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Chapter 18 Real Estate Finance Tools: Present Value and Mortgage Mathematics

Chapter 18 Real Estate Finance Tools: Present Value and Mortgage Mathematics. Major Topics. Mortgage balance calculations Point charges and their effects on borrowing costs or yields Annual Percentage Rate Effective Cost of Borrowing Refinancing decisions Adjustable Rate Mortgages.

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Chapter 18 Real Estate Finance Tools: Present Value and Mortgage Mathematics

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  1. Chapter 18Real Estate Finance Tools: Present Value and Mortgage Mathematics

  2. Major Topics • Mortgage balance calculations • Point charges and their effects on borrowing costs or yields • Annual Percentage Rate • Effective Cost of Borrowing • Refinancing decisions • Adjustable Rate Mortgages

  3. Loan Calculations 30-year, $100K loan @ 7%  Compute PMT 12 p/yr 30 yrs * 12 months = 360 payments  360 N 7 I/YR $100,000 PV (0 FV) Hit PMT key to compute PMT = $665.30

  4. Loan Calculations Each payment = $665.30 = principal + interest 1st payment: 1 INPUT 1 <color> AMORT = = = $665.30 = $81.97 principal + $583.33 interest New loan balance = $100K - $81.97 = $99,918

  5. Loan Calculations Each payment = $665.30 = principal + interest 2nd payment: 2 INPUT 2 <color> AMORT = = = $665.30 = $82.45 principal + $582.85 interest New loan balance = $99,918 - $82.45 = $99,836

  6. Loan Calculations 1st year  12 payments = $665.30*12 = $7,984 12 payments: 1 INPUT 12 <color> AMORT = = = $7,984 = $1,016 principal + $6,968 interest New loan balance = $100,000 - $1015.81 = $98,984

  7. Loan Calculations • 30-year $150,000 loan @ 7.5% • How long before loan is halfway paid off? • If you pay $100/month extra, how long will it take to pay the loan completely off?

  8. Loan Costs and Fees • Interest • Administrative costs • Third party costs • Appraisal • Survey • Title insurance • Points (elective) to buy down r • 1 point = 1% of loan amount • Effect: Borrower nets less than lender’s actual disbursement • Effective borrowing cost > stated r

  9. Effective Borrowing Cost • 30-year, $200K loan • 6.25%, 0 points, $4000 fees • 6.00%, 2 points, $3000 fees • Which is cheaper? • Find PMT • Plug “proceeds” into PV and solve for I/YR

  10. Effective Borrowing Cost • 30-year, $200K loan • 6.25%, 0 points, $4000 fees • 6.00%, 2 points, $3000 fees • Which is cheaper if we sell in 5 years? • Find PMT • Find balance after 5 years (60 N  FV?) • Plug “proceeds” into PV and solve for I/YR

  11. Points/Fees, etc • Raise Effective Borrowing Cost > nominal rate • Prepay  Effective Borrowing Cost >>> nominal rate Points = cost spread over shorter period When is paying points a good idea?

  12. APR • Disclosure required by Truth in Lending Act • APR = Effective Borrowing Cost assuming no prepayment

  13. Points – Lender’s Yield • Lender’s Profit • Interest • Points • Other fees go to cover costs or to 3rd parties

  14. How Lenders Use Points A lender is considering what terms to offer on a loan. Current market rates are 5.5% for 30 years, and the borrower has requested a loan of $100K. The lender believes that the borrower is somewhat of a risk because of his spotty credit history, so he wants to charge points to make the mortgage loan yield 6.25%. Assuming no prepayment, how much in points must he charge?

  15. Lending Risks • Default Risk • Interest Rate Risk • “Lender is unable to charge the market rate” • Initial rate depends on both, but r risk dominates

  16. Mortgage Types • Fixed Rate Mortgage • 30-year and 15-year • Adjustable Rate Mortgage • Index rate: Market-determined rate • Spread (Margin): Lender’s markup • Change Date: Date that interest rate changes each time • 3-1 ARM, 5-1 ARM • Teaser rate: Initial, temporarily reduced interest rate • http://www.bankrate.com/brm/news/mtg/mtg_blurbs/rates.asp

  17. Interest Rate Caps • Annual rate caps = maximum increase in the rate that is possible per year • 1%-2% annual rate cap is common • Life time caps = maximum total increase in the rate that is possible during the loan term • 5%-6% lifetime cap is common • Effect on initial interest rate?

  18. Refinancing • Refinancing can save borrower money if there is a drop in mortgage interest rates • Situations when refinancing is not advisable: • Remaining term of the loan is short or expected tenure with new loan is short • Mortgage rates are expected to further drop • Deciding whether refinancing is profitable or not: • NPV of expected savings exceeds the cost of refinancing then it is advisable and vice-versa

  19. PV of loan payment reductions − Cost of refinancing = NPV PV of old loan −PV of new loan = PV of loan payment reductions Mortgage Decisions:Refinancing An NPV Problem:

  20. n I/YR PV Pmt FV Refinancing Example • Existing loan: • Amount: $90,000 • Remaining term: 15 years • Interest rate: 8% • Expected time to prepayment: 6 years • New loan interest rate: 6% • Payment on old loan? 180 8 90,000 -$860.09

  21. n n I/YR I/YR PV PV Pmt Pmt FV FV Present Value of Old Loan Balance in 6 years? 72 -$66,065.42 Present value discounted at 6%? 72 6 -$860.09 -$66,065.42 $98,036.87

  22. Present Value of New Loanand Final Result Question: What is the value of any loan discounted at its own interest rate? Answer: The balance on the loan Therefore, PV of new loan is $90,000 PV of payment reductions = $98,037.87 − 90,000 = $8,037.87

  23. Number of Years to Prepayment of New Loan 2 4 6 8 10 15 Present value of old loan $93,269 $95,960 $98,031 $99,635 $100,785 $101,923 Present value of new loan 90,000 90,000 90,000 90,000 90,000 90,000 P Vof paymentreductions 3,269 5,960 8,031 9,635 10,785 11,923 Cost of refinancing 6,300 6,300 6,300 6,300 6,300 6,300 Net refinancing benefit (NPV) (3,031) (340) 1,731 3,335 4,485 5,623 Existing loan is $90,000, 15 years remaining, 8% interest rate. Current market interest rate is 6% NPV of Refinancing for Various Times to Loan Prepayment

  24. Refinancing Ten years ago, you took out a 30-year, $150K mortgage with a 7% rate and a $997.95 monthly payment. Today, you can refinance the remaining $128,719 balance for the remaining 20 years at 6% for a fee of $4500. If you expect to prepay in 6 years, what is the NPV of refinancing?

  25. Refinancing Rules of Thumb • Interest rate spread rule: Refinance if “spread” between old loan interest rate and current rate is 2% • Correct? Why or why not? • Payback period rule: Divide cost of refinancing by monthly savings to find “payback period” • What SHOULD determine whether you should refinance?

  26. END

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