# Leasing

## 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 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 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.