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.
1/1/X1 | 1.1.X1 |
|
|
|
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 |
|
||
|
|
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 |
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 |
|||
|
Depreciation expense |
1,800 |
|
|
|
|
Accrued lease payment |
|
|
|
|
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 |
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 |
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.
|
1/1/X1 | 1.1.X1 |
|
|
|
|
|
|||
|
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 |
|
||
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) |
|
||
|
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.
|
|
|
||
|
Interest expense |
52 |
||
|
Lease liability |
|
||
|
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 |
|
||
|
|
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) |
|
||
|
|
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 |
|
|
|
271 |
|
||
Lease liability |
|
||
|
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 |