How Much House Should You Buy?

 16 August 2004, Reviewed August 8, 2007

Buying more house builds wealth the greater is future price appreciation, the smaller the price premium that must be paid for a larger mortgage, the longer the buyer expects to own the house, the higher the buyer's income tax bracket, the weaker the buyer's tendency to save the difference in monthly payment if the purchase is less, and the lower the return on any such savings.

"My wife and I are arguing about whether to buy the $150,000 house we set out to buy, or the upgraded version for $185,000 that she fell in love with. She argues that we can afford the more expensive house with an interest-only mortgage, and that appreciation in the area will make the more expensive house a better investment. I’m concerned about biting off more than we can chew, especially with interest rates heading up."

This issue is emerging in many households these days because they have more leeway than they used to in how much they spend on a house. To be sure, lenders still apply maximum ratios of housing expense to income when they underwrite a loan. These ratios limit the mortgage payment, which in turn limits the loan amount, which in turn limits the house price. But these ratios are not nearly as rigid as they used to be, especially for borrowers with good credit.

At the same time, the more widespread use of adjustable rate mortgages (ARMs) with flexible payment arrangements, including an interest-only option, allows borrowers to shift part of the financing burden into the future. And strong price appreciation in most parts of the country encourages a mindset that equity in the home will grow even without paying down the loan balance.

To shed some light on the financial wisdom of buying more or less house, I used the net worth spreadsheet on my web site to analyze the twins Con and Agg, short for "conservative" and "aggressive." They are identical in every respect (income, assets, credit) except one. Con wants to buy a $100,000 house and Agg wants to spend $150,000. The question I pose is, which one ends up wealthier?

They have $20,000 in assets, which is used as down payment. Because Con’s $80,000 loan is only 80% of sale price while Agg’s $130,000 loan is 87% of price, Con pays only 6% on his 30-year fixed-rate mortgage, while Agg pays 6.5%. (Another possibility is that Agg pays 6% plus a mortgage insurance premium that would be roughly the equivalent of 6.5% interest). Higher financing cost is one likely, though not an inevitable, disadvantage of buying more house.

A second disadvantage is the higher mortgage payment, reflecting both the larger loan and the higher rate. This means that Con has more income left over, which I assume is invested. The higher the investment rate on surplus income, the better Con does relative to Agg.

On the other hand, Agg earns appreciation on a more costly house. The higher the appreciation rate, the better Agg does relative to Con.

High income taxes also work in Agg’s favor. Agg has larger tax savings on his mortgage, and the after-tax return on investment income, which Agg has less of than Con, is smaller.

I measure the wealth of Con and Agg every month over 360 months. Wealth in any month is: house value + the accumulated value of after-tax investment income + the accumulated value of tax savings on the mortgage - the mortgage balance.

Since Con’s wealth grows more rapidly relative to Agg’s in the early years, the bottom line question is how long it takes for Agg’s wealth to be larger?

Assuming a 4% appreciation rate, 2.5% investment rate before taxes, and 15% tax rate, it take 316 months. At 5%, 6% and 7% appreciation, the period falls to 135, 19 and 1 month, respectively. If the tax rate is 35% while appreciation remains at 4%, it takes only 126 months, and at 5% appreciation (and greater), it takes only one month. On the other hand, the 126 months with 4% appreciation and 35% tax rate becomes 299 months if the investment rate jumps from 2.5% to 5%.

In summary, the case for an aggressive purchase policy as a means to build wealth is stronger: a) The greater your confidence in future price appreciation; b) The smaller the price premium you must pay for the larger mortgage; c) The longer you expect to be in your house; d) The higher your income tax bracket; e) The weaker your confidence that if you adopted a conservative policy, you would save the difference in monthly payment; and f) the lower the return on any such savings.

Even if these factors are favorable, I would not adopt an aggressive policy if it required a flexible payment or interest-only ARM to make it affordable. The risk is just too great.

Number of Months Before An "Aggressive" Buyer Accumulates More Wealth Than           a "Cautious" Buyer

 Income Tax Rate of Buyer 15%

  Investment Rate
Property Appreciation Rate Zero 2.5% 5% 7.5% 10%
3% 318 Never Never Never Never
4% 186 316 Never Never Never
5% 84 135 358 Never Never
6% 13 19 40 Never Never
7% 1 1 1 1 1
8% 1 1 1 1 1

Income Tax Rate of Buyer 35%

  Investment Rate
Property Appreciation Rate Zero 2.5% 5% 7.5% 10%
3% 229 Never Never Never Never
4% 80 126 299 Never Never
5% 1 1 1 1 1
6% 1 1 1 1 1
7% 1 1 1 1 1
8% 1 1 1 1 1

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