Intangible assets are recorded at cost when purchased externally
What are intangible assets?
Intangible assets with no physical substance such as goodwill, patents and copyrights.
The fact that goodwill is an intangible asset means that first option is incorrect.
There are intangible assets with definite life and non-definite life, which means that the statement that they always have definite life is wrong
For those that do not have definite life, they are only tested for impairment annually with no amortization, in essence, intangible are recognized at their external purchase cost is correct
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