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Investments
 9 Months Ended
Jun. 30, 2021
Investments, Debt and Equity Securities [Abstract]  
Investments Investments
Our investments consist of (in millions):
June 30, 2021September 30, 2020
Fixed income securities$0.6 $0.6 
Equity securities1,494.8 875.3 
Other94.6 78.2 
Total investments1,590.0 954.1 
Less: Short-term investments(1)
(0.6)(0.6)
Long-term investments$1,589.4 $953.5 
(1) Short-term investments are included in other current assets in the Consolidated Balance Sheet.
Equity Securities
On July 19, 2018, we purchased 10,582,010 shares of PTC Inc. ("PTC") common stock (the "PTC Shares") in a private placement at a purchase price of $94.50 per share for an aggregate purchase price of approximately $1.0 billion. The PTC Shares are considered equity securities. On May 11, 2021, we entered into an amendment to the securities purchase agreement with PTC, which amended, among other things, our entity-specific transfer restrictions through September 2023, subject to certain exceptions. We have the ability to transfer in open market transactions, in the aggregate in any 90-day period, a number of PTC Shares equal to up to 1.0 percent of PTC's total outstanding shares of common stock as of the first day in such 90-day period. We also have the ability to transfer in marketed underwritten public offerings, in the aggregate in any one-year period, a number of PTC Shares equal to up to 5.0 percent of PTC's total outstanding shares of common stock as of the closing date of the first such offering.
Fair Value of Investments
U.S. GAAP defines fair value as the price that would be received for an asset or paid to transfer a liability (exit price) in an orderly transaction between market participants in the principal or most advantageous market for the asset or liability. U.S. GAAP also classifies the inputs used to measure fair value into the following hierarchy:
Level 1: Quoted prices in active markets for identical assets or liabilities.
Level 2: Quoted prices in active markets for similar assets or liabilities, quoted prices for identical or similar assets or liabilities in markets that are not active, or inputs other than quoted prices that are observable for the asset or liability.
Level 3: Unobservable inputs for the asset or liability.
The methods described above may produce a fair value calculation that may not be indicative of net realizable value or reflective of future fair values. Furthermore, while we believe our valuation methods are appropriate and consistent with other market participants, the use of different methodologies or assumptions to determine the fair value of certain financial instruments could result in a different fair value measurement at the reporting date. We did not have any transfers between levels of fair value measurements during the period presented.
The PTC Shares are classified as level 1 in the fair value hierarchy and recognized at fair value in the Consolidated Balance Sheet using the most recent closing price of PTC common stock quoted on Nasdaq. At June 30, 2021, the fair value of the PTC Shares was $1,494.8 million, which was recorded in long-term investments in the Consolidated Balance Sheet. For the three and nine months ended June 30, 2021, we recorded gains of $38.2 million and $619.5 million related to the PTC Shares, respectively. For the three and nine months ended June 30, 2020, we recorded gains of $175.5 million and $101.7 million related to the PTC Shares, respectively.