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 8422020: 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 rightofuse assets are, technically speaking, intangible assets.
IFRS 15 Appendix A  ASC 8422020 define a rightofuse 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 (rightofuse asset) 
1,800 



Accumulated depreciation (rightofuse 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 (rightofuse asset) 
10,800 


Cash 
1,250 



Production machine (rightofuse 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 madetoorder 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 8422020: 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 8422030 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 8422020: 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 rightofuse assets are, technically speaking, intangible assets.
IFRS 15 Appendix A  ASC 8422020 define a rightofuse 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 6year 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=(120004116/(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 



Rightofuse 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 



Rightofuse 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 84210252 were met, XYZ applied the guidance in ASC 84210253.a recognizing the acquisition as an operating lease.
ASC 84210252: A lessee shall classify a lease as a finance lease and a lessor shall classify a lease as a salestype 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 84210305(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 84210253 When none of the criteria in paragraph 84210252 are met:
a. A lessee shall classify the lease as an operating lease...
1/1/X1  1.1.X1 



Prepaid rent 
271 


Rightofuse 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 



Prepaid rent 

271 

Rightofuse asset (Leased vehicle) 

219 
ASC 84220256 (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 straightline 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 righttouse asset is intangible, XYZ did not use an accumulated amortization account.
2/1/X1  1.2.X1 



Prepaid rent 
271 



Cash 

271 
12/31/X3  31.12.X3 



Rental expense 
271 


Lease liability 
269 



Prepaid rent 

271 

Rightofuse asset (Leased vehicle) 

269 