Thursday, February 11, 2010

Appreciation and the Total Cost of Buying vs. Renting - Part 4 of 4

This is Part 4 of our 4-part series in toward establishing a methodology for determining whether renting or owning is more financially advantageous.  Part 1 can be found here.  Part 2 can be found here.  Part 3 can be found here.  In Part 4, we will be discussing Appreciation and Transaction Costs and working though some specific examples of calculating the cost of renting vs. owning.  Part 4 starts below:

Long-term, housing has appreciated at a rate about equal to the rate of inflation.  However, we have experienced wide-spread home price reduction in recent years.  Alternatively, as we noted in Part 1, housing prices and value changes vary widely geographically.  Consequently, you may wish to do one of the following with regard to your Appreciation value:
  1. Not use it.  That would be good if you are making a conservative calculation or are not planning on living in the house a long time.  However, recognize that at 3% inflation, the value of your house will double in 24 years.  Consequently, you are likely to be significantly off if you neglect all appreciation and remain in the house for several years.
  2. Use the 3% historical, nation-wide inflation
  3. Use 2.5% because you think inflation will be lower going forward - or use a higher value if you think inflation will be higher.
  4. Analyze your local market and see if you can figure out what housing is doing there.  You can use sites like Redfin (while not available everywhere) can be very useful in that regard.
  5. If you are being very honest, use a negative inflation rate if you think housing costs will continue to fall.  Of course, you may wish to ask yourself why you are buying a house if housing costs are going to continue falling.

Transaction Costs
When I was first thinking about a cost comparison for buying vs. renting, I recognized that there would be additional transaction expenses associated with buying and selling the home - like the cost of real estate agents, appraisals, etc.  My initial impression was that if you planned to be in the home only a short while, then those expenses should be considered.  However, if you were going to be in the home for many years, then those expenses can be amortized over the entire home ownership period - and would thus likely be quite low.  For example, if puchasing a new home costs you 1% of its value in expenses and selling it costs you 5% of its value in expenses, then if you both buy and sell the home in the same year, then it can be seen to be a huge cost.  On the other hand, if you buy a house and keep it until death, then you avoid the 5% hit from selling the house.

However, it turns out that even if you live in the home for quite a long time, the transaction costs of buying and selling the home can still be significant.  Let's use the example of a house that I buy for $300K, live in for ten years, and then sell.  You incur about $3K (1%) in expenses buying the house - think lawyer, home inspection, transfer tax, title company fees, etc.  Assuming a 3% rate of inflation, after 10 years the price of the house has risen to $403K.  The 5% cost to sell the house is thus about 20K.  The total in-and-out cost of owning the house is thus about $23K.  Amortizing this in a straight line over 120 months (10 years) gives me about $193/month.  Thus, as you can see, the transaction costs can actually be pretty sizable even if you live in the house for a long time.

However, the transaction costs can vary widely depending on the individual situation.  For example, if you buy a house for $300K and live in it until you die in 30 years, then you are amortizing about $3000 over 360 months - and $8.33/month is pretty negligable.  Alternatively, you may choose to list and sell your house "by owner" - which would cut down or eliminate the selling fee.  Similarly, there are discount brokerages that will list your property for $1000 up front instead of the contingency-fee style of being paid when-and-if the sale closes.  (Disclosure - I used this service in 2007 and it worked our great!)

The bottom line here is that depending on how long you are going to own your home and how you are going to sell it, the transaction costs can be pretty significant, but they are going to vary widely depending on your specific situation.  A good estimate of the cost if you are not doing anything fancy may be 1% to get in, 5% (inflation adjusted) to get out, and then amortize that expense over the expected ownership period.

Financial Impact Of Owning A Home
Finally, we can take our calculation of Ownership Cost from Part 2, and Equity Cost and Financing Cost from Part 3, combine it with the Appreciation and Transaction costs and determine the financial impact of owning a home. The formula is:

Total cost of owning a home = Ownership Costs + Equity Costs + Financing Costs - Appreciation + Transaction Costs

More specifically
Total cost of owning a home = Ownership costs (with real estate taxes adjusted to take into account tax deduction) + (equity in the house * municipal bond rate of return) + interest paid on the mortgage (also adjusted to take into account tax deduction) - appreciation + Transaction costs

How does this work in practice?  Let's see some examples.

Example 1
You are thinking of buying a $300K home with 20% down.  Municipal bonds are at 6%.  You determine that long-term appreciation is likely to be 3%.  You are in the 33% tax bracket.  Real estate taxes are $6K/year.

Your alternative rental costs are $2000/month and you would pay only the electic bill.

Thus, you first calculate the Ownership cost of your prospective house (not including the electric bill becuase you would have to pay that in the rental).  You also adjust the real estate tax cost from $6K to $4K to take account of the tax deductability. You arrive at a total ownership cost of $1100/month.

Second, calculate the Equity cost - 20% of 300K is $60K.  60K times 6% is $3600/year or $300/month.

Third, calculate the Financing cost - you are financing $240K.  Let's assume that you get a rate of 5%.  $240K times 5% is $12000/year or $1000/month.  Remember that we only use the interest paid in the Financing cost - not the principal.  Also, I realize that the Financing cost for the first year is going to be less than 12K because our mortgage payments are going to reduce the amount of principal.  However, note that 1) those same mortgage payments will increase the Equity Cost, and 2) the mortgage payments in a 30 year fixed mortgage really only reduce the principal by about 1% over the first year, so I feel OK about ignoring the difference here.

Further, with regard to tax deduction, we note that the interest paid is typically tax deductible.  However, it is tax deductible only to the extent that it would exceed the standard deduction.  For a married couple, the standard deduction in 2009 is $11,400 (for singles, it's $5,700).  Consequently, for the sake of this example, let's assume that you are married and that your interest paid is about equal to your standard deduction.  Consequently, we will consider all of the $12,000 in interest as an expense.  However, we will continue to deduct the $6K in real estate taxes because they would be on top of the $12K in interest.

Now, calculate appreciation - $300K at 3% is $9000/year or $750/month.

Finally, Transaction costs - let's say that you intend to live in the home for 20 years.  The 1%/5% cost is $3000 on the front end and 5% of $542K or $27K on the back end for a total of about $30K.  Amortized over 20 years - 240 months - it's $113/month.

Our total costs of ownership therefore equal $1100/month + $300/month + $1000/month - $750/month (note the MINUS on the appreciation) + $113/month.  Adding these all up, we arrive at a monthly cost of $1763/month.  We note that $1763/month compares favorably with the $2000/month in rent that we were originally considering - consequently it is cheaper to own than it is to rent for our specific examples.

Conversely, if you can rent an equivalent unit for less than $1763, then it would be more financially advantageous to rent than to own.

Another thing that we note is that if we were just looking at cash out of pocket, we would have gotten the wrong idea.  For example, the actual principal + interest mortgage payment for $240K at 5% is $1288.  Toss on $500/month for taxes and $250/month for assessment and you are at $2038 - which is more than the $2000 in rent for the other unit.

Example 2
Watch what happens, though, if we only intend to stay in the house for 2 years.  The total 1%/5% cost becomes $788/month - which makes the monthly total ownership cost $2438.  In this case, it would have been much better to rent at $2000/month

What if we paid for the house in full?  What would our monthly cost be then?
Ownership costs stay the same at $1100/month.  Equity costs become (300K *.06/12) = $1500/month.
Financing cost goes to zero.  Appreciation stays the same at $750/month.  Transaction costs stay the same at $113/month.

The total cost thus becomes $1963/month.  But wait you say!  How can it actually cost MORE per month when I have 100% paid for the house in cash?? It only cost me $1763/month ($200 less per month) when I was financing 80%!

Answer - rate arbitrage between the corporate bonds rate and the interest rate on the home loan.  Your equity cost is at a 6% rate while your financing cost is at a 5% rate (or really only 3.35% considering the tax deductability).  In the first example your costs were 80% at 5% (but really at 3.35% considering the tax deductability) and 20% at 6% - in the second example, your costs were 100% at 6%.

This is one reason why it may not be most financially advantageous to you to pay off your house - at least during your working years.

These posts have been pretty complicated, but I hope that it will help you calculate the true cost of ownership so that you can make an accurate comparison with rentals.  The comparison of vost of owning vs. renting is actually a pretty complicated question - as you can see.  I highly recommend doing the numbers before making the decision.  Good luck!


  1. Do your examples take into account the fact that rents tend to go up over time, sometimes dramatically?

    When I bought a house 8 or 9 years ago, my landlord had started jacking up my rent and it was very attractive to me that my monthly payment was locked in.

  2. Hi, Good post overall, but just a couple of observations.
    1. The tax deduction for property taxes might be overstated. Remember, the taxpayer that does not itemize still gets the standard deduction (I think it's almost $6K on the '09 1040). So, any benefit of doing an itemized deduction would need to exceed the standard deduction (and, so, there might likely be no benefit at all).

    2. The interest portion of any mortgage payment is also deductible (& relatively large, but goes to 0 as the mortgage is paid off); and this would make itemizing beneficial. (I don't see any mention of this in the post.)

    3. In an all-cash purchase, the example charges the buyer the equity cost for those funds used to make the purchase. But, to be fair, the buyer should then be able to save (or get credit for) the imputed rent for similar housing, compounding at xx% (6%) year after year. This factor would greatly lower the cost of home ownership when there is no mortgage.

    For the most thorough "Rent v. Buy" analysis I've ever seen, check out the link below. It even considers start-up initial repairs and the $8K new home buyer tax credit.

  3. Hi Nycsolo - Factoring in the rents going up over time was one of those things that I considered, but it started getting too complicated. For example, rents for many higher-end properties in Chicago decreased from 2003-2006 as the rental pool decreased as people bought condos. Rents are now rising again even though the economy is bad.

    As I really started to get into this, I found myself wanting to make a huge calculator program to take absolutely everything into account. For example, right now for the financing and equity costs I ignore the monthly changes. I found myself saying ok - is this going to be 1) really complicated and try to estimate all the costs over the entire lifetime of ownership, or 2) pretty decent, but could still be worked out by hand. I went with the latter.

  4. 3:16 - Thank you very much for your comment! I appreciate your help in helping me deliver a better product. With regard to the specific items that you raise:
    1) Tax deduction for property taxes - Excellent point and I thought I had mentioned it. The tax savings for the deductable real estate taxes and interest payments should be your actual tax savings. If your specific tax position does not give you any savings, then you are not entitled to any. For example, if you previously used the standard deduction (let's say 6K), but this year you itemize deducte 15K, then only the 9K difference is really a tax savings - and that's what you should include in your numbers.
    2) Whoops. I actually mention it in the Financing post, but then did not take it into account in the calculation above. This actually gives me the opportunity to fix two birds with one stone - I revised the post above to include the approximately $12k standard deduction for married couples and used that to prevent the deductability of the $12K in taxes.
    3) I don't think I agree, but I would be happy to review your reasoning. Here's why - I don't give an imputed rent credit when the buyer has 20% equity, so why should the buyer get an imputed rent credit when they own 100% equity? To put it another way, I am comparing owning cost to renting cost. If you apply an imputed rent, wouldn't that just be like subtracting the renting cost from the housing cost to arrive at a single number? You certainly would not want to include rental cost in the equation twice.
    4) I had not seen this calculator before. It certainly seems impressive at first glance. I am going to have to research it further - thanks for linking to it!

  5. I agree that you should minus out the standard deduction when you factor in the mortgage interest deduction tax savings.

    At the same time, you also have to add in the other itemized deductions. For instance, if you are just taking the standard deduction, your state and local income taxes go to waste (as in, they are not deducted for federal income tax purposes). Because your mortgage interest bumps up the amount you are itemizing, now it brings a whole bunch of other itemizable (is that a word?) deductions into play. It gets complicated, of course. So yea, the mortgage interest tax deduction isn't as much as you might thing because you're giving up your standard deduction, but also isn't as little as just the mortgage interest minus standard.

    Sorry for the run-on sentences. lol.

    Have a wonderful Valentine's Day!! Happy Chinese New Year!! and have enjoy the excitement of the Snowlympics.

  6. "Factoring in the rents going up over time was one of those things that I considered, but it started getting too complicated. For example, rents for many higher-end properties in Chicago decreased from 2003-2006 as the rental pool decreased as people bought condos. Rents are now rising again even though the economy is bad. "

    Maybe it makes the calculation more complicated but it's an important factor to weigh in favor of buying.

  7. Coder Emeritus - You are right! There can be additional deductions - and the more prevalent one is probably state income tax. It looks like everyone will have to find their own value using their own specific situation.

  8. nycsolo - You know, when I initially went into this, I was thinking more of a system for determining the price differential between renting and owning at any one specfic point in time. More along the lines of the question "How much more expensive is it to own rather than rent *right now*" as opposed to "over time." However, as we talk more about it, it is really leading to a conclusion that you have to trace the value over time if you are going to get the full impact of the economic decision - and in order to do that, I agree that you need to take the rental increases into account. I think that an additional post may be in order!