoids a neg.-NPV transaction).

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Fundamentals Underlying Expected Return & Contract Yield ("int"):1) Inflation Expectation (yield curve):

"Fisher" Effect: int = (1+real)(1+infl) – 1

"Darby" Effect: int = [(1+ATreal)(1+infl) - 1] / (1-taxrate)

2) Time Value of Money (Riskless S.T.Interest Rate)

3) Interest Rate Risk (yield curve)

4) Prepayment Risk (related to interest rate risk)

5) Default Risk ("Credit Risk")

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e.g., 1-yr loan:(1+Er) = (1-PrDef)(1+int) + (PrDef)(1-Loss%)(1+int)==>1+int = (1+Er) / [(1-PrDef)+(PrDef)(1-Loss%)]

6) Illiquidity Premium

Note: These considerations apply to loan underwriting in general, not just residential mortgages, and underlie the market yields that come out of the secondary mortgage market (RMBS, CMBS), the primary source of capital.

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Simplified summary of residential qualification criteriaStandards set largely by FNMA, FHLMC (2ndary

mortgage market - MBS):Typical Income Requirements:

L/V<=80% L/V>80%Fraction of Gross Income:1)Mortg PMT # 28% 25%2)PITI # 30% 28%3)Mort PMT+LTDS # 36% 33%4)PITI+util&main+child

+LTDS+STDS # 50% 45%(3 out of 4 OK if 4th close)

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Borrower Criteria:1) Level of Household Income2) Stability, Growth of Income3) Financial Condition (Net Worth,

Liquidity)4) Other considerations (credit hist, svgs

hist, dependents, etc., but age, gender, race etc. not legal considerations, according to "Regulation B" of FRB)

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Property (Collateral) Criteria:1) Loan/Value Ratio (min: price,

appraisal)

2) Location, but "Redlining" illegal