Question

Tom got a 30 year fully amortizing FRM for $1,500,000 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 2 points and $1000 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 stays until maturity?

Answer 1

Tom’s old payment:

[360, N], [8/12, I], [-1,500,000, PV], [CPT, PMT] PMT=11,006.47

Tom’s balance after 3 years:

[324, N], [8/12, I], [-11,006.47, PMT] , [CPT, PV] PV=1,459,202.23

Tom’s payment if he refinances.

[324, N], [5/12, I], [-1,459,202.23, PV], [CPT, PMT] PMT=8,215.88

Difference in payments = $11,006.47 - $8,215.88 = $2,790.59

Tom’s cost of refinancing = [0.02*$1,459,202.23] + $1,000 = $29,184.04 + $1,000 = $30,184.04

Now, To find the IRR we need to put the following values in the financial calculator:

[324, N], [-30,184.04, PV], [2,790.59, PMT], [0,FV],[CPT, I/Y*12] IRR=110.94%