The rules describing how to account for all leases were drastically revised on February 25, 2016. That is when the accounting rule setters, FASB, issued their document called Accounting Standards Update 2016-02 – Leases (Topic 842).
You will be hearing a lot more about these changes over the next few years.
In extremely brief summary, the new rules require all entities preparing financial statements (including nonprofit organizations) to record all leases as an asset and liability. The assets will be called right to use assets and will be amortized over the life of the lease. An offsetting liability will be recorded. Whether the asset will be reported at the sum of total future payments or at the discounted present value of future payments would depend on the nature of the lease.