Monday, May 20, 2019

Modeling Choice between a Jumbo and Conventional Mortgage



This post describes a problem that I was recently asked to analyze.   An applicant for a mortgage refinance had to choose between refinancing the entire current mortgage with either a jumbo loan or a small conventional loan and a cash paydown.  He needed my advice on what option was best.

Question:  A person refinancing a $650,000 30-year Adjustable Rate Mortgage loan into a 15-year Fixed Rate Mortgage has two options.   The first option involves refinancing the current $650,000 30-year ARM with a $650,000 jumbo 15-year FRM.   The second option involves reducing the loan balance by $100,000 and taking out a $550,000 conventional FRM.

Note many people lack an extra $100,000 and don’t have two options.

The advantages of the jumbo loan are greater liquidity and earnings on the $100,000, which is invested in financial assets.

The advantage of the conventional loan is lower lifetime interest payments.

Create a spreadsheet to evaluate these two options for base case assumptions and for modifications to the base case.

The Base Case:

Both mortgages have a 3.75% interest rate,

Invested funds under the jumbo bond option are invested in Treasury bills and receive a 2.5% rate of return,

The marginal tax rate applied to both investment income and gains from mortgage interest deduction is 30%.

What option – the jumbo mortgage or the conventional mortgage – is preferable under the base case assumption?

Alternative Scenarios:

Often conventional mortgage interest rates are lower than jumbo interest rates.    Assume the conventional mortgage interest rate is 3.25% and the jumbo mortgage interest rate is 3.75%.  
What option is preferable?

The investor chooses to invest partially in stock and partially in Treasury bonds.   Accounting for risk, the certainty equivalent rate of return on invested funds is 6.5%.  Assume a 3.25% conventional interest rate and a 3.75% jumbo interest rate   What option is preferable?



Analysis:  


The measure  of the most affordable mortgage is  after-tax lifetime interest costs minus after tax investment income plus


Here is a table describing base case results.


Base Case Results
Jumbo Loan No Paydown
Conventional Loan $100,000 Paydown
Interest Rate
3.75%
3.75%
Loan Term Years
15
15
Paydown Amount
$0
$100,000
Initial Loan Balance
$650,000
$550,000
Invested Cash
$100,000
$0
Interest Rate on Invested Cash
2.50%
NA
Monthly Mortgage Payment
$4,712
$3,987
Mortgage Payments over 15 years
$848,199.63
$717,707.38
Annual Earnings On Cash Invested
$2,500
NA
Cumulative Earnings
$37,500
NA
Mortgage Payments - Cumulative Earnings
$810,700
$717,707
Cumulative Interest
$198,199.63
$167,707.38
Principle
$650,000
$550,000
Total Payments
$848,199.63
$717,707.38
Tax  Rate
0.3
0.3
Tax Savings from Deduction of Mortgage Interest
$59,459.89
$50,312.21
Tax Paid on  Investment Income
$11,250
0
After Tax Mortgage Payments Minus After Tax investment Income
$762,490
$667,395


·      The conventional mortgage appears to save the home buyer around $95,000 ($762k- $667k )over fifteen years.    This is a bit more than $6,300 per year.

Lower conventional mortgage interest rates

Typically interest rates on conventional mortgages can be lower than interest rates on jumbo mortgages.   The differential is currently fairly small because demand for large houses is at this time lower than demand for mid-size houses.  

The results below pertain to a situation where the conventional mortgage interest rate is 3.25%, the jumbo mortgage interest rate is 3.75% and all other variables are set by base rate assumptions.

Lower Conventional Mortgage Rate Results
Jumbo
Conventional
Diff.
After Tax Mortgage Payments Minus After Tax investment Income
$762,490
$650,634
$111,856
Assumed Conventional Mortgage has 3.25% interest all other assumptions are base case

·      The conventional option appears to save the borrower close to $112,000 over $9,300 per year.


Lower Conventional Mortgage Rates  

A person who takes out the jumbo loan and invests in stocks could get higher returns. The final scenario assumes a 6.5% return, a conventional mortgage rate of 3.25%, a jumbo rate of 3.75% and all other variables determined by the base case. 


Higher Returns & Lower Conventional Mortgage Rates
Jumbo
Conventional
Diff.
After Tax Mortgage Payments Minus After Tax investment Income
$720,490
$667,395
$53,095

·      The conventional option appears to save the borrower around $53,000 or around $3,500 per year. 


Concluding Remarks:   The conventional loan & pay down option beats the jumbo loan option in all three scenarios considered here.   The jumbo loan option could win after the fact if borrower buys risky assets and these assets experience large returns but this scenario does not consider risk. 

The best justification for the jumbo loan option would be fear of losing so much liquidity.  

Authors Note:   Please consider my books on Kindle.


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