1. Mortgage Calculations and Decisions
Chapter 15:
Mortgage Calculations and Decisions
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2. Five Vital Features of a Mortgage
Payment
Remaining balance (at any point in time)
Lender’s yield (internal rate of return-IRR)
Borrower’s effective borrowing cost (EBC)
Present value of the loan payments
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3. Valuing a Series of Loan Payments
What would the value of these payments be to a lender who can earn 6% on other loans?
360 level payments
$1,000 each
/ , PV
PMT I N FV
166,791.61
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4. Payment on a Loan
What would be the fixed level payment on the following $166, loan?
Level payment
360 months
6% per year
/ , PV
PMT I N FV
1,000
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5. Another Example of Finding a Payment
Loan amount: $100,000
Term:15 years (monthly payments)
Interest rate: 6% annual
Find fixed level payment
180 6/ , PV
PMT I N FV
843.86
Note: /100,000= is the monthly mortgage constant
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6. Finding the Remaining Mortgage Balance (RMB)
Balance of a level payment loan at any point in time:
Equal to the present value of the remaining payments, discounted at the contract interest rate
Balance after one month? /
Original term: 180 months PV
PMT I N FV
99,656.14
$99, is remaining balance (RMB) after 1 year (12 payments)
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7. Finding the Remaining Balance: Manually
What is the balance (RMB) after two payments?
Principal = $ – Interest reduction = – (0.005 x 99,656.14)
= $345.58
Balance after 2 payments
= 99, – = 99,310.56
Confirm with keystrokes… / PV
PMT I N FV
99,310.57
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8. Finding the Remaining Balance: Calculators & Excel
Financial calculators have functions/keystrokes to find remaining loan balance
May also use Excel
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9. Finding RMB: Example
For a loan of $100,000, at 7% (annual) interest for 30 years with monthly payments, what will be the balance of the loan at the end of four years?
Confirm using Excel or the appropriate function of your financial calculator
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10. Lender’s Yield (IRR) Consider the following mortgage:
Term: 360 months
Required discount rate/yield: 7%
Monthly payment: $1,000
Initial loan balance: $150,307.57
Discount points: 3.53%
Points = x 150, = 5,307.57
Net loan proceeds = $150, – 5,307.57
= $145,000
What lender disburses (net) at loan closing
What payments are based on
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11. Lender’s Yield (continued)
What interest rate makes the present value of the payments = $145,000
, , PV
PMT I N FV
7.36%
(0.6133x12)
Implicit yield is 7.36%; that is, the lender’s yield (IRR), charging 3.53 discount points, is 7.36%
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12. Lender’s Yield (continued)
, , PV
PMT I N FV
7.36%
Lender’s yield:
implicit interest rate received on a loan
also lender’s expected IRR on loan
is based on:
actual cash loaned out by lender
actual cash payments received by lender
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13. Effective Borrowing Cost (EBC)
Third-party expenses: up-front expenses incurred by borrower but not paid to lender:
Mortgage insurance premium
Lender’s title insurance
Charges to record your mortgage (county)
Appraisal
Survey
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14. Effective Borrowing Cost (cont)
Effect of 3rd party payments:
Borrower net less cash at loan closing than lender’s actual net disbursement to borrower
Result?
EBC > lender’s yield/IRR
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15. Effective Borrowing Cost (cont)
Example: Same loan, but with additional borrower expenses
Points to lender: $5,307.57
Borrower’s 3rd party loan expenses: $2,692.43
Total deducted from borrower’s loan proceeds at closing: $8,000 (5, $2,692.43)
Net loan proceeds received by borrower:
= $150, – $8,000
= $142,307.57
Note: net loan proceeds < amount disbursed by lender
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16. Effective Borrowing Cost (cont)
What is EBC? (N = 360; PMT = $1,000)
Net loan proceeds: $142,307.57
, , PV
PMT I N FV
7.55%
( x 12)
With $8,000 in borrower expenses, EBC of loan is 7.55%
Recall lender’s yield is 7.36%
3rd party expenses create a 0.19% “wedge” between EBC & lender’s yield
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17. Special Case of EBC: APR
Federal Truth in Lending Act requires disclosure of annual % rate (APR) on most home mortgage loans
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
What inadequacy might you see in the APR as a measure of true borrowing cost?
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18. Effect of Prepayment on Lender’s Yield & Borrower’s EBC?
Suppose example loan will be prepaid at end of 7 years (84 months)
Loan balance at end of 7 years?
Amount: $150,307.57
Payment: $1,000
Interest rate: 7%
Term: 360 mos.
/ ,
# of months remaining after 7 yrs. (23 x 12) PV
PMT I N FV
137,001.46
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19. Summary of Effect of Prepayment on Lender’s Yield & EBC
,000 1, ,001.46 PV
PMT I N FV
7.69% (7.36% w/o prepayment)
Effective Borrowing Cost
, , ,001.46 PV
PMT I N FV
8.03% (7.55% w/o prepayment)
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20. Interaction of EBC, Points, & Holding Period
Exhibit 15-1
Based on 30-year, $200,000, fixed payment mortgage with contract interest rate of 6.0% and other up-front financing costs of $3,000
Note: Interest rate is held constant in Exhibit 15-1; actually, contract interest rates would decrease as points paid by borrower increase
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21. Implications of Up-Front Financing Costs?
Borrowers who expect to move relatively soon should
pay few or no discount points & a slightly higher contract rate
Borrowers who expect to keep loan outstanding for a long period should
consider paying discount points to buy down the contract interest rate
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22. 30-Year Loans vs. 15-Year Loans
Exhibit 15-2: Total interest paid on 6% LPM of $250,000
Question: Which is the better loan for a borrower?
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23. Implications for 30-Year & 15-Year Loans
What is PV of $250,000, 30-yr 6%?
What is PV of $250,000, 15-yr 6%?
Conclusion: borrower is indifferent between the two loans, assuming:
both loans are at a market interest rate
borrower is unconstrained in borrowing (i.e., can afford higher monthly payment with 15-year loan)
But…15-year mortgages usually have lower interest rates, all else equal
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24. 30-Year vs. 15-Year Mortgage with Borrower Constrained
Suppose household has large credit card balances at a 12% interest rate
Assume this 12% rate indicates the appropriate opportunity cost, or discount rate, to value the mortgage choices
Which of these home loans would the household prefer?
$250,000, 30-year at 6% (monthly payment = $1,498.88)
$250,000, 15-year at 6% (monthly payment = $2,109.64)
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25. 30-Year vs. 15-Year Mortgage with Borrower Constrained: Answers
Assumptions: $250,000 loan, 6% contract rate, and up-front financing costs equal between loans
PV of 6%, 30-year 12%
/ , PV
PMT I N FV
145,718
PV of 6%, 15-year 12%
/ , PV
PMT I N FV
175,779
Conclusion: 30-yr loan has lowest PV (cost) and is best option
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26. Alternative Amortization Schedules
Interest-only mortgage
Not typically observed with home loans
More common with income property (CRE) loans
Partially amortized mortgage
Loan maturity/term is shorter than amortization period
Results in “balloon” payment at end of term
Very common in CRE lending
Early payment mortgage
Most home loans allow borrowers to make unscheduled (“extra”) payments along with their monthly payment
These extra payments go toward reduction of the principal balance
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27. Adjustable Rate Mortgages without Caps: Exhibit 15-3
Be sure you can replicate each calculation with your calculator or Excel
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28. Adjustable Rate Mortgages with Caps: Exhibit 15-5
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29. Adjustable Rate Mortgages: Other Options
3 year/1 year ARM
Interest rate fixed for 3 years
Adjusts annually thereafter on the anniversary of loan
Loan is fully amortized over, say, 25 or 30 yrs.
5/1 ARM
7/1 ARM
10/1 ARM
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30. Other Things to Consider When “ARM Wrestling”
Annual cap on interest rate changes?
Life of loan cap?
# of discount points?
Other up-front financing costs charged by lender?
Important question: Do borrowers receive benefit of "caps" for free?
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31. End of Chapter 15
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