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Mortgage Basics

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

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/V80, unless private mortgage

insurance (PMI) - Majority of all loans

Terminology

- Owner begins with O, so ...or gt Owner
- Lessor is Owner (Landlord), Lessee is Renter.
- Mortgagor is Owner (Borrower), Mortgagee is

Lender.

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.

TYPICAL COVENANTS CLAUSES

- Promise to Pay
- Specifies principal, interest, penalties, etc.,

along with date, names, etc. - 2) Covenant to Avoid Liens w Priority

over the Mortgage - For example, if borrower fails to pay property

tax, she is in default of mortgage too, because

property tax lien has priority over mortgage lien.

- 3) Hazard Insurance
- Borrower must insure value of the property (at

least up to mortgage amount) against fire, storm,

etc. - 4) Mortgage Insurance
- Borrower must hold mortgage insurance (usually

only if loan is not Govt insured and Loan/Value

ratio gt 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.

- 5) Escrow
- Borrower 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 Payments
- First to penalties and expenses, then to

interest, then to principal balance. (This

implements the 4 Rules.) - 7) Good Repair Clause
- Borrower must maintain property in good repair.

- 8) Lenders Right to Inspect
- Lender has right to enter property, with prior

notice and at the owners convenience, to verify

that borrower is keeping property in good repair. - 9) Joint Several Liability
- Each party signing the mortgage is individually

completely liable for the entire mortgage debt.

- 10) Acceleration Clauses
- Allow 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.

- 11) Due-on-Sale Clause
- Lender 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.

- 12) Borrowers Right to Reinstate
- Allows 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 Possession
- Provision 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.

- 14) Release Clauses
- States 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.

- 15) Estoppel Clause
- Requires 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.

- 16) Prepayment Clause
- Provision 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).

- 17) Lenders 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.

- 18) Subordination Clause
- A 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.

- 19) Future Advances
- Provision 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 Removal
- Borrower (property owner) is not permitted to

remove from the property any part of the

collateral, such as fixtures attached to the

building.

- 21) Personal Property Clauses
- Provisions 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 Clause
- Requires borrower to live in the house.

- 23) Sale in One Parcel Clause
- Prevents the collateral property from being

broken up into parcels sold separately. - 24) Exculpatory Clause
- Removes 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.

- etc., etc. . . .Anything the borrower and lender

mutually agree on to include in the contract.

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.

Priority of Claims in Foreclosure

- Lien Priority established by Date of Recording,

except - Property Tax Lien comes firstSometimes Mechanics

LiensExplicit Subordination ClauseBankruptcy

Proceedings may modify debtholder rights - First Mortgage (earlier recording) Senior

Debt - 2nd (etc) Mortgage Junior Debt

- Example
- 1st Mortgage 90,000
- 2nd Mortgage 20,000
- 3rd Mortgage 10,000
- Property sells in foreclosure for 100,000
- 1st Mortgagee gets 90,000
- 2nd Mortgagee gets 10,000
- 3rd Mortgagee gets 0.

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.

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

- (With calculator set to pmts at END of periods,

and P/YR12) - Mortgage Math Keys DCF Keys
- 15----gt N key 10----gt I/YR key
- 10----gt I/YR key 0 ----gt CFj key
- 1000 ----gt PMT key 1000----gt CFj key
- 10000----gt FV key 14 ----gt Nj key
- PV ----gt -22,875 11000----gtCFj key
- NPV ----gt 22,875

- How the Calculator Mortgage Math Keys Work. . .
- The five mortgage math keys on your calculator

(N,I,PV,PMT,FV) solve

- or0 -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).

- 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.

THE BASIC RULES OF CALCULATING LOAN PAYMENTS

BALANCES

- Let
- 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

THE FOUR BASIC RULES

- IEt rt(OLBt-1)
- PPt PMTt IEt
- OLBt OLBt-1 - PPt
- Equivalent to PV of remaining loan payments
- OLB0 P
- Know 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.)

APPLICATION OF THE FOUR RULES TO SPECIFIC LOAN

TYPES

- Fixed-Rate loans (FRMs)
- The contract interest rate is constant throughout

the life of the loan - rtr, all t.
- 2) Constant-Payment loans (CPMs)
- The payment is constant throughout the life of

the loan - PMTtPMT, all t.

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

the life of the loan - PPtPP, all t.
- 4) Fully-Amortizing loans
- Initial contract principal is fully paid off by

maturity of loan - PPtP over all t1,,N.
- 5) Partially-Amortizing loans
- Loan principal not fully paid down by due date of

loan - PPtltP, so OLBN must be paid as balloon at

maturity.

- 6) Interest-Only loans
- The principal is not paid down until the end
- PMTtIEt, all t
- (equivalently OLBtP, all t, and in calculator

equation FV -PV). - 7) Graduated Payment loans (GPMs)
- The initial payment is low, usually initial PMT1

lt IE1, so OLB at first grows over time (negative

amortization), followed by higher payments

scheduled later in the life of the loan.

- 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).

Classical Fixed-Rate Mortgage

- The classical mortgage is both FRM CPM
- PMT P/(PVIFAr,N) P / (1 1/(1r)N )/r

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

- 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.)

Using Your Calculator

- Calculate Loan Payments
- Example 100,000 30-year 10 mortgage with

monthly payments - ----gt N
- 10----gt I/YR
- 100000 ----gt PV
- 0 ----gt FV
- PMT----gt - 877.57

- 2) Calculate Loan Amount (Affordability)
- Example You can afford 500/month payments on

30-year, 10 mortgage - 360----gt N
- 10----gt I/YR
- 500----gt PMT
- 0----gt FV
- PV----gt - 56,975.41 Amt you can borrow.

- If you can borrower 80 of house value, how much

can you afford to purchase - Purchase Price 56,975 / 0.80
- Purchase Price 71,218

- 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
- ----gt N
- 10----gt I/YR
- 100000----gt PV
- 0----gt FV
- PMT----gt - 877.57
- Then calculate remaining balance either way

below - N ----gt 60 N----gt 300
- FV ----gt - 96,574.32 PV----gt 96,574.32

- 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,
- ---gt I/YR,
- 100000 ---gt PV,
- -100000---gt FV,
- PMT ---gt -833.33

- 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

- 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.

- 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.)

Loan Yields and Mortgage Valuation

- Loan Yield Effective Interest Rate
- Yield IRR of loan
- Recall IRR based on cash flows.

- Using calculator equation

- Let
- PV CF0
- PMT CFt , t1,2,...,N-1
- PMT FV CFN
- N Holding Period
- where CFj represents actual cash flow at end of

period j.

- Then, by the definition of r in the equation

above, we have

- (bearing in mind that
- Expressed in nominal per annum terms (imr, where

mP/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.

- In 2ndary mkt, loans are priced so their yields

equal the mkts required yield (like expected

total return, E(r)rfRP, 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)

- The tricky part in loan yield calculation
- 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

- (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 PMTOLBN - So we must make sure that the amounts in the N,

PV, and FV registers reflect the actual cash

flows

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.

- 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 - (N360, I10, PV200000, FV0, Compute

PMT1755.14) - (2)Alter the amounts in the registers to reflect

the actual cash flows - (3)Compute yield.
- (You must do these steps in this order.)

- Step 1)
- ----gt N
- 10----gt I/YR
- 200000 ----gt PV
- 0 ----gt FV
- PMT----gt - 1755.14
- Step 2)
- 48----gt N
- FV----gt - 194804 X 1.03 - 200,649 ----gt

FV - 196000 ----gt PV
- Step 3)
- I/YR----gt 11.22

- 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.)

- General rule to calculate yield
- Change the amount in the PV Register last,
- (just prior to computing the yield).

- Equivalent solution to previous problem
- Use CF keys instead of mortgage math keys
- 196000 ----gt CFj key
- - 1755.14 ----gt CFj key
- 47 ----gt Nj key
- - 202404 ----gt CFj key
- IRR ----gt 11.22

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 NPV0.

Markets required yield is r, the opportunity

cost of capital for the loan.)

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

- Step 1)
- 360---gtN,
- 10---gtI/YR,
- 100000---gtPV,
- 0---gtFV,
- Compute PMT---gt -877.57.

- Step 2)
- 48---gtN,
- FV---gt -97,402 1.03 -100,324 ---gtFV.
- Step 3)
- I/YR----gt11.00.
- Step 4)
- PV----gt 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.)

- Determining required discount points (or

origination fee) - To avoid lender doing NPV lt 0 deal in making

loan, we need - (100,000 - 98,697) / 100,000 1.30

1.30 points

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.

- 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
- 48N, FV97402, 99000PV, 12I/YR, FV105883,
- so in this case Penalty 105883 97402

8,481.

- 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

PMT877.57 - Next change 48N, Compute FV97402
- Next change 11I/YR, Compute PV96811
- So NPV 100,000 - 96,811 3189.
- This is before-tax market value based NPV.

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 (m2P/YR) - Mortgages typically have monthly pmts 12 pmts/yr

(m12P/YR). - Apples vs oranges in comparing yields between

mortgages bonds.

- 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 - 1m

- For bonds m2
- For mortgages m12.
- Thus, BEY ENAR with m2.
- Mortgage Equivalent Yield (MEY) ENAR with

m12.

- Example
- What is MEY equivalent to 10 BEY
- 2----gt P/YR
- 10----gt I/YR
- EFF----gt 10.25 (1 .10/2)2 -1 .1025
- 12----gt P/YR
- NOM----gt 9.80 (1 .1025)1/12 - 112

.0980 - Thus, 9.80 monthly MEY 10.00 BEY

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.

- Overview of solution steps
- Compute NPV of incremental CFs of having New Loan

instead of Old Loan (keeping in mind the apples

vs apples principles). - 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 - 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.)

- 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.

- 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).

- 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).

- (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.)

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

- 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).

- 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 97,540
- Write 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 FV
- Now change to 84 N.

- 3rd) Find PV of those CFs at new market yield
- 8.3905 I/YR
- Compute 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.)

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.)

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.)

- 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.

- 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.

- 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 . . .

- 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.

- 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.

- 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.

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).

- 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.

- 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

NPV0 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 - E0refin1 (50)(17774) (50)(0) 8,887.

- 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 - PVrefin1 8887 / 1.25 7,110.

- 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 - NPVrefin0 NPV0 - PVrefin1 5940 - 7110

-1,170

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.

- 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.

- 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).

- 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.

- 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.)

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 NPV0 transaction from the

lenders 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.

- 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.

- 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.

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.

- Purpose
- 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).

- Fundamentals Underlying Expected Return

Contract Yield (int) - Inflation Expectation (yield curve)
- Fisher Effect int (1real)(1infl) 1
- Darby Effect int (1ATreal)(1infl) - 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)

- e.g., 1-yr loan
- (1Er) (1-PrDef)(1int) (PrDef)(1-Loss)(1i

nt) - gt1int (1Er) / (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.

- Simplified summary of residential qualification

criteria - Standards set largely by FNMA, FHLMC (2ndary

mortgage market - MBS) - Typical Income Requirements
- L/Vlt80 L/Vgt80
- Fraction of Gross Income
- 1)Mortg PMT 28 25
- 2)PITI 30 28
- 3)Mort PMTLTDS 36 33
- 4)PITIutilmainchild
- LTDSSTDS 50 45
- (3 out of 4 OK if 4th close)

- Borrower Criteria
- Level of Household Income
- Stability, Growth of Income
- Financial Condition (Net Worth, Liquidity)
- Other considerations (credit hist, svgs hist,

dependents, etc., but age, gender, race etc. not

legal considerations, according to Regulation B

of FRB)

- Property (Collateral) Criteria
- Loan/Value Ratio (min price, appraisal)
- Location, but Redlining illegal

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