Tuesday, May 10, 2011

How the furniture calculator works

The new furniture calculator is an awesome tool for helping you move out of an old apartment. As we mentioned in the introductory post, the calculator takes three things into account:
  • The purchase price of the furniture
  • The change in condition/quality of the furniture
  • How long the furniture has been in use since it was bought
It uses this information to calculate the current value of the furniture so that you can sell it to your housemates, or split up furniture fairly when moving out.  But how does it work?

To see what condition my condition was in
The difference in value between a "Like New" couch and a "Good condition" couch is a subjective question, and there wasn't an off-the-shelf formula we could use. So we asked our survey respondents what would be a fair price of a $1000 couch in various conditions, and we extrapolated this response to be a fixed percentage of the purchase cost for all types of furniture.

Clearly, assuming all furniture is the same as a $1000 couch is a simplifying assumption, but we have a reason to think it will work better than you might expect. For instance, you might say wear and tear on a kitchen table or a TV stand is just different from wear and tear on a couch. But our survey revealed that the average life of those items is similar, and experts such as the IRS and our accounting panel downplay differences between furniture in accounting purposes. For instance, while tables and arm-chairs tend to "last longer" against wear and tear than couches according to our survey, people still typically replace them over roughly the same time-frame. What matters to fairness is how an owner is likely going to keep something, not how long it could hypothetically last.

But what about a TV? TV's and other pieces of electronics don't usually get "damaged" - they become obsolete or the prices fall really fast. According to our survey, it takes about 5-6 years for respondents to replace such items. That's where the other part of the calculator kicks in.

The persistence of furniture
No matter what condition the item is in, it loses value to you with time, because eventually, you want to replace it with something newer, nicer, or more to your taste. Since this typically happens over a 5-6 year cycle for both electronics and furniture, the fair value of any shared item declines similarly regardless of type or condition. We could quibble about seven years vs. four in the most extreme cases, but in the interest of simplicity we did not worry about these issues.  After all, there is a lot of individual variation in quality between brands and individual items. Personally, Jon would guess that five years is probably also a good time scale for replacement of basic kitchen appliances like blenders, but we did not test this assumption at all.

To calculate this effect, we depreciate the value of furniture using a somewhat standard accounting formula. This is more of a planning-guide than a solid fact, and it probably isn't exactly what you could get for the item on the open market.  But what it does do is try and approximate a market via the survey, while creating a consistent guideline for your housemates. After the program calculates the time-depreciated value and the difference-in-quality value, it takes the lesser of the two numbers: being old or being broken both devalue an item.

In order to chose a depreciation formula for the calculator, we have to pick both a basis-period (length of time) and a kind of depreciation: typically straight-line or declining balance, in which it loses a fixed percentage of its value each year. We settled on a 24% decline in value per year with a 5% scrap value, which would be called an "8.3-year double declining balance" method for you accounting nerds out there. Why these numbers? We calibrated them to the survey data:

The five data points represent New, Like New, Very Good,
Good and Acceptable values for a $1000 couch in their average time-frame.
Error bars are 1-sigma (assuming central limit theorem)
  • This calibration matched real-world data, given the average time period it takes for a couch to reach a given condition, and the average fair value of a piece of furniture in that condition.
  • The furniture should lose most if its value (~75%) over the 5-6 years before its expected replacement
  • We wanted to use a standard formula commonly used by accountants, so we restricted ourselves to straight-line depreciation and double-declining balance
We are not too concerned about the discrepancy between 1-year depreciation and the true value at that time.  The survey and expert opinion indicates that the resale value of a couch plummets as soon as it leaves the store, even more than any declining balance formula which correctly captures the medium-term value of the couch. However, this is probably because a non-roommate would not know what actually happened to the couch (for instance, "did someone hook up on it?"), or whether or not the person was lying about how old it was. It also includes the trouble of hauling the couch out of someone's place. Buying a new couch would be more attractive than buying a supposedly-like new couch at the price point recommended by the formula, but a roommate knows who physically sees the couch in front of them and roughly knows what the couch has been through over the past year should probably pay more. (The parallel situation would be buying a leased car after the lease expires.)

To summarize the FAQs:
  • The calculator will NOT necessarily predict how much the furniture would really sell for on the open market, but represents a fair value of the product over its lifecycle of expected replacement
  • The calculator WILL help you pick a fair value for your furniture, for resale to your roommates, suitemates or housemates who share it with you
  • The formula is based on standard accounting procedures that are fit to real-world data
  • Split up furniture you originally bought communally
  • Set a price for selling furniture to your roommate or friend
  • Figure out what rate to charge for renting furniture in a furnished apartment
  • Figure out how much to pay if you damage a piece of furniture
We hope to document the methodology more technically in a later blog post - for now, you can email Jon at split.the.rent.jb@gmail.com with questions.

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