Accordingly
| V₁ - Vₙ |
| D = ———(1) |
| n |
The amount to be written off each year is thus seen to be constant. The percentage to be applied to the original cost in order to determine the periodic depreciation D is, therefore, found by dividing D by V₁. Hence the formula:
| D |
| r = —(2) |
| V₁ |
Having determined by careful estimate the method of calculating the periodic amount of depreciation, the problem of valuation of the asset at any given time during its life is ordinarily simple. In the case of renewal of any parts, the question of betterment comes in and requires careful handling. In unusual cases it may often be necessary to revise the rate of depreciation in order to write off the betterment during the remaining life of the asset. Depreciation is at the best but an estimate and unless there are major betterment items it is not usually necessary because of them to revise the estimate of depreciation. When a renewal takes place it is theoretically necessary to determine the value of the replaced part at the time of its replacement. The excess of the cost of the new part over this value is the amount of the betterment, when only the values of the old and new parts are considered. In such cases, however, the new part will not usually have value apart from the asset to which it is attached. In practice, therefore, the amount of the betterment recorded is the difference between original—not present—value of the old part and the cost of the new part. An example will illustrate the problems involved and the accounting treatment.
Problem. Assume that an asset—office equipment—costing $1,000 has an estimated life of ten years and no scrap value. After six years of this life it becomes necessary to replace a part of the asset, estimated to have cost originally $100, the cost of the new part being $150. At the time of the replacement the depreciation reserve carries an amount of $600.
The first step in booking the transaction is to transfer from the reserve account to the asset account the original cost of the part replaced. Just as in the case of bad debts, now that a part of the asset has been discarded and the amount of the decrease in value of the asset is definitely known, this amount held in suspense until the present time in the reserve account must be applied as a definite reduction in the carrying value of the asset. The entry to effect the transfer is:
| Depreciation Reserve, Office Appliances | 100.00 | ||
| Office Appliances | 100.00 | ||
The next step is to set up the cost of the new part which replaces that discarded. This follows the usual entry at the time of purchase of any equipment. The entry needed is:
| Office Appliances | 150.00 | ||
| Cash | 150.00 | ||