Mortgage Basics
1
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
2
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
3
Terminology
Owner begins with "O", so: "...or" ===>
Owner
"Lessor" is Owner (Landlord), "Lessee"
is Renter.
"Mortgagor" is Owner (Borrower),
"Mortgagee" is Lender.
4
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.
5
TYPICAL COVENANTS &
CLAUSES
1) 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.
6
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 > 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.
7
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
8) Lender's Right to Inspect
Lender 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 Liability
Each party signing the mortgage is
individually completely liable for the entire
mortgage debt.
9
*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.
10
*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.
11
*12) Borrower's 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.
12
*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.
13
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.
14
*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).
15
*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 lienholder. 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.
16
*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.
17
*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.
18
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.
19
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.
20
etc., etc. . . .
Anything the borrower and lender
mutually agree on to include in the
contract.
21
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.
22
Priority of Claims in
Foreclosure
Lien Priority established by Date of Recording,
except:
Property Tax Lien comes first
Sometimes Mechanics Liens
Explicit Subordination Clause
Bankruptcy Proceedings may modify debtholder
rights
"First Mortgage" (earlier recording) = "Senior
Debt“
"2nd (etc) Mortgage" = "Junior Debt“
23
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.
24
"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.
25
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?
$22,875 
$1,000
$1,000

1  .10 12
1  .10 1215

$10,000
1  .10 1215
= (14.045)1000 + (0.8830)10000
= $14,045 + $8,830
= (PVIFA.00833,15)*PMT + (PVIF.00833,15)*FV
26
(With calculator set to pmts at “END” of periods,
and P/YR=12…)
Mortgage Math Keys:
DCF Keys:
15----> N key
10----> I/YR key
10----> I/YR key
0 ----> CFj key
1000 ----> PMT key
1000----> CFj key
10000----> FV key
14 ----> Nj key
PV ----> -22,875
11000---->CFj key
NPV ----> 22,875
27
How the Calculator "Mortgage Math"
Keys Work. . .
The five "mortgage math" keys on your
calculator (N,I,PV,PMT,FV) solve:
0   PV
PMT
PMT
PMT



2
1  r 1  r 
1  r N

FV
1  r N
28
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 (mP/YR).
29
Example:
10%, 20-yr fully-amortizing mortgage with payments
of $1000/month.
The calculator solves the following equation for PV:
0   PV 
1000
1000
1000




1.00833 1.008332
1.00833240

0
1.00833240
The result is: PV = 103625.
30
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“
31
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 = 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.)
32
APPLICATION OF THE FOUR RULES TO
SPECIFIC LOAN TYPES
1) 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.
33
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.
34
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.
35
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).
36
Classical Fixed-Rate
Mortgage
The “classical” mortgage is both FRM &
CPM:
PMT = P/(PVIFAr,N) = P / [(1 – 1/(1+r)N )/r]
37
$60,000, 12%, 30-year CPM...
MONTH
BEG.
BAL.
INTERES
T
PMT
PRIN
END BAL.
1
$60,000.0
0
$600.00
$617.17
$17.17
$59,982.8
3
2
$59,982.8
3
$599.83
$617.17
$17.34
$59,965.4
9
3
$59,965.4
9
$599.65
$617.17
$17.51
$59,947.9
8
38
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.)
39
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
40
2) Calculate Loan Amount
(Affordability):
Example: You can afford $500/month
payments on 30-year, 10% mortgage:
360----> N
10----> I/YR
500----> PMT
0----> FV
PV----> - 56,975.41 = Amt you can borrow.
41
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
42
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:
----> N
10----> I/YR
100000----> PV
0----> FV
PMT----> - 877.57
360
Then calculate remaining balance either way below:
N ----> 60
N----> 300
FV ----> - 96,574.32 PV----> 96,574.32
43
4) Calculate payments & balloon on partially
amortizing loan:
Same as (3) above.
5) Calculate the payments on an interestonly 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
44
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?
45
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 30year partially-amortizing loan, with balloon
of $20,325 due after 30 years.
46
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.)
47
Loan Yields and Mortgage
Valuation
Loan Yield = Effective Interest Rate
Yield = IRR of loan
Recall: IRR based on cash flows.
48
Using calculator equation:
0   PV
PMT
PMT
PMT



2
N
1  r 1  r 
1  r 

FV
1  r 
N
49
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".
50
Then, by the definition of "r" in the
equation above, we have:
0  NPV   CF0
CFN
CF1
CF2



2
N
1  r 1  r 
1  r 
51
(bearing in mind that:
PMT
1  r 
N

FV
1  r 
N

PMT  FV
1  r 
N

CFN
1  r N
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.
52
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…)
53
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 ;
(a)
54
(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…
55
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.
56
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.)
57
Step 1)
360----> N
10----> I/YR
200000 ----> PV
0 ----> FV
PMT----> - 1755.14
Step 2)
48----> N
FV----> - 194804 X 1.03 = - 200,649 ----> FV
196000 ----> PV
Step 3)
I/YR----> 11.22%
58
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.)
59
General rule to calculate yield:
Change the amount in the PV Register
last,
(just prior to computing the yield).
60
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%
61
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.)
62
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%?
63
Step 1)
360--->N,
10--->I/YR,
100000--->PV,
0--->FV,
Compute PMT---> -877.57.
64
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.)
65
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 points
=
1.30% =
66
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.
67
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.
68
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:
360N, 10I/YR, 100000PV, 0FV, Compute
PMT=877.57
Next change: 48N, Compute FV=97402
Next change: 11I/YR, Compute PV=96811
So NPV = $100,000 - $96,811 = +$3189.
This is before-tax market value based NPV.
69
Determining Market Yields
Market yields come from market prices in the
bond market.
Quoted in "bond-equivalent" (BEY) or "couponequivalent" (CEY) terms,
Based on the classical bond format which is 2
pmts/yr (m=2P/YR)
Mortgages typically have monthly pmts: 12
pmts/yr (m=12P/YR).
“Apples vs oranges” in comparing yields
between mortgages & bonds.
70
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
71
For bonds m=2;
For mortgages m=12.
Thus, BEY = ENAR with m=2.
"Mortgage Equivalent Yield" (MEY) = ENAR
with m=12.
72
Example:
What is MEY equivalent to 10% BEY?
2----> P/YR
10----> I/YR
EFF%----> 10.25
12----> P/YR
NOM%----> 9.80
│
│
│(1 + .10/2)2 -1 = .1025
│
│[(1 + .1025)1/12 - 1]12 = .0980
Thus, 9.80% monthly MEY = 10.00% BEY
73
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.
74
Overview of solution steps:
1.
2.
3.
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.)
75
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.
76
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:
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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 = 97,540
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.
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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.)
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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 criteria
Standards set largely by FNMA, FHLMC (2ndary
mortgage market - MBS):
Typical Income Requirements:
L/V<=80%
Fraction of Gross Income:
1)Mortg PMT #
28%
2)PITI #
30%
3)Mort PMT+LTDS #
36%
4)PITI+util&main+child
+LTDS+STDS #
50%
(3 out of 4 OK if 4th close)
L/V>80%
25%
28%
33%
45%
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Borrower Criteria:
1)
2)
3)
4)
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)
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Property (Collateral) Criteria:
1)
2)
Loan/Value Ratio (min: price,
appraisal)
Location, but "Redlining" illegal
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