1. Overview & Key Terms
Lease financing is a significant source of medium- and long-term funding. In this arrangement, the owner of an asset grants another party the right to use that asset in exchange for periodic payments. The owner of an asset (the Lessor) grants another party (the Lessee) the right to use that asset in exchange for periodic payments known as Lease Rents.
Every lease contract rests on four basic elements:
- Two parties (Lessor and Lessee)
- The leased asset
- The lease period
- The lease rent
Types of leases include: Operating lease, Financial lease, Direct leasing, Sale-and-leaseback, and Leveraged leases.
2. Merits of Leasing
WHY LEASING CAN BE ATTRACTIVE
Mnemonic: A Fine Horse is in Action
- Avoids cost of obsolescence – The lessor bears the risk of the asset becoming outdated.
- Avoids restrictive covenants – Lease contracts rarely impose tight operational restrictions.
- Financial flexibility – Leasing frees up capital and keeps borrowing lines intact.
- Hundred percent financing – No down payment is usually required.
- Increases liquidity – Little or no upfront cash is tied up.
- Improves ratios – Keeps debt off the balance sheet.
- Advances in case of bankruptcy – Lease obligations may be treated more favorably than secured debt.
3. Demerits of Leasing
LIMITATIONS TO REMEMBER
Mnemonic: Every Lease Prohibits Loss
- Expensive – Lease rentals often exceed the asset’s purchase price.
- Loss of salvage value – Residual value goes to the lessor.
- Prohibited from making improvements – Lessees usually cannot alter the asset.
- Loss of ITC and tax saving on depreciation – The lessee misses out on tax benefits.
4. Repair & Maintenance: Lease vs. Buy
Under Leasing: If the lease is "maintenance-inclusive", the lessee pays a single consolidated lease rental. The lessor bears the upkeep, making the cost fixed and predictable.
Under Borrowing & Buying: The firm assumes full responsibility for repairs. These are real cash outflows, and although tax-deductible, they increase the net after-tax cost of borrowing.
Conclusion: The purchase option incurs additional after-tax maintenance outflows, making the borrowing route relatively more expensive.
5. Why After-Tax Cost of Debt is Used as Discount Rate
The appropriate discount rate for evaluating lease-versus-buy decisions is the firm's after-tax cost of debt. The rationale rests on two core points:
- Comparable Risk: Most lease-related cash flows—such as lease rentals, maintenance costs, and residual obligations—are fixed by contract and legally binding. They are not speculative like equity returns. Hence, the risk profile of these cash flows closely matches the risk associated with the firm's debt obligations, not its equity.
- Debt Substitute: Leasing is widely viewed as a substitute for borrowing. When a firm enters into a lease, it commits to a stream of fixed payments, much like servicing a loan. Therefore, the discount rate should reflect the cost of the financing option it replaces—i.e., debt.
Additionally, we use the after-tax cost of debt (Kd × (1 − Tax rate)) to account for the tax shield on interest payments. Since lease rentals are typically tax-deductible, and debt interest also enjoys tax deductibility, applying the after-tax rate ensures consistency and a fair comparison between the two alternatives.
6. Evaluation Formulas & Formats (For Exam)
EXAM CALCULATION FLOW
1. Identify Data→
2. Calculate After-Tax Kd→
3. Find PV / NAL / IRR→
4. Apply Decision Rule
*Use these exact tables and formulas for your exam paper. Kd = After-tax cost of debt.
I. Net Advantage to Leasing (NAL)
NAL = Cost of owning - Cost of leasing
NAL = -Io + [ITC + Dt × T × PVIF(kd, n)] + [SVn × PVIF(kd, n)] - [Lt(1 - T) × PVIF(kd, n)] - [Ot(1 - T) × PVIF(kd, n)]
NAL = -Io + [ITC + Dt × T × PVIF(kd, n)] + [SVn × PVIF(kd, n)] - [Lt(1 - T) × PVIF(kd, n)] - [Ot(1 - T) × PVIF(kd, n)]
Where:
- Io = Investment cost
- ITC = Investment Tax Credit
- Dt = Depreciation for the t-th year
- SVn = Estimated after-tax salvage value of the asset in year n
- Ot = Operating costs at time t
- Lt = Lease rentals at time t
- T = Tax rate
| Decision Rule | Action |
|---|---|
| NAL is positive | Lease the asset |
| NAL is negative | Buy the asset |
II. Internal Rate of Return (IRR) for Leasing
Io - ITC - Dt(T) × PVIF(IRR, n) - SVn × PVIF(IRR, n) - Lt(1-T) × PVIF(IRR, n) = 0
| Decision Rule | Action |
|---|---|
| IRR < Kd (After-tax cost of debt) | Lease the asset |
| IRR > Kd | Buy the asset |
III. Evaluation of Lease by Lessor
Step 1: Compute the present value of cash outflows from ownership benefits (PV of ownership benefits) using the lessor's after-tax required rate of return.
PV of ownership benefits = [ITC + Dep × T × PVIF(A kd, n)] + [SVn × PVIF(kd, n)]
Step 2: Net amount to be recovered = Io - PV of ownership benefits.
Step 3: After-tax Lease (ATL) = Net amount to be recovered / PVIF(A kd, n).
Step 4: Lt = ATL / (1 - T)
PV of ownership benefits = [ITC + Dep × T × PVIF(A kd, n)] + [SVn × PVIF(kd, n)]
Step 2: Net amount to be recovered = Io - PV of ownership benefits.
Step 3: After-tax Lease (ATL) = Net amount to be recovered / PVIF(A kd, n).
Step 4: Lt = ATL / (1 - T)
Alternative Method for Lessor:
NPV(lessor) = -Io + [ITC + Dep × T × PVIF(A kd, n)] + [SVn × PVIF(kd, n)] + [Lt(1-T) × PVIF(A kd, n)]
Or, Lt = [Io - SVn × PVIF(kd, n) - ITC - Dep × T × PVIF(A kd, n)] / [PVIF(A kd, n) × (1-T)]
Or, Lt = [Io - SVn × PVIF(kd, n) - ITC - Dep × T × PVIF(A kd, n)] / [PVIF(A kd, n) × (1-T)]
IV. Cost of Owning vs. Buying (Case 1: Payments at End of Year)
Step 1: PV of Lease alternative.
PV(L) = Lt(1 - T) × PVIF(A kd, n)
Step 2: PV of Purchase alternative (Borrow and Buy).
PV(L) = Lt(1 - T) × PVIF(A kd, n)
Step 2: PV of Purchase alternative (Borrow and Buy).
- Calculate annual loan payment: PVA = PMT × PVIF(A kd, n)
- Prepare Loan Amortization Schedule:
Due to rounding, the calculated value of the final principal reduction would not fully repay the loan; therefore the actual remaining principal repayment has been included.
Year Installment Interest Principal Loan Balance 0 - - - - 1 - - - - 2 - - - - 3 - - - - - Calculate After-tax cash flows:
Year (1) Installment (2) Dep (3) Int (4) Tax Shield (5) = [(3)+(4)]×T After-tax maint. cost (6) Salvage Value (7) After-tax cash outflows (8) = (2)+(6)-(5)-(7) 1 - - - - - - - 2 - - - - - - - 3 - - - - - - - - Calculate PV of purchase alternative:
Year (1) After-tax cash flow (2) PVIF @ kd (3) PV (4) = (2)×(3) 1 - - - 2 - - - 3 - - -
Step 3: Choose the alternative with the lower present value of cash outflows.
Alternative Method for PV of Borrow-Purchase:
PV(P) = Io - [ITC + D × T × PVIF(A kd, n)] + [After-tax maintenance costs × PVIF(A kd, n)] - [Salvage value × PVIF(kd, n)]
PV(P) = Io - [ITC + D × T × PVIF(A kd, n)] + [After-tax maintenance costs × PVIF(A kd, n)] - [Salvage value × PVIF(kd, n)]
V. Case 2: If Lease and Loan Payments are Made in Advance
Step 1: PV of Lease alternative.
PV(L) = Lt + Lt(1-T) × PVIF(A kd, n-1) - Lt × T × PVIF(kd, n)
Step 2: PV of Purchase alternative.
i) Calculate payment: PVA = PMT × PVIF(A kd, n) × (1 + kd)
ii) Prepare Amortization Schedule
PV(L) = Lt + Lt(1-T) × PVIF(A kd, n-1) - Lt × T × PVIF(kd, n)
Step 2: PV of Purchase alternative.
i) Calculate payment: PVA = PMT × PVIF(A kd, n) × (1 + kd)
ii) Prepare Amortization Schedule
7. Sources of Value in Leasing
Capital Market
Bankruptcy Cost
Different Taxes
Market Equilibrium
- Lease financing in perfect capital markets.
- Bankruptcy costs to lender or lessor.
- Effect of differing taxes.
- Market equilibrium process.
8. Factors Affecting Leasing vs. Owning Decision
Quick memory point: When comparing leasing and owning, focus on rate of return, maintenance, salvage value, obsolescence, tax and depreciation.
- Different required rate of return of lessee and lessor.
- Maintenance cost.
- Expected salvage value.
- Obsolescence cost.
- Tax rate.
- Method of depreciation.
9. Solved Exam Numerical Examples
PRACTICE PROBLEMS & STEP-BY-STEP SOLUTIONS
Example 1: Payments Payable at End of Each Year (Case 1)
Question: A firm wishes to acquire a machine costing Rs 1,000,000 with a useful life of 5 years. It can lease the asset for annual lease payments of Rs 300,000, payable at the end of each year for 5 years. Alternatively, the firm can borrow funds at a 10% interest rate to buy the machine, repayable in 5 equal annual end-of-year installments. The machine is depreciated using the straight-line method to zero, with an expected salvage value of Rs 150,000 at the end of Year 5. The corporate tax rate is 40%. Which alternative should the firm choose using the after-tax cost of debt as the discount rate?
Solution:
Given:
- Cost of machine (Io) = Rs 1,000,000
- Life of machine (n) = 5 years
- Annual lease rental (Lt) = Rs 300,000 (payable at end of year)
- Before-tax interest rate (Kd) = 10%
- Tax rate (T) = 40% (0.40)
- Expected salvage value (SV5) = Rs 150,000
- Annual depreciation = Cost / n = Rs 1,000,000 / 5 = Rs 200,000
- After-tax cost of debt (KdT) = Kd × (1 − T) = 10% × (1 − 0.40) = 6%
Step 1: PV of Lease Alternative
PV(L) = Lt × (1 - T) × PVIFA(6%, 5 yrs)
PV(L) = Rs 300,000 × (1 - 0.40) × 4.2124
PV(L) = Rs 180,000 × 4.2124 = Rs 758,232.00
PV(L) = Rs 300,000 × (1 - 0.40) × 4.2124
PV(L) = Rs 180,000 × 4.2124 = Rs 758,232.00
Step 2: PV of Borrowing and Buying Alternative
i) Calculate Annual Loan Payment (PMT):
Loan = PMT × PVIFA(10%, 5 yrs)
Rs 1,000,000 = PMT × 3.7908
PMT = Rs 1,000,000 / 3.7908 = Rs 263,796.56
Rs 1,000,000 = PMT × 3.7908
PMT = Rs 1,000,000 / 3.7908 = Rs 263,796.56
ii) Loan Amortization Schedule:
| Year | PMT (Installment) | Interest (10%) | Principal Repayment | Balance of Loan |
|---|---|---|---|---|
| 0 | - | - | - | Rs 1,000,000.00 |
| 1 | Rs 263,796.56 | Rs 100,000.00 | Rs 163,796.56 | Rs 836,203.44 |
| 2 | Rs 263,796.56 | Rs 83,620.34 | Rs 180,176.22 | Rs 656,027.22 |
| 3 | Rs 263,796.56 | Rs 65,602.72 | Rs 198,193.84 | Rs 457,833.38 |
| 4 | Rs 263,796.56 | Rs 45,783.33 | Rs 218,013.22 | Rs 239,820.16 |
| 5 | Rs 263,796.56 | Rs 23,976.40 | Rs 239,820.16 | Rs 0.00 |
iii) Calculate After-Tax Cash Flows (CFAT):
| Year | PMT | Interest | Depreciation | Tax Shield = (Dep + Int) × T | CFAT = PMT - Tax Shield |
|---|---|---|---|---|---|
| 1 | Rs 263,796.56 | Rs 100,000.00 | Rs 200,000.00 | Rs 120,000.00 | Rs 143,796.56 |
| 2 | Rs 263,796.56 | Rs 83,620.34 | Rs 200,000.00 | Rs 113,448.14 | Rs 150,348.42 |
| 3 | Rs 263,796.56 | Rs 65,602.72 | Rs 200,000.00 | Rs 106,241.09 | Rs 157,555.47 |
| 4 | Rs 263,796.56 | Rs 45,783.33 | Rs 200,000.00 | Rs 98,313.33 | Rs 165,483.23 |
| 5 | Rs 263,796.56 | Rs 23,976.40 | Rs 200,000.00 | Rs 89,590.56 | Rs 174,206.00 |
iv) Calculate Present Value of Outflows (@ KdT = 6%):
| Year | CFAT | PVIF @ 6% | Present Value (PV) |
|---|---|---|---|
| 1 | Rs 143,796.56 | 0.9434 | Rs 135,657.67 |
| 2 | Rs 150,348.42 | 0.8900 | Rs 133,810.09 |
| 3 | Rs 157,555.47 | 0.8396 | Rs 132,283.57 |
| 4 | Rs 165,483.23 | 0.7921 | Rs 131,079.27 |
| 5 | Rs 174,206.00 | 0.7473 | Rs 130,184.13 |
| PV of Purchasing Cost before Salvage Value: | Rs 663,014.73 | ||
| Less: PV of After-Tax Salvage Value | Rs 150,000 × 0.7473 | (Rs 112,095.00) | |
| Net Present Value of Purchasing Cost: | Rs 550,919.73 | ||
Decision: Since the Present Value of cash outflows for borrowing and buying (Rs 550,919.73) is less than the PV of leasing (Rs 758,232.00), the company should borrow and buy the machine.
Example 2: Payments Made in Advance with MACRS Depreciation (Case 2)
Question: Nepal Leasing Company wishes to acquire an asset of Rs 100,000. It has a useful life of 8 years with a scrap value of Rs 8,000. The asset falls into the 5-year property class under MACRS (Depreciation rates: Year 1 = 20%, Year 2 = 32%, Year 3 = 19%, Year 4 = 12%, Year 5 = 11%, Year 6 = 6%). The company can use either lease or debt financing; lease payments of Rs 16,000 at the beginning of each of the 8 years are required. If debt-financed, the interest rate would be 14%, and mortgage payments would be due at the beginning of each of the 8 years. Tax rate = 40%. Which financing method has the lower present value of cash outflows?
Solution:
Given:
- Cost of asset (Io) = Rs 100,000
- Life of asset (n) = 8 years
- Annual advance lease rent (Lt) = Rs 16,000
- Interest rate on debt (Kd) = 14% (Payment in advance)
- Tax rate (T) = 40% (0.40)
- Scrap value (SV8) = Rs 8,000
- After-tax cost of debt (KdT) = Kd × (1 − T) = 14% × (1 − 0.40) = 8.4%
Step 1: PV of Lease Alternative (Advance Payments)
PV(L) = L0 + Lt × (1 - T) × PVIFA(8.4%, n-1) - Lt × T × PVIF(8.4%, n)
PV(L) = Rs 16,000 + Rs 16,000 × (1 - 0.40) × PVIFA(8.4%, 7) - Rs 16,000 × 0.40 × PVIF(8.4%, 8)
PV(L) = Rs 16,000 + Rs 9,600 × 5.1359 - Rs 6,400 × 0.5245
PV(L) = Rs 16,000 + Rs 49,304.64 - Rs 3,356.80 = Rs 61,947.84
PV(L) = Rs 16,000 + Rs 16,000 × (1 - 0.40) × PVIFA(8.4%, 7) - Rs 16,000 × 0.40 × PVIF(8.4%, 8)
PV(L) = Rs 16,000 + Rs 9,600 × 5.1359 - Rs 6,400 × 0.5245
PV(L) = Rs 16,000 + Rs 49,304.64 - Rs 3,356.80 = Rs 61,947.84
Step 2: PV of Borrowing & Buying Alternative (Advance Loan Payments)
i) Calculate Annual Advance Loan Installment (PMT):
Loan = PMT × PVIFA(14%, 8 yrs) × (1 + Kd)
Rs 100,000 = PMT × 4.6389 × 1.14
Rs 100,000 = PMT × 5.2883
PMT = Rs 100,000 / 5.2883 = Rs 18,909.67
Rs 100,000 = PMT × 4.6389 × 1.14
Rs 100,000 = PMT × 5.2883
PMT = Rs 100,000 / 5.2883 = Rs 18,909.67
ii) Loan Amortization Schedule (Advance Installments):
| Year | PMT | Interest (14%) | Principal Repayment | Loan Balance |
|---|---|---|---|---|
| 0 | Rs 18,909.67 | - | Rs 18,909.67 | Rs 81,090.33 |
| 1 | Rs 18,909.67 | Rs 11,352.65 | Rs 7,557.02 | Rs 73,533.31 |
| 2 | Rs 18,909.67 | Rs 10,294.66 | Rs 8,615.01 | Rs 64,918.30 |
| 3 | Rs 18,909.67 | Rs 9,088.56 | Rs 9,821.11 | Rs 55,097.19 |
| 4 | Rs 18,909.67 | Rs 7,713.61 | Rs 11,196.06 | Rs 43,901.13 |
| 5 | Rs 18,909.67 | Rs 6,146.16 | Rs 12,763.51 | Rs 31,137.62 |
| 6 | Rs 18,909.67 | Rs 4,359.27 | Rs 14,550.40 | Rs 16,587.22 |
| 7 | Rs 18,909.67 | Rs 2,322.45 | Rs 16,587.22 | Rs 0.00 |
| 8 | - | - | - | - |
iii) Calculate After-Tax Cash Outflows & Present Value Schedule (@ KdT = 8.4%):
*After-tax Salvage Value (SV8) = Cash Salvage Value × (1 − T) = Rs 8,000 × (1 − 0.40) = Rs 4,800.
| Year | PMT (1) | Interest (2) | Depreciation (3) | Tax Shield (4) = [(3)+(2)]×T | After-tax SV (5) | CFAT (6) = (1)-(4)-(5) | PVIF @ 8.4% (7) | PV (8) = (6)×(7) |
|---|---|---|---|---|---|---|---|---|
| 0 | Rs 18,909.67 | - | - | - | - | Rs 18,909.67 | 1.0000 | Rs 18,909.67 |
| 1 | Rs 18,909.67 | Rs 11,352.65 | Rs 20,000 | Rs 12,541.06 | - | Rs 6,368.61 | 0.9225 | Rs 5,875.04 |
| 2 | Rs 18,909.67 | Rs 10,294.66 | Rs 32,000 | Rs 16,917.86 | - | Rs 1,991.81 | 0.8510 | Rs 1,695.03 |
| 3 | Rs 18,909.67 | Rs 9,088.56 | Rs 19,000 | Rs 11,235.42 | - | Rs 7,674.25 | 0.7851 | Rs 6,025.05 |
| 4 | Rs 18,909.67 | Rs 7,713.61 | Rs 12,000 | Rs 7,885.44 | - | Rs 11,024.23 | 0.7242 | Rs 7,983.75 |
| 5 | Rs 18,909.67 | Rs 6,146.16 | Rs 11,000 | Rs 6,858.46 | - | Rs 12,051.21 | 0.6681 | Rs 8,051.41 |
| 6 | Rs 18,909.67 | Rs 4,359.27 | Rs 6,000 | Rs 4,143.71 | - | Rs 14,765.96 | 0.6163 | Rs 9,100.26 |
| 7 | Rs 18,909.67 | Rs 2,322.45 | - | Rs 928.98 | - | Rs 17,980.69 | 0.5686 | Rs 10,223.82 |
| 8 | - | - | - | - | Rs 4,800 | (Rs 4,800.00) | 0.5245 | (Rs 2,517.60) |
| Present Value of Cost of Buying: | Rs 65,346.43 | |||||||
Decision: The lease financing method has the lower present value of cash outflows (Rs 61,947.84 vs. Rs 65,346.43). Therefore, the company should choose to lease the asset.
Chapter Summary: Lease Financing at a Glance
ConceptLessor gives the lessee the right to use an asset for lease rent.
Core ComparisonCompare the present value of leasing with the present value of buying.
NAL RulePositive NAL → Lease | Negative NAL → Buy.
IRR RuleIRR below Kd → Lease | IRR above Kd → Buy.
Key Discount RateUse the after-tax cost of debt for the comparison.
Exam ApproachIdentify timing first: payments at end or payments in advance.
