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So if a company is depreciating an asset faster for tax purposes, and slower for Financial statements. This would result in a lower actual tax bill vs. a higher financial statement tax bill.

The liability is thus created; the question is since the actual tax bill has already been paid so
what does this liability mean in an economic sense?

Its a temporary timing difference. Its a liability because cash taxes will be higher in the future unless the company continues its CAPEX at a high enough rate to offset

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so to your point, lets say this was the only asset and company doesn't invest after this. My confusion is now the liability is there, but who is the liability to because the IRS has been paid the appropriate taxes already.

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I understand the theory, but I am asking from a practical standpoint how would this work.
For example, if an accelerated dep. schedule is used for taxes over 5 yrs vs. a slower one for
financial statements.

In the later yrs the depreciation on the tax schedule will be lower as compared to the one on the financial statements. but the question is that since IRS is ok with the accelerated depreciation who do you owe the cash taxes to in the later years?

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