Question

Tom got a 30 year fully amortizing frm for $400,000 at 6%, 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 2 points and $1500 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 in 5 years? (clarification: tom will prepay the new loan 5 years after the house is purchased)

Answer 1

Tom’s old payment:
[360, N],[6/12, I],[400000, PV],[CPT, PMT] PMT = $2398.20

Tom’s balance after 3 years:
[324, N],[6/12, I],[2398.20, PMT] , [CPT, PV]PV = $384,335.94

Tom’s payment if he refinances.
[324, N],[5/12, I],[384,335.94, PV],[CPT, PMT]PMT = $2163.96

Difference in payments:
2398.20−2163.96 = 234.24

Tom’s cost of refinancing:
0.02∗384,335.94+1500 = 9186.72

Tom’s NPV:
NPV = (−9186.72+(234.24/(1+IRR12)^1)) +...+ (234.24/(1+IRR12)^360−36 = 324)

CF0 = -9186.72,
CF1 = 234.24, F01 = 324,
[IRR, CPT]IRR = 30.59%