For purposes of notation and reference the following symbols will be used:
- V = original cost
- V₁ = depreciated value at end of first period
- V₂ = ” ” ” ” ” second period
- Vₙ = ” ” ” ” ” last period, i.e., scrap value
- n = length of service life
- d = rate of depreciation per period
- D = total amount of depreciation, i.e., V - Vₙ
- D₁ = amount of depreciation during first period
- Dₙ = ” ” ” ” last ”
- r = rate of interest
- R = 1 + r, i.e., 100% plus the rate
- 1 - r = 100% minus the rate
- A = annual amount to be paid under the compound interest methods
It should be noted that the foregoing factors are all estimates, with the exception of original cost, and that when making these estimates the principles of depreciation as discussed in preceding chapters must be taken into consideration. Thus, a decision must be made as to whether physical or functional depreciation is the controlling factor in determining service life. In the determination of service life, the policy as to repairs, renewals, and maintenance has a very important bearing. In fixing the scrap value, the relation of inadequacy, obsolescence, wear and tear, and age to the values remaining in the asset must be considered.
1. Proportional Methods
Proportional methods include all those in which the periodic depreciation is calculated as a proportional part of some fixed basic value. These may be grouped under the following subclass titles, each of which will be separately considered:
- (a) Straight Line
- (b) Working Hours
- (c) Composite Life
- (d) Service Output
(a) Straight Line Method
The “Straight Line” method, so called because its graphical representation is a straight line, is perhaps the simplest of all methods for calculating the periodic depreciation charge and is therefore the most widely used. Under it the loss of value for each period is proportioned to the length of service life. Thus, an asset whose service life is reckoned as 10 years will have depreciated one-tenth by the end of the first year, two-tenths by the end of the second year, and so on. The depreciation for each year is the same. Shown by formula, using the notation above, this will be:
| D₁ = | (V - Vₙ) | or | D | and, evidently, |
| n | n |
V₁ = V - D₁; V₂ = V₁ - D₂; etc.