## 16.2. Estimating Valuation

A central issue with depreciation is to determine how you will estimate the future value of the asset. Compared to the often uncertain estimates one has to do where appreciation of assets is concerned, we are on somewhat firmer ground here. Using sources listed below should make it fairly straight forward to estimate the future value of your depreciating assets.

• Tax Codes: For businesses that want to use depreciation for tax purposes, governments tend to set up precise rules as to how you are required to calculate depreciation. Consult your local tax codes, which should explicitly state how to estimate depreciation.

• Car Blue Book: For automobiles, it is easy to look up in references such as Blue Books estimates of what an automobile should be worth after some period of time in the future. From this you will be able to develop a model of the depreciation.

### 16.2.1. Depreciation Schemes

A depreciation scheme is a mathematical model of how an asset will be expensed over time. For every asset which undergoes depreciation, you will need to decide on a depreciation scheme. An important point to keep in mind is that, for tax purposes, you will need to depreciate your assets at a certain rate. This is called tax depreciation. For financial statement purposes you are free to choose whatever method you want. This is book depreciation. Most small businesses use the same rate for tax and book depreciation. This way there is less of a difference between your net income on the financial statements and your taxable income.

This section will present 3 of the more popular depreciation schemes: linear, geometric, and sum of digits. To simplify the examples, we will assume the salvage value of the asset being depreciated is zero. If you choose to use a salvage value, you would stop depreciating the asset once the net book value equals the salvage value.

1. Linear depreciation diminishes the value of an asset by a fixed amount each period until the net value is zero. This is the simplest calculation, as you estimate a useful lifetime, and simply divide the cost equally across that lifetime.

Example: You have bought a computer for \$1500 and wish to depreciate it over a period of 5 years. Each year the amount of depreciation is \$300, leading to the following calculations:

Table 16.1. Linear Depreciation Scheme Example

 Year Depreciation Remaining Value 0 - 1500 1 300 1200 2 300 900 3 300 600 4 300 300 5 300 0

2. Geometric depreciation is depreciated by a fixed percentage of the asset value in the previous period. This is a front-weighted depreciation scheme, more depreciation being applied early in the period. In this scheme the value of an asset decreases exponentially leaving a value at the end that is larger than zero (i.e.: a resale value).

Example: We take the same example as above, with an annual depreciation of 30%.

Table 16.2. Geometric Depreciation Scheme Example

 Year Depreciation Remaining Value 0 - 1500 1 450 1050 2 315 735 3 220.50 514.50 4 154.35 360.15 5 108.05 252.10

Note Beware: Tax authorities may require (or allow) a larger percentage in the first period. On the other hand, in Canada, this is reversed, as they permit only a half share of “Capital Cost Allowance” in the first year. The result of this approach is that asset value decreases more rapidly at the beginning than at the end which is probably more realistic for most assets than a linear scheme. This is certainly true for automobiles.
3. Sum of digits is a front-weighted depreciation scheme similar to the geometric depreciation, except that the value of the asset reaches zero at the end of the period. This is a front-weighted depreciation scheme, more depreciation being applied early in the period. This method is most often employed in Anglo/Saxon countries. Here is an illustration:

Example: First you divide the asset value by the sum of the years of use, e.g. for our example from above with an asset worth \$1500 that is used over a period of five years you get 1500/(1+2+3+4+5)=100. Depreciation and asset value are then calculated as follows:

Table 16.3. Sum of Digits Depreciation Scheme Example

 Year Depreciation Remaining Value 0 - 1500 1 100*5=500 1000 2 100*4=400 600 3 100*3=300 300 4 100*2=200 100 5 100*1=100 0