## 3. Salvage value and double-declining depreciation method

Assume the same scenario, but this time we will talk about the double-declining depreciation method:

 Original cost \$120,000 Useful life 5 years Salvage value \$20,000

As this is the double-declining depreciation method, the annual depreciation rate is double the straight-line rate:

 Double-declining Depreciation Rate = Straight-line Rate x 2 = (1 ÷ 5 years) x 2 = 40%

The annual depreciation is calculated by multiplying the net book value at the beginning of the year by the double-declining depreciation rate. The net book value to which the rate is applied will decline each year. The salvage value is ignored in determining the amount to which the rate is applied, but it will limit the total depreciation that can be taken. Depreciation will stop when the net book value equals the salvage value (in other words, net book value can’t be depreciation below its salvage value). Refer to the table below to see the calculation:

 Year Beginning Net Book Value x Double the Straight- line Rate = Depreciation Expense Ending Net Book Value 1 \$120,000 x 40% = \$48,000 \$72,000 2 \$72,000 x 40% = \$28,800 \$43,200 3 \$43,200 x 40% = \$17,280 \$25,920 4 \$25,920 x 40% = \$10,368 (Use \$5,920) \$20,000 5 \$15,552 x 40% = \$6,221 (Use \$0) \$20,000

During the fourth year, the calculated depreciation expense would have reduced the net book value below \$20,000 – the salvage value – so only \$5,920 of the calculated depreciation was recognized. During the fifth year, no depreciation was recognized at all because the net book value was reduced to the salvage value during the fourth year.

Now, let’s return to our question of why the salvage value is not subtracted from the original cost in calculating depreciation under the double-declining balance.

To answer the question, let us go ahead and see what will happen if we do subtract the salvage value from the original cost. In this hypothetical situation, note that the depreciable basis (original cost less salvage value or \$120,000 - \$20,000 = \$100,000) will need to be depreciated fully since the salvage value will already be deducted from the original cost. This is similar to the straight-line depreciation method:

 Year Beginning Net Depreciable Basis x Double the Straight- line Rate = Depreciation Expense Ending Net Depreciable Ending Net Book Value * 1 \$100,000 x 40% = \$40,000 \$60,000 \$80,000 2 \$60,000 x 40% = \$24,000 \$36,000 \$56,000 3 \$36,000 x 40% = \$14,400 \$21,600 \$41,600 4 \$21,600 x 40% = \$8,640 \$12,960 \$32,960 5 \$12,960 x 40% = \$5,184 \$7,776 \$27,776 … … … … … … 10 \$1,008 x 40% = \$403.1 \$604.7 \$20,604.7 … … … … … … 25 \$0.47 x 40% = \$0.19 \$0.28 \$20,000.28 … … … … … …

(*) Calculated as the net depreciable basis plus the salvage value (\$20,000).

As you can see from the table above, the depreciation will technically never reduce the net depreciable basis to zero (of course, the annual depreciation will become very negligible after a number of years, but we will ignore this fact for this hypothetical situation). For example, it will take 10 years to depreciate the asset net book value to \$20,604.7 (i.e., \$604.7 more than the salvage value) and 25 years to depreciate it to \$20,000.28 (i.e., \$0.28 than the salvage value). Ten and 25 years periods are much longer than the estimated useful life of the asset.

The conclusion from this hypothetical exercise is that the salvage value should not be subtracted from the original cost of the asset under the double-declining depreciation method; otherwise, depreciation will take substantially longer to reduce the net book value to the asset salvage value than the useful life of the asset.

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