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Note 9. Leases

Operating lease assets are right-of-use assets, which represent the right to use an underlying asset for the lease term. Operating lease liabilities represent the obligation to make lease payments arising from the lease. Operating leases are included in the Operating Lease Assets, net, and Operating Lease Liabilities, Current and Long-term on the unaudited Consolidated Balance Sheet at July 31, 2019. ÌýThese assets and lease liabilities are recognized based on the present value of remaining lease payments over the lease term. When the lease does not provide an implicit interest rate, the Company uses an incremental borrowing rate to determine the present value of the lease payments. The right-of-use asset includes all lease payments made and excludes lease incentives. Lease expense for operating leases is recognized on a straight-line basis over the lease term. There are no variable lease payments. Lease expense for the three month period ended July 31, 2019 was $612,597. These costs are primarily related to long-term operating leases, but also include amounts for short-term leases with terms greater than 30 days that are not material.

The following is a schedule by years of future minimum rental payments required under operating leases that have initial or remaining non-cancelable lease terms in excess of one year as of July 31, 2019.

Cash Flows

An initial ROU asset of $8.0 million was recognized as a non-cash asset addition with the adoption of the standard. There were no additional ROU assets recognized as non-cash asset additions during the quarter ended July 31, 2019. Cash paid for amounts included in the present value of operating lease liabilities at adoption and for the quarter ended July 31, 2019 was $1.7 million and $0.5 million, respectively, and is included in operating cash flows.