INTANGIBLE ASSETS AND GOODWILL

The following table details the composition of our intangible assets at year-end 2018 and 2017:



($ in millions)	At Year-End 2018			At Year-End 2017
Definite-lived Intangible Assets
Costs incurred to obtain contracts with customers	$	1,347		$	1,137
Contracts acquired in business combinations and other	1,983			2,052
	3,330			3,189
Accumulated amortization	(674		)	(499		)
	2,656			2,690
Indefinite-lived Intangible Brand Assets	5,724			5,854
	$	8,380		$	8,544

We capitalize direct costs that we incur to obtain management, franchise, and license agreements. We amortize these costs on a straight-line basis over the initial term of the agreements, ranging from 15 to 30 years.

For acquired definite-lived intangible assets, we recorded amortization expense of $111 million in 2018, $116 million in 2017, and $31 million in 2016 in the “Depreciation, amortization, and other” caption of our Income Statements. For these assets, we estimate that our aggregate amortization expense will be $111 million for each of the next five fiscal years.

The following table details the carrying amount of our goodwill at year-end 2018 and 2017:



($ in millions)	North American Full-Service			North American Limited-Service			Asia Pacific			Other International			Total Goodwill
Balance at year-end 2017	$	3,585		$	1,769		$	1,928		$	1,925		$	9,207
Foreign currency translation	(19		)	(14		)	(66		)	(69		)	(168		)
Balance at year-end 2018	$	3,566		$	1,755		$	1,862		$	1,856		$	9,039