# Chapter 18 Real Estate Finance Tools Present Value and Mortgage Chapter 18 Real Estate Finance Tools Present

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```					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

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

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

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

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

Loan Calculations
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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?

Loan Costs and Fees
  

Interest Administrative costs Third party costs
  

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Points (elective) to buy down r


Appraisal Survey Title insurance

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Effect: Borrower nets less than lender’s actual disbursement


1 point = 1% of loan amount

Effective borrowing cost > stated r

Effective Borrowing Cost

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30-year, \$200K loan
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6.25%, 0 points, \$4000 fees 6.00%, 2 points, \$3000 fees

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Which is cheaper? Find PMT Plug “proceeds” into PV and solve for I/YR

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

Points/Fees, etc

1.

2.

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?

APR


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



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

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?

Lending Risks
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Default Risk Interest Rate Risk
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“Lender is unable to charge the market rate”

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Initial rate depends on both, but r risk dominates

Mortgage Types
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Fixed Rate Mortgage
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  

30-year and 15-year

Index rate: Market-determined rate Spread (Margin): Lender’s markup Change Date: Date that interest rate changes each time




Teaser rate: Initial, temporarily reduced interest rate

3-1 ARM, 5-1 ARM

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http://www.bankrate.com/brm/news/mtg/mtg_blurbs/rates.asp

Interest Rate Caps
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Annual rate caps = maximum increase in the rate that is possible per year
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1%-2% annual rate cap is common

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Life time caps = maximum total increase in the rate that is possible during the loan term
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Effect on initial interest rate?

Refinancing
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Refinancing can save borrower money if there is a drop in mortgage interest rates Situations when refinancing is not advisable:
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Remaining term of the loan is short or expected tenure with new loan is short Mortgage rates are expected to further drop

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Deciding whether refinancing is profitable or not:


NPV of expected savings exceeds the cost of refinancing then it is advisable and vice-versa

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

Refinancing Example
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Existing loan:
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
 

Amount: \$90,000 Remaining term: 15 years Interest rate: 8% Expected time to prepayment: 6 years

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New loan interest rate: 6% Payment on old loan?
180
n

8
I/YR

90,000
PV Pmt FV

-\$860.09

Present Value of Old Loan
Balance in 6 years?
72
n
I/YR

PV

Pmt

FV

-\$66,065.42

Present value discounted at 6%?
72
n

6
I/YR

-\$860.09 -\$66,065.42
PV Pmt FV

\$98,036.87

Present Value of New Loan and 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

NPV of Refinancing for Various Times to Loan Prepayment
Number of Years to Prepayment of New Loan
2 4 6 8 10 15

Present value of old loan
Present value of new loan P V of payment reductions Cost of refinancing Net refinancing benefit (NPV)

\$93,269 90,000 3,269 6,300 (3,031)

\$95,960 90,000 5,960 6,300 (340)

\$98,031 90,000 8,031 6,300 1,731

\$99,635 90,000 9,635 6,300 3,335

\$100,785 90,000 10,785 6,300 4,485

\$101,923 90,000 11,923 6,300 5,623

Existing loan is \$90,000, 15 years remaining, 8% interest rate. Current market interest rate is 6%

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?

Refinancing Rules of Thumb
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Interest rate spread rule: Refinance if “spread” between old loan interest rate and current rate is 2%
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Correct? Why or why not?

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Payback period rule: Divide cost of refinancing by monthly savings to find “payback period” What SHOULD determine whether you should refinance?

END

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Jun Wang Dr
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