“Is Mortgage Refinancing a Wise Financial Move? Analyzing Costs and Benefits”

QUESTION

Two years ago, you purchased a house of $300,000. You borrow a mortgage with 80% of LTV (loan to value ratio). The interest rate on the mortgage is 6.25%.  Payment terms are being made monthly to amortize the loan over 30 years. You have found another lender who will refinance the current outstanding loan balance plus all the costs associated with the new loan at 5% with monthly payments for 30 years. Suppose that the new lender will charge 2.5 discount points on the new loan and other refinancing costs will equal $9,555.51.

1. What is the new loan amount if you choose to refinance?
2. Should you refinance if you hold the loan for 30 years?
3. If you choose to refinance, at least how many years should you stay in the house (do not prepay)? Why?

ANSWER

Refinancing a mortgage is a financial decision that should be made carefully, taking into consideration various factors such as interest rates, costs, and how long you plan to stay in your home. In this scenario, you are considering refinancing your existing mortgage, and we will explore whether it makes financial sense to do so.

First, let’s calculate the new loan amount if you choose to refinance:

1. Current Mortgage Details:
   • Original Loan Amount: $300,000
   • Loan-to-Value Ratio (LTV): 80%
   • Interest Rate: 6.25%
   • Amortization Period: 30 years

To calculate the current outstanding loan balance, we can use an amortization calculator or formula. However, I’ll provide you with the approximate balance after two years of payments. Keep in mind that actual values may vary slightly due to the specifics of your mortgage agreement.

• After 2 years of payments, the remaining balance on the current mortgage is approximately $292,637.62.

2. New Mortgage Offer:
   • Interest Rate: 5%
   • Amortization Period: 30 years
   • Discount Points: 2.5% of the loan amount
   • Refinancing Costs: $9,555.51

Now, let’s calculate the new loan amount with the refinancing costs included:

• New Loan Amount = Current Balance + Refinancing Costs + Discount Points
• New Loan Amount = $292,637.62 + $9,555.51 + (2.5% of $292,637.62)

Calculating this, the new loan amount for refinancing is approximately $312,278.21.

Next, let’s consider whether you should refinance if you plan to hold the loan for 30 years. To determine this, we need to compare the total costs of the current mortgage over 30 years with the total costs of the new mortgage after refinancing.

Total Costs of Current Mortgage (30 years):

• Monthly Payment = $1,848.43 (calculated based on the original mortgage terms)
• Total Payments over 30 years = $1,848.43 * 12 months * 30 years = $665,535.48

Total Costs of New Mortgage (30 years):

• Monthly Payment = To calculate the monthly payment for the new mortgage at 5% interest over 30 years, we can use a standard loan amortization formula. The monthly payment comes out to approximately $1,678.60.
• Total Payments over 30 years = $1,678.60 * 12 months * 30 years = $604,296.00

Now, let’s compare the total costs:

• Total Cost with Current Mortgage: $665,535.48
• Total Cost with New Mortgage (including refinancing costs): $604,296.00 + $9,555.51 = $613,851.51

Comparing these costs, it’s evident that refinancing will save you money over 30 years, as the total cost with the new mortgage is lower. Therefore, it makes financial sense to refinance if you plan to hold the loan for 30 years.

However, you asked about the minimum number of years you should stay in the house without prepaying the mortgage. This depends on when the savings from refinancing surpass the costs. In this case, the savings are the difference in total costs between the two mortgages.

• Savings = Total Cost with Current Mortgage – Total Cost with New Mortgage = $665,535.48 – $613,851.51 = $51,683.97

To find out how many years it takes to recoup the refinancing costs and start saving money, you can divide the refinancing costs by the annual savings:

• Break-even period = Refinancing Costs / Annual Savings = $9,555.51 / ($51,683.97 / 30 years) ≈ 5.53 years

Therefore, it will take approximately 5.53 years for you to recoup the refinancing costs and start saving money. As long as you plan to stay in the house for more than 5.53 years, refinancing is a financially sound decision. If you anticipate staying for a shorter period, it may not be as beneficial.

In conclusion, refinancing your mortgage to the new lender with a 5% interest rate is a prudent financial move if you intend to hold the loan for 30 years, as it will result in lower overall costs. However, it’s essential to consider your long-term housing plans and evaluate the break-even point to make an informed decision based on your specific circumstances.