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

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Chapter 18Real Estate Finance Tools Present
Value and Mortgage Mathematics
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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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Loan Calculations

• 30-year, 100K loan _at_ 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

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Loan Calculations

• Each payment 665.30 principal interest
• 1st payment
• 1 INPUT 1 AMORT
• 665.30 81.97 principal 583.33 interest
• New loan balance 100K - 81.97 99,918

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Loan Calculations

• Each payment 665.30 principal interest
• 2nd payment
• 2 INPUT 2 AMORT
• 665.30 82.45 principal 582.85 interest
• New loan balance 99,918 - 82.45 99,836

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Loan Calculations

• 1st year ? 12 payments 665.3012 7,984
• 12 payments
• 1 INPUT 12 AMORT
• 7,984 1,016 principal 6,968 interest
• New loan balance 100,000 - 1015.81 98,984

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Loan Calculations

• 30-year 150,000 loan _at_ 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?

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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 lenders actual
  disbursement
• Effective borrowing cost stated r

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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

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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

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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?

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APR

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

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Points Lenders Yield

• Lenders Profit
• Interest
• Points
• Other fees go to cover costs or to 3rd parties

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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?

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Lending Risks

• Default Risk
• Interest Rate Risk
• Lender is unable to charge the market rate
• Initial rate depends on both, but r risk
  dominates

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Mortgage Types

• Fixed Rate Mortgage
• 30-year and 15-year
• Adjustable Rate Mortgage
• Index rate Market-determined rate
• Spread (Margin) Lenders 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/ra
  tes.asp

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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?

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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

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Mortgage DecisionsRefinancing
An NPV Problem
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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
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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
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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

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NPV of Refinancing for Various Times to Loan
Prepayment
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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?

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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?

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END