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Mortgage Basics

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**Types of Mortgages Types of Collateral: Permanent vs. Construction**

Residential 1 to 4 family homes (up to 4 units) Commercial Larger apartments & non-residential Permanent vs. Construction Perm on completed existing buildings Construction loans finance development projects

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**Government Involvement**

Government-Insured (FHA, VA) Include “mortgage insurance”, allows higher L/V ratio More “red tape”, longer approval process No “due-on-sale” clause, may be assumable Conventional Normally max L/V=80%, unless private mortgage insurance (PMI) Majority of all loans

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

"Lessor" is Owner (Landlord), "Lessee" is Renter. "Mortgagor" is Owner (Borrower), "Mortgagee" is Lender.

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**Legal Structure of Mortgages**

Mortgages have 2 parts (documents): Promissory Note: Contract establishing debt. Mortgage Deed: Secures debt with real property collateral (potentially conveys title). Two legal bases of mortgages: "Lien Theory" (most states): borrower holds title, lender gets lien. "Title Theory" (a few states): Lender holds title.

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**TYPICAL COVENANTS & CLAUSES**

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.

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**3) Hazard Insurance *4) Mortgage 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.

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***6) Order of Application of Payments**

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.

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**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.

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***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.

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*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.

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***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.

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*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.

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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.

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*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).

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***17) Lender's Right to Notice (Jr Loans)**

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

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***18) Subordination 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.

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**20) Covenant against Removal**

*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.

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**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.

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**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.

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

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**More Terminology “Purchase Money Mortgage" vs Refinancing**

"Land Contract" Title does not pass until contract paid off "Wraparound Mortgage" ("wrap") 2nd Mortgage issued by seller to buyer, seller keeps 1st Mortgage alive, using wrap pmts to cover (smaller) 1st Mortgage pmts.

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**Priority of Claims in Foreclosure**

Lien Priority established by Date of Recording, except: Property Tax Lien comes first Sometimes Mechanics Liens Explicit Subordination Clause Bankruptcy Proceedings may modify debtholder rights "First Mortgage" (earlier recording) = "Senior Debt“ "2nd (etc) Mortgage" = "Junior Debt“

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**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.

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**"Redeem up, Foreclose down"**

Senior Lien Holders obtain their claim (to the extent foreclosure sale proceeds and their priority allows), even if they did not bring the suit. Junior Lien Holders lose claims after foreclosure, provided they are included in the foreclosure suit. Lien Holder bringing foreclosure suit normally buys the property in the foreclosure sale, for amount sufficient to cover its claim.

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Mortgage Math What is PV of $1000 per month for 15 months plus $10,000 paid 15 months from now at 10% nominal annual interest? = (14.045) (0.8830)10000 = $14,045 + $8,830 = (PVIFA.00833,15)*PMT + (PVIF.00833,15)*FV

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

Mortgage Math Keys: DCF Keys: 15----> N key > I/YR key 10----> I/YR key > CFj key > PMT key > CFj key > FV key > Nj key PV ----> -22, >CFj key NPV ----> 22,875

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

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

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

where: r = i / m, where: i = Nominal annual interest rate m = Number of payment periods per year (mP/YR).

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Example: 10%, 20-yr fully-amortizing mortgage with payments of $1000/month. The calculator solves the following equation for PV: The result is: PV =

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**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“

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**THE FOUR BASIC RULES: IEt = rt(OLBt-1) PPt = PMTt – IEt**

OLBt = OLBt 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.)

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**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: rt=r, all t. 2) Constant-Payment loans (CPMs): The payment is constant throughout the life of the loan: PMTt=PMT, all t.

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**3) Constant-Amortization loans (CAMs):**

The principal amortization is constant throughout the life of the loan: PPt=PP, all t. 4) Fully-Amortizing loans: Initial contract principal is fully paid off by maturity of loan: PPt=P over all t=1,…,N. 5) Partially-Amortizing loans: Loan principal not fully paid down by due date of loan: PPt<P, so OLBN must be paid as “balloon” at maturity.

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**6) Interest-Only loans:**

The principal is not paid down until the end: PMTt=IEt, all t (equivalently: OLBt=P, all t, and in calculator equation: FV = -PV). 7) Graduated Payment loans (GPMs): The initial payment is low, usually initial PMT1 < IE1, so OLB at first grows over time (“negative amortization”), followed by higher payments scheduled later in the life of the loan.

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**8) Adjustable-Rate loans (ARMs):**

The contract interest rate varies over time (rt not constant, not known for certain in advance, loan payment schedules & expected yields must be based on assumptions about future interest rates).

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**Classical Fixed-Rate Mortgage**

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

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**$60,000, 12%, 30-year CPM... MONTH BEG. BAL. INTEREST PMT PRIN**

END BAL. 1 $60,000.00 $600.00 $617.17 $17.17 $59,982.83 2 $599.83 $17.34 $59,965.49 3 $599.65 $17.51 $59,947.98

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

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**Using Your Calculator Calculate Loan Payments:**

Example: $100, year 10% mortgage with monthly payments: ----> N 10----> I/YR > PV 0 ----> FV PMT---->

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**2) Calculate Loan Amount (Affordability):**

Example: You can afford $500/month payments on 30-year, 10% mortgage: > N 10----> I/YR > PMT 0----> FV PV----> - 56, = Amt you can borrow.

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**3) Calculate Outstanding Loan Balance:**

Example: What is the remaining balance on $100,000, 10%, 30-year, monthly-payment loan after 5 years (after 60 payments have been made)? First get loan terms in the registers: ----> N 10----> I/YR > PV 0----> FV PMT----> Then calculate remaining balance either way below: N ----> 60 N----> 300 FV ----> - 96, PV----> 96,574.32

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**4) Calculate payments & balloon on partially amortizing loan:**

Same as (3) above. 5) Calculate the payments on an interest-only loan: Example: A $100,000 interest-only 10% loan with monthly payments: N can be anything, ---> I/YR, > PV, > FV, PMT --->

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**6) Meet affordability constraint by trading off payment amount with amortization rate:**

Example: Go back to example #2 on the previous page. The affordability constraint was a $500/mo payment limit. Suppose the $56,975 which can be borrowed at 10% with a 30-year amortization schedule falls short of what the borrower needs. How much slower amortization rate would enable the borrower to obtain $58,000?

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

Enter: I/YR = 10, PV = , PMT = 500, FV = 0, Compute: N = 410. Thus, the amortization rate would have to be 410 months, or 34 years. Note: This does not mean loan would have to have a 34-year maturity, it could still be a 30-year partially-amortizing loan, with balloon of $20,325 due after 30 years.

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**7) Determining principal & interest components of payments:**

Example: For the $100,000, 30-year, 10% mortgage in problem #1 on the previous page, break out the components of the 12 payments numbering 50 through 61. In the HP-10B, after entering the loan as in problem #1, enter: 50, INPUT, 61, AMORT, = $9, int, = $ prin, =$96,501 OLB61. To get the corresponding values for the subsequent calendar year, press AMORT again, to get: = $9, int, = $ prin, =$95,579 OLB73. (Other business calculators can do this too.)

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**Loan Yields and Mortgage Valuation**

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

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**Using calculator equation:**

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**Let: PV= CF0 PMT= CFt , t=1,2,...,N-1 PMT + FV = CFN N= Holding Period**

where: CFj represents actual cash flow at end of period "j".

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

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

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In 2ndary mkt, loans are priced so their yields equal the “mkt’s required yield” (like expected total return, E(r)=rf+RP, from before). At the time when a loan is originated (primary market), the loan yield is usually approximately equal to its contract interest rate. (But not exactly…)

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**The tricky part in loan yield calculation:**

The holding period over which we wish to calculate the yield may not equal the maturity of the loan (e.g., if the loan will be paid off early, so N may not be the original maturity of the loan): N maturity ; (b) The actual time-zero present cash flow of the loan may not equal the initial contract principal on the loan (e.g., if there are "points" or other closing costs that cause the cash flow disbursed by the lender and/or the cash flow received by the borrower to not equal the contract principal on the loan, P): CF0 P ;

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(c)The actual liquidating payment that pays off the loan at the end of the presumed holding period may not exactly equal the outstanding loan balance at that time (e.g., if there is a "prepayment penalty" for paying off the loan early, then the borrower must pay more than the loan balance, so FV is then different from OLB): CFN PMT+OLBN So we must make sure that the amounts in the N, PV, and FV registers reflect the actual cash flows…

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**Example $200,000 mortgage, 30-year maturity, monthly payments**

10% annual interest The loan has “2 points” (‘discount points’ or prepaid interest) Also a 3 point prepayment penalty through end of 5th year.

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**Break this problem into 3 steps:**

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=$ ); (2)Alter the amounts in the registers to reflect the actual cash flows; (3)Compute yield. (You must do these steps in this order.)

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**Step 1) Step 2) Step 3) ----> N 10----> I/YR 200000 ----> PV**

0 ----> FV PMT----> Step 2) 48----> N FV----> X = , > FV > PV Step 3) I/YR----> %

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**Expected yield (like E(r) or “going-in IRR”) is 11**

Expected yield (like E(r) or “going-in IRR”) is 11.22%, even though “contractual interest rate” on the loan is only 10%. (When closing costs and prepayment penalties are quoted in "points", you do not need to know the amount of the loan to find its yield.)

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**General rule to calculate yield:**

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

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**Equivalent solution to previous problem:**

Use CF keys instead of mortgage math keys… > CFj key > CFj key > Nj key > CFj key IRR ----> %

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**Using Market Yields to Value Mortgages**

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

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Example $100,000 mortgage, 30-year, 10%, 3 points prepayment penalty before 5 years. Expected time until borrower prepays loan = 4 years. How much is the loan worth today if the market yield is 11.00%?

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**Step 1) 360--->N, 10--->I/YR, 100000--->PV, 0--->FV,**

Compute PMT--->

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**Step 2) Step 3) Step 4) The loan is worth $98,697. 48--->N,**

FV---> -97,402 * 1.03 = -100, >FV. Step 3) I/YR---->11.00%. Step 4) PV----> 98,697. The loan is worth $98,697. (Watch out for order of steps. Cash flows first, then input the market yield, then compute the loan value as the PV.)

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**Determining required “discount points” (or “origination fee”):**

To avoid lender doing NPV < 0 deal in making loan, we need: (100, ,697) / 100, = % = points

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**Yield-Maintenance Prepayment Penalty**

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

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**Answer: Original loan in registers, then:**

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 = – = $8,481.

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**Valuing a "seller loan" or subsidized loan:**

(Been there, done that.) Example: $100,000, 10%, 30-yr amort loan, no points or ppmt penalty, maturing in 48 months with a balloon: 360N, 10I/YR, PV, 0FV, Compute PMT=877.57 Next change: 48N, Compute FV=97402 Next change: 11I/YR, Compute PV=96811 So NPV = $100,000 - $96,811 = +$3189. This is before-tax market value based NPV.

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**Determining Market Yields**

Market yields come from market prices in the bond market. Quoted in "bond-equivalent" (BEY) or "coupon-equivalent" (CEY) terms, Based on the classical bond format which is 2 pmts/yr (m=2P/YR) Mortgages typically have monthly pmts: 12 pmts/yr (m=12P/YR). “Apples vs oranges” in comparing yields between mortgages & bonds.

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e.g., “10% yield”: For a bond, for each $1 you invest at the beginning of the year you would have: (1.05)(1.05)= (1.05)2= $1.1025 For a mortgage, you would have: ( )( )...( )=( )12= $1.1047 To make “apples vs apples” comparisons, define: Effective Annual Yield EAY = (1 + ENAR/m)m -1 Equivalent Nominal Annual Rate ENAR = [(1 + EAY)1/m - 1]m

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**For bonds m=2; For mortgages m=12. Thus, BEY = ENAR with m=2. **

"Mortgage Equivalent Yield" (MEY) = ENAR with m=12.

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** Thus, 9.80% monthly MEY = 10.00% BEY**

Example: What is MEY equivalent to 10% BEY? 2----> P/YR │ 10----> I/YR │ EFF%----> │( /2)2 -1 = .1025 12----> P/YR │ NOM%----> │[( )1/12 - 1]12 = Thus, 9.80% monthly MEY = 10.00% BEY

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**Refinancing This is essentially a comparison of two loans.**

NPV is the evaluation (decision) framework. OCC (disc.rate, “r”) = Eff. int. rate in current loan market (“mkt yield”). Basic principles (“apples vs apples”): 1) Compare over same time horizon; 2) Compare over the same debt amount.

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**Overview of solution steps:**

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.)

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**Steps (1) & (2) are all that is presented in typical R. E**

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

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**Step 1) The NPV of the incremental cash flows.**

Compare the two loans: Old vs New. Note: In principle, this analysis should be based on “investment value” on an after-tax basis. Requires use of computer spreadsheet. (See “frmrefin.xls”, downloadable from course web site.) The after-tax NPV will be less than the before-tax NPV, but generally it will be quite a bit greater than (1-taxrate)*BTNPV, the more so the longer the holding period (approaching BTNPV in the limit).

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**Most convenient way to do Step 1...**

NPV = PV(Benefit) - PV(Cost) Benefit = Remaining cash flows on old loan you save by paying off old loan. Cost = Amount you must pay to pay off old loan today. Discount rate = Market rate today = Yield (over expected holding period) on new loan. Analysis horizon = Expected holding period (same under either loan, also applies to calculate market opportunity cost of capital as yield on new loan).

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

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**Example of Step 1 Loan refinancing NPV calculation:**

Old loan was $100, 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 = Now change to: 84 = N, and compute FV = Now change to: .98 = PV, and compute I/YR = % 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, = PV, 0 = FV, and compute PMT = 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:**

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: = + $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**

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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**How much is this option worth? . . .**

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] = = -$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**

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: = -$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: 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"):**

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% L/V>80% Fraction of Gross Income: 1)Mortg PMT # 28% 25% 2)PITI # 30% 28% 3)Mort PMT+LTDS # 36% 33% 4)PITI+util&main+child +LTDS+STDS # 50% 45% (3 out of 4 OK if 4th close)

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**Borrower Criteria: 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:**

Loan/Value Ratio (min: price, appraisal) Location, but "Redlining" illegal

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