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## APR - Annual Percentage Rate

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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**• 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 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.**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**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.**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**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.**An Example from the Text**Refinance Analysis • Original Loan of $200,000 at 9% for 30 years with monthly payments • Calculate Monthly Payments • Loan Amount=$200,000 IR=9.0 N=30 Years, Monthly • PMT= $1,609.25**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**Refinance Analysis**• AMOUNT OF THE POINTS:$191,760 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**Refinance Analysis**• Calculate the monthly payment for the new loan Loan Amount=$196,595 IR=8.0 N=25 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.**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 = $11,906.98**But what if the new loan is for a term that extends the**original term of the loan? Refinance Analysis • If the new loan is for 30 years at 8.0% with 2 points the new loan would extend the payoff date be 5 years. • The monthly payment would be with the Loan Amount=$ 196,595 IR=8.0 N=30 years with payments occurring monthly • PMT = $1,442.54**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.**TO EVALUATE THE REFINANCE IN THIS SITUATION, WE NEED TO USE**DISCOUNTING. Refinance Analysis • FOR PAYMENTS 1 – 300 (25 YEARS) • Monthly savings=$166.71 IR=8.0 N=25 years Paid monthly • PV= $21,599.70 • THIS REPRESENTS THE PRESENT VALUE OF THE SAVINGS OVER THE 25 YEARS**Refinance Analysis**• NEXT WE NEED TO CALCULATE THE PRESENT VALUE OF THE ADDITIONAL PAYMENTS. • FOR PAYMENTS 301 - 360 (5 YEARS) • PMT= $1,442.54 IR=8.0 N=5 years, paid monthly • PV= $71,143.81 • THIS REPRESENTS THE PRESENT VALUE OF THE ADDITIONAL PAYMENTS BACK TO YEAR 25.**Refinance Analysis**• NEXT WE NEED TO DISCOUNT THIS AMOUNT ($71,143.81) TO THE PRESENT. • FV= 71,143.81 IR=8.0 N=25 years, paid monthly • PV= $9,692.38 • THE PRESENT VALUE (BACK TO YEAR 0) OF THE ADDITIONAL PAYMENTS IS $9,692.38.**SO, WHAT IS THE NET RESULT?**Refinance Analysis • LET’S 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**Refinance Analysis**• Therefore, the net result is a benefit from refinancing of $11,907.32 • This means that refinancing would be useful.