Question

9. 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 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

Amortization formula is

.........Formula A

and for Principal

..........Formula B

Now With explanation of Notation,we right given information in question

A= Amortization payment

P= Principle or say balance of amount = 500000(Given in Questions)

r= Rate =8%(Given in question)

T= term

n= multiply as per quarterly,half-yearly,monthly (For example, for Quarterly (4), Monthly (12))

As per Amortization formula A, we will find Monthly payment for the first 3 years (36 months) as rate start to fall after 3 years.

=3668.82

Now, Assumption Tom Prepay the new loan after 5 years of refinancing. therefore we have to compare all the data for it.

CASE 1 : IF he is not going to refinancing way...........

Remaining Balance after 8 years (3 years already gone + 5 years as per assumption) as per formula B

  

= 455088.14

CASE 2 : IF he is going to refinancing way...........

Remaining Balance after 3 years Because going to refinancing	As per Formula B		=486400.36
Cost of One time for Refinancing			= 54048.03
Next 5 years' Payment	per Formula A		= 2738.62
Balance after 5 years	per Formula B		=437982.45

We can Make a table for CASH FLOW as follow ............

Months	Cash Flow If Tom do not refinance	Cash Flow If Tom refinance	B-A	Remarks
0	500000	500000	0	Cash Inflow
1 to 35	-3668.82	-3668.82	0	Cash outflow Payment
36	-3668.82	-3668.82	0
36	0	-54048.03	-54048.03
37 to 95	-3668.82	-2738.62	930.20
96	-3668.82	-2738.62	930.20
96	-455088.14	-437982.45	17105.69	In total at 96 month =18035.89

FOR IRR

Multiply IRR with 12 month

by putting

CF0	-54048.03
CFt	930.20
CFt+1	18035.89
For 1 -36 month	t=0
For 36 -95 month	t=59
for 96th month	t=1

by solving it with scientific method,

IRR*12 = IRR in Year term = IRR for Solution = 10.8%