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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. Points.

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Apr annual percentage rate
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.


Points
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.


Calculation of apr with points
Calculation of APR 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.


Calculate the monthly payment on the loan amount after making the down payment of 50 000
Calculate the monthly payment on the loan amount after making the down payment of $50,000.

  • PV = 200,000

  • FV = 0

  • PMT = ? -1,199.10

  • I/Y = 6.0

  • N = 30x12 = 360

  • P/Y = 12


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.


Calculate the apr i y based on the calculated payment and a funded loan amount of 196 000
Calculate the APR (I/Y) based on the calculated payment and a funded loan amount of $196,000.

  • PV = 196,000

  • FV = 0

  • PMT = -1,199.10

  • I/Y = ? 6.18948% APR

  • N = 30x12 = 360

  • P/Y = 12


Refinance analysis
REFINANCE ANALYSIS a funded loan amount of $196,000.

  • THE PROPER PERSPECTIVE FOR REFINANCING IS TO WEIGH THE DISCOUNTED CASH FLOW SAVINGS OF THE NEW, LOWER PAYMENT AGAINST THE COST OF THE TRANSACTION


Example problem from textbook
EXAMPLE PROBLEM FROM TEXTBOOK a funded loan amount of $196,000.

  • ORIGINAL LOAN$200,000 AT 9% FOR 30 YEARS WITH MONTHLY PAYMENTS

  • CALCULATE MONTHLY PAYMENTS PV=200,000 FV=0 I/Y=9.0 N=360 P/Y=12

  • PMT= -$1,609.25


  • 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 FOR THE ORIGINAL LOAN?USING THE AMORTIZATION FUNCTION THE PRINCIPAL BALANCE FOLLOWING THE 60TH PAYMENT IS $191,760.27 WHICH IS ≈$191,760


  • AMOUNT OF THE POINTS: $1,000 IN OTHER LOAN FEES FOR 25 YEARS WITH MONTHLY PAYMENTS. THE LENDER WILL FINANCE THE COST OF THE POINTS AND FEES.191,760 + 1,000 = 192,760 *0.02 = $3,855

  • AMOUNT OF NEW LOAN = $191,760 1,000 3,855TOTAL OF NEW LOAN = $196,615


  • CALCULATE THE MONTHLY PAYMENT FOR THE NEW LOAN $1,000 IN OTHER LOAN FEES FOR 25 YEARS WITH MONTHLY PAYMENTS. THE LENDER WILL FINANCE THE COST OF THE POINTS AND FEES.

    PV=196,615 FV=0 I/Y=8.0 N=300

    P/Y=12

  • PMT = -$1,517.50

  • 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.


Calculate the present value of the savings from refinancing
CALCULATE THE PRESENT VALUE OF THE SAVINGS FROM REFINANCING $1,000 IN OTHER LOAN FEES FOR 25 YEARS WITH MONTHLY PAYMENTS. THE LENDER WILL FINANCE THE COST OF THE POINTS AND FEES.

  • ORIGINAL PAYMENT = $1,609.25

  • NEW PAYMENT = $1,517.50 91.75

  • FV=0 PMT=91.90 I/Y=8.0 N=300 P/Y=12

  • PV= -$11,887.54


But what if the new loan is for a term that extends the original term of the loan
BUT, WHAT IF THE NEW LOAN IS FOR A TERM THAT EXTENDS THE ORIGINAL TERM OF THE LOAN?

  • IF THE NEW LOAN IS FOR 30 YEARS AT 8.0% WITH 2 POINTS THE NEW LOAN WOULD EXTEND THE PAYOFF DATE BY 5 YEARS.

  • THE MONTHLY PAYMENT WOULD BE

    PV=196,615 FV=0 I/Y=8.0 N=360

    P/Y=12

  • PMT = -$1,442.69



To evaluate the refinance in this situation we need to use discounting
TO EVALUATE THE REFINANCE IN THIS SITUATION, WE NEED TO USE DISCOUNTING.

  • FOR PAYMENTS 1 – 300 (25 YEARS)

    • FV=0 PMT=166.56 I/Y=8.0 N=300 P/Y=12

    • PV= -$21,580.27

  • THIS REPRESENTS THE PRESENT VALUE OF THE SAVINGS OVER THE 25 YEARS




So what is the net result
SO, WHAT IS THE NET RESULT? PRESENT.

  • LETS EXPRESS THE PV IN TERMS WHERE A SAVINGS IS POSITIVE AND AN ADDITIONAL COST IS NEGATIVE.

  • PV OF SAVINGS FOR 25 YEARS =$21,580.27

  • PV OF ADDITIONAL PAYMENTS FOR 5 YEARS = -$9,693.39



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