Subject: Real Estate - Renting versus Buying a Home

Last-Revised: 21 Nov 1995
Contributed-By: Jeff Mincy (mincy at rcn.com), Chris Lott (contact me)

This note will explain one way to compare the monetary costs of renting vs. buying a home. It is strongly oriented towards the US system, taking into account tax code issues.

1. Abstract

  • If you are guaranteed an appreciation rate that is a few points above inflation, buy.
  • If the monthly costs of buying are basically the same as renting, buy.
  • The shorter the term, the more advantageous it is to rent.
  • Tax consequences in the US are fairly minor in the long term.

2. Introduction

The three important factors that affect the analysis the most are the following:
  1. Relative cash flows; e.g., rent compared to monthly ownership expenses
  2. Length of term
  3. Rate of appreciation

The approach used here is to determine the present value of the money you will pay over the term for the home. In the case of buying, the appreciation rate and thereby the future value of the home is estimated. For home appreciate rates, find something like the tables published by Case Schiller that show changes in house prices for your region. The real estate section in your local newspaper may print it periodically. This analysis neglects utility costs because they can easily be the same whether you rent or buy. However, adding them to the analysis is simple; treat them the same as the costs for insurance in both cases.

Opportunity costs of buying are effectively captured by the present value. For example, pretend that you are able to buy a house without having to have a mortgage. Now the question is, is it better to buy the house with your hoard of cash or is it better to invest the cash and continue to rent? To answer this question you have to have estimates for rental costs and house costs (see below), and you have a projected growth rate for the cash investment and projected growth rate for the house. If you project a 4% growth rate for the house and a 15% growth rate for the cash then holding the cash would be a much better investment.

First the analysis for renting a home is presented, then the analysis for buying. Examples of analyses over a long term and a short term are given for both scenarios.

3. Renting a Home.

Step 1: Gather data
You will need:
  • monthly rent
  • renter's insurance (usually inexpensive)
  • term (period of time over which you will rent)
  • estimated inflation rate to compute present value (historically 4.5%)
  • estimated annual rate of increase in the rent (can use inflation rate)

Step 2: Compute present value of payments
You will compute the present value of the cash stream that you will pay over the term, which is the cost of renting over that term. This analysis assumes that there are no tax consequences (benefits) associated with paying rent.

3.1 A long-term example of renting

Rent = 990 / month
Insurance = 10 / month
Term = 30 years
Rent increases = 4.5% annually
Inflation = 4.5% annually
For this cash stream, present value = 348,137.17.

3.2 A short-term example of renting

Same numbers, but just 2 years.
Present value = 23,502.38

4. Buying a Home

Step 1: Gather data.
You need a lot to do a fairly thorough analysis:
  • purchase price
  • down payment and closing costs
  • other regular expenses, such as condominium fees
  • amount of mortgage
  • mortgage rate
  • mortgage term
  • mortgage payments (this is tricky for a variable-rate mortgage)
  • property taxes
  • homeowner's insurance (Note: this analysis neglects extraordinary risks such as earthquakes or floods that may cause the homeowner to incur a large loss due to a high deductible in your policy. All of you people in California know what I'm talking about.)
  • your marginal tax bracket (at what rate is the last dollar taxed)
  • the current standard deduction which the IRS allows

Other values have to be estimated, and they affect the analysis critically:

  • continuing maintenance costs (I estimate 1/2 of PP over 30 years.)
  • estimated inflation rate to compute present value (historically 4.5%)
  • rate of increase of property taxes, maintenance costs, etc. (infl. rate)
  • appreciation rate of the home (THE most important number of all)

Step 2: Compute the monthly expense
This includes the mortgage payment, fees, property tax, insurance, and maintenance. The mortgage payment is fixed, but you have to figure inflation into the rest. Then compute the present value of the cash stream.

Step 3: Compute your tax savings
This is different in every case, but roughly you multiply your tax bracket times the amount by which your interest plus other deductible expenses (e.g., property tax, state income tax) exceeds your standard deduction. No fair using the whole amount because everyone, even a renter, gets the standard deduction for free. Must be summed over the term because the standard deduction will increase annually, as will your expenses. Note that late in the mortgage your interest payments will be be well below the standard deduction. I compute savings of about 5% for the 33% tax bracket.

Step 4: Compute the present value
First you compute the future value of the home based on the purchase price, the estimated appreciation rate, and the term. Once you have the future value, compute the present value of that sum based on the inflation rate you estimated earlier and the term you used to compute the future value. If appreciation is greater than inflation, you win. Else you break even or even lose.

Actually, the math of this step can be simplified as follows:

                          /periods + appr_rate/100\ ^ (periods * yrs)
 prs-value = cur-value * | ----------------------- |
                          \periods + infl_rate/100/

Step 5: Compute final cost
All numbers must be in present value.
Final-cost = Down-payment + S2 (expenses) - S3 (tax sav) - S4 (prop value)

4.1 Long-term example Nr. 1 of buying: 6% apprecation

Step 1 - the data
  • Purchase price = 145,000
  • Down payment etc = 10,000
  • Mortgage amount = 140,000
  • Mortgage rate = 8.00%
  • Mortgage term = 30 years
  • Mortgage payment = 1027.27 / mo
  • Property taxes = about 1% of valuation; I'll use 1200/yr = 100/mo (Which increases same as inflation, we'll say. This number is ridiculously low for some areas, but hey, it's just an example!)
  • Homeowner's ins. = 50 / mo
  • Condo. fees etc. = 0
  • Tax bracket = 33%
  • Standard ded. = 5600 (Needs to be updated)

Estimates:

  • Maintenance = 1/2 PP is 72,500, or 201/mo; I'll use 200/mo
  • Inflation rate = 4.5% annually
  • Prop. taxes incr = 4.5% annually
  • Home appreciates = 6% annually (the NUMBER ONE critical factor)

Step 2 - the monthly expense
The monthly expense, both fixed and changing components:
Fixed component is the mortgage at 1027.27 monthly. Present value = 203,503.48. Changing component is the rest at 350.00 monthly. Present value = 121,848.01. Total from Step 2: 325,351.49

Step 3 - the tax savings
I use my loan program to compute this. Based on the data given above, I compute the savings: Present value = 14,686.22. Not much when compared to the other numbers.

Step 4 - the future and present value of the home
See data above. Future value = 873,273.41 and present value = 226,959.96 (which is larger than 145k since appreciation is larger than inflation). Before you compute present value, you should subtract reasonable closing costs for the sale; for example, a real estate broker's fee.

Step 5 - the final analysis for 6% appreciation
Final = 10,000 + 325,351.49 - 14,686.22 - 226,959.96
= 93,705.31

So over the 30 years, assuming that you sell the house in the 30th year for the estimated future value, the present value of your total cost is 93k. (You're 93k in the hole after 30 years, which means you only paid 260.23/month.)

4.2 Long-term example Nr. 2 of buying: 7% apprecation

All numbers are the same as in the previous example, however the home appreciates 7%/year.
Step 4 now comes out FV=1,176,892.13 and PV=305,869.15
Final = 10,000 + 325,351.49 - 14,686.22 - 305,869.15
= 14796.12

So in this example, 7% was an approximate break-even point in the absolute sense; i.e., you lived for 30 years at near zero cost in today's dollars.

4.3 Long-term example Nr. 3 of buying: 8% apprecation

All numbers are the same as in the previous example, however the home appreciates 8%/year.
Step 4 now comes out FV=1,585,680.80 and PV=412,111.55
Final = 10,000 + 325,351.49 - 14,686.22 - 412,111.55
= -91,446.28

The negative number means you lived in the home for 30 years and left it in the 30th year with a profit; i.e., you were paid to live there.

4.4 Long-term example Nr. 4 of buying: 2% appreciation

All numbers are the same as in the previous example, however the home appreciates 2%/year.
Step 4 now comes out FV=264,075.30 and PV=68,632.02
Final = 10,000 + 325,351.49 - 14,686.22 - 68,632.02
= 252,033.25

In this case of poor appreciation, home ownership cost 252k in today's money, or about 700/month. If you could have rented for that, you'd be even.

4.5 Short-term example Nr. 1 of buying: 6% apprecation

All numbers are the same as long-term example Nr. 1, but you sell the home after 2 years. Future home value in 2 years is 163,438.17
Cost = down+cc + all-pymts - tax-savgs - pv(fut-home-value - remaining debt)
= 10,000 + 31,849.52 - 4,156.81 - pv(163,438.17 - 137,563.91)
= 10,000 + 31,849.52 - 4,156.81 - 23,651.27
= 14,041.44

4.6 Short-term example Nr. 2 of buying: 2% apprecation

All numbers are the same as long-term example Nr. 4, but you sell the home after 2 years. Future home value in 2 years is 150,912.54
Cost = down+cc + all-pymts - tax-savgs - pv(fut-home-value - remaining debt)
= 10,000 + 31,849.52 - 4,156.81 - pv(150912.54 - 137,563.91)
= 10,000 + 31,849.52 - 4,156.81 - 12,201.78
= 25,490.93

5. A Question

Q: Is it true that you can usually rent for less than buying?

Answer 1: It depends. It isn't a binary state. It is a fairly complex set of relationships.

In large metropolitan areas, where real estate is generally much more expensive than elsewhere, then it is usually better to rent, unless you get a good appreciation rate or if you are going to own for a long period of time. It depends on what you can rent and what you can buy. In other areas, where real estate is relatively cheap, I would say it is probably better to own.

On the other hand, if you are currently at a market peak and the country is about to go into a recession it is better to rent and let property values and rent fall. If you are currently at the bottom of the market and the economy is getting better then it is better to own.

Answer 2: When you rent from somebody, you are paying that person to assume the risk of homeownership. Landlords are renting out property with the long term goal of making money. They aren't renting out property because they want to do their renters any special favors. This suggests to me that it is generally better to own.

6. Conclusion

Once again, the three important factors that affect the analysis the most are cash flows, term, and appreciation. If the relative cash flows are basically the same, then the other two factors affect the analysis the most.

The longer you hold the house, the less appreciation you need to beat renting. This relationship always holds, however, the scale changes. For shorter holding periods you also face a risk of market downturn. If there is a substantial risk of a market downturn you shouldn't buy a house unless you are willing to hold the house for a long period.

If you have a nice cheap rent controlled apartment, then you should probably not buy.

There are other variables that affect the analysis, for example, the inflation rate. If the inflation rate increases, the rental scenario tends to get much worse, while the ownership scenario tends to look better.

7. Resources

Here are some resources to help you run your own analyses.
  • The New York Times offers an interactive feature "Is it Better to Buy or Rent" where you can enter monthly rent, home price, down payment, mortgage rate, annual property taxes, and annual home price change. The graph updates itself to show how the numbers work over time.
    http://www.nytimes.com/interactive/business/buy-rent-calculator.html
  • For those who prefer command-line programs over GUIs, a few small C programs for computing future value, present value, and loan amortization schedules (used to write this article) are available. See the article "Software - Investment-Related Programs" elsewhere in this FAQ for information about obtaining them.

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