# Accountancy/Depreciation

Depreciation relates to an entity's change in fair market value and how the fluctuation in value is processed as a tax-deductible expense.

## Depreciation

Depreciation occurs over a period of useful economic life, in which the property, plant or equipment is used to generate income for the business.
Several methods can be used to calculate the depreciable cost of an asset over its life, the most commonly used are:
* Straight-line method
* Reducing balance method

### Straight-line Method

The Straight-line Method reduces the Net-Book value of an asset by the same amount each period. This amount is determined by dividing the total value of said asset by some number of periods, then subtracted from the balance at the end of each period.
For example,if you purchased a sewing machine for $12,000 and you wrote it off over 12 months using the Straight-line method, you would divide the original cost ($12,000) by the term of useful life (12 months). In this case, $12,000 / 12 months = $1,000/month. To apply depreciation on this item, you would deduct $1,000 at the end of the first month to leave a balance of $11,000. The second month you would deduct another $1,000 leaving a balance of $10,000. At the end of the 12th month, you would deduct the last $1,000 from the previous (11th months) balance of $1,000, leaving you with a balance of $0.
At this point you would say that you have written off the sewing machine. In practice, things get a little more complicated. In this example it would not be fair to assume that at the end of the 12th month the machine would suddenly stop working, or be absolutely worthless, though for tax purposes it is considered to have zero basis. It is possible you could still sell the completely written off sewing machine for $1,000, causing you to recognize a $1,000 taxable gain.
The economic reasoning behind the Straight-line method is, essentially, the acceptance that depreciation is an approximation of the rate at which an asset transfers value to the Operations of a business by participating productively in it, and so we should use the most economical one (regarding computational effort) to calculate and record it in the accounting books. There are certain Intangible Assets for which the Straight-Line method can be considered the relatively more accurate one. But for most Tangible Assets there is good argument that the Declining Balance method is more suitable (see below). Nevertheless, the simplicity of the Straight-line method had made it the prevailing one, accepted by economists, accountants, analysts, businesses, and even state authorities (for tax purposes).

### Declining (or Reducing) Balance Method

The Net-Book value of an asset is reduced by the same proportion each period. That is, at the end of every period you reduce the value by a fixed percentage. Each period uses the previous period's balance to work out the amount.
For example, we purchase a motor-vehicle for $10,000 and we depreciate it by 10% per month. At the end of the first month we take $10,000 * 10% = $1,000, making the balance $9,000. At the end of the second month, we take the balance from the previous month and apply the 10% factor: $9,000 * 10% = $900. Note the change in depreciation: in the first month the expense was $1,000, but in this month it is $900. At the end of this second month, you subtract the new depreciation amount, resulting in $9,000 - $900 = $8,100. The depreciation for the third month, then, is $8,100 * 10% = $810; the remaining value at the end of the third month is $8,100 - $810 = $7,290. At the end of 12 months the balance would be $3138.11.
The economic reasoning behind the Declining Balance Method of Depreciation is that any asset (think of machinery to stay focused), no matter how carefully serviced by its user, is most productive during the earlier periods of its productive use. Mathematically, the same depreciation rate will extinguish the value of an asset much more quickly under The Straight Line Method than under the Declining Balance Method. In the above example, a $10,000 value with a 10% monthly depreciation rate will be extinguished after 10 months of calculating and recording depreciation by the Straight Line method. But it will take ~22 months to extinguish 9/10 of the value under depreciation using the Declining Balance Method on the same value and with the same depreciation rate. So caution should be exercised when choosing the Declining Balance Method.

### The "Useful Life" approach

Since Accounting Depreciation attempts to capture a real economic phenomenon, it must be based on economic reasoning. It is not a mechanical procedure or an arithmetic exercise. The prevailing concern when determining depreciation methodology should not be to "guess" the correct depreciation rate, but to estimate reasonably the useful life of the asset under depreciation in time-units, and then calculate the corresponding depreciation rate that will result in extinguishing the value of the asset from the books when the estimated useful life ends too, given the Depreciation method chosen.
In the Straight-Line method, the mapping of Useful Life to Depreciation Rate is easy. If "x" is the estimated useful life, say in years, then the Yearly Depreciation Rate "d" is d = 1/x. For example, if you expect that the company will use a vehicle for 10 years, then the Yearly Depreciation Rate for this vehicle is 1/10 = 0,1 = 10%, under the Straight-line method.
In the Declining Balance Method, things are trickier. First we must note that from a mathematical point of view, the value of the asset is never fully extinguished under the Declining Balance method, but it approaches arbitrarily close to zero. In practice, companies that use the Declining Balance Method, decide on a "materiality threshold" for the non-depreciated (residual) value of the asset, usually up to 10% of its initial purchase value. Essentially then, they calculate the depreciation rate which, under the Declining Balance method, will extinguish the largest part of the Value of the asset (i.e. 90% or 95%) at the end of its economic useful life. When they reach that point in time, they depreciate what's left in the next accounting period.
Now, the Declining Balance method is expressed as a Difference Equation. Denote "d" the depreciation rate, "r" the remaining value at the end of the estimated useful life, as a percentage of initial purchase value (=> 0 < r < 1) and V(t) the nondepreciated value of the asset at the end of period t. Denote also "n" the useful life of the asset, say in years. Then you have
Going backwards in the Difference equation and writing for period "n" you get
Solving together the two equations you get
So we see that by estimating the useful life of the asset (the "n"), and given that we have chosen a residual value (the "r", as a percentage of the initial purchase value of the asset), we can uniquely determine the required depreciation rate "d" to use in our depreciation calculations so that our accounting books reflect, at least approximately, what happens in actual economic activity.

### Review Questions

Volume 1 - Chapter 27
1. A firm buys equipment on 1 July 20X3 for £6,500. The equipment is to be depreciated on a monthly basis at 20% on cost. On 31 December 20X5 the equipment is sold for £2,700 cash.
(a) Show the provision for depreciation on equipment account for 20X3, 20X4 and 20X5. (b) Show the equipment disposal account as at 31 December 20X5
2. A company depreciates its machinery at the rate of 10% per annum using the reducing balance method. A machine is sold on 30 June 20X7 for £900 which had originally been purchased for £5,000 on 1 January 20X4. No depreciation is to be provided for in the year of sale.
(a) Show the provision for depreciation on machinery account for 20X4 to 20X7. (b) Show the asset disposal account to record the sale of the machinery (c) Show the entry in the profit and loss account for 20X7.
3. A firm sells equipment which had cost £15,000 for cash proceeds of £3,200. At the date of the sale, the balance on the account for depreciation for this equipment stood at £9,700.
Construct the asset disposal account for the equipment sold.
4. A firm purchases machinery on 1 January 20X5. The machinery cost £12,000 and is to be depreciated using the reducing balance method – using a rate of 25%.
Show the depreciation account for the first three years of the asset’s life

### Typical Policies

| Type of Asset | Policy |
| Motor Vehicles | Reducing Balance 25% |
| Leasehold Property | Straight-line over the length of the lease |
| Freehold land | Never depreciated. Only fixtures on land can be depreciated as land never loses its "useful life" |
| Fixtures and Fittings | Reducing Balance 15% |
| Computer Equipment | Straight-line 3 years or companies may expense it when purchased |

### Answers to Review Questions

Volume 1 - Chapter 27
1. (a) Provision for depreciation on equipment 20X3 £ 20X3 £ Dec 31 Balance c/d 650 Dec 31 Profit & Loss 650
20X4 20X4 Dec 31 Balance c/d 1,950 Jan 1 Balance b/d 650
20X5 20X5 Dec 31 Equipment disposal 3,250 Jan 1 Balance b/d 1,950
1. (b) Equipment Disposal 20X5 £ 20X5 £ Dec 31 Equipment at cost 6,500 Dec 31 Provision for depreciation 3,250
2. (a) Provision for depreciation on machinery 20X4 £ 20X4 £ Dec 31 Balance c/d 500 Dec 31 Profit & Loss 500
20X5 20X5 Dec 31 Balance c/d 950 Jan 1 Balance b/d 500
20X6 20X6 Dec 31 Balance c/d 1,355 Jan 1 Balance b/d 950
20X7 20X7 Jun 30 Machinery disposal 1,355 Jan 1 Balance b/d 1,355
2. (b) Machinery Disposal 20X7 £ 20X7 £ Jun 30 Equipment at cost 5,000 Jun 30 Provision for depreciation 1,355
3. Equipment disposal account
Equipment at cost 15,000 Depreciation 9,700
4. Provision for depreciation – Machinery 20X5 £ 20X5 £ Dec 31 Balance c/d 3,000 Dec 31 Profit & Loss 3,000
20X6 20X6 Dec 31 Balance c/d 5,225 Jan 1 Balance b/d 3,000
20X7 20X7 Dec 31 Balance c/d 6,919 Jan 1 Balance b/d 5,225