Is Real Estate a Good Investment? A mathematic model

Since real estate is a very hot investment sector, I try to figure out if the investment is mathematically viable. Here is the assumption I used in my model:

• Home cost of P dollars ($200,000)
• Yearly interest rate r (6.5%) fixed over N years (30)
• Down pay rate (10%)
• Marginal income tax rate rIT (30%)
• Property tax rate rPT (assumed to be 1.5% of P),
• Yearly maintenance cost rate & insurance rate rM (assumed to be 1.5% of P)

Therefore, the monthly cost of home ownership is approximately ($1,187) by using following formula:

Cost = ((r/(1-(1+r)^(-N)+ rPT)*(1- rIT)+ rM)*P/12

Let us also assume
• 90% of the monthly cost is covered by renting income
• cost increases 2.5% annually
• renting income increases 2.5% as well
• Mortgage application fee 1%
• Attorney fee: 0.5%
• Agent fee when you sell: 6%

Here comes the big assumption, annual house market appreciation rate. Since historical data showed long term real return for real estate is about 0.7%, so I assume the nominal return rate is 3.5%.

By plugging in all this number and assume you sell the house in year 10, the calculated IRR is 15%!!!

I also run Monte Carlo simulation. In majority of the simulations, 10-Year IRR is positive, even when the annual appreciation rate is 0%. Of course the key is: NO SIGNIFICANT DECREASE OF HOUSE PRICE during the holding period.

So I guess the conclusion is Real estate is a good investment in long run based on the fact you need spend time and energy to manage and take some risk. However, is now the right time to jump in?