May 21st, 2002, 4:50 pm
This is a nice spreadsheet, but I have a couple of minor carps. First, you discount to PV using monthly rates, then compound to the horizon using annual. This only makes a difference of $2,720 with the numbers on the sheet, but could matter more with a longer horizon, lower tax rates or higher reinvestment rate. Second, you oversimplify the taxes. You can only deduct the mortgage interest by giving up your standard deduction, and only to the point that your deductions phase out. That's why the mortgage tax deduction is valuable only to moderate high income taxpayers (joint income $120,000 to $300,000). This probably describes a lot of people who might use the spreadsheet, but by no means all. Similarly, you assume state and local income tax is deductible from federal, this is not true in all states and, in any case, has the same limitation as mortgage interest.I prefer to approach the problem differently. In the numbers you supplied, a $1,200,000 apartment gives monthly savings of $2,600, which is 2.6% per year. Since the savings go up by 3% per year, that's a yield of 5.6%. The alternative, after tax, is 5.4%. So if the apartment value goes up by 3% per year, buying is 0.2% per year better than renting. The breakeven price appreciation for the apartment is about 2.8% per year. You compute 1.1% by doing a more elaborate analysis, but you have to introduce lots of assumptions (a mortgage, a horizon and tax splits). Thinking about those things, in my opinion, focuses attention on the wrong variables and does not result in a better answer since most people have little idea about these things. In fact, I would leave it as the apartment returns 2.6% per year inflation-adjusted, tax-free and leave it to the buyer to decide if that is a good or bad return.I don't like incorporating the mortgage in the analysis. If buying something is a good investment, leverage may make it better. If it's a bad investment, leverage might make it worse. But leverage does not change whether it is good or bad. So putting it in the analysis complicates things without changing the result.Finally, the natural way to think about this spreadsheet is to compare the apartment to an investment in securities. 10% implies you consider the apartment about as risky as large-cap stocks. That might be true over a fixed five-year horizon, although I think it exaggerates the risk. But for someone who is willing to live in the apartment long-term (basically, someone who does not expect to have to move for a job and has correctly anticipated family changes), the risk is much lower. Usually it is the risk element that is crucial to the decision, someone stable will find buying attractive, others will not.