Goodwill

Goodwill represents the difference between the purchase price and the estimated fair value of identifiable assets acquired and liabilities assumed. We are required to perform impairment tests related to our goodwill annually, which we perform during the third quarter of each fiscal year, or when we identify certain triggering events or circumstances that would more likely than not reduce the estimated fair value of the goodwill of the Company below its carrying amount. The following table represents the changes in the carrying amount of goodwill for the nine months ended October 31, 2018 (amounts in thousands):

In the second quarter of fiscal 2019, we determined there to be a triggering event that prompted us to test our goodwill for impairment as of July 31, 2018. The triggering event was a decline in actual revenue for the quarter compared to projected amounts, which was reported in a Current Report on Form 8-K furnished to the SEC on August 21, 2018. The Company performed a quantitative goodwill impairment test, utilizing the single-step approach under ASU 2017-04, “Intangibles-Goodwill and Other (Topic 350): Simplifying the Test of Goodwill Impairment,” comparing the carrying value of the reporting unit to its estimated fair value, which was calculated using a discounted cash flow analysis, a form of income approach. We considered three generally accepted approaches for valuing businesses: the market approach, the income approach and the asset-based (cost) approach to arrive at fair value. The discounted cash flow analysis relied on certain assumptions regarding future net free cash flows based on industry market data, historical performance and expected future performance. Future net free cash flows were discounted to present value using a risk-adjusted discount rate, which reflects the Weighted Average Cost of Capital (“WACC”). The WACC was developed using information from same or similar industry participants and publicly available market data. As a result of the quantitative goodwill impairment test performed as of July 31, 2018, the Company determined that the estimated fair value of the reporting unit exceeded its carrying value, including goodwill, by 28.7%. Therefore, no impairment charges on our goodwill or other long-lived assets were recorded in the second quarter of fiscal 2019.

Intangible Assets

Intangible assets, net, consisted of the following at October 31, 2018 and January 31, 2018:

Amortization expense for intangible assets was $0.4 million and $1.2 million, respectively, for the three and nine months ended October 31, 2018 and $0.6 million and $1.8 million, respectively, for the three and nine months ended October 31, 2017.

As of October 31, 2018, the estimated future amortization expense for our finite-life intangible assets is as follows (amounts in thousands):