BUSI 121 Foundations of Real Estate Mathematics

Transcription

1 BUSI 121 Foundations of Real Estate Mathematics SESSION 5 Chapter 6 Graham McIntosh Sauder School of Business

2 Outline Introduction PV vs I/YR Vendor Financing Mortgage Assumption 2

3 Objectives Understand what is Vendor Financing Calculate the Market Value of the Mortgage and the Offer Understand what is a Mortgage Assumption Calculate the market value of an assumed mortgage 3

4 Pre requisites Ability to perform interest rate conversions Ability to solve for a mortgage payment (PMT) or mortgage amount (PV) Ability to calculate outstanding balances 4

5 Introduction Chapters 6 and 7 are for the most part based on the relationship between PV vs I/YR Ideally, you should read these chapters together In essence, most of the questions in Ch. 6 and 7 involve changing one the inputs (PV or I/YR) and analyzing the impact on the other (I/YR or PV) while keeping the payments the same 5

6 Present Value and I/YR PV and I/YR are Inversely Related (they move in opposite directions) I/YR Increases I/YR Decreases PV Decreases PV Increases This is the important relationship to remember when finding the market value of vendor take-back and analyzing bonused mortgages. 6

7 Mortgage Markets Primary Market = where mortgages are initiated Secondary Mortgage Market = where existing mortgages are traded 7

8 Vendor Mortgage Financing The vendor in this situation has two relationships with the purchaser: 1. As seller of the property. 2. As lender to the purchaser. Typically these types of loans occur when it is necessary to enhance the sale of the property: developers providing an incentive via below market financing in order to sell condos or homes in a new subdivision or condos. (avoid alienating previous purchasers, who paid full price) Incentive of lower financing costs in slow market, therefore encourage sales Lender of last resort The mortgage could be an investment for the vendor 8

9 Vendor Mortgage Financing 9

10 Vendor Mortgage Financing Vendor should be aware of potential risks (default and foreclosure) tax implications (interest income is taxable) admin costs These deals involve interests rates on the mortgage contracts which are usually less than (could be more than as well) than the rates prevailing in the market. Therefore this leads to a difference in value of the vendor mortgage versus the value of market mortgages. The vendor should be aware of the value of their price versus the market: this is accomplished by determining the market value of the offer or cash equivalent price of the offer 10

11 Vendor Mortgage Financing Down Payment Amount (Cash or Equity) + Market Value of the Mortgage = Market Value of the Offer The market value of a Vendor mortgage is the present value of the payments and OSB as determined under the Vendor mortgage contract discounted at the market rate of interest. What it would cost the purchaser if they had to go out and arrange a mortgage in today's market based on the same level of payments? (Remember PV of Pmts. vs. I/YR) 11

12 VTB Steps The following steps could be followed when calculating the market value of the offer of a Vendor loan: 1. Calculate the loan information with the "contract rate": perform an interest rate conversion (if necessary) calculate the required payment and enter the rounded payment if there is a term, calculate the OSB and enter the rounded OSB into FV and change N = length of the term 2. Calculate the market value of the mortgage with the "market rate": perform an interest rate conversion (if necessary) compute the market value ( PV ) of the mortgage 3. Calculate the market value of the offer: add the cash down payment to the market value of the mortgage to calculate the market value of the offer 12

13 VTB Mortgage Example 1 Example 1: Fully Amortized Vendor Loan Joe Buyer has offered to purchase Jane Seller's house for $350,000. Joe has offered to pay $100,000 of the total purchase price as a cash down payment. He wants Jane to offer vendor financing on the remaining $250,000. If Jane "takes back" the $250,000 as a first mortgage on the property, Joe says he will pay her a rate of j 2 = 5% on the funds. He has requested that the mortgage be fully amortized over a 25 year period by constant monthly payments (rounded up to the next higher cent). Calculate the market value of this offer if the current market rate of interest is j 2 = 8% 13

14 VTB Mortgage Example 1 Calculate the Market Value of the Offer: Cash down = $100,000 Vendor loan = $250,000 Contract Rate = j 2 = 5% Monthly Payments (Round up to the next higher cent) 25-year Amortization period and Term Market Rate = j 2 = 8% 14

15 VTB Mortgage Example 1 Step 1: Interest Rate Conversion - Contract Rate j 2 =5% Calculator Steps Press Display Comments 5 NOM% 5 2 P/YR 2 EFF% P/YR 12 NOM% j 12 rate j 2 = 5% Stored in I/YR 15

16 VTB Mortgage Example 1 Step 2: Solve for Payment Calculator Steps Press Display Comments P/YR Already entered NOM% Already entered I/YR PV 250,000 Loan amount 25 X 12 = 300 N 300 Amort. period 0 FV 0 PMT -1, /- PMT -1, Enter rounded PMT N recalculated N 16

17 VTB Mortgage Example 1 Step 3: Discount the PMTS = $ at the market interest rate j 2 =8% (Solve for the MV of the Mortgage) Calculator Steps Press Display Comments 8 NOM% 8 2 P/YR 2 EFF% P/YR 12 NOM% j 12 rate j 2 = 8% Stored in I/YR PV 190, MV of the Mortgage 17

18 VTB Mortgage Example 1 Step 4: Market Value of the Offer $190, MV of the Mortgage + $100, Cash Down Payment = $290, MV of the Offer 18

19 VTB Mortgage Example 1 Conclusion: PMT = $ Can Borrow $250, at j 2 = 5% PMT = $ Can Borrow $190, at j 2 = 8% Difference in PV s $59,

20 VTB Mortgages - Example 1 Equation: Fully Amortized VTB Loan i = periodic MARKET interest rate per month equivalent to j 2 =8% in this case to j 12 = % = i mo = % = ) Solve for PV = Market Value of the Mortgage = $190, PV 1 (1 + i) = PMT i n = 1 ( ) 190, = 1,

21 Step 1: Convert j 2 = 8% to j 12 Calculator Steps VTB Mortgage Example 1 (another Method) Calculate the Difference in PMTS PV = $250,000 at j 2 =5%; PMT = $ Calculate the PMT for $250,000 at j 2 = 8% Press Display Comments 8 NOM% 8 2 P/YR 2 EFF% P/YR 12 NOM% j 12 rate j 2 = 8% Stored in I/YR 21

22 VTB Mortgage Example 1 (another Method) Step 2: Solve for Payment at j 2 = 8% Calculator Steps Press Display Comments P/YR Already entered NOM% Already entered I/YR PV 250,000 Loan amount 25 X 12 = 300 N 300 Amort. period 0 FV 0 PMT /- PMT -1, Enter rounded PMT N recalculated N 22

23 VTB Mortgage Example 1 (another Method) Step 3: Solve for the PV of the difference in PMTS at j 2 = 8% $ $ = $ Calculator Steps Press Display Comments P/YR Already entered NOM% Already entered I/YR N Already entered N FV Already entered FV /- PMT Enter difference in PMTS PV 59, PV of the difference in PMTS 23

24 VTB Mortgage Example 1 (another Method) Conclusion: PV = $250,000.00; PMT = $ at j 2 = 5% PV = $250,000.00; PMT = $ at j 2 = 8% Difference in PMT s $ PV s of the difference in PMTS = $59, If the borrower needs $250,000, the vendor mortgage interest rate (5%) will save them $ per month in payment costs 24

25 VTB Mortgage Example 2 Example 2: Partially Amortized Vendor Loan Referring back to Example 1, what is the market value of the offer if the loan now has a 5-year term? Calculate the Market Value of the Offer: Cash down = $100,000 Vendor loan = $250,000 Contract Rate = j 2 = 5% Monthly Payments (Round up to the next higher cent) 25-year Amortization period 5-year Term Market Rate = j 2 = 8% 25

26 VTB Mortgage Example 2 Step 1: Interest Rate Conversion - Contract Rate Calculator Steps Press Display Comments 5 NOM% 5 2 P/YR 2 EFF% P/YR 12 NOM% j 12 rate j 2 = 5% Stored in I/YR 26

27 VTB Mortgage Example 2 Step 2: Solve for Payment and OSB term Calculator Steps Press Display Comments P/YR Already entered NOM% Already entered I/YR PV 250,000 Loan amount 25 X 12 = 300 N 300 Amort. period 0 FV 0 PMT -1,

28 VTB Mortgage Example 2 Step 2: Solve for Payment and OSB term (cont d) Calculator Steps Press Display Comments /- PMT -1, Enter rounded PMT 60 INPUT AMORT Find OSB after the 60 th payment = = = 221, OSB /- FV -221, Enter rounded OSB into FV 60 N 60 Set N = Term 28

29 VTB Mortgage Example 2 Step 3: Discount the Payments at the market interest rate (MV of the Mortgage) Interest Rate Conversion: Market Rate Calculator Steps Press Display Comments 8 NOM% 8 2 P/YR 2 EFF% P/YR 12 NOM% j 12 rate j 2 = 8% Stored in I/YR PV 221, MV of the Mortgage 29

30 VTB Mortgage Example 2 Step 4: Market Value (MV) of the Offer $221, MV of the Mortgage + $100, Cash Down Payment = $321, MV of the Offer 30

31 VTB Mortgages - Example 2 Equation: Partially Amortized VTB Loan t = length of the term = 60 i = periodic MARKET interest rate per month equivalent to j 2 =8% in this case to j 12 = % = i mo = % = ) Solve for PV = Market Value of the Mortgage = $221, (1 + i) PV = PMT i t + OSB (1 + i) t 1 ( ) 221, = 1, t ,268.26( ) 60 31

32 VTB Mortgage Common Errors: Forgetting to add back the down payment (offer) Forgetting to calculate the OSB at term Mixing up the contract and market rates of interest 32

33 Mortgage Assumption Mortgage Assumption is where the purchaser assumes (takes over responsibility) the remaining payments (the regular payments and the OSB at the end of the term) of the vendor s mortgage from the bank (third party lender). Usually occurs when interest rates have been increasing (a form of below market financing). Not all mortgages are assumable, it requires a clause in the mortgage contract and is at the option of the bank. Analysis is similar to partially amortized vendor loans, the only difference being the timeframe N for discounting is shorter. 33

34 Mortgage Assumption Steps The following steps could be followed when calculating the market value of the offer of an assumed loan: 1. Calculate the loan information with the "contract rate": perform an interest rate conversion (if necessary) calculate the required payment and enter the rounded payment calculate the OSB at the end of the term and enter rounded OSB into FV be sure to enter the number of payments remaining (the assumed payments) into N 2. Calculate the market value of the assumed mortgage with the "market rate": perform an interest rate conversion (if necessary) compute the market value ( PV ) of the assumed mortgage 3. Calculate the market value of the offer: add the cash to the market value of the mortgage to calculate the market value of the offer 34

35 Mortgage Assumption - Example Three years ago the Smiths arranged a mortgage with their bank with the following terms: Loan Information: Smith and Weston Example Face Value $325,000 Contract Interest Rate j 2 = 4.75% Amortization Period 20 years Term 5 years Term remaining 2 years Monthly payments (round up to the next higher cent) Today the Westons have offered to purchase the Smiths property, providing they can assume the existing mortgage. Calculate the market value of the mortgage being assumed if current market interest rates are j 2 = 6% 35

36 Mortgage Assumption - Example 36

37 Mortgage Assumption - Example Step 1: Interest Rate Conversion - Contract Rate Calculator Steps Press Display Comments 4.75 NOM% P/YR 2 EFF% P/YR 12 NOM% j 12 rate j 2 = 4.75% Stored in I/YR 37

38 Mortgage Assumption - Example Step 2: Solve for Payment and OSB term(60) Calculator Steps Press Display Comments P/YR Already entered NOM% Already entered I/YR PV 325,000 Loan amount 20 X 12 = 240 N 240 Amort. period 0 FV 0 PMT -2, , /- PMT -2, Enter rounded PMT 38

39 Mortgage Assumption - Example Step 2: Solve for Payment and OSB term(60) (cont d) Calculator Steps Press Display Comment 36 INPUT AMORT OSB 36 (amount of Debt the purchaser is receiving) = = = 293, For comparison purposes only 60 INPUT AMORT Find the OSB after the 60 th PMT (end of term) = = = 269, OSB , /- FV -269, Enter Rounded OSB into FV 24 N 24 Set N = Remaining PMTS 39

40 Mortgage Assumption - Example Step 3: Discount the Remaining Payments and the OSB TERM at the market interest rate (MV of the Assumed Mortgage) Interest Rate Conversion: Market Rate Calculator Steps Press Display Comments 6 NOM% 6 2 P/YR 2 EFF% P/YR 12 NOM% j 12 rate j 2 = 6% Stored in I/YR PV 286, MV of the Mortgage Market Value of the Mortgage = $286,

41 Mortgage Assumption - Example Q. How much benefit is the purchaser receiving? Benefit = OSB 36 (TODAY) Market Value of the assumed mortgage $293, $286, = $6,

42 Mortgage Assumption - Equation i = periodic MARKET interest rate per month equivalent to j 2 =6% in this case to j 12 = % = i mo = % = Solve for PV = Market Value of the Mortgage = $286, term _ remaining 1 (1 + i) PV = PMT + OSBt (1 + i) i term _ remaining 24 1 ( ) 286, = 2, , ( )

43 Mortgage Assumption - Example This example is similar to solving for the value of a mortgage to an investor, at the investor s desired yield or discount rate. 43

44 Feedback and Questions For further questions related to the course content presented in this session, contact your tutor (please include the course number in the subject): For all other feedback about the webinar please contact the Real Estate Division: 44