Tom got a 30 year fully amortizing FRM for $500,000 at 8%, with constant monthly payments. After 3 years of payments rates fall and he can get a 27 year FRM at 5%, but he must pay 7 points and $20000 in closing costs to get the new loan. Think of the refinancing decision as an investment for Tom, he pays a fee now but saves money in the future in the form of lower payments. What is the annualized IRR of refinancing for Tom assuming he prepays the new loan 5 years after refinancing? (Clarification: Tom will prepay the new loan 3+5=8 years after the house is purchased)
Tom’s old payment: | |
Principal | $500,000.00 |
Rate = 8%/12 | 0.67% |
Period = 30 x 12 | 360 |
Monthly Payment = PMT(.67%,360-500000) | $3,668.82 |
Loan Balance after 3 years | |
PMT | $3,668.82 |
Rate = 8%/12 | 0.67% |
Period = 27 x 12 | 324 |
Loan Balance after 3 years = PV(.67%,324,-3668.82) | $486,400.74 |
Tom’s payment if he refinances | |
Principal | $486,400.74 |
Rate = 5%/12 | 0.42% |
Period = 30 x 12 | 324 |
Monthly Payment = PMT(.67%,360-500000) | $2,738.63 |
Difference in payments = 3668.82 − 2738.63 = | $930.20 |
Tom’s cost of refinancing = 0.07 x 486,400.74 + 20000 = | $54,048.05 |
New Loan Balance after 5 years | |
PMT | $2,738.63 |
Rate = 5%/12 | 0.42% |
Period = 22 x 12 | 264 |
Loan Balance after 5 years = PV(.42%,264,-2738.63) | $437,983.40 |
Old Loan Balance after 5 years | |
PMT | $3,668.82 |
Rate = 5%/12 | 0.67% |
Period = 22 x 12 | 264 |
Loan Balance after 5 years = PV(.42%,264,-2738.63) | $455,088.49 |
Difference in Balances = $455,088.49 - $437,983.40 | $17,105.09 |
Present Value = PV | $54,048.05 |
PMT | $930.20 |
Period = 5 x 12 | 60 |
Final balance | $17,105.09 |
Monthly IRR = Rate (60,930.20,-54048,17105.09) | 0.84% |
Annual IRR = 12 x 0.84% | 10.08% |
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