The company recorded net gains on sale and leaseback transactions of $41 million for the year ended December 31, 2019.

The following table presents supplemental information relating to the cash flows arising from lease transactions. Cash payments related to variable lease costs and short-term leases are not included in the measurement of operating and finance lease liabilities, and, as such, are excluded from the amounts below.

* Includes opening balance additions as a result of the adoption of the new lease guidance effective January 1, 2019. The post adoption addition of leases for the year ended December 31, 2019 was $1,679 million for operating leases and immaterial for finance leases.

The following table presents the weighted-average lease term and discount rate for finance and operating leases.


At December 31:	2019
Finance leases
Weighted-average remaining lease term	4.8	yrs.
Weighted-average discount rate	1.62	%
Operating leases
Weighted-average remaining lease term	5.4	yrs.
Weighted-average discount rate	3.03	%

The following table presents a maturity analysis of expected undiscounted cash flows for operating and finance leases on an annual basis for the next five years and thereafter.

Imputed

($ in millions)

2020

2021

2022

2023

2024

Thereafter

Interest*

Total**

Finance leases

(54)

204

Operating leases

1,486

1,198

928

673

514

806

(346)

5,259

* Imputed interest represents the difference between undiscounted cash flows and discounted cash flows.

** The company entered into lease agreements for certain facilities and equipment with payments totaling approximately $181 million that have not yet commenced as of December 31, 2019, and therefore are not included in this table.

At December 31, 2019, the total amount of finance leases recognized in the Consolidated Balance Sheet for ROU assets in property, plant and equipment was $187 million and lease liabilities in short-term debt and long-term debt was $52 million and $151 million, respectively.

Prior to the adoption of the new lease guidance on January 1, 2019, ROU assets and lease liabilities for operating leases were not recognized in the Consolidated Balance Sheet. The company elected the practical expedient to not provide comparable presentation in the Consolidated Balance Sheet for periods prior to adoption. Rental expense, including amounts charged to inventory and fixed assets, and excluding amounts previously reserved, were $1,944 million and $1,821 million for the years ended December 31, 2018 and 2017, respectively.

The following table, which was included in the company’s 2018 Annual Report, depicts gross minimum rental commitments under noncancelable leases, amounts related to vacant space associated with workforce transformation, sublease income commitments and capital lease commitments.



											Beyond
($ in millions)	2019		2020		2021		2022		2023		2023
Operating lease commitments
Gross minimum rental commitments (including vacant space below)	$	1,581	$	1,233	$	914	$	640	$	445	$	815
Vacant space		29		23		14		9		5		8
Sublease income commitments		11		7		5		4		4		2
Capital lease commitments		3		3		3		3		2		28

The difference between the company’s total lease commitments as reported at December 31, 2018 compared to the January 1, 2019 ROU asset balance in the Consolidated Balance Sheet is primarily due to the required use of a discount factor (imputed interest) under the new lease guidance and certain amounts that are not included in the ROU assets under the new lease guidance (e.g. tenant incentives and vacant space).

Accounting for Leases as a Lessor

The following table presents amounts included in the Consolidated Income Statement related to lessor activity:


($ in millions)
For the year ended December 31:	2019
Lease income–sales-type and direct financing leases
Sales-type lease selling price	$	1,509
Less: Carrying value of underlying assets excluding unguaranteed residual value		591
Gross profit		918
Interest income on lease receivables		303
Total sales-type and direct financing lease income		1,221
Lease income–operating leases		324
Variable lease income		56
Total lease income	$	1,601

Sales-Type and Direct Financing Leases

At December 31, 2019, the unguaranteed residual value of sales-type and direct financing leases was $652 million. For further information on the company’s net investment in leases, including guaranteed and unguaranteed residual values, refer to note K, “Financing Receivables.”

For the years ended December 31, 2019 and 2018, impairment of residual values was immaterial.

The following table presents a maturity analysis of the lease payments due to IBM on sales-type and direct financing leases over the next five years and thereafter, as well as a reconciliation of the undiscounted cash flows to the financing receivables recognized in the Consolidated Balance Sheet at December 31, 2019:


($ in millions)	Total
2020	$	2,632
2021		1,921
2022		1,053
2023		382
2024		82
Thereafter		7
Total undiscounted cash flows	$	6,077
Present value of lease payments (recognized as financing receivables)		5,567	*
Difference between undiscounted cash flows and discounted cash flows	$	(509)

* The present value of the lease payments will not equal the financing receivables balances in the Consolidated Balance Sheet, due to certain items including IDCs, allowance for credit losses and residual values, which are included in the financing receivable balance, but are not included in the future lease payments.

Operating Leases

The following table presents a maturity analysis of the undiscounted lease payments due to IBM on operating leases over the next five years and thereafter, at December 31, 2019:


($ in millions)	Total
2020	$	145
2021		35
2022		4
2023		0
2024		0
Thereafter		—
Total undiscounted cash flows	$	184

There were no material impairment losses incurred for equipment provided to clients under an operating lease for the year ended December 31, 2019.

At December 31, 2019, the unguaranteed residual value of operating leases was $81 million.