The Mathematics of Refinancing

Dr. Youngna Choi and Crystal Dahlhaus (2009)

Presented by Amara Yeb

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

Picking up the Old Loan

Starting a New Loan

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.

Reference

Choi, Youngna, and Crystal Dahlhaus, “The Mathematics of Refinancing,” UMAP Journal 30(4) (2009): 429-456.