Mortgage Basics

1
Mortgage Basics
2
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

3
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

4
Terminology

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

5
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.

6
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.

7

• 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.

8

• 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.

9

• 8) Lender's 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

• 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

• 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

• 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.

13

• 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.

14

• 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.

15

• 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).

16

• 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.

17

• 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.

18

• 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.

19

• 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.

20

• 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.

21

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

22
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.

23
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

24

• 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.

25
"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.

26
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

27

• (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

28

• How the Calculator "Mortgage Math" Keys Work. . .
• The five "mortgage math" keys on your calculator
  (N,I,PV,PMT,FV) solve

29

• 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 (m?P/YR).

30

• 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.

31
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

32
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.)

33
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.

34

• 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.

35

• 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.

36

• 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).

37
Classical Fixed-Rate Mortgage

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

38
60,000, 12, 30-year CPM...
39

• 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.)

40
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

41

• 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.

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
• ----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

43

• 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

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 30-year
  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

49

• 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".

50

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

51

• (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.

52

• 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)

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

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 ? PMTOLBN
• 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
• (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.)

57

• 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

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 ----gt CFj key
• - 1755.14 ----gt CFj key
• 47 ----gt Nj key
• - 202404 ----gt CFj key
• IRR ----gt 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 NPV0.
  Markets 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---gtN,
• 10---gtI/YR,
• 100000---gtPV,
• 0---gtFV,
• Compute PMT---gt -877.57.

64

• 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.)

65

• 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

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
• 48N, FV97402, 99000PV, 12I/YR, FV105883,
• 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
  PMT877.57
• Next change 48?N, Compute FV97402
• Next change 11?I/YR, Compute PV96811
• 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
  "coupon-equivalent" (CEY) terms,
• Based on the classical bond format which is 2
  pmts/yr (m2?P/YR)
• Mortgages typically have monthly pmts 12 pmts/yr
  (m12?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 - 1m

71

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

72

• 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

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
• 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).

77

• 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).

78
 

• (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.)

79
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?

80

• 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).

81

• 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.

82

• 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? . . .

88

• 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.

89
 

• 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.

90

• 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.

91
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).

92

• 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
  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.

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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
• PVrefin1 8887 / 1.25 7,110.

95
 

• 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

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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.

97

• 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.

98

• 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).

99

• 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.

100

• 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.)

101
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.

102

• 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.

103

• 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.

104
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.

105

• 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).

106

• 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")

107

• 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.

108

• 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)

109

• 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)

110

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