Lecture 9: Leasing

Overview of Lease Contracts

• A lease is a contractual agreement between a lessee and a lessor, granting the lessee the right to use an asset for a specified period in exchange for regular payments.
• The lessor retains legal ownership of the asset.
• Lease contracts may include:
  • End-of-term purchase or renewal options
  • Cancellation conditions
  • Responsibilities for maintenance and servicing

Types of Lease Contracts

• Sales-type leases: The lessor is the manufacturer or authorized dealer, often bundled with services.
• Direct leases: A third-party leasing company buys an asset and leases it to the lessee.
• Sales and leasebacks: A firm sells an asset it owns and leases it back.
• Leveraged leases: A lender funds the asset acquisition, and lease payments cover principal and interest.
• Synthetic leases: A special-purpose entity (SPE) acts as lessor for specific accounting or tax treatment.

Leasing Versus Borrowing in a Perfect Capital Market

• In a perfect capital market:

  • No taxes, transaction costs, or information asymmetries
  • Competitive pricing among lessors

• The fair lease payments ensures that the lessor breaks even:

  $PV(Lease payments) = Purchase price - PV(Residual value)$

• Alternative Option: Borrow to purchase, where:

  $PV(Loan repayments) = Purchase price$

• Combined Expression (Law of One Price):

  $PV(Lease payments) + PV(Residual value) = PV(Loan repayments)$

• In a perfect capital market, leasing with a residual value purchase is equivalent to borrowing to buy, costing the same.

• A loan finances the entire asset; a lease only finances the depreciation over the lease term.

• Lease payments are typically made at the beginning of each period (annuity due).

• The present value of lease payments:

  $PV(Lease payments) = (1 + i)L \frac{1 - (1 + i)^{-n}}{i}$

  • Where:
    • $L$ is the periodic lease payment
    • $i$ is the discount rate per lease period
    • $n$ is the number of lease periods

Example

• A logistics firm needs a $12,000 drone for three years; the residual value is $3,000.

• The risk-free interest rate is 4.8% p.a. with monthly compounding ($i = 0.4$ per month).

• There are $n = 3 \times 12 = 36$ monthly lease payments.

• Calculation of the monthly lease payment:

  L^* = \frac{0.004}{1.004 \times (1 - 1.004^{-36})} \times (12,000 - \frac{3,000}{1.004^{36}}) \approx $281.77

• If the firm borrowed $12,000, monthly loan repayments would be:

  PMT = \frac{12,000 \times 0.004}{1 - 1.004^{-36}} \approx $358.57

• Loan repayments exceed lease payments as they fund the drone's full value.

End-of-Term Lease Options and Other Lease Provisions

Fair Market Value Leases

• The lessee can purchase the asset at the end of the lease at its fair market value (FMV).
• The contract specifies a procedure for determining FMV, often involving an independent valuation.
• In a perfect capital market, this option has no impact on lease value.
  • Buying at fair market value is a zero-NPV transaction.

Finance Leases

• A finance lease (or $1 out lease) transfers ownership to the lessee at lease-end for a nominal price.
• The lessee pays for the asset over its full useful life through lease installments.
• Economically similar to a loan-financed purchase.

Fixed Price Leases

• The lessee has the option to buy the asset for a fixed price written into the lease contract.
• Common in consumer markets (e.g., car leases).
• The lessee benefits from a valuable option:
  • If the market value exceeds the fixed price, the asset can be purchased at a discount.
  • If the market value is less than the fixed price, the lessee can walk away.
• The lessor typically charges a higher lease rate to compensate for this embedded option.

Fair Market Value Cap Leases

• The lessee can buy the asset for whichever is less:
  • The fair market value of the asset
  • A predetermined cap price
• Combines flexibility of an FMV lease with the price protection of a fixed price lease.

Other Lease Provisions

• Early cancellation options
• Buyout options
• Upgrade options
• These features are tailored to the lessee’s needs, asset characteristics, and preferences.

Valuation Effects of Lease Provisions

• Provisions that enhance lessee flexibility (e.g., early termination, upgrade options) increase lease payments.
• Provisions that restrict lessee flexibility reduce lease payments.
• In a perfect capital market, leasing remains a zero-NPV financing method, even with additional lease provisions.
• The Modigliani-Miller proposition applies.
• A lease simply reallocates cash flows and risks between the lessee and lessor.

Example

• A firm leases a server worth $25,000 for 3 years, with monthly payments made in advance.
• The residual value of the server at the end of the lease is $7,000.
• The risk-free rate is 5.4% p.a. with monthly compounding (i = 0.045% per month).
• There are n = 3 × 12 = 36 monthly lease payments.
• Comparison of three leases:
  • Fair market value lease
  • Finance lease with a $1 buyout
  • Fixed price lease with a $5,000 purchase option

Option A: Fair Market Value Lease

• The lessee returns the asset or may purchase it at the fair market value of $7,000.

• The fair lease is:

  L^* = \frac{0.0045}{1.0045 \times (1 - 1.0045^{-36})} \times (25,000 - \frac{7,000}{1.0045^{36}}) \approx $574.21

Option B: Finance Lease with $1 Buyout

• The lessee obtains full ownership for a nominal residual value ($1).

• The entire asset value must be recovered via lease payments.

• The fair lease using the same formula:

  L^* = \frac{0.0045}{1.0045 \times (1 - 1.0045^{-36})} \times (25,000 - \frac{1}{1.0045^{36}}) \approx $750.37

Option C: Fixed Price Lease

• The lessee can buy the server for $5,000 at lease end.

• Purchase is assumed to occur, given a known market value of $7,000.

  L^* = \frac{0.0045}{1.0045 \times (1 - 1.0045^{-36})} \times (25,000 - \frac{5,000}{1.0045^{36}}) \approx $622.71

Tax and Accounting Aspects of Leases

Operating Leases

• Treated like a rental agreement for accounting purposes.
• The lessee:
  • Reports lease payments as operating expenses on the income statement.
  • Does not report the leased asset or lease liability on the balance sheet.
  • Does not claim depreciation; the asset remains off-balance-sheet.
• Lease details are disclosed in the footnotes of the financial statements.
• Tax treatment:
  • Lease payments are fully tax-deductible for the lessee, providing a tax shield.
  • The lessor includes the payments as taxable income and claims depreciation deductions.
  • The lessor receives the depreciation tax shield as the asset owner.

Capital Leases

• A capital lease (or finance lease) is treated as if the lessee purchased the asset.
• The asset appears on the lessee's balance sheet, with depreciation recorded over its useful life.
• The present value of lease payments is recorded as a liability.
• Each lease payment is split into:
  • Interest expense (reported on the income statement)
  • Principal repayment (reduces the lease liability)
• Tax treatment:
  • The lessee claims depreciation and receives a depreciation tax shield.
  • The interest component of payments is tax-deductible, creating an interest tax shield.
  • The lessor treats interest as taxable income; principal repayment is not taxed.

Accounting standards

• Capital leases increase reported leverage by adding both an asset and a liability to the balance sheet.
• Firms have often preferred operating leases to keep obligations off-balance-sheet.
• Criteria to classify a lease as a capital lease:
  • Ownership transfers to the lessee at lease end.
  • The lessee can purchase the asset at a bargain price.
  • The lease term spans 75% or more of the asset’s useful life.
  • The present value of lease payments is 90% or more of the asset’s fair market value.
• These criteria identify leases that effectively transfer the risks and rewards of ownership.
• Accounting standards were reformed to require most leases longer than one year to appear on the balance sheet.
• Updated rules improve transparency by better reflecting a firm's total lease-related commitments.

The Leasing Decision

Leasing with Taxes

• In a perfect capital market, leasing does not affect firm value.
• Market frictions such as taxes can make leasing more or less attractive.
• The impact of taxes on the leasing decision from the lessee’s perspective.

Case Study: TasTech Ltd

• TasTech Ltd is an Australian manufacturer evaluating whether to purchase or lease a surface-mount assembly machine.
• Corporate tax rate: 30%
• Before-tax cost of borrowing: 6% p.a.
• Lease option: five annual payments of $27,000 (operating lease).
  • First payment due immediately.
  • Full lease payment is tax-deductible.
  • No option to purchase the asset at lease end.
• Purchase option:
  • Purchase price: $120,000
  • Depreciated straight-line over 5 years
  • Annual depreciation deduction: $24,000
  • No salvage value expected.

Free Cash Flows

• Compare the free cash flow impact of each option, focusing only on differing cash flows.
• Under leasing:
  • Lease payments are fully tax-deductible.
  • Tax shield: 0.30 \times 27,000 = $8,100 per year.
  • Net cash outflow = $18,900 annually.
• Under purchasing:
  • Initial capital outlay: $120,000 at time 0.
  • Annual straight-line depreciation: $24,000 per year.
  • Tax savings from depreciation: 0.30 \times 24,000 = $7,200 per year.
  • No salvage value at end of year 5.

Free Cash Flow

• Free Cash Flow Consequences of Leasing the Machine

• Free Cash Flow Consequences of Purchasing the Machine

• Leasing spreads costs evenly across the asset’s life through deductible payments.
• Purchasing requires a large upfront outlay and generates tax savings via depreciation over time.

Naive Approach

• Compare the present value of after-tax free cash flows under each option.

• Lease payments are discounted at the firm’s secured borrowing rate.

• TasTech’s cost of borrowing is 6% p.a.

• Present value of the free cash flows from leasing the machine:

  PV(Lease) = -18,900 + \frac{18,900}{1.06} + \frac{18,900}{1.06^2} + \frac{18,900}{1.06^3} + \frac{18,900}{1.06^4} = -18,900 + 18,900 \times \frac{1 - 1.06^{-4}}{0.06} \approx -$84,390

• Present value of the free cash flows from buying the machine:

  PV(Buy) = -120,000 + \frac{7,200}{1.06} + \frac{7,200}{1.06^2} + \frac{7,200}{1.06^3} + \frac{7,200}{1.06^4} + \frac{7,200}{1.06^5} = -120,000 + 7,200 \times \frac{1 - 1.06^{-5}}{0.06} \approx -$89,671

• Leasing appears preferable, but this overlooks that lease obligations increase a firm’s fixed financial commitments.

• Leasing adds leverage to the firm’s capital structure.

• Compare lease versus borrow-and-buy as a more valid method.

Lease-Equivalent Loan

• The lease-equivalent loan has the same financial commitments as the lessee.
• Incremental Free Cash Flows from leasing versus buying

• Treat incremental free cash flows as repayments on the lease-equivalent loan.

• Value the loan using the firm’s after-tax cost of borrowing $r<em>d(1 - \tau</em>c)$.

• Comparison:

  • If the value of the lease-equivalent loan is less than the initial saving from leasing, then leasing is a financial advantage.
  • If the value of the lease-equivalent loan exceeds the initial saving, then borrowing and buying is a financial advantage.

• TasTech’s after-tax cost of borrowing is $0.06 \times (1 - 0.25) = 4.2\%$ p.a.

• Value of the lease-equivalent loan:

  $\frac{26,100}{1.042} + \frac{26,100}{1.042^2} + \frac{26,100}{1.042^3} + \frac{26,100}{1.042^4} + \frac{7,200}{1.042^5} = 26,100 \times \frac{1 - 1.042^{-4}}{0.042} + \frac{7,200}{1.042^5} \approx 100,157$

• Since the value of the lease-equivalent loan is less than the initial saving, leasing is financially more attractive.

• The financial advantage of leasing is 101,100 - 100,157 = $943.

Direct Approach

• Simplify the analysis by directly comparing leasing with a debt-financed purchase.
• Calculate the NPV of incremental free cash flows, using the firm’s after-tax cost of borrowing.
• Comparison:
  • If the NPV is positive, then leasing is advantageous.
  • If the NPV is negative, then borrowing and buying is advantageous.
• The NPV of the incremental free cash flows in the TasTech case:

NPV = 101,100 - \frac{26,100}{1.042} - \frac{26,100}{1.042^2} - \frac{26,100}{1.042^3} - \frac{26,100}{1.042^4} - \frac{7,200}{1.042^5} = 101,100 - 26,100 \times \frac{1 - 1.042^{-4}}{0.042} - \frac{7,200}{1.042^5} \approx $943

• Since the NPV is positive, leasing is financially preferable.

Effective After-Tax Borrowing Rate

• Compare leasing and buying using the effective after-tax borrowing rate implied by a lease.
• This is the IRR on the incremental cash flows from leasing relative to buying.
• Comparison:
  • If the effective after-tax borrowing rate is less than the firm’s after-tax cost of borrow, then leasing is an advantage.
  • If the effective after-tax borrowing rate is greater than the firm’s after-tax cost of borrow, then borrowing and buying is an advantage.
• In the TasTech example, solve for the IRR that sets the NPV of incremental cash flows to zero:

$101,100 - \frac{26,100}{1 + IRR} - \frac{26,100}{(1 + IRR)^2} - \frac{26,100}{(1 + IRR)^3} - \frac{26,100}{(1 + IRR)^4} - \frac{7,200}{(1 + IRR)^5} = 0$

• Solving give $IRR \approx 3.83\%$ p.a.
• Since this is less than TasTech’s after-tax cost of borrowing, leasing offers a financial advantage.

Breakeven Lease

• The breakeven lease identifies when leasing is more cost-effective than borrowing to purchase.
• Assume lease payments $L$ are unknown, the free cash flows from leasing are $-(1 - \tau_c)L$.
• Present value of lease free cash flows:

$PV(Lease FCFs) = -(1 + r<em>d(1 - \tau</em>c))(1 - \tau<em>c)L \frac{1 - (1 + r</em>d(1 - \tau<em>c))^{-n}}{r</em>d(1 - \tau_c)}$

• Compute $PV(Purchase FCFs)$ using the same discount rate.
• The breakeven lease payment $L^*$ is determined by solving the equation $PV(Lease FCFs) = PV(Purchase FCFs)$
• This is the lease payment that makes the firm indifferent between leasing and buying.
• Comparison:
  • If the breakeven lease exceeds the lease specified in the contract, then leasing offers a financial advantage.
  • If the breakeven lease is less than the lease specified in the contract, then borrowing and buying offers a financial advantage.
• For the TasTech example:

• Present value of lease free cash flows:

$PV(Lease FCFs) = -1.042 \times 0.7 \times L\frac{1 - 1.042^{-5}}{0.042} \approx -3.229 \times L$

• Present value of purchase free cash flows:

PV(Purchase FCFs) = -120,000 + \frac{7,200}{1.042} + \frac{7,200}{1.042^2} + \frac{7,200}{1.042^3} + \frac{7,200}{1.042^4} + \frac{7,200}{1.042^5} = -120,000 + 7,200 \times \frac{1 - 1.042^{-5}}{0.042} \approx -$88,126

• The breakeven lease payment:

L^* \approx \frac{88,126}{3.229} \approx $27,292

• Since this exceeds the lease payment of $27,000, leasing is more attractive.

Reasons for Leasing

Valid Arguments for Leasing

Tax Differences

• A tax benefit arises if a lease reallocates the more valuable deductions to the party in the higher tax bracket.
  • If tax depreciation is faster than the lease payment schedule, then leasing is advantageous when the lessor is in a higher tax bracket than the lessee.
  • If tax depreciation is slower than the lease payment schedule, then leasing may offer tax savings when the lessor is in a lower tax bracket than the lessee.

Reduced Resale Costs

• Leasing shifts resale responsibility to the lessor, who is typically more efficient at handling it.
• Leases can reduce adverse selection in resale markets.

Efficiency Gains from Specialisation

• Lessors often operate more efficiently than lessees in maintaining or operating specialised assets.
• Bundling assets with services enables lessors to realise economies of scale and pass on cost savings.
• Leasing bundled services preserves a firm’s flexibility to switch providers, maintaining bargaining power.

Reduced Distress Costs and Increased Debt Capacity

• Lease obligations carry higher priority and lower credit risk than even secured debt.
• The lower risk and higher recovery potential of leases allow lessors to offer more favourable financing terms.
• This advantage is especially important for small firms and firms facing capital constraints.

Transferring Risk

• Leasing allows the risk, such as the uncertainty about the assets residual value, to be shifted to the party best equipped to manage it.
• Small firms with limited capacity to absorb financial uncertainty may prefer to lease rather than buy.

Mitigating Debt Overhang

• Leasing can mitigate debt overhang by providing financing that is effectively senior to existing debt.
• Leasing may enable firms to pursue value-enhancing investments that would otherwise be blocked by debt overhang.

Improved Incentives

• When the lessor is also the manufacturer, retaining residual value risk can align incentives and reduce agency costs.
• However, leasing may also introduce agency problems:
  • Lessees may underinvest in maintenance
• This misalignment can increase costs for the lessor.

Invalid Arguments for Leasing

Avoiding Capital Expenditure Controls

• Managers may prefer leasing to avoid scrutiny associated with large capital expenditures.
• However, this strategy can lead to higher long-term costs if leasing is more expensive than buying.

Preserving Capital

• Leasing is often promoted as offering "100% financing"
• For leasing to provide a real advantage, market imperfections must be present.
  • Financial distress costs
  • Debt overhang
  • Tax asymmetries

Off-Balance-Sheet Financing

• Firms can structure leases to avoid classification as capital leases, keeping them off the balance sheet.
• However, lease obligations are economically equivalent to loans and represent real liabilities.