the mathematics of refinancing dr. youngna choi and crystal dahlhaus (2009) presented by amara yeb
TRANSCRIPT
What is Refinancing?
Finance something again
Continue the same loan at a lower interest rate
Paying off an existing loan and replacing it with a new one at a lower interest rate
Modeling Objective How to make an intelligence decision on
refinancing
Model the effects of refinancing loans at lower interest rates
• Should the borrower always refinance if there is a lower interest rate?
• Can various fees make refinancing at lower interest rate worse than the original loan?
Questions to be Answered
Basic Financial Background Compound interest
Present Value
Net Present Value
+…++
Effective Rate of Interest is when the NPV is zero
Payment
Model Assumptions Specifically looking at automobile (Short term
loan) and Real Estate (Long Term Loan)
Compound interest is used and assume that the interest is compounded at the end of each term
Number of payments made by the time of refinancing: N-n
Interest rate per month for refinancing: which is lower than
Model Assumptions (Cont.) All the equity built to date is used for refinancing
Refinancing fee: F
Discount points for refinancing: x
is remaining debt at time
is new loan principal
are new monthly payment
Modeling Strategy
Picking up the old loan: Short-term Refinancing
Starting a new loan: long-term Refinancing
Amortization with combined Fees are used
Result A lower Interest rate alone does not guarantee a
profitable refinancing (because there are other factors that should be taken into consideration such as the remaining number of payments, the refinancing fee etc.)
Refinancing is not always a good idea, because we might end up paying more interest throughout the refinanced loan.
This is not bad if there is a tax exemption on the interest.
Conclusion
When refinancing, all the variables of the NPV function should be considered.
Other investment opportunity should be considered (ex. The borrower may take advantage of the lower monthly payment and invest the savings for higher return.
If there is no tax benefit and/or other investment options, the borrower should keep the old loan.