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Yes depreciation is a fixed cost of business which is an allocation of fixed asset cost over period of asset life.
Allocation of cost of intangible asset is called as amortization.
Depreciation spreads the cost of a fixed asset over the useful life of that asset so a portion of that cost is recognized as an expense in each period that the asset is in service. The original cost, less the accumulated depreciation is the net book value of the asset. The net book value may not represent the actual market value of the asset. Depreciation is not concerned with the market value but rather the value of the contribution that the asset makes to the business.
The income tax expense on the income statement is the sum of the income taxes payable for the year and the changes in deferred tax asset or liability balances for the year.
No depreciation is not included as depreciation is allocation of part of assets cost to income statement while in capital budgeting, full cost of asset is already included so if depreciation will also be included then there would be double counting of same asset.