Question

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)

Answer 1

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%