Real Estate Ch. 15
What two things is the lender yield based on? (maybe not concentrate too much on)
1. Actual cash loaned out by lender 2. Actual cash payments received by lender
What are the implications of up-front financing costs?
1. Borrowers who expect to move relatively soon should pay few or no discount points and a slightly higher contract rate 2. Borrowers who expect to keep loan outstanding for a long period should consider paying discount points to buy down the contract interest rate -Monthly savings from paying the discount points to reduce the contract rate will be greater the longer the loan remains outstanding
Find the Borrower's Effective Borrowing Cost for this loan: $125,000 15-year loan interest rate= 6.25% annually Lender points and origination fee= $2,500 Other up-front cost paid by borrower to 3rd party= $3,500 Assume no prepayment
1. Find PMT on loan" N= 15*12= 180 i= 6.25/12= .5208 FV= 0 PV= -125,000 PMT= 1,071.75 2. Reduce the amount of loan by lender's discount points and other up-front fees: $125,000-$2,500-$3,500= $119,000 3. Find Borrower's yield using new loan amount: PV= -119,000 PMT= 1,071.75 FV=0 N= 180 ANSWER: i= .5860*12= 7.03%
Find the lender's interest on this loan: $125,000 15-years interest rate is 6.25% annually Lender "points" equal to $2,500 Assume no prepayment
1. Find PMT: i= 6.25/12=.5208 N= 15*12= 180 FV= 0 PV= -125,000 PMT= 1,071.75 2. Decrease amount of loan by lender's discount: 125,000- 2,500= $122,500 3. Find lender's yield using new loan amount: PV= -122,500 PMT= 1,071.75 N= 180 FV=0 ANSWER: i=.5474*12= 6.57%
Find the Effective borrowing cost for this loan: $125,000 15 year loan Annual 6.25% interest rate Lender points and origination fee= $2,500 Other up-front costs= $3,500 (Assume prepayment after 4 years (11 years remaining)
1. Find PMT: Same process as always, PMT= 1071.78 2. Find PV of loan after 4 years (11 years remaining): N=132 PMT= 1071.78 i=0.5208 FV=0 PV= 102,123.41 3. Subtract total upfront costs from amount of loan: $125,000-$2,500-$3,500= $119,000 4. Find borrower cost after 4 years, using loan balance after 4-years as FV, and loan balance after fees as PV: N= 12*4=48 PV= -119,000 PMT= 1071.78 FV= 102,123.28 ANSWER: i=.6478*12= 7.77%
Find the balloon payment of this mortgage loan: $100,000 6.5% annual interest 30-year amortization but 7-year term to maturity
1. Find monthly pament: N=30*12=360 i=6.5/12 PV= -100,000 FV=0 PMT= 632.068 2. Find loan balance at end of year 7 (Balloon payment): N= 360-(7*12)=276 i=6.5/12 FV=0 PMT=632.068 ANSWER: PV= 90,416.25
Given the following information for a 30-year $75,000 CAPPED ARM loan, find the interest rate and ending balance for year 2: Margin= 2.75% Index for year 1= 2.50% Index for year 2= 2.75% Teaser rate= 4% Periodic cap= 1% Overall cap= 5% Assume that the cap applies to the teaser rate
1. Find the PMT for year 1 using teaser: N=30*12=360 i=4/12 PV= -75,000 FV= 0 PMT= 358.0615 2. Find the loan balance at the end of year 1: N= 360-12= 348 i= 4/12 PMT= 358.0615 FV=0 PV end of year 1= 73,679.23 3. Find the PMT for year 2, keeping in mind periodic cap: -Interest rate is lower of 4%+1%= 5% (highest interest rate can be for this period) and 2.75% (index)+ 2.75% =5.5% N=348 i=5/12 PV end of year 1= 73,679.23 FV=0 PMT= 401.45 4. Find the loan balance at the end of year 2: N=360-12-12=336 i=5/12 FV=0 PMT= 401.45 ANSWER: PV= 72,519.67
How do you find the lender's yield when a loan is prepayed? (Example later)
1. Find the balance at the end of the prepayment period -ex.) Prepayed at 7 years with original 30 years. So find PV of 23 years. 2. Set this loan balance up as FV, and set PV as the amount of disbursement to the borrower when originated and find I -ex.) Lender originated loan with a net disbrsement to borrower of $145,000, so this is PV, while PV of 23 years is FV
Given the following information for a 30-year $75,000 uncapped ARM loan, find the loan balance at the end of year 2: Margin=2.75% Index for year 1= 2.50% Index for year 2= 2.75% Teaser rate= 4%
1. Find the initial payment at the teaser rate (ignore the index rate for y1): i=4/12 pv= -75,000 Fv=0 N=30*12=360 PMT= 358.0615 2. Find loan balance at the end of year 1: N=360-12=348 i=4/12 FV=0 PMT= 358.0615 PV= 73,679.22 3. Find payment at year 2 using year 2 interest rate (Interest rate= index rate+margin) N=348 i= (2.5+2.5)/12 PV (loan balance at end of year 1)= 73,679.22 FV=0 PMT=424.0549 4. Find loan balance at end of year 2: N= 360-12-12= 336 i= (2.5+2.5)/12 PMT= 424.0549 FV=0 ANSWER: PV= 72,616.39
What are the 2 important differences between effective borrowing cost and APR?
1. For APR, the expense items required to be included, although extensive, may still omit some significant ones. 2. APR is always based on the assumption of no prepayment
What are the 5 vital financial features of a mortgage?
1. Payment 2. Remaining balance (At any point in time) 3. Lender's yield (Internal rate of return- IRR) 4. Borrower's effective borrowing cost (EBC) 5. Present value of loan payments
Find the lender's yield for this loan: $125,000 15-year loan 6.25% annual interest rate Lender's "points" and origination fee: $2,500 (Assume Prepayment after 4 years)
1.) Find PMT: N= 180, i=.5208, PV= -125,000, FV=0, PMT= 1,071.78 2.) Find the balance of the loan after 4 years: N=180-(4*12)= 132 PMT= 1,071.78 i= .5208 FV=0 PV= 102,123.28 3.) Find Subtract the up-front fees from the amount of the loan: $125,000-$2,500= $122,500 4. Find lender's yield by setting the time horizon as 4 years, using the loan amount after fees, and setting the balance of the loan after 4 years as the FV: N=4*12=48 PV= -122,500 FV= 102,123.28 PMT= 1,071.78 ANSWER: i= .5729*12= 6.87%
Find the balance on this loan at the end of 6 years: $125,000 15-year loan interest rate is 6.25% annually
1.) Find the PMT of the loan" N= 15*12= 180 PV= -125,000 i= 6.25/12= 0.5208 FV=0 PMT= 1,071.78 2. Find balance after 6 years have passed: N= 180-(6*12)= 108 PMT= 1071.78 i= .5208 FV=0 ANSWER: PV= $88,359.56
What is the effect of prepayment on lender's yield and a borrower's effective borrowing cost? (MAY NOT BE TRUE OR MAY NEED TO ADD FROM LECTURE, GO BACK)
1.) With lender's yield, prepayment causes the lender's yield to increase because the loan is being paid off in a shorter amount of time 2.) With prepayment, effective borrowing costs increase
15 year loans generally have lower interest rates than 30-year loans, all else equal (Just understand)
15 year loans generally have lower interest rates than 30-year loans, all else equal (Just understand)
How can you compare if loans are better when they have different maturities?
Can only compare if loans are better when they have different maturities by comparing their present values -If they have the same discount rate, they will be equivalent
Life of loan cap (Just understand)
Can only raise that % past the initial rate over the life of the loan -ex.) initial rate= 5.5% life of loan cap= 5% 10.5% is the highest rate that can ever be paid on the loan
Effective Borrowing Costs depend on 2 aspects of prepayment: 1.) How large the up-front financing costs are 2.) Hold long until the loan is prepayed (Holding Period) (Just understand)
Effective Borrowing Costs depend on 2 aspects of prepayment: 1.) How large the up-front financing costs are 2.) Hold long until the loan is prepayed (Holding Period) (Just understand)
How do you find the balance of a level payment loan at any point in time?
Find the present value of the remaining payments, discounted at the contract interest rates -Just subtract the time passed from N, and then find PV
Holding the contract interest rate constant, adding discount points to other up-front fees increases the effective borrowing rate (Just understand) -Because it decreases the loan proceeds WITHOUT altering the scheduled monthly payment or remaining loan balance
Holding the contract interest rate constant, adding discount points to other up-front fees increases the effective borrowing rate (Just understand) -Because it decreases the loan proceeds WITHOUT altering the scheduled monthly payment or remaining loan balance
Lender's yield
Implicit interest rate received on a loan -The internal rate of return for the lender, given all cash flows on the loan -Must be annualized at the end
How does the use of rate caps in an ARM loan shift the risk between borrower and lender? (Understand but don't spend a ton of time on)
In a level-payment mortgage, if interest rates rise, borrower's payments are unaffected while tje value of the lender's asset (loan) falls because the market now discounts the loan's payment streams at a higher discount rate -Unconstrained ARM shifts this risk away from the lender -Use of caps reallocates this shift between the extremes
What is the interest rate on a given year for an adjustable rate mortgage (ARM)?
Interest rate of ARM= index rate+margin -Except for initial teaser rate, then ignore this
Monthly loan constant (Probably don't have to concentrate much on)
Monthly loan constant= Monthly mortgage payment (PMT)/ Loan amount
What would the value of these payments be to a lender who can earn 6% on their loans (annually)? 360 level payments $1,000 each
N= 360 i= 6/12=0.5 PMT= 1,000 FV= 0 ANSWER: PV= 166,791.61
Problem: Loan Amount= $100,000 Term: 15 years (monthly payments) Interest Rate= 6% Find fixed level monthly payment!
PV= -100,000 N=15*12=180 I= 6/12= 0.5 FV=0 ANSWER: PMT= $843.86
Early Payment Mortgage (EPM)
Principal payments may exceed the schedule of principal payments for a level-payment mortgage -Making more than required principal payments -There is significant opportunity costs associated with paying down a loan early
Interest-only mortgages
Repaid in full with one payment at maturity of the loan (During life of loan only interest payments are made, no principal) -Seldom with home loans, but are often used with income property loans
Partially amortizing loans
Requires periodic payments of principal as well as interest, but are not paid off completely over loan's term to maturity, so a balloon payment is necessary at end of maturity -Maturity is shorter than amortization paeriod
Simple test of estimating closing expenses: (Just understand) If the expense would be incurred even if no mortgage financing were obtained, it is an expense associated with obtaining ownership of the property and should not be involved in the Effective Borrowing Cost calculation -ex.) title insurance, attorney fees, etc.
Simple test of estimating closing expenses: (Just understand) If the expense would be incurred even if no mortgage financing were obtained, it is an expense associated with obtaining ownership of the property and should not be involved in the Effective Borrowing Cost calculation -ex.) title insurance, attorney fees, etc.
What is the maximum amount the lender should be willing to pay on a fixed-payment loan at closing?
The Present value of expected future payments
How does the presence of interest rate caps affect the calculations for ARMs?
The change in interest rate from one year to the next cannot be above periodic cap -Have to use the lesser of margin+index rate for the year, or the previous year's interest rate+periodic cap
The effects of up-front financing costs on effective borrowing cost decrease as the holding period increases (Just understand) -The father out the holding period is, the closer EBC approaches contract interest rate.
The effects of up-front financing costs on effective borrowing cost decrease as the holding period increases (Just understand) -The father out the holding period is, the closer EBC approaches contract interest rate.
The less interest rate risk that the borrower assumes, the higher interest rate charged during the initial period (Understand) -3-year ARMS (interest rate is fixed for 3-years and then adjusts) have higher initial interest rates than standard 1-year ARMS -5-year ARMS have higher initial interest rates than 3-year ARMS, and so on
The less interest rate risk that the borrower assumes, the higher interest rate charged during the initial period (Understand) -3-year ARMS (interest rate is fixed for 3-years and then adjusts) have higher initial interest rates than standard 1-year ARMS -5-year ARMS have higher initial interest rates than 3-year ARMS, and so on
Discount rate (Probably don't need to concentrate too much on)
The opportunity cost, the return that we can get on alternative investments at similar risk
Borrower's effective borrowing cost
The true borrowing cost, including the effect of all up-front financing costs -Borrower pays these costs so does not get as income, meaning we subtract them from the amount of the loan -Subtract the lender's discount points along with other up-front costs
How are 3-year ARMs, 5-year ARMs, and so forth a creative truce in the "interest rate tug-o-war" between borrower and lender?
They allow a borrower to select an ARM where the payment is fixed for approximately the amount of time the borrower expects to keep the loan -ex.) Borrowers who expect to refinance or move in 5 years can get a 5-year ARM and their payments won't increase for that period -So, borrowers are paying only for the protection they value, while the lender's interest rate risk is much less than the standard level-payment mortgage
How do lenders balance the pricing of ARMs with rate caps relative to ARMs without such caps? (understand)
They must in some fashion increase their expected returns on the ARMs with caps -Borrowers who choose ARMs with rate caps can expect a higher initial contract interest rate, a higher margin, more up-front financing costs, or some combination of the three
Third party expenses
Up-front expenses incurred by borrower but NOT paid by lender *Examples: -Mortgage insurance premium -Taxes on the loan -Lender's title insurance -Appraisal -Survey
Discount points
Upfront financing costs charged charged by lenders to increase yield on loans (Advanced interest) -These are subtracted from the amount of the loan when calculating lender's yield
Level payment mortgage (Just review)
When fully amortizing loans call for periodic payments -At maturity, loan balance is 0
Annual Percentage Rate (APR)
Yield to maturity after adjusting for : All loan finance charges All compensation to originating brokers All other charges controlled by lender Premiums for any required insurance -An approximation of the mortgage loan's annual effective borrowing cost in the absence of early payoff -Includes the effect of up-front financing costs on the true cost of borrowing -Computed under the assumption of no prepayment
