## Tuesday, August 19, 2014

### Should you list or rent out your house?

Interest rates and the house listing decision

A recent CNBC article found that many people who move are now choosing to maintain ownership and rent out their current home rather than sell.

There are many factors impacting the decision to rent out the first home and buy a second one.   This math post looks at one factor (lower interest rates), which may be spurring some people to own two homes rather than one.

Question

A house sale today would go for \$700,000.

The rent on the house is expected to be \$3,000 per month.

Taxes and insurance are \$7,000.

Expenses on house maintenance are \$5,000.

Consider two homeowners.

Both homeowners borrowed \$600,000 10 years ago.

The first has a 10-year old 30-year mortgage with a 5.5% interest rate.

The second has a 10-year old 30-year mortgage with a 3.5% interest rate.

Explain why the low-interest borrower is more likely to hold the house than the high-interest borrower?

Discuss wider implications for the house listing decision.

Analysis:

The mortgage holder with the lower interest rate has paid off a larger portion of his mortgage than the high-rate borrower.

The chart below contains information on the mortgage balance and house equity for the two borrowers after holding the property for 10 years.

 House Equity After 10 Years Borrower 1 Borrower 2 Mortgage Interest Rate 0.035 0.055 Value of House \$700,000 \$700,000 Mortgage 10 Years Ago \$600,000 \$600,000 Monthly Payment on Mortgage (\$2,694) (\$3,407) Current Mortgage Balance (\$464,561) (\$495,246) Equity in House \$235,439 \$204,754

Note the person with the lower interest rate mortgage has around \$30,000 in additional equity because equity build up is quicker when interest rates are low.

A person will be indifferent between selling the home today and selling the home in one year if the net present value of the proceeds in one year is identical to the amount that could be received today.

There are three differences between the high-rate and low-rate borrower that are likely to increase the probability the low-rate borrower continues to hold the property.

First, the low-interest borrower makes lower mortgage payments and will net more cash flow from rent.   Second, equity build is larger at lower interest rates.  Third, the cost of capital is lower for the borrower with the low interest rate.

Below is information on loss (rent-expenses) from holding this property for one more year.

 Mortgage Interest Rate 0.035 0.055 Revenue 36000 36000 Taxes and Insurance 7000 7000 Maintenance 5000 5000 Mortgage Payment \$32,331.22 \$40,880.81 Loss on House From Rent (\$8,331.22) (\$16,880.81)

Note that the only difference in rental income from the two borrowers stems from the lower interest rate.  Rent income and other expenses like taxes and maintenance are identical for the two borrowers.

Below is the mortgage balance at the end of the year under the two mortgage interest rate assumptions.

 Borrower 1 Borrower 2 Difference Value of Mortgage Today (\$464,561) (\$495,246) (\$30,685) Value of Mortgage in One More year (\$448,229.34) (\$481,254.46) (\$33,025) Reduction of Mortgage by Holding the Property One More Year (\$16,331.91) (\$13,991.49) \$2,340

The borrower with low interest rates should be more likely to hold onto the property for two direct pecuniary reasons --- around \$8,500 per year in additional rental income and around \$2300 per year in additional equity build up.

In addition, the borrower with the low rate has the lower cost of capital.

Other Considerations:

There are always other considerations.

People have other uses for funds including equity and bond investments.  However, given the low interest rates and a stock market nearing record highs real estate exposure seems ok.

There are always tax considerations.  Higher-income taxpayers are not allowed to deduct all mortgage interest on tax

Managing a rental property takes time as well as money.  Most property owners are going to hire a professional manager and the quality of professional property managers vary widely.   Many property managers use a contract that indemnifies themselves against their own mistakes and misdeeds.

Many homeowners will want to reduce their exposure to real estate by owning one home rather than two.

Also, homes are large items subject to neighborhood risk, which can’t be fully diversified.

However, home sales differ from stock in that with the later there is a clearly observed price on a homogenous item while in the former there are wide disagreements in price on heterogeneous items.   My view in a recent post is that the housing market still appears soft.

Most realtors are going to want you to list and sell your old home and buy a new one.   This may not be in your best interest.