Leasing

Lessee

Basic lease, implicit rate

1/1/X1, XYZ leased a production machine for five years. Annual payments (in arrears) were 2,927 and XYZ retained the asset. Prices of comparable machines were readily available. On this basis, XYZ determined the machine's fair value was 12,000 and rate implicit in the lease was 7%. XYZ intended to use the machine 6 years, then sell it for 1,200. It actually sold it for 1,250 on 3/31/X7.

Put simply, the rate implicit in the lease is the rate that will cause the present value of the lease payments to equal the asset's fair value.

IFRS 16.Appendix A: [The] interest rate implicit in the lease [is] the rate of interest that causes the present value of (a) the lease payments and (b) the unguaranteed residual value to equal the sum of (i) the fair value of the underlying asset and (ii) any initial direct costs of the lessor.

ASC 842-20-20: The rate of interest that, at a given date, causes the aggregate present value of (a) the lease payments and (b) the amount that a lessor expects to derive from the underlying asset following the end of the lease term to equal the sum of (1) the fair value of the underlying asset minus any related investment tax credit retained and expected to be realized by the lessor and (2) any deferred initial direct costs of the lessor.

A rate implicit in the lease can thus be (readily) determined if, and only if, the asset's fair value can be (readily) determined.

The simplest way to calculate an implicit rate is using Excel's =rate function:

7.0039771424884% =RATE(5,-2927,12000,0,0,10%).

The syntax for the function is =RATE(number of periods, -payment, present value, future value, type of payment (0 beginning of period, 1 arrears), initial guess.

A collection of other useful Excel formulas and functions can also be downloaded on our formula page.

Dr/Cr

1/1/X1 | 1.1.X1

 

 

Production machine (right-of-use asset)

12,000

 

 

Lease liability

 

12,000


Current common practice is to recognize leased tangible assets as PP&E. This practice is expected to continue under IFRS 16 | ASC 842 even though right-of-use assets are, technically speaking, intangible assets.

IFRS 15 Appendix A | ASC 842-20-20 define a right-of-use asset as "An asset that represents a lessee's right to use an underlying asset for the lease term".

12/31/X1 | 31.12.X1

 

 

Interest expense (leasing)

840

 

Lease liability

2,087

 

 

Cash

 

2,927

Depreciation expense (right-of-use asset)

1,800

 

 

Accumulated depreciation (right-of-use asset)

 

1,800



P

Liability

Discount rate

Interest expense

Payment

Liability amortization

A

B (B+1) = B - F

C

D = B x C

E

F = E - D

1

12,000

7.00%

840

2,927

2,087

2

9,913

7.00%

694

2,927

2,233

3

7,681

7.00%

538

2,927

2,389

4

5,292

7.00%

370

2,927

2,556

5

2,735

7.00%

191

2,927

2,735

 

 

 

 

 

12,000

 

 

 

 

 

 


31/3/X7 | 3.31.X7

 

 

Accumulated depreciation (right-of-use asset)

10,800

 

Cash

1,250

 

 

Production machine (right-of-use asset)

 

12,000

 

Asset disposal gain

 

50


Upfront payments

Same facts except payments of 2,735 were paid up front.

1/1/X1 | 1.1.X1

 

 

Production machine

12,000

 

 

Cash

2,735

 

 

Lease liability

 

9,265


12/31/X1 | 31.12.X1

 

 

Interest expense

649

 

Lease liability

2,087

 

Depreciation expense

1,800

 

 

Accrued lease payment

 

2,735

 

Accumulated depreciation

 

1,800


P

Liability

Discount rate

Interest expense

Payment

Liability amortization

A

B (B+1) = B - F

C

D = B x C

E

F = E - D

0

12,000

7.00%

0

2,735

2,735

1

9,265

7.00%

649

2,735

2,087

2

7,178

7.00%

502

2,735

2,233

3

4,945

7.00%

346

2,735

2,389

4

2,556

7.00%

179

2,735

2,556

 

 

 

 

 

12,000

 

 

 

 

 

 


7.00%=RATE(5,-2735,12000,0,1,10%)

A collection of other useful Excel formulas and functions can be downloaded on our formula page.

Principal and interest can also be recognized separately:

 

Accrued lease payment: Principal

 

2,087

 

Accrued lease payment: Interest

 

649


1/1/X2 | 1.1.X2

 

 

Accrued lease payment

2,735

 

 

Cash

 

2,735


Interim entries

Same facts except XYZ made quarterly accruing entries.

3/31/X1 | 31.3.X1

 

 

Interest expense

162

 

Lease liability

522

 

Depreciation expense

450

 

 

Accrued lease payment

 

684

 

Accumulated depreciation

 

450


Implicit rate not determinable, monthly payments, purchase option

1/1/X1, XYZ leased a made-to-order machine for 3 years. Monthly payments were 342 and XYZ had an option to buy the machine for 1,000. Prices of comparable machines were not available so XYZ could not determine the machine's fair value. Its incremental borrowing rate was 7.5%. XYZ kept the machine 6 years and scrapped it 31/12/X6.

Put simply, the rate implicit in the lease is the rate that will cause the present value of the lease payments to equal the asset's fair value.

IFRS 16.Appendix A: [The] interest rate implicit in the lease [is] the rate of interest that causes the present value of (a) the lease payments and (b) the unguaranteed residual value to equal the sum of (i) the fair value of the underlying asset and (ii) any initial direct costs of the lessor.

ASC 842-20-20: The rate of interest that, at a given date, causes the aggregate present value of (a) the lease payments and (b) the amount that a lessor expects to derive from the underlying asset following the end of the lease term to equal the sum of (1) the fair value of the underlying asset minus any related investment tax credit retained and expected to be realized by the lessor and (2) any deferred initial direct costs of the lessor.

A rate implicit in the lease can thus be (readily) determined if, and only if, the asset's fair value can be (readily) determined.

As the machine's fair value could not be determined, XYZ used its incremental borrowing rate instead.

IFRS 16.26: At the commencement date, a lessee shall measure the lease liability at the present value of the lease payments that are not paid at that date. The lease payments shall be discounted using the interest rate implicit in the lease, if that rate can be readily determined. If that rate cannot be readily determined, the lessee shall use the lessee’s incremental borrowing rate.

ASC 842-20-30 1: At the commencement date, a lessee shall measure both of the following: a. The lease liability at the present value of the lease payments not yet paid, discounted using the discount rate for the lease at lease commencement ...

ASC 842-20-20: For a lessee, the discount rate for the lease is the rate implicit in the lease unless that rate cannot be readily determined. In that case, the lessee is required to use its incremental borrowing rate.

Dr/Cr


1/1/X1 | 1.1.X1

 

 

Production machine (right-of-use asset)

11,916

 

 

Cash

 

342

 

Lease liability

 

11,574


Current common practice is to recognize leased tangible assets as PP&E. This practice is expected to continue under IFRS 16 | ASC 842 even though right-of-use assets are, technically speaking, intangible assets.

IFRS 15 Appendix A | ASC 842-20-20 define a right-of-use asset as "An asset that represents a lessee's right to use an underlying asset for the lease term".

XYZ calculated the asset's value using this table:

P

Payment

Discount rate

Present value

A

B

C = (1 + 7.5%)1/12 - 1

D = B ÷ (1 + C)A

0

342

0.604%

342

1

342

0.604%

340

-

-

-

-

34

342

0.604%

279

35

1,342

0.604%

1,087

 

 

 

11,916

 

 

 

 


Alternatively, it could have also calculated this value manually (a collection of useful formulas and functions can be downloaded in Excel format on our formula page):

11,916.04(rounded) = (1 + ((1 + 7.5%)(1/12) - 1)) x 342.15 x ((1 - (1 + ((1 + 7.5%)(1/12) - 1))-36) ÷ ((1 + 7.5%)(1/12) - 1)) + 1,000 ÷ (1 + ((1 + 7.5%)(1/12) - 1))35

In Excel syntax:

11916.0356707745=(1+((1+7.5%)^(1/12) - 1))*342.15*((1-(1+((1+7.5%)^(1/12) - 1))^-36)/((1+7.5%)^(1/12) - 1))+1000/(1+((1+7.5%)^(1/12) - 1))^35

1/31/X1 | 31.1.X1

 

 

Interest expense

70

 

Lease liability

272

 

Depreciation expense

166

 

 

Accrued lease payment

 

342

 

Accumulated depreciation

 

166



P

Liability

Discount rate

Interest expense

Payment

Liability amortization

A

B (B+1) = B - F

C

D = B x C

E

F = E - D

0

11,916

0.604%

0.00

342

342

1

11,574

0.604%

70

342

272

-

-

-

-

-

-

34

1,666

0.604%

10

342

332

35

1,334

0.604%

8

1,342

1,334

35

1,000

 

 

 

10,916

 

 

 

 

 

 


2/1/X1 | 1.2.X1

 

 

Accrued lease payment

342

 

 

Cash

 

342


12/1/X3 | 1.12.X3

 

 

Accrued lease payment

342

 

Lease liability

1,000

 

 

Cash

 

1,342


12/31/X6 | 31.12.X6

 

 

Accumulated depreciation

11,916

 

 

Production machine

 

11,916


Asset returned

1/1/X1, XYZ leased a vehicle for three years for 271 per month. Comparable vehicles sold for 12,000, had 6-year economic lives and lost 30% or their value annually. While the lessor used this information and its own required return of 8% to calculate the lease payments, much of this information was not available to XYZ, so XYZ applied its own incremental borrowing rate of 7.5% instead.

217 (rounded) = (12,000 - 4,116 ÷ (1 + (1 + 8%)(1÷12) - 1)(3 x 12)) ÷ ((1 - (1 + ( (1 + 8%)(1÷12) - 1))(-3 x 12)) ÷ ( (1 + 8%)(1÷12) - 1)) x (1 ÷ (1 + ( (1 + 8%)(1÷12) - 1)))

4,116 = 12,000 + 12,000 x -30% + (12,000 + 12,000 x -30%) x -30% + (12,000 + 12,000 x -30% + (12,000 + 12,000 x -30%) x -30%) x -30%

In Excel syntax:

270.782081171774=(12000-4116/(1+(1+8%)^(1/12) - 1)^(3*12))/((1-(1+( (1+8%)^(1/12) - 1))^(-3*12))/( (1+8%)^(1/12) - 1))*(1/(1+( (1+8%)^(1/12) - 1)))

4,116=12000+12000*-30%+(12000+12000*-30%)*-30%+(12000+12000*-30%+(12000+12000*-30%)*-30%)*-30%

A collection of easy to use Excel formulas and functions can be downloaded on our formulas page.

IFRS (finance lease) / US GAAP (operating lease)

1/1/X1 | 1.1.X1

 

 

Right-of-use asset (leased vehicle)

8,797

 

 

Cash

 

271

 

Lease liability

 

8,526


The current practice of recognizing returned tangible assets as PP&E is expected to change with IFRS 16 | ASC 842 to better reflect the substance of the transactions.

XYZ calculated the asset's value using its incremental borrowing rate and this table:

P

Payment

Discount rate

Present value

A

B

C = (1 + 7.5%)1/12 - 1

D = B ÷ (1 + C)A

0

271

0.604%

271

1

271

0.604%

269

-

-

-

-

34

271

0.604%

221

35

271

0.604%

219

 

 

 

8,797

 

 

 

 


Alternatively, it could have also calculated this value manually:

8,797 = (1 + 0.604%) x 271 x (1 - (1 + 0.604%)-36) ÷ 0.604%

A collection of easy to use Excel formulas and functions can be downloaded on our formulas page.

1/31/X1 | 31.1.X1

 

 

Interest expense

52

 

Lease liability

219

 

Amortization expense

244

 

 

Cash

 

271

 

Accumulated amortization

 

244

 

Alternatively    

XYZ elected to make payments the 31st instead of the 1st to avoid accruing entries.


P

Liability

Discount rate

Interest expense

Payment

Liability amortization

A

B (B+1) = B - F

C=(1+7.5%)(1/12)-1

D = B x C

E

F = E - D

0

8,796

0.604%

0

271

271

1

8,526

0.604%

52

271

219

-

-

-

-

-

-

34

537

0.604%

3

271

268

35

269

0.604%

2

271

269

 

 

 

 

 

8,797

 

 

 

 

 

 


XYZ could have recognized amotization of the asset each quarter:

3/31/X1 | 31.3.X1

 

 

Amortization expense

732

 

 

Accumulated amortization

 

732


or annually:

12/31/X1 | 31.12.X1

 

 

Amortization expense

2,932

 

 

Accumulated amortization

 

2,932


12/31/X3 | 31.12.X3

 

 

Interest expense

2

 

Lease liability

269

 

Amortization expense

244

 

 

Cash

 

271

 

Accumulated amortization

 

244


Accumulated amortization

8,797

 

 

Right-of-use asset (leased vehicle)

 

8,797


Note: 244 x 36 = 8,784. The difference is due to rounding as 8,797÷ 36 = 244.36.

Since none of the criteria outlined in ASC 842-10-25-2 were met, XYZ applied the guidance in ASC 842-10-25-3.a recognizing the acquisition as an operating lease.

ASC 842-10-25-2: A lessee shall classify a lease as a finance lease and a lessor shall classify a lease as a sales-type lease when the lease meets any of the following criteria at lease commencement:

a. The lease transfers ownership of the underlying asset to the lessee by the end of the lease term.

b. The lease grants the lessee an option to purchase the underlying asset that the lessee is reasonably certain to exercise.

c. The lease term is for the major part of the remaining economic life of the underlying asset. However, if the commencement date falls at or near the end of the economic life of the underlying asset, this criterion shall not be used for purposes of classifying the lease.

d. The present value of the sum of the lease payments and any residual value guaranteed by the lessee that is not already reflected in the lease payments in accordance with paragraph 842-10-30-5(f) equals or exceeds substantially all of the fair value of the underlying asset.

e. The underlying asset is of such a specialized nature that it is expected to have no alternative use to the lessor at the end of the lease term.

ASC 842-10-25-3 When none of the criteria in paragraph 842-10-25-2 are met:

a. A lessee shall classify the lease as an operating lease...

1/1/X1 | 1.1.X1

 

 

Pre-paid rent

271

 

Right-of-use asset (leased vehicle)

8,797

 

 

Cash

 

271

 

Lease liability

 

8,797


XYZ calculated the asset's value using its incremental borrowing rate and this table:

P

Payment

Discount rate

Present value

A

B

C = (1 + 7.5%)1/12 - 1

D = B ÷ (1 + C)A

0

271

0.604%

271

1

271

0.604%

269

-

-

-

-

34

271

0.604%

221

35

271

0.604%

219

 

 

 

8,797

 

 

 

 


Alternatively, it could have also calculated this value manually:

8,797 = (1 + 0.604%) x 271 x (1 - (1 + 0.604%)-36) ÷ 0.604%

A collection of easy to use Excel formulas and functions can be downloaded on our formulas page.

The current practice of recognizing returned tangible assets as PP&E is expected to change with IFRS 16 | ASC 842 to better reflect the substance of the transactions.

1/31/X1 | 31.1.X1

 

 

Rental expense

271

 

Lease liability

219

 

 

Pre-paid rent

 

271

 

Right-of-use asset (Leased vehicle)

 

219



ASC 842-20-25-6 (Operating Leases): After the commencement date, a lessee shall recognize ... A single lease cost, calculated so that the remaining cost of the lease ... is allocated over the remaining lease term on a straight-line basis unless another systematic and rational basis is more representative of the pattern in which benefit is expected to be derived from the right to use the underlying asset ...


P

Liability

Discount rate

Deduction

Rental exp.

Asset and liability amort.

A

B (B+1) = B - F

C=(1+7.5%)(1/12)-1

D = B x C

E

F = E - D

0

8,796

0.604%

0

271

271

1

8,526

0.604%

52

271

219

-

-

-

-

-

-

35

269

0.604%

2

271

269

 

 

 

 

 

8,797

 

 

 

 

 

 


Under US GAAP an ambulated amortization account is not required for an intangible asset. As a right-to-use asset is intangible, XYZ did not use an accumulated amortization account.

2/1/X1 | 1.2.X1

 

 

Pre-paid rent

271

 

 

Cash

 

271


12/31/X3 | 31.12.X3

 

 

Rental expense

271

 

Lease liability

269

 

 

Pre-paid rent

 

271

 

Right-of-use asset (Leased vehicle)

 

269


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