Sunday, April 12, 2009

Buy or Rent: an NPV of the Birmingham Housing Market

My wife and I sold our house in May 2008. With our equity, we could afford to set the price aggressively to sell. It was better to sell our house for less, than it was to hold on for a mythical price.

After we sold our house, we moved into an apartment. When selling, the buyer’s agent asked, “Why are you selling?” And my reply was, “I don’t want to be in a house right now.” I can’t say that I foresaw the economic meltdown last fall; my projections were 10% interest rates as the supply money for mortgages decreased. Either way, it was a good move.

Trade-Offs: Apartment v. House

Apartments are cramped, and most “features” of a house are indirect to the features of an apartment. For instance, in an apartment you don’t have yard work, in a house you have to do yard work; the trade-off is a yard where you can play. Other trade-offs include maintenance, cost of utilities, trash, taxes, etc. The costs of a house are explicit, but most benefits are implicit.

Like most personal finance decisions, we have decided we want to live in a house for non-financial reasons. We made the decision based on non-financial metrics, but financial metrics determine our price range and feasibility of living in a house.

Assumptions & Data

As, we are not speculators; therefore, we are not betting on aggressive increases housing price. Remember this when I am talking about owning a house, and appreciation.

We will start with our known information and assumptions:

Principal on House$120,000.00
Interest Rate4.85%
Mortgage Months360
Tax Rate12.00%
PMI Rate1.00%
Pay PMI Until20%
Variable Utilities (House / Rent)50.00%
Property Taxes1.00%
Repairs (Mortgage Payment)50.00%
Rent Increase2.15%
Corporate Bond Yield6%
Growth of House Value1%
Closing Costs3%

Currently, our rent is $830, marginal tax rate is 12%, monthly variable utilities average $215, and fixed utilities average $100. I’m using the corporate bond yield of 6% to discount the costs. Marginal tax rate is included because of the beneficial treatment of mortgage interest by the IRS. I'm using 6% discount rate because I can receive that on a relatively safe bond.

One bit of contention is the 2% growth of house value; it is the long-term growth of housing values—-I read that recently somewhere. Include anticipated repairs and upfront repairs that must be made prior to move-in. Monthly repairs of "50%" assumes costs are half the mortgage payment, which is a best guess. Owning would significantly outweigh renting if no repairs were needed.


First, buying a house with a 30-year mortgage is not a positive NPV project.

Given the assumptions above, the following NPV’s exists for renting and owning after the following durations:

1 years($19,315.04)($13,381.76)
5 years($73,679.56)($61,384.46)
10 years($126,077.78)($110,696.20)
20 years($191,423.27)($182,415.45)
30 years($231,285.04)($229,245.59)

Throughout the duration of the project, renting always has a higher NPV than buying. From year 1 through year 20, renting actually has gains on buying. Only from year 20 through year 30 when principal has been reduced, does buying gain on renting.

I've heard people claim, "At least with owning a house, you receive a check when you leave." If he rented and saved the rest, he would have more money than the closing check. Seeing that most people are moving houses less than every 10 years, most are making poor financial decisions.


In order to maintain our current economic position on housing, we cannot buy a $120,000 house. Also, the value of housing is a function of time, and the indeterminate market value of the house. As people have recently found, the owner receives the benefit/detriment of changes in house prices.

We continue to look for houses, but I don't expect to make any money in the process.

1 comment:

Andrew said...

When you estimate 50% of monthly payment for Repairs, how are you arriving at this figure? That just seems a touch high, unless you are counting "remodling" in repairs, but then I would think you would have to offset with value gained in assessment price.

And, like you stated earlier, the main thing that makes this somewhat problematic ist hat owning a home is not purely a financial decision, but there are unfortunatly no reliable financial models to calculate "the joy of owning".