Leasing: formula sheet

Key formulas

Definition of a lease

Lease = contract conveying the right to control the use of an identified asset for a period of time in exchange for consideration

All parts must be met. If any one fails, it is a service contract, not a lease.

Three-part control test

Identified asset + right to obtain substantially all economic benefits + right to direct the use

Apply in this order. Stop as soon as one part fails.

Substitution right

Supplier's right is substantive only if it can practically substitute AND would benefit economically

If the right is not substantive, the asset is treated as identified.

Short-term lease

Lease term ≤ 12 months at commencement and no purchase option

A lessee election made by class of underlying asset. Payments are expensed, usually straight-line.

Low-value asset exemption

Assessed on the value of the asset when new, not on the lease payments

Election is made lease by lease. Examples are tablets, small office furniture and phones. Cars and most machinery are not low value.

Lease liability at commencement

Lease liability = Σ [ lease payment ÷ (1 + r)^t ] for all unpaid payments

r is the implicit rate or incremental borrowing rate. t is the number of periods until each payment. Payments in advance have t = 0 for the first one.

Annuity of equal payments in arrears

PV = payment × [1 − (1 + r)^−n] ÷ r

Use the cumulative discount factor if the question provides one.

Right-of-use asset at commencement

ROU asset = lease liability + payments made at or before commencement + initial direct costs + restoration cost estimate − incentives received

Add all items in this list that apply. Ignore the ones the question does not mention.

Payments included in the liability

Fixed payments (less incentives receivable) + variable payments based on an index or rate + amounts under residual value guarantees + purchase option price if reasonably certain to be exercised + termination penalties if the term assumes termination

Variable payments linked to sales or usage are excluded and expensed when incurred.

Lease term

Lease term = non-cancellable period + optional periods if reasonably certain to be used

Extension options reasonably certain to be exercised extend the term.

ROU depreciation

Annual depreciation = (ROU cost − residual value) ÷ shorter of lease term and useful life

Use useful life if ownership transfers or a purchase option is reasonably certain to be exercised.

Finance cost (arrears)

Finance cost = opening liability × interest rate

Payment at year end. Closing = opening + finance cost − payment.

Finance cost (advance)

Finance cost = (opening liability − payment made at start) × interest rate

Payment at start of year. Closing = opening − payment + finance cost.

Current liability

Current portion = liability at this year end − liability at next year end

This is the principal repaid in the next 12 months. Non-current = total liability − current portion.

Initial liability

Liability = present value of lease payments not yet paid, discounted at the rate

Initial ROU asset = liability + payments made at or before start + initial direct costs + restoration costs − incentives received.

Is it a sale?

Sale only if the buyer obtains control (IFRS 15 test)

If not a sale: keep the asset and recognise a financial liability equal to the proceeds.

Right-of-use asset retained

ROU asset = Carrying amount × (PV of lease payments ÷ Fair value of asset)

Use this when the sale is at fair value and it is a genuine sale.

Total gain on sale

Total gain = Fair value − Carrying amount

Only part of this is recognised.

Gain recognised

Gain recognised = Total gain × (Fair value − PV of lease payments) ÷ Fair value

This is the gain relating to rights transferred to the buyer.

Below-market sale price

Adjustment = Fair value − Sale price → treat as prepaid lease payments

Add to the ROU asset. Also adjust where lease rentals are below market.

Above-market sale price

Adjustment = Sale price − Fair value → treat as additional financing

Add to the lease liability. Gain is then based on fair value, not the inflated price.

Opening lease liability

Lease liability = PV of lease payments (plus any additional financing)

Cash received is debited to bank at the actual proceeds.

Short-term lease test

Lease term ≤ 12 months at commencement AND no purchase option

Both conditions must be met. Elected by class of underlying asset.

Low-value test

Value of the asset when new is low, judged in absolute terms

Elected lease by lease. Independent of the lessee's size. Use a threshold only if the question gives one.

Expense for exempt leases

Total payments ÷ lease term in months × months in the period = expense for the period (straight line)

Applies if payments are uneven, for example rent-free periods or stepped rents. Use the monthly rate when the term is not a whole number of years. Another systematic basis is allowed if it is more representative.

Accrual or prepayment

Cash paid − expense = prepayment (if positive) or accrual (if negative)

Carry the balance in current assets or current liabilities.

Non-exempt lease expense in profit or loss

Depreciation of right-of-use asset + interest on lease liability

Do not also charge the rental payments to profit or loss.

Lease liability split

Current = principal repaid within 12 months; Non-current = remainder

Current portion is the next year's liability reduction, not the next payment.

Quick revision

• A contract contains a lease if it gives the right to control the use of an identified asset for a period in exchange for consideration.
• A supplier's substantive right to substitute the asset means there is no identified asset.
• Lessee initial liability is the present value of unpaid lease payments, discounted at the rate implicit in the lease if known, otherwise the incremental borrowing rate.
• Right-of-use asset starts at the liability, plus payments made before or at commencement and initial direct costs, less incentives received.
• Payments in arrears: interest = opening liability × rate; closing = opening + interest − payment.
• Payments in advance: interest = (opening liability − payment made at the start) × rate; closing = opening − payment + interest. The payment reduces the liability before interest accrues for that year.
• Current and non-current split, arrears: non-current = closing liability at the end of next year; current = closing liability now less that figure.
• Current and non-current split, advance: non-current = liability after the next payment is deducted, before next year's interest; current = liability now less that figure. Do not use the end-of-next-year closing balance.
• Depreciate the right-of-use asset over the shorter of lease term and useful life, unless ownership passes.
• Short-term leases (lease term of twelve months or less at commencement, no purchase option) may be expensed if the lessee elects, and the election is made by class of underlying asset. Low-value asset leases may be expensed, elected lease by lease, but the exemption cannot apply if the lessee subleases the asset. Expense the payments straight-line, or on another systematic basis if it is more representative of the benefit pattern.
• In a sale and leaseback, if the transfer is not a sale under IFRS 15, keep the asset and record a financial liability for proceeds.
• If it is a sale at fair value, right-of-use asset = carrying amount × (PV of lease payments ÷ fair value). Gain recognised = total gain × (fair value − PV of lease payments) ÷ fair value, where total gain = fair value − carrying amount. If the sale price differs from fair value, adjust first: a shortfall is a prepayment of lease payments, and an excess is additional financing.
• Statement of cash flows: interest is classified as operating or financing in line with the entity's IAS 7 policy; the capital element of the payment is a financing outflow.

Common mistakes

• Treating any contract to use an asset as a lease. Fix: Always run the three control tests. A service contract can involve an asset without conveying control.
• Ignoring the supplier's substitution right. Fix: Check it first. If the right is substantive, there is no identified asset and no lease.
• Adding initial direct costs to the lease liability. Fix: Direct costs are paid to third parties. They increase only the right-of-use asset, with the credit going to cash.
• Discounting the first payment when it is made on day one. Fix: A payment at commencement has t = 0, so its present value is the full payment. Discount only later payments.
• Charging interest on the full opening balance when payments are in advance. Fix: Deduct the first-day payment first, then multiply the remainder by the rate.
• Using the annual payment as the current liability. Fix: The payment includes interest. Current liability is the fall in the liability: this year's closing less next year's closing.
• Treating every sale and leaseback as a sale. Fix: Always test for control first. A repurchase option at a fixed price is a red flag. If it is not a sale, record a financial liability and recognise no gain.
• Recognising the whole gain in profit or loss. Fix: Under IFRS 16 recognise only the gain relating to the rights transferred: total gain × (FV − PV) ÷ FV.
• Treating a lease as short-term because only part of it falls in the current year. Fix: Measure the lease term from commencement. A 24-month lease is not short-term even if only 6 months fall in this period.
• Judging low value by the age or current value of the asset. Fix: Use the value of the asset when new. A used asset that was costly new is not low value.

Exam tips

• In scenarios, hunt for the substitution clause, the exclusivity wording and who decides use. These are the facts the examiner plants.
• Write the conclusion for each of the three tests in a short line. Marks follow each test, not just the final answer.
• In objective tests, check the exemption traps: purchase option, value when new, and whether the asset is part of a larger set.
• Say that the exemptions are elections and the expense is normally straight-line. Do not say they are compulsory.
• When a contract bundles services, say the price is allocated between lease and non-lease components.
• Write the list of included and excluded items first. OT questions often hide a deposit or a sales-based rent to trap you.
• Check whether payments are in advance or in arrears before choosing any factor. This is the most common slip in annuity questions.
• In constructed response, show each component of the right-of-use asset on its own line. Marks are given for each item.