A borrower has had a 30 year, 8%, $600,000 mortgage for 6 years. Closing fees on
ID: 2726781 • Letter: A
Question
A borrower has had a 30 year, 8%, $600,000 mortgage for 6 years. Closing fees on this mortgage were 4% of the loan amount, and the prepayment penalty is 4% of OLB. The borrower is considering a refi into a 20 year mortgage at 7.25%. She will finance the payoff and all fees, and take out an additional $50,000 in cash. The closing fees on the new mortgage are 4% of the loan amount. Also assume the homeowner could borrow the extra $50,000 elsewhere at 7.5% for a fee of 2% in the form of a 10 year monthly installment loan with no prepayment penalty. The borrower will sell the house and pay off any remaining mortgage 7 years from now.
What is the NPV of refinancing, and should the borrower refinance? Assume the homeowner's opportunity cost is 7.5%.
Explanation / Answer
The payment for the old loan =pmt(rate,nper,pv) = pmt(0.08/12,30*12,600000) = $4,402.59
The amount of loan left off at the end of 6 years is as shown in the amortization table.
The loan remaining is $562,951.76
4% closing fees and 4% prepayment penalty = 45,036. This amount will be financed using the additional 50,000 borowed at 7.5%
The monthly payment for the new loan = pmt(0.0725/12,20*12,562,951.76 ) = $4,449.44
The monthly payment for the 50,000 loan for 10 years at 7.5% = pmt(0.075/12,10*12,50000) = 593.91
The remaining mortgage after 7 years is calculated in the amortization table and the same is :$448,680.59 ( We have not included the amortization table due to lakh of space)
The savings of the loan = pmt(0.08/12,360,600000) - pmt(0.0725/12,360,600000) = 309.53
Hence NPV =pv(0.075/12,7*12,309.53) -45,036 = -24,855.77
The lower rate is attractive, but the higher fee of exiting makes the refianance unattratcive
Month Payment Interest Amortized amount Principal 0 600000 1 $ 4,402.59 $ 4,000.00 $ 402.59 $ 5,99,597.41 2 $ 4,402.59 $ 3,997.32 $ 405.27 $ 5,99,192.14 3 $ 4,402.59 $ 3,994.61 $ 407.97 $ 5,98,784.17 4 $ 4,402.59 $ 3,991.89 $ 410.69 $ 5,98,373.48 5 $ 4,402.59 $ 3,989.16 $ 413.43 $ 5,97,960.04 6 $ 4,402.59 $ 3,986.40 $ 416.19 $ 5,97,543.86 7 $ 4,402.59 $ 3,983.63 $ 418.96 $ 5,97,124.90 8 $ 4,402.59 $ 3,980.83 $ 421.75 $ 5,96,703.14 9 $ 4,402.59 $ 3,978.02 $ 424.57 $ 5,96,278.57 10 $ 4,402.59 $ 3,975.19 $ 427.40 $ 5,95,851.18 11 $ 4,402.59 $ 3,972.34 $ 430.25 $ 5,95,420.93 12 $ 4,402.59 $ 3,969.47 $ 433.11 $ 5,94,987.82 13 $ 4,402.59 $ 3,966.59 $ 436.00 $ 5,94,551.81 14 $ 4,402.59 $ 3,963.68 $ 438.91 $ 5,94,112.91 15 $ 4,402.59 $ 3,960.75 $ 441.83 $ 5,93,671.07 16 $ 4,402.59 $ 3,957.81 $ 444.78 $ 5,93,226.29 17 $ 4,402.59 $ 3,954.84 $ 447.75 $ 5,92,778.54 18 $ 4,402.59 $ 3,951.86 $ 450.73 $ 5,92,327.81 19 $ 4,402.59 $ 3,948.85 $ 453.74 $ 5,91,874.08 20 $ 4,402.59 $ 3,945.83 $ 456.76 $ 5,91,417.32 21 $ 4,402.59 $ 3,942.78 $ 459.81 $ 5,90,957.51 22 $ 4,402.59 $ 3,939.72 $ 462.87 $ 5,90,494.64 23 $ 4,402.59 $ 3,936.63 $ 465.96 $ 5,90,028.69 24 $ 4,402.59 $ 3,933.52 $ 469.06 $ 5,89,559.62 25 $ 4,402.59 $ 3,930.40 $ 472.19 $ 5,89,087.43 26 $ 4,402.59 $ 3,927.25 $ 475.34 $ 5,88,612.10 27 $ 4,402.59 $ 3,924.08 $ 478.51 $ 5,88,133.59 28 $ 4,402.59 $ 3,920.89 $ 481.70 $ 5,87,651.89 29 $ 4,402.59 $ 3,917.68 $ 484.91 $ 5,87,166.98 30 $ 4,402.59 $ 3,914.45 $ 488.14 $ 5,86,678.84 31 $ 4,402.59 $ 3,911.19 $ 491.40 $ 5,86,187.45 32 $ 4,402.59 $ 3,907.92 $ 494.67 $ 5,85,692.78 33 $ 4,402.59 $ 3,904.62 $ 497.97 $ 5,85,194.81 34 $ 4,402.59 $ 3,901.30 $ 501.29 $ 5,84,693.52 35 $ 4,402.59 $ 3,897.96 $ 504.63 $ 5,84,188.89 36 $ 4,402.59 $ 3,894.59 $ 507.99 $ 5,83,680.89 37 $ 4,402.59 $ 3,891.21 $ 511.38 $ 5,83,169.51 38 $ 4,402.59 $ 3,887.80 $ 514.79 $ 5,82,654.72 39 $ 4,402.59 $ 3,884.36 $ 518.22 $ 5,82,136.50 40 $ 4,402.59 $ 3,880.91 $ 521.68 $ 5,81,614.82 41 $ 4,402.59 $ 3,877.43 $ 525.16 $ 5,81,089.67 42 $ 4,402.59 $ 3,873.93 $ 528.66 $ 5,80,561.01 43 $ 4,402.59 $ 3,870.41 $ 532.18 $ 5,80,028.83 44 $ 4,402.59 $ 3,866.86 $ 535.73 $ 5,79,493.10 45 $ 4,402.59 $ 3,863.29 $ 539.30 $ 5,78,953.80 46 $ 4,402.59 $ 3,859.69 $ 542.90 $ 5,78,410.90 47 $ 4,402.59 $ 3,856.07 $ 546.51 $ 5,77,864.39 48 $ 4,402.59 $ 3,852.43 $ 550.16 $ 5,77,314.23 49 $ 4,402.59 $ 3,848.76 $ 553.83 $ 5,76,760.41 50 $ 4,402.59 $ 3,845.07 $ 557.52 $ 5,76,202.89 51 $ 4,402.59 $ 3,841.35 $ 561.23 $ 5,75,641.65 52 $ 4,402.59 $ 3,837.61 $ 564.98 $ 5,75,076.68 53 $ 4,402.59 $ 3,833.84 $ 568.74 $ 5,74,507.93 54 $ 4,402.59 $ 3,830.05 $ 572.53 $ 5,73,935.40 55 $ 4,402.59 $ 3,826.24 $ 576.35 $ 5,73,359.05 56 $ 4,402.59 $ 3,822.39 $ 580.19 $ 5,72,778.85 57 $ 4,402.59 $ 3,818.53 $ 584.06 $ 5,72,194.79 58 $ 4,402.59 $ 3,814.63 $ 587.96 $ 5,71,606.84 59 $ 4,402.59 $ 3,810.71 $ 591.88 $ 5,71,014.96 60 $ 4,402.59 $ 3,806.77 $ 595.82 $ 5,70,419.14 61 $ 4,402.59 $ 3,802.79 $ 599.79 $ 5,69,819.35 62 $ 4,402.59 $ 3,798.80 $ 603.79 $ 5,69,215.56 63 $ 4,402.59 $ 3,794.77 $ 607.82 $ 5,68,607.74 64 $ 4,402.59 $ 3,790.72 $ 611.87 $ 5,67,995.87 65 $ 4,402.59 $ 3,786.64 $ 615.95 $ 5,67,379.92 66 $ 4,402.59 $ 3,782.53 $ 620.05 $ 5,66,759.87 67 $ 4,402.59 $ 3,778.40 $ 624.19 $ 5,66,135.68 68 $ 4,402.59 $ 3,774.24 $ 628.35 $ 5,65,507.33 69 $ 4,402.59 $ 3,770.05 $ 632.54 $ 5,64,874.79 70 $ 4,402.59 $ 3,765.83 $ 636.76 $ 5,64,238.03 71 $ 4,402.59 $ 3,761.59 $ 641.00 $ 5,63,597.03 72 $ 4,402.59 $ 3,757.31 $ 645.27 $ 5,62,951.76Related Questions
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