Jack's Jumpin' Junk Joint has a 5.64% APR mortgage on his shop, which has a remaining balance of $203,044.90. The loan has 9.25 more years (111 payments) of $2,351.89 per month until the current mortgage will be paid off. Interest is a tax-deductible expense for Jack, and Jack's tax rate is 28%. Jack can refinance the mortgage with a 4.68% APR 15-year mortgage for a total after-tax cost to refinance of $7,245. What is Jack's net advantage to refunding (NA) to refinance the mortgage, to the nearest dollar?
NOTE: The mortgages are installment loans (not like bonds, which are interest-only loans), so you cannot simply plug values into Equation (20.4) to get the correct answer. Instead, this situation is just like a home mortgage.
Existing Mortgage scheme:
Total payments = N x PMT = 111 x 2,351.89 = $ 261,059.79
Interest payment = total payment - loan amount = 261,059.79 - 203,044.90 = 58,014.89
Post tax interest outflow = Interest payment x (1 - T) = 58,014.89 x (1 - 28%) = $ 41,770.72
New Mortgage Scheme:
Monthly payment, = PMT (Rate, Nper, PV, FV) = PMT (4.68%/12, 12 x 15, -203044.90, 0) = 1,572.02
Total payments = N x PMT = 15 years x 12 months per year x 1,572.02 = $ 282,964.27
Interest payment = total payment - loan amount = 282,964.27 - 203,044.90 = 79,919.37
Post tax interest outflow = Interest payment x (1 - T) = 79,919.37 x (1 - 28%) = $ 57,541.94
Total post tax interest outflow differential = 57,541.94 - 41,770.72 = 15,771.22
Post tax closing cost = 7,245
Hence, Jack's net advantage to refunding (NA) to refinance the mortgage, to the nearest dollar = 15,771.22 - 7,245 = $ 8,526.22
Jack's Jumpin' Junk Joint has a 5.64% APR mortgage on his shop, which has a remaining...