Note 5. Goodwill and Other Intangible Assets

Goodwill

Changes in the carrying amount of the Company’s goodwill for the six-months ended June 30, 2019 were as follows:

During the fourth quarter of 2018, the Company performed a quantitative assessment for goodwill impairment for its Stratasys-Objet reporting unit.

Following its quantitative assessment, the Company concluded that the fair value of its Stratasys-Objet reporting unit exceeded its carrying amount by approximately 8%, with a carrying amount of goodwill assigned to this reporting unit in an amount of $386 million.

When evaluating the fair value of its Stratasys-Objet reporting unit the Company used a discounted cash flow model which utilized Level 3 measures that represent unobservable inputs into the valuation method. Key assumptions used to determine the estimated fair value include: (a) expected cash flows for five years following the assessment date which were based on, among other factors, expected revenue growth, costs to produce, operating profit margins and estimated capital needs; (b) an estimated terminal value that utilized a terminal year growth rate of 3.1% that was determined based on the growth prospects of the reporting unit; and (c) a discount rate of 14.0% based on management’s best estimate of the after-tax weighted average cost of capital. If any of these were to vary materially from the Company's estimates, the Company could face impairment of goodwill allocated to this reporting unit in the future.

Actual results may differ from those assumed in the Company's valuation method. It is reasonably possible that the Company's assumptions described above could change in future periods. If any of these were to vary materially from the Company's plans, it may record impairment of goodwill allocated to this reporting unit in the future.

A hypothetical decrease in the growth rate of 1% or an increase of 1% to the discount rate would have reduced the fair value of Stratasys-Objet reporting unit by approximately $48 million and $80 million, respectively.

Based on the Company’s assessment as of December 31, 2018, no goodwill was determined to be impaired.

During the second quarter of 2019 the Company reaffirmed that no significant events or circumstances occurred that contradict the assumptions and data used in the annual impairment test performed in the fourth quarter of 2018.

Determining the fair value of the Stratasys-Objet reporting unit requires significant judgment, including judgments about the appropriate discount rates, terminal growth rates, weighted average costs of capital and the amount and timing of projected future cash flows. The Company will continue to monitor the fair value of its Stratasys-Objet reporting unit to determine whether events and changes in circumstances such as a deterioration in the business climate or operating results, significant decline in the Company's share price, changes in management’s business strategy or downward changes of the Company's cash flows projections, warrant further interim impairment testing.

Other Intangible Assets

Other intangible assets consisted of the following:

Amortization expense relating to intangible assets for the three-month periods ended June 30, 2019 and 2018 was approximately $6.0 million and $8.0 million, respectively. Amortization expense relating to intangible assets for the six-month periods ended June 30, 2019 and 2018 was approximately $12.1 million and $16.1 million, respectively.

As of June 30, 2019, the estimated amortization expense relating to intangible assets for each of the following periods was as follows: