1. 課程六 : Real Estate Financing

2. Flow of Real Estate Financial Capital The issues: Real estate is capital intensive Typical capital structure is dominated by debt That is a major portion of the funds to purchase a home or construct an office building, etc must be borrowed The segment of the capital markets where these funds come from are called mortgage markets This sector of the debt market is by far the largest in the US and in some respect the world

3. Flow of Real Estate Financial Capital Potential developers, homeowners etc. must obtain financing in order to build, own and operate properties Funds are supplied by a variety of individuals, firms, institutions and government as shown in the figure Between the users and the sources of funds are a number of service organizations that make the raising of capital easier and more efficient Financial capital flows from suppliers to users in the form of debt (mortgage) and equity Providers of debt have priority claim on the revenue from operation Equity holders have residual claim on cash flow

4. The Flow of Real Estate Financial Capital Thrifts Commercial Banks Insurance companies Pension Funds REITs Credit Unions Governments Nonfinancial business Households Foreign Investors Mortgage Bankers Mortgage Brokers Real Estate Brokers Investment Bankers Government agencies Syndicators Developers Owners of Homes Owners of income Properties Land Owners SUPPLIES OF CAPITAL SERVICE GROUPSUSERS OF CAPITAL Equity Debt E D

5. 3Q 1994 total: $12,309 Billion Total Credit Outstanding in U.S

6. The Supply of Mortgage Debt Types of lenders –Portfolio lenders –Non-portfolio lenders –Depository institutions –Contractual or non-depository institutions –Specialized mortgage market intermediaries mortgage companies federally related agencies or GSEs real estate investment trusts Types of loans –Construction Loans –Permanent loans

7. Total Mortgage Outstanding 75.2% 16.1% 1.6% 6.8% Total $4,279 (billions, 3rd Q 1994)

8. Total Mortgage Debt Outstanding The total mortgage outstanding is around $4.3 trillion –single family mortgage debt accounts for the biggest share 75.2% or $3.2 trillion ($3,217.5 billion) –Commercial and multifamily accounts for roughly 23% or $1 trillion Residential Mortgages –Commercial banks and S&Ls are the major portfolio lenders of whole loans –Roughly 49% or $1.6 trillion of the mortgages are securitized mainly by GNMA, FNMA FHLMC or GSEs –GSEs hold 7.6% or $246.1 billion of whole loans –GSEs account for roughly 57% or $1.75 trillion of 1-4 family residential mortgages

9. Mortgage Market Participants In Billions of Dollars

10. Why Study Mortgage Market ? Shed light on how traditional method of financing assets by financial intermediaries is rapidly changing securitization is the new BIG BROTHER Demonstrates how financial engineering can redirect cash flows to create securities that more closely satisfy the asset/liability needs of investors Government agencies provide Credit guarantees for mortgage backed securities should government agencies continue to provide guarantee

11. Supply of loanable funds The amount of funds borrowed and lent depends on interest rates. –As rates rise many spending units save more and spend less –Simultaneously when interest rates rise many spending units demand less credit –The figure following illustrates the operation of supply and demand for loanable funds –The demand schedule is downward sloping, reflecting greater willingness to borrow at lower rates. –The supply schedule, s 1, rise to the right, because people have more to lend at higher rates –The intersection of the of the two schedules determines the amount of funds lent, f 1, and the prevailing interest rate, i 1

12. Supply and demand for loanable funds d1d1 s2s2 s1s1 f1f1 f2f2 i1i1 i2i2 Amount of loanable funds Interest rate

13. Real Estate Financial Instrument When ever real estate is financed, the property is pledged as collateral or security creating a financial instrument known either as MORTGAGE or DEED OF TRUST Power of secured debt: attempting to buy a $300 suit on credit versus obtaining $200,000 loan to build a house –Mortgage : Two Parties –Deed of Trust : Three Parties –Promissory Note –Title Pledge

14. Note + Pledge Funds Pledge and lien are extinguished with performance of mortgage contract MORTGAGE Borrower (Mortgagor) Lender (Mortgagee) A bilateral financial contract

15. Note Funds pledge of title Title goes to borrow if no default if default property is sold and proceeds goes to lender DEED OF TRUST Borrower (Trustor) Lender (Beneficiary) Trustee A three-party financial contract

16. Important Contractual Provisions in Real Estate Financial Instruments Parties to the contract Loan amount Term of loan Interest rate Amortization period Property description Priority of loan Acceleration clause Escalation clause Prepayment clause callable mortgage non-callable mortgage

17. Important Contractual Provisions in real estate financial instrument Due-on-Sale Clause Default Clause (put option) Personal Liability Clause Deficiency Judgment Foreclosure Redemption Rights –Equitable right –Statutory right Escrow Provisions

18. Loan Termination Termination by satisfying contract ending lien against pledged property trustee provides deed of release defeasance clause Termination by mutual agreement Refinance Recasting Deed in lieu of foreclosure Termination by foreclosure

19. Redemption Rights date of default Foreclosur e suite filed Foreclosure sale End of Statutory period Equitable Right of Redemption Period Statutory Right of Redemption Period FORECLOSURE PROCESS

20. Alternative mortgage contracts Fixed Rate Mortgage (FRM) Adjustable Rate Mortgage (ARM) Graduated Payment Mortgage (GPM) Shared Appreciation Mortgage (SAM) Reverse Annuity Mortgage (RAM) Growing Equity Mortgage (GEM) Balloon Mortgage

21. Other Mortgages Junior Mortgage Purchase Money Mortgage Land Contract Wraparound Mortgage

22. Types of mortgage amortization Interest only mortgage (bullet loans) Partially amortizing or balloon mortgage Fully amortizing

23. Risks faced by mortgage finance intermediaries Credit risk: risk that money borrowed might not returned timely Default risk: risk that money lent might not be repaid Cash flow risk: risk that market conditions will alter scheduled cash flows –prepayment risk –inflation risk –exchange risk –interest rate risk Liquidity risk: risk that money will be needed before it is due

24. Mortgage Contract Rate Generalized Mortgage Contract Rate R j = R* + (1-a)D + a E(P) where: R j = contract interest rate on mortgage of type j. R* = real rate of return a = risk sharing parameter D = risk loading P = pure interest rate risk component j = term of loan

25. n a = 1 R j = R* + E(P) Uncapped ARM or free floating rate. n 0 < a < 1 R j = R* + (1-a)D + aE(P) Capped ARM n a = 0 R j = R* + D FRM Contact rate = risk free rate + liquidity + default + prepayment + inflation + interest rate risk + origination and servicing cost Mortgage Contract Rate

26. Mathematics of level-payment mortgages Mortgage investors must be able to calculate scheduled cash flows associated with mortgages. Servicers of mortgages must be able to calculate servicing fee We also need to know cash flow from mortgage pools to price MBS

27. Monthly Mortgage Payment Mortgage payment requires the application of PVA PVA = A[1-(1+i) -n ]/i –where: –A = amount of annuity –n = number of periods –PVA = present value of annuity –i = periodic interest rate The term in the outer bracket is called the present value of annuity factor (PVAF)

28. Redefine terms for level pay mortgage MB 0 = DS([1-(1+i) -n ]/i) –where: –DS = monthly mortgage payment –n = amortization period or term or mortgage –MB 0 = original mortgage amount –i = simple monthly interest (annual/12) Solving for DS gives DS = MB 0 {[i(1+i) n ]/[(1+i) n -1 )]} The term in outer bracket is called mortgage constant or payment factor So what is a mortgage constant (MC)?

29. Illustration Original mortgage balance (MB 0 ) = $100,000, term/amortization period (n) = 360 mons., interest rate (i) = 9.5 or.095/12 =.0079167 DS = MB 0 {[i(1+i) n ]/[(1+i) n -1 )]} DS = $1,000,000{[.0079167(1.007967) 360 ]/[(1.0079167) 360 - 1]} = $100,000(.0084085) = $840.85 Illustration using calculator: -$100,000 = PV ; 9.5/12 = I; 30x12 = n; PMT = ?

30. Mortgage Balance Mortgage Balance each period is given by the ff. formula MB t = MB 0 {[(1+i) n - (1+i) t ]/[(1+i) n - 1]}, where MB 0 = mortgage balance after t months Example: Mortgage balance in 210th month is t = 210; n = 360; MB 0 = $100,000; i =.095/12 =.0079167 MB 210 = 100,000{[(1.0079167) 360 - (1.0079167) 210 ]/[(1.0079167) 360 - 1]} = $73,668 Check (calculator): $840.85 = PMT 9.5/12 = i ; 150 = n PV =? $73,668

31. Scheduled principal payment (P t ) is P t = MB 0 {[i(1+i) t-1 ]/[(1+i) n - 1] Example: Scheduled principal payment for 210th month is P 210 = {[.0079167(1.0079167) 210 - 1 ]/[(1.0079167) 360 -1]} = 100,000{.0079167(5.19696) = $255.62 CHECK: 840.85 = PMT ; 9.5/12 = i ; 13x12 = n ; PV = $75,171.72 Balance at end of month 210 = $73,667.78 Scheduled principal paid = $75,171.72 - $73,667.78 = $1503.94 Scheduled Principal Payment

32. Scheduled Interest Scheduled interest is as follows: I t = MB 0 {i[(1+i) n - (1+i) t-1 ]/[(1+i) n - 1]} where I t = interest in month t Example: scheduled interest in month t is I 210 = 100,000{.0079167[(1.0079167) 360 - (1.0079167) 210 - 1 ]/ [(1.0079167) 360 - 1]} = 100,000{.0079167[(17.095 - 5.19696)]/[17.095 - 1]} = $585.23 CHECK Debt Service = 255. 62(p) + 585.23 (i) = $840.85

33. Monthly Mortgage Cash flow If the mortgage investor services the mortgage the investor’s cash flow is principal, interest payment If the investor sells the right to service the mortgage the interest income is net of servicing fee Servicing fee = [MB t (servicing fee rate)]/12 Example: assume servicing fee rate is.5%, then servicing fee for month 211 is = [(73,668)(.005)]/12 = 368.34/12 = $30.70 Note the balance at end of month 210 ($73,668)is the beginning balance for month 211 Net interest payment for month 211 = $583.21 - 30.70 = $552.51

34. Mortgage Amortization Schedule Loan Amount = $100,000 Interest Rate = 10% Term of Loan or amortization period = 30 yrs. Mortgage Constant =.10608 Yearly payment Debt Service = Loan Amount x Mortgage Constant = 100,000 x.10608 Yearly Payment = $10,608

35. Amortization Schedule A.INTEREST RATE METHOD BOY1 principal balance = $100,000 EOY1 interest (100,000 x.1)= $10,000 EOY1 principal repaid = $608 (10,608 - 10,000) EOY1 balance (100,000 - 608)= $99,392 BOY2 principal balance= $99,392 EOY2 interest (99,392 x.1)= $9,939.2 EOY2 principal repaid = $668.2 (10,608 - 9,939.2) EOY2 balance (99,302 - 668.8)= $98,723.2

36. Amortization Schedule Amount YearOutstandingPayment InterestPrincipal 0$100,000 199,392$10,608 $10,000$608 298,723.210,608 9,939.2668.2 397,987.5210,008 9,872.32735.68

37. Amortization Schedule B. PRESENT VALUE METHOD Loan Amount = $100,000 Annual Interest Rate = 10% Frequency of Payments = Monthly Term of Loan = 30 yrs. (360 months) Monthly Mortgage Constant =.00877572 Monthly Debt Service = 100,000 x.00877572 = $877.57 Annual Payment = 100,000 x.00877572 x 12 = $10,530.86

38. Amortization Schedule BOY1 principal balance=$100,000 EOY1 balance = [PVAF 10/12, 348 ] x 877.57 = 113.3174 x 877.57 = $99,443.95 EOY1 prin. repaid = 100,000 - 99,443.95 = $556.05 EOY1 interest = 10,530.86 - 556.05 = $9,974.81 BOY2 principal balance = $99,443.95 EOY2 balance = [PVAF 10/12, 336 ] x 877.57 = 112.6176 x 877.57 = $98,829.83 EOY2 prin. repaid = 99,443.95 - 98,829.83 = $614.12 EOY2 interest = 10,530.86 - 614.12 = $9,916.74

39. Amortization Schedule Amount YearOutstandingPayment InterestPrincipal 0$100,000 199,443.95$10,530.86 $9,974.81$556.05 298,829.83 10,530.86 9,916.74 614.12 398,151.47 10,530.86 9,852.50 678.36

40. Alternatives For Determining Mortgage Balance 1. Present value of annuity factor (PVAF) PVAF i%, n - t Proportion Outstanding = --------------------------- PVAF i%, n where n = the period over which the loan is amortized t = period in which balance is desired n - t = remaining life of the loan

41. Alternative method of determining mortgage balance 2. Mortgage Constant (MC) MC i%, n Proportion Outstanding = --------------------------- MC i%, n - t

42. Example What is the proportion outstanding at the end of 10th year for a loan which is fully amortizing, with a term of 30 years, interest rate of 10%, monthly payments. The original loan amount is $100,000 PVAF 10/12%, 240 mon. 103.624619 PO = ------------------------------- = --------------- =.909380195 PVAF 10/12%, 360 mon 113.950820 Therefore balance outstanding = (.909380195)(100,000) = $90,938.02

43. Example Mortgage Constant Approach MC 10/12%, 360 mon.008776 PO = -------------------------- = ------------- =.909430051 MC 10/12%, 240 mon.009650 Proportion paid off = (1 -.909430051) =.0905699 Outstanding loan amount = 100,000x.909430051 = $90,943.0051

44. Alternatives for Determining %of Loan Outstanding 3. Future value of annuity factor (FVAF): FVAF t, i PO = 1 - ------------------------ FVAF n, i 204.844979 = 1 - --------------------- =.909380194 2260.487925 where: FVAF t = future value of annuity factor in period t FVAF n = future value of annuity factor in period n t = year in which balance is desired n = term or amortization period of loan