APR - Annual Percentage Rate

1
APR - Annual Percentage Rate

• APR is the true or effective interest rate for a
  loan. It is the actual yield to the lender.
• The APR is calculated using the stated interest
  rate, any prepaid interest (points) or other
  lender fees.

2
Points

• Points are loan fees that are viewed as prepaid
  interest and raise the APR of the loan. One
  point is 1 of the loan amount.

3
Calculation of APR from a loan with Points

• Your are purchasing a residence that has a
  purchase price of 250,000. You plan on making a
  down payment of 20. Your mortgage lender has
  agreed to finance the loan at 6 for 30 years,
  monthly payments, and wants 2 points.

4
Calculate the monthly payment on the loan amount
after making the down payment of 50,000.
Calculation of APR from a loan with Points

• Loan Amount 200,000
• Payment 1,199.10
• IR 6.0
• N 30 years
• P/Y 12 payments per year

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Calculation of APR from a loan with Points

• The amount of the points that is being required
  is 200,000 x 0.02 4,000.
• Therefore the amount of the funded loan is
  200,000 less the 4,000 196,000.

6
Calculate the APR based on the calculated payment
and a funded loan amount of 196,000.
Calculation of APR from a loan with Points

• Loan Amount 196,000
• PMT 1,199.10
• IR 6.19 APR
• N 30 years
• P/Y 12 payments per year

7
Refinance Analysis

• The proper perspective for refinancing is to
  weigh the discounted cash flow savings of the
  new, lower payment against the cost of the
  transaction.

8
An Example from the Text
Refinance Analysis

• Original Loan of 200,000 at 9 for 30 years with
  monthly payments
• Calculate Monthly Payments
• Loan Amount200,000 IR9.0 N30 Years, Monthly
• PMT 1,609.25

9
Refinance Analysis

• Refinance the balance after 5 years at 8 with 2
  Points and 1,000 In other loan fees for 25 years
  with monthly payments. The lender will finance
  the cost of the points and fees.
• What is the payoff amount of the original loan?
• Calculating the principal balance following the
  60th using the Loan Balance Equation the payment
  is 191,760.27. Which is 191,760

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Refinance Analysis

• AMOUNT OF THE POINTS191,760 x 0.02
  3,835
• LOAN FEES 1,000
• TOTAL 4,835
• AMOUNT OF NEW LOAN 191,760
  4,835TOTAL OF NEW LOAN 196,595

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Refinance Analysis

• Calculate the monthly payment for the new loan
• Loan Amount196,595 IR8.0 N25 years
• Paid monthly
• PMT 1,517.35
• Since the new loan is paid off at the same time
  as the original loan, the fact that the new
  monthly payment is less means the refinance would
  be profitable.

12
Calculate the Present Value of the Savings from
Refinancing
Refinance Analysis

• Original Payment 1,609.25
• New Payment 1,517.35 91.90
• PMT 91.90 IR 8.0 N 25 Years, Paid monthly
• PV 11,906.98

13
But what if the new loan is for a term that
extends the original term of the loan?
Refinance Analysis

• If the new loan is for 30 years at 8.0 with 2
  points the new loan would extend the payoff date
  be 5 years.
• The monthly payment would be with the
• Loan Amount 196,595 IR8.0 N30 years with
  payments occurring monthly
• PMT 1,442.54

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Refinance Analysis

• The new loan would reduce the payment by 166.71
  per month from the original loan over 25 Years or
  300 Payments.
• However, there would be an additional 5 years or
  60 payments in the amount of 1,442.54 each.

15
TO EVALUATE THE REFINANCE IN THIS SITUATION, WE
NEED TO USE DISCOUNTING.
Refinance Analysis

• FOR PAYMENTS 1 300 (25 YEARS)
• Monthly savings166.71 IR8.0 N25 years Paid
  monthly
• PV 21,599.70
• THIS REPRESENTS THE PRESENT VALUE OF THE SAVINGS
  OVER THE 25 YEARS

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Refinance Analysis

• NEXT WE NEED TO CALCULATE THE PRESENT VALUE OF
  THE ADDITIONAL PAYMENTS.
• FOR PAYMENTS 301 - 360 (5 YEARS)
• PMT 1,442.54 IR8.0 N5 years, paid monthly
• PV 71,143.81
• THIS REPRESENTS THE PRESENT VALUE OF THE
  ADDITIONAL PAYMENTS BACK TO YEAR 25.

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Refinance Analysis

• NEXT WE NEED TO DISCOUNT THIS AMOUNT (71,143.81)
  TO THE PRESENT.
• FV 71,143.81 IR8.0 N25 years, paid monthly
• PV 9,692.38
• THE PRESENT VALUE (BACK TO YEAR 0) OF THE
  ADDITIONAL PAYMENTS IS 9,692.38.

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SO, WHAT IS THE NET RESULT?
Refinance Analysis

• LETS EXPRESS THE PV IN TERMS WHERE SAVINGS IS
  POSITIVE AND AN ADDITIONAL COST IS NEGATIVE.
• PV OF SAVINGS FOR 25 YEARS 21,599.70
• PV OF ADDITIONAL PAYMENTS FOR 5 YEARS -9,692.38

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Refinance Analysis

• Therefore, the net result is a benefit from
  refinancing of 11,907.32
• This means that refinancing would be useful.