FORMULAS
CHAPTER 10: LESSEE ACCOUNTING
(Basic Principles)
Interest (Effective Interest Method) = Face
amount of Gross Fixed Payments - Present
Value
Ex: (refer to page 331)
Interest=(100,000x4)-303,730
= 400,000-303,730
= 96,270
Carrying Amount at Year End of RUA= Right of
use asset - Accumulated depreciation
Ex: (refer to page 332)
Carrying Amount = 303,730-75,932
= 227,798
Cost of Right of Use Asset & Lease Liability (w/
purchase option) = Present Value of Lease
Payments + Present Value of Purchase Option
Ex: (refer to page 333)
Cost of Right of Use
Asset=(1,000,000x5.65)+(500,000x0.322)
= 5,650,000+161,000
= 5,811,000
NONEXERCISE OF PURCHASE OPTION
*Note: Nonexercise of Purchase Option
Depriciable Years=Lower of useful life and lease
term
Loss on Finance Lease = (Right of use asset Accumulated Depreciation) - Lease Liability at
the Lease Expiration (Purchase Option)
Ex: (refer to page 335)
Loss on Finance Lease=(5,811,000-4,342,500)500,000
=1,468,500-500,000
=968,500
Cost of Right of Use Asset & Lease Liability (w/
residual value guarantee) = Present Value of
Lease Payments + Present Value of Residual
Value Guarantee
Ex: (refer to page 335)
Cost of Right of Use
Asset=(1,000,000x3.16987)+(200,000x0.683)
= 3.169,870+136,600
= 3,306,470
Cost of Right of Use Asset (w/ residual value
guarantee & initial direct cost) = Initial Lease
Liability + Initial Direct Cost - Lease Incentive
Received
Ex: (refer to page 338)
Initial Lease
Liability=(1,000,000x4.3121)+(300,000x0.6806)
=4,312,100+204,180
=4,516,280
Cost of Right of Use Asset=4,516,280+250,000150,000
=4,616,280
Net Cash Payment at the start of the Lease =
Initial Direct Cost - Lease Incentive Received
Ex: (refer to page 338)
Net Cash Payment=250,000-150,000
=100,000
Cost of Right of Use Asset (w/ unguaranteed
residual value, lease payment for long term
lease, restoration cost) = Initial Lease Liability +
Payment to Lessor + PV of restoration cost
Ex: (refer to page 341)
Initial Lease Liability=(600,000x4.36)
=2,616,000
*Note: Residual Value was excluded because it
is unguaranteed
Cost of Right of Use
Asset=2,616,000+224,000+(634,920x0.63)
=2,616,000+224,000+400,000
=3,240,000
Cost of Equipment actually purchased =
Carrying Amount + Cash Payment - Balance of
Lease Liability
Ex: (refer to page 343)
Cost of Equipment=(5,000,0001,500,000)+4,000,000-3,800,000
=3,500,000+4,000,0003,800,000
=3,700,000
CHAPTER 11: LESSEE ACCOUNTING
(Remeasurement of Lease Liability)
EXTENSION OPTION
Initial Lease Liability/Right of use asset = Annual
Rental (old) x PV of an ordinary annuity (old)
Ex: (refer to page 372)
Initial Lease Liability=500,000x3.791
=1,895,500
New Carrying Amount of Right of Use Asset =
(Right of Use Asset (old) - Accumulated
depreciation) + Increase in Lease Liability
*Note: Depreciable year=years expired
Ex: (refer to page 373)
New Carrying Amount=(1,895,5001,137,300)+2,076,790
=758,200+2,076,790
=2,834,990
REMEASUREMENT OF LEASE LIABILITY
Present Value of remaining rentals of old lease
term = Annual Rental (old) x PV of an ordinary
annuity (new: remaining period)
Ex: (refer to page 373)
Present Value of remaining rentals of old lease
term=500,000x1.783
Depreciation of Remeasured Liability = New
Carrying Amount / (Total Lease Term - Years
Expired)
Ex: (refer to page 374)
Depreciation of Remeasured
Liability=2,834,990/(10-3)
=2,834,990/7
=404,999
=891,500
Present Value of new rentals of extended lease
term = Annual Rental (new) x PV of an ordinary
annuity (new: extended period) x PV of 1 (new:
remaining period)
Ex: (refer to page 373)
Present Value of new rentals of extended lease
term=600,000x3.993x0.857
VARIABLE PAYMENTS
Present Value of Annual Rentals for first years =
Annual rental for first years x PV of an ordinary
annuity (for first years period)
Ex: (refer to page 375)
Present Value of Annual Rentals for first
years=300,000 x 2.487
=746,100
=2,053,200
Present Value (new)/Lease Liability (new) =
Present Value of remaining rentals of old lease
term + Present Value of new rentals of
extended lease term
Ex: (refer to page 373)
Present Value (new)=891,500+2,053,200
=2,944,700
Increase in lease liability = Present Value (new) Carrying Amount of liability before extension
Ex: (refer to page 373)
Increase in Lease Liability=2,944,700-867,910
=2,076,790
NOTE: Increase in lease liability is an addition to
the carrying amount of the right of use asset. So
in the date of extension Right of Use Asset and
Lease Liability will be recognized.
Present Value of Annual Rentals for next years =
(Annual rental for next years x PV of an ordinary
annuity (for next years period)) x PV of 1 (for
first years period)
Ex: (refer to page 375)
Present Value of Annual Rentals for next
years=(400,000x3.791)x0.751
=1,138,816
Initial Lease Liability = Present Value of Annual
Rentals for first years + Present Value of Annual
Rentals for next years
Ex: (refer to page 375)
Initial Lease Liability=746,100+1,138,816
=1,884,916
LEASE MODIFICATION
Lease Liability/Right of Use Asset = Annual
Rental (old) x PV of an Ordinary Annuity (old)
Ex: (refer to page 378)
Lease Liability=100,000x5.34
=534,000
Present Value of the Additional Lease Rentals =
Increase in Rental Payable x PV of an Ordinary
Annuity (new)
*Note: the modification is accounted as a
separate lease.
Ex: (refer to page 378)
PV of the Additional Lease Rentals=200,000x4.62
=924,000
LEASE MODIFICATION-EXTENSION OF
LEASE TERM
Initial Lease Liability = Annual Rental Payable
(old) x PV of an Ordinary Annuity (old)
Ex: (refer to page 379)
Initial Lease Liability=200,000x3.89
=778,000
Lease Liability (new) = Annual Rental Payable
Ex: (refer to page 379)
Lease Liability (new)=200,000x4.231
=846,200
Increase in Lease Liability = Lease Liability (new)
- Carrying amount of liability before extension
Ex: (refer to page 379)
Increase in Lease Liability=846,200-506,342
=339,858
LEASE MODIFICATION-DECREASE IN
SCOPE OF LEASE
*Note: Depreciable year=years expired
Carrying Amount of Right of Use Asset before
Amendment = Right of Use Asset - Accumulated
Depreciation
Ex: (refer to page 382)
Carrying Amount=268,400-53,680
=214,720
Termination Gain = Decrease in Carrying
Amount of Lease Liability before amendment Decrease Carrying Amount of RUA before
amendment
Ex: (refer to page 382)
Termination Gain=(229,862x40%)-(214,720x40%)
=91,945-85,888
=6,057
Remaining Old Lease Liability = Lease Liability
before amendment - Decrease in Lease Liability
before amendment
Ex: (refer to page 382)
Remaining Old Lease Liability =229,862-91,945
=137,917
Increase in Lease Liability = Lease Liability (new)
- Remaining Old Lease Liability
Ex: (refer to page 382)
Increase in Lease Liability=(30,000x5.335)137,917
=160,050-137,917
=22,133
New Carrying Amount of Right of Use Asset =
(Right of Use Asset (old) - Accumulated
depreciation) + Increase in Lease Liability
*Note: Depreciable year=years expired
Ex: (refer to page 380)
New Carrying Amount=(778,000311,200)+339,858
=466,800+339,858
=806,658
LEASE MODIFICATION-CHANGE IN
RENTAL
Decrease in Lease Liability = (New Lease
Payment x New PV of Ordinary Annuity) - Lease
Liability before amendment
Ex: (refer to page 385)
Decrease in Lease Liability=(70,000x2.53)210,285
=177,100-210,285
=33,185
Depreciation of Extended Liability = New
Carrying Amount / (Total Lease Term - Years
Expired)
Ex: (refer to page 380)
Depreciation of Remeasured
Liability=806,658/(8-2)
=134,443
New Carrying Amount of Right of Use Asset =
(Right of Use Asset (old) - Accumulated
depreciation) - Decrease in Lease Liability
Ex: (refer to page 385)
New Carrying Amount=(381,600-190,800)-33,185
=190,800-33,185
=157,615
CHAPTER 12: OPERATING LEASELESSOR
Total Carrying Amount = (Cost - Accumulated
Depreciation) + Deferred Initial Direct Cost
(unamortized)
Ex: (refer to page 399)
Total Carrying Amout=(3,000,000300,000)+225,000
=2,700,000+225,000
=2,925,000
Annual Rental = (Cost of asset - PV of residual
value) / PV of an Ordinary Annuity
Ex: (refer to page 423)
Annual Rental=(3,194,410-341,500)/3.1699
=2,852,910/3.1699
=900,000
Unamortized Initial Direct Cost = Deferred Initial
Direct Cost - Amortization for first year
Ex: (refer to page 399)
Unamortized balance=300,000-75,000
=225,000
Residual Value, whether guaranteed or
unguaranteed should be added to the gross
rentals to get the Gross Investment.
UNEQUAL RENTAL PAYMENTS
Average Annual Rental = Rent Income / no. of
years
Ex: (refer to page 400)
Average Annual Rental =3,000,000/3
=1,000,000
On Accounting for Lessee, if the residual value is
unguaranteed it is automatically IGNORED. While
in Accounting for Lessor, as long as the asset will
revert back to the lessor at the end of lease term,
whether GUARANTEED or UNGUARANTEED it is
NOT IGNORED. IGNORED only if it will not revert
back to lessor.
DIRECT FINANCING LEASE-LESSOR
Gross Investment (Gross Rentals) = Annual
Rental Payable x Lease Term
Ex: (refer to page 417)
Gross Investment=500,000x4
=2,000,000
CHAPTER 13: SALES TYPE LEASELESSOR
Gross Income on Sale = Net Investment - Cost
of Machinery
Ex: (refer to page 445)
Gross Income on Sale=1,440,000-1,000,000
=440,000
Net Investment (Present Value of Gross Rentals)
= Annual Rental Payable x PV of Annuity
Ex: (refer to page 417)
Net Investment=500,000x3.0373
=1,518,650
Note: If the machinery will revert back to the
lessor, add the PV of residual value. If it will not
revert back, IGNORE RESIDUAL VALUE.
Initial Direct Cost has no PV
Unearned Interest Income = Gross Investment Net Investment
Ex: (refer to page 417)
Unearned Interest Income=2,000,000-1,518,650
=481,350
SALES TYPE LEASE W/ RESIDUAL
VALUE & INITIAL DIRECT COST
Note: In sales type lease, initial direct cost is
expensed in COGS
Gross Investment = Gross Rentals + Residual
Value Guarantee
Ex: (refer to page 447)
Gross Investment=(800,000x5)+200,000
=4,000,000+200,000
=4,200,000
DIRECT FINANCING LEASE W/ INITIAL
DIRECT COST
Net Investment = PV or Cost of Machinery +
Initial Direct Cost
Ex: (refer to page 419)
Net Investment=1,518,650+66300
=1,584,950
Net Investment = PV of Gross Rentals + PV of
Residual Value
Ex: (refer to page 447)
Net Investment
=(800,000x3.7908)+(200,000x0.6209)
=3,032,640+124,180
=3,156,820
Cost of Goods Sold = Cost of Machinery + Initial
Direct Cost
Ex: (refer to page 447)
Cost of Goods Sold=2,000,000+100,000
=2,100,000
Pretax Total Income = Gross Income + Interest
Income
Ex: (refer to page 464)
Pretax Total Income=400,000+204,492
=604,492
Gross Income = Net Investment - COGS
Ex: (refer to page 447)
Gross Income=3,156,820-2,100,000
=1,056,820
CHAPTER 15: SALE AND LEASEBACK
Cost of right of use asset = PV of Lease Liability /
Fair Value x Carrying Amount
Ex: (refer to page 476)
Cost of Right of Use
Asset=2,536,000/6,000,000x4,500,000
=1,902,000
UNGUARANTEED RESIDUAL VALUE
Cost of Goods Sold = (Cost of Machinery - PV of
Unguaranteed Residual Value) + Initial Direct
Cost
Ex: (refer to page 449)
Cost of Goods Sold=(2,000,000124,180)+100,000
=1,875,820+100,000
=1,975,820
Gross Income = (Net Investment - PV of
Unguaranteed Residual Value) - COGS
Ex: (refer to page 449)
Gross Income=(3,156,820-124,180)-1,975,820
=3,032,640-1,975,820
=1,056.820
CHAPTER 14: SALES TYPE LEASE W/
PURCHASE OPTION
Gross Investment-Lease Receivable = Gross
Rentals + Purchase Option
Ex: (refer to page 452)
Gross Investment=(500,000x4)+200,000
=2,000,000+200,000
=2,200,000
Net Investment = PV of Gross Rentals + PV of
Purchase Option
Ex: (refer to page 452)
Net
Investment=(500,000x3.312)+(200,000x0.735)
=1,656,000+147,000
=1,803,000
ACTUAL SALE OF UNDERLYING ASSET
Loss on Sale of Leased Equipment = Sale Price (Lease Receivable - Unearmed Interest Income)
Ex: (refer to page 455)
Loss on Sale=3,500,000-(5,000,000-1,200,000)
=3,500,000-3,800,000
=300,000
Total Gain = Fair Value - Carrying Amount
Ex: (refer to page 477)
Total Gain=6,000,000-4,500,000
=1,500,000
Right Transferred to Buyer-Lessor = Fair Value PV of Lease Liability
Ex: (refer to page 477)
Right transferred to buyer-lessor=6,000,0002,536,000
=3,464,000
Gain to be Recognized = Right transferred / Fair
Value x Total Gain
Ex: (refer to page 477)
Gain to be
Recognized=3,464,000/6,000,000x1,500,000
=866,000
SALE PRICE ABOVE FAIR VALUE
Excess sale price over fair value = Sale price Fair Value of Building
Ex: (refer to page 479)
Excess sale price=20,000,000-18,000,000
=2,000,000
PV of Lease Liability related to rentals = PV of
Lease Liability - Excess Sale Price
Ex: (refer to page 479)
PV of Lease Liability=5,400,000-2,000,000
=3,400,000
Annual Rental related to Lease = PV Related to
Rentals / Initial Lease Liability x Annual Rental
given
Ex: (refer to page 481)
Annual Rental related to
Lease=3,400,000/5,400,000x1,500,000
=944,444
Annual Rental related to Financing = Excess Sale
Price / Initial Lease Liability x Annual Rental
given
Ex: (refer to page 481)
Annual Rental related to Financing =
2,000,000/5,400,000x1,500,000
=555,556
SALE PRICE BELOW FAIR VALUE
Excess Fair Value = Fair Value - Sale Price
Ex: (refer to page 483)
Excess Fair Value=6,000,000-5,000,000
=1,000,000
Total Lease Liability = PV of Lease Liability +
Excess Fair Value
Ex: (refer to page 483)
Total Lease Liability=3,591,000+1,000,000
=4,591,000
SALE PRICE AT FAIR VALUE WITH LOSS
Total Loss = Sale Price - Carrying Amount
Ex: (refer to page 486)
Total Loss=10,000,000-12,000,000
=2,000,000