Understanding Depreciation & Taxes

The post comparing the cost of buying versus leasing a new car introduced the term “book value” to refer to the value of the car as an asset, that the leasing car will carry on their books, but never explained exactly why the leasing company would do any such thing.  It’s not clear that the leasing company should be concerned with the book value at all, given that book value is not the same as market value, and in any case they aren’t allowed to sell the asset.

Rather than worrying about book value, the leasing company might consider the entire purchase price of the vehicle as an expense as soon as it is incurred.  Thus, they would deduct the full cost of the car against any revenues they have during the year, as this video from the Khan Academy illustrates:

Slaman Khan highlights the problem that this sort of accounting creates for the business, which is to say that profits appear highly variable.  That by itself may not be a problem, until you consider the tax implications.  Businesses only pay income taxes on their profits.  When the business operates at a loss, there are no profits to tax.  So you can see that deducting the full cost of the car (or truck) in the same year that it is purchased results in a loss, which results in no tax bill during the year the vehicle was purchased, and then larger tax bills in future years.

But the IRS does not recognize the full purchase price of the car as being “lost” as soon as it is paid.  After all, the business didn’t really lose the money — they simply traded money for a new vehicle.  If they wanted to (or had to), they could sell the vehicle at the end of the tax year and recover whatever the market value of that asset is.  The proceeds of the sale would increase revenues, and might result in a profit that is taxable.

The IRS takes a dim view of businesses that appear to be “losing” money, when they are actually using the money to purchase tangible assets, simply so that the business can defer payment of taxes. So, the IRS require businesses to depreciate the assets, which in the ideal would mean that they can only expense the portion of the asset purchase price which represents the loss of market value (called, mark-to-market accounting).

However, the true market value of used goods cannot be determined without an actual sale.  And selling something just to try and figure out what someone will pay for it is expensive (due to transactions costs), inconvenient, and usually pointless.  Therefore, the there IRS specifies a depreciation schedule for different types of assets that requires businesses to record the “book” value (an assumed market value) for the purpose of computing profits, and thereby taxes.

In this next video from Khan Academy, Salman Khan explains how to depreciate the truck on the businesses books (using straight-line depreciation).  The impact of depreciation is to report the same total profit, but to report it earlier.  The fact that profits come sooner means that taxes are paid earlier.  From our understanding of time preference, we know that businesses would prefer to delay tax payments, but the IRS would likely prefer to accelerate them.

Khan uses the terms “capitalization”, and “depreciation” as if they were interchangeable.  Another term is called “amortization” which also refers to the process of spreading out a large payment into multiple instalments.  Although this terms are very similar, they aren’t identical.  In this video, Khan explains that depreciation is a term that is used to refer to the declining value of tangible assets, like equipment.  However, intangible assets, such as a fee paid for a multi-year license are not subject to depreciation.  In this case, the word for doing the exact same mathematics as depreciation (spreading the cost out over the useful life of the asset) is called amortization.  Both depreciation and amortization are specific examples of the more general term, capitalization.

The simplest method for calculating depreciation is straight line.  However, we know that tangible (or hard) assets are likely to lose more value at the beginning of their useful lives than they are at the end.  That is, straight line depreciation does not reflect market value well, and as a consequence businesses using straight line will pay taxes too soon.  The real market value curve fluctuates, but likely takes the general form of exponential decay, meaning it declines rapidly at first and more slowly in each subsequent year.

Perhaps because exponential decay was too complicated to calculate before the introduction scientific calculators, several accelerated methods of depreciation have been invented that approximate exponential decay.  These are the Sum Of the Years Digits (SOYD), the Double Declining Balance (DDB), the units of production method, and the Modified Accelected Cost Recovery System (MACRS — pronounced “makers” in the video below).  This video shows how to calculate the straight line, the SOYD, DDB and units of production using Excel.

The key parameters in depreciation calculations are the initial value (price paid for the good), the residual value (also called the salvage value), the lifetime of the good.  The book value in a given year is the initial value minus the depreciation that has accumulated since the purchase.

This video explains the straight line and SOYD methods graphically.  Most errors on the Fundamentals of Engineering Exam come from confusing book value in a given year with the depreciation in a given year.  Depreciation is the change in book value.

It’s important to note that depreciation is of little practical importance in not-for-profit operations, and for businesses that chronically lose money.  These businesses likely keep books that record the initial purchase prices, book values, and depreciation amounts anyway, but because they do not pay taxes, there are no tax implications.

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