You are borrowing $250,000 to buy a house, using a standard, 30- year mortgage.

Question

You are borrowing $250,000 to buy a house, using a standard, 30- year mortgage. Your mortgage lender offers a 5.50% mortgage with no points, or a 5.20% mortgage with X points. You plan on living in the house for exactly 72 months, paying only the required payment each month, and without refinancing your mortgage. What points will make you indifferent between the two mortgages? Use the 5.50% rate to discount cash flows between the two options. Note: all rates in the problem are nominal annual rates with monthly compounding. 0 0.67 0.80 0.98 1.14 1.28

Explanation / Answer

OPTION 1 5.5% mortgage with no points A Initial loan $250,000 B InitialCash outflow $0 (No points) C Monthly Interest rate=(5.5/12)% D Number of months 360 (30 years*12) E Monthly payment $1,419.47 (Using PMT function of excelwithRate=(5.5/12)%,Nper=360,PV=-250000) F Present Value of Monthly Payment of 72 months $86,882.26 (Using PV function of excelwithRate=(5.5/12)%,Nper=72,PV=-1419.47) G Future Value of Monthly Payment of 72 monthsat end of 72 months $120,759.37 (Using FV function of excelwithRate=(5.5/12)%,Nper=72,Pmt=-1419.47) H Future Value of initial Loan at end of 72 months $347,479.95 (Using FV function of excelwithRate=(5.5/12)%,Nper=72,PV=-250000) I=H-G Loan Balance at the end of 72 months $226,720.58 J Present value of Terminal payment $163,117.74 (Using PV function of excelwithRate=(5.5/12)%,Nper=72,FV=-226720.58) Present Value of Total payment=Present Value of monthly Payment +Present Value of Terminal Payment K=F+J PRESENT VALUE OF TOTAL PAYMENTS $250,000.00 OPTION 2 5.2% mortgage with X points Amount of Point payment=X*250000 Y Additional InitialCash out Flow for this option X*250000 A Initial loan $250,000 Y InitialCash outflow X*250000 X points) C Monthly Interest rate=(5.2/12)% D Number of months 360 (30 years*12) E Monthly payment $1,372.78 (Using PMT function of excelwithRate=(5.2/12)%,Nper=360,PV=-250000) F Present Value of Monthly Payment of 72 months at 5.5% discont rate $84,024.16 (Using PV function of excelwithRate=(5.5/12)%,Nper=72,PV=-1372.78) G Future Value of Monthly Payment of 72 months at end of 72 months(5.2% interest) $115,704.25 (Using FV function of excelwithRate=(5.2/12)%,Nper=72,Pmt=-84024.16) H Future Value of initial Loan at end of 72 months(5.2% interest) $341,308.54 (Using FV function of excelwithRate=(5.2/12)%,Nper=72,PV=-250000) I=H-G Loan Balance at the end of 72 months $225,604.28 J Present value of Terminal payment(5.5% dicount) $162,314.60 (Using PV function of excelwithRate=(5.5/12)%,Nper=72,FV=-225604.28) Present Value of Total payment=Present Value of monthly Payment +Present Value of Terminal Payment+Cash flow for point payment K=F+J+Y PRESENT VALUE OF TOTAL PAYMENTS=84024.16+162314.60+X*250000 PRESENT VALUE OF TOTAL PAYMENT OPTION 1 $250,000.00 $246,338.76 84024.16+162314.60+X*250000= $250,000.00 246338.76+X*250000=250000 X*250000=(250000-246338.76)= $3,661.24 X=3661.24/250000= 0.014644959 Number of Points Required to be indifferent = 1.46 Nearest Value =1.28 ANSWER: 1.28

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