CMA Final · Strategic Financial Management

Leasing Decisions: formula sheet

Full chapter guide

Key formulas

Classification test: Risks and rewards of ownership substantially with lessee → Finance lease; otherwise → Operating lease; Decide by substance. Indicators: lease term covers most of asset life, ownership or purchase option at a low price, non-cancellable, lessee bears maintenance.
Leveraged lease structure: Asset cost = Lessor's equity + Lender's loan; Three parties. Lender usually has recourse only to the asset and rentals, not to the lessor's other assets.
Sale and leaseback cash effect: Cash inflow to seller-lessee = Sale price; then outflow = periodic lease rentals; Use of the asset continues without a break.
Discount rate for lease vs buy: Kd (after tax) = Kd × (1 − t); Lease and loan flows are fairly certain, so the after-tax cost of debt is the usual discount rate.
Net advantage of leasing (NAL): NAL = PV of cost of buying − PV of cost of leasing; Positive NAL means lease. Express both as costs on the same basis.
After-tax lease rental: Rental × (1 − t); Use when rentals are tax-deductible and the firm pays tax.
Tax shield on depreciation: Depreciation × t; Applies only under buying, since the lessee does not claim depreciation on a leased asset.
After-tax cost of debt (discount rate): Kd after tax = Pre-tax interest rate × (1 − t); Use this to discount both the lease and the buy cash flows, unless the question gives a different rate.
After-tax lease rental: Rental × (1 − t); The rental is tax-deductible. If rentals are paid at the start of each year, discount them from year 0.
Depreciation tax shield: Depreciation × t; Depreciation itself is not a cash flow. Use the depreciation as per the question's method (SLM or WDV).
Present value of cost of buying: Purchase price − PV of depreciation tax shield − PV of after-tax salvage value; Add maintenance or other costs only if they differ between the two options. Interest on the loan is ignored because the discount rate already covers it.
Present value of cost of leasing: Σ [Rental × (1 − t)] ÷ (1 + Kd after tax)^n; Add lessee-borne costs (such as a security deposit, net of its refund) if the question gives them.
Net advantage to leasing (NAL): NAL = PV cost of buying − PV cost of leasing; If NAL > 0, lease. If NAL < 0, buy. The same result comes from PV of leasing outflows vs PV of buying outflows.
Net outflow at time zero: Outflow = Cost of asset + initial expenses (if given); Treat it as a cash outflow at year 0. Ignore it if the question gives no initial expenses.
After-tax rental: After-tax rental = Rental × (1 − t); t is the lessor's tax rate. Rentals are taxable income.
Depreciation tax shield: Tax shield = Depreciation × t; Use the depreciation method and rate stated in the question. It is a tax saving, not depreciation itself.
Lessor's NPV: NPV = Σ [Rental × (1 − t) + Depreciation × t] ÷ (1 + k)^n + PV of residual value − Cost of asset; k is the post-tax required return. Tax on residual value applies only if the question or tax rules give it. Add tax effects only where the problem supports them.
Lessor's IRR (yield): IRR is the k at which NPV = 0; Find it by trial at two rates and interpolate: IRR ≈ L + NPV(L) ÷ [NPV(L) − NPV(H)] × (H − L).
Break-even (minimum) rental: After-tax rental = [Cost − PV of tax shield − PV of residual value] ÷ PV annuity factor; Pre-tax rental = After-tax rental ÷ (1 − t); Valid when rentals are level. If rentals fall at the beginning of each year, use the matching factors.
Equated annual charge: EAC = PV of net cash outflows ÷ PVAF(r, n); Use the after-tax discount rate and the asset's own life n. Choose the option with the lower EAC when the options are costs only.
Break-even lease rental (annual, in arrears): L × (1 − t) × PVAF(r, n) = PV of net cost of buying; Solve for L. Use this form when rentals are fully tax-deductible and paid at year end. Adjust the timing if rentals are paid in advance.
Net cost of buying: Cost of asset − PV of depreciation tax shield − PV of after-tax salvage value + PV of after-tax costs borne only under purchase; Include running costs only if they differ between lease and buy.
Lease liability (Ind AS 116): Lease liability = Σ [Lease payment ÷ (1 + r)^t]; r is the rate implicit in the lease, or the incremental borrowing rate if that cannot be readily determined.
Lessee's subsequent charges: Interest = Opening lease liability × r; Depreciation = Right-of-use asset ÷ shorter of lease term and useful life; Depreciation applies to the right-of-use asset. Where ownership transfers at the end, use the asset's useful life.

Quick revision

In a finance lease the lessee bears most risks and rewards of ownership; an operating lease is short term and the lessor bears them.
Sale and leaseback means selling an owned asset and taking it back on lease.
Lease or buy: compare present values of after-tax cash outflows under each option.
Rentals are tax deductible, so the lessee's relevant outflow is rental × (1 − tax rate), unless the question states otherwise.
Under buying, count the loan repayment or purchase cost, depreciation tax shield and salvage value.
Discount at the after-tax cost of debt when the lease is treated as a debt substitute.
Choose the option with the lower present value of net cost.
Lessor's view: accept if the NPV of rentals, tax and residual value is not negative against the asset cost.
Equated annual charge = present value of cost ÷ annuity factor; the lower charge is preferred.
Break-even lease rental is the rental at which the lessee is indifferent between leasing and buying.
Cross-border leasing adds exchange rate, tax treaty and legal issues.
State the recommendation clearly at the end of every numerical answer.

Common mistakes

Classifying a lease by its name in the contract. Fix: Classify by substance: look at who bears the risks and rewards of ownership.
Saying ownership always transfers in a finance lease. Fix: Legal title may stay with the lessor. What passes is substantially all risks and rewards, with or without title transfer.
Mixing lessee and lessor advantages in one list. Fix: Write the role at the top of the answer and keep points separate.
Claiming leasing is always cheaper. Fix: Say the total cost is decided by comparing PV of after-tax costs. Leasing often costs more overall.
Discounting at the company's WACC or the pre-tax interest rate Fix: Use the after-tax cost of debt, pre-tax rate × (1 − t), unless the question names a different rate.
Treating depreciation as a cash outflow or inflow Fix: Only the tax saved, depreciation × t, is a cash flow. Add nothing for the depreciation itself.
Discounting at a pre-tax rate while using after-tax cash flows. Fix: Check the rate. Post-tax flows need a post-tax rate. Convert as pre-tax × (1 − t) if the question gives only a pre-tax rate.
Treating the full depreciation as a cash inflow. Fix: Only the tax saved is a cash inflow: depreciation × t. Depreciation itself is non-cash.
Comparing the NPV of costs of assets with unequal lives without adjusting for life. Fix: Convert each present cost to EAC using its own life. Then compare the yearly figures.
Dividing by the annuity factor for the wrong number of years. Fix: Use each asset's own life and the same discount rate. Write n beside each division.

Exam tips

In case scenarios, quote the facts that decide the classification, such as lease term, cancellability and who maintains the asset.
Write differences between finance and operating lease as a two-column style list of points: term, cancellation, maintenance, risk, recovery of cost.
Know one real-life example for each type; examiners like application.
Leveraged lease is often asked in short notes. Mention three parties, partial equity, non-recourse loan and costly assets.
This topic leads into lessee and lessor evaluation numericals, so be ready to link the type of lease to the rental calculation.
Read whether the question asks for the lessee, the lessor or both, and structure the answer accordingly.
In theory answers, give 4 to 5 points each for advantages and limitations, then add the evaluation factors.
In numericals, state the discount rate and why you chose it.