OK-mathematicians, where are you??

[Rich Weese]

A reply on another thread made me wonder about something. Mikeoh mentioned fannie mae is showing 5% appreciation annually over the past 50 years on average. The Rule Of 72 says that to find out how long it takes to double your money, divide the % rate(5) into 72. Your money would double in 14.4 years.
Here is my question. At the same rate, what would be my value of property in 30 years when loan is paid off, with no extra principal payments?
If you put the standard 20% down as an investor, what would be your "annual " rate of return for the 30 years on the 20% down ? Much more than the 5% we've chatted about above!!
When someone posts the calculations, it will help the newbies to understand why we love this stuff. Leverage is truly an amazing thing, especially for those young enuff to enjoy the 30 year ride.
Now, what will your estate be worth if you buy one a year , each year for the 30 years??? Probably too difficult to calculate, but it might be enuff to stay ahead of the changes current administration is making... Someone, do the math for us. Thanks. Rich.

[Jon Holdman]

Not sure I buy the 5% annual appreciation number, if you factor out the recent bubble, but we'll go with it. Inflation over that period has averaged 4.07%.

After 30 years of averaging 5% appreciation per year, a property will be worth 4.32 times its initial price, in nominal terms. However, during that time, assuming 4.07% inflation, inflation has made overall prices 3.31 times what they were at the start of the time. So, in real terms (real means inflation adjusted, that's, what you can buy with the money), the property is worth only 1.3 times its initial value.

The calculation is down as a power function in Excel: Power (1+rate, term) where rate is the appreciation rate (5%) and term is the number of years (30).

There's not quite enough information to fully answer you second question, so I'll make a few assumptions. Say you purchase a house for $100K with a 30 year loan at 6%. You put down 20%. Your payment is $599.55. After 30 years, in nominal terms (i.e., the price you would sell it for in current dollars) would be $432,194. The total of your payments would be $215,838. So, in nominal terms, you would have just about doubled your money. To apply the rule of 72, you've doubled you cash in 30 years, so your return was 72/30=2.4%. Pretty crummy.

Another way to consider this is to compare it to putting the money in CDs. I don't have historical CD rates, so lets back into the equivalent rate. Say instead of buying the house you used the $599.55 to buy one CD a month for 30 years. What rate would you need to get to end up with the $432K? 4.275%.

Now, of course, with a property you don't just pay. You have rent coming in. My rule of thumb is I assume 40% for expenses because I manage them myself, and I'm not looking for monthly cash flow. So, if I could rent this house for $1000 with this payment, it would meet my bare minimum criteria. I have an asset that's (at least in nominal terms) increasing in value and I'm not out of pocket anything.

If I bought one house a year at $100,000, put nothing down, got a loan as above, and rented it for $1000 a month, then after 30 years I'd have total equity of $5.1 million. The properties themselves would be worth a total of $7 million, but I'd have $1.9 million in debt.

Note that most of the value is in the earliest purchases. If I just bought one a year for 10 years, then waited for 20 more years, I'd have a worth of $3.2 million and only $270K in debt.

Now that's all in nominal terms, and if you want real comparison, you have to convert to real terms. If you adjust for inflation, the one house a year for 30 years gives you the equivalent of $1.6M in todays dollars, and the one for 10 years and wait 20 gives you just under $1M in todays dollars.

Again, I don't buy that 5% is the right number, so what if we use the same 4.07% for both inflation and appreciation. In nominal terms I end up with $4.0 M in the 30 house scenario and $2.5M in the 10 house scenario. In real terms, I have $1.2M with 30 houses and $760K with 10 houses.

Either of those would make for a decent retirement. In fact, I'd have to say that's pretty much my plan.