Introduction & Learning Objectives
This guide is your interactive companion to understanding the core concepts of **Leasing**, based on **Chapter 27 of Ross's textbook**. Leasing is a form of financing that is often an alternative to long-term borrowing. This chapter focuses on how to evaluate the lease-versus-buy decision from a financial perspective.
Learning Objectives (Ross, page 900)
- Define the types of leases and how the IRS qualifies leases.
- Explain the reasons for leasing and the reasons for not leasing.
- Show how to calculate the net advantage of leasing and related issues.
1. Leases and Lease Types
Leasing vs. Buying
The key difference between leasing and buying is that with buying, the firm finances, purchases, and holds title to the asset. With leasing, a separate company (the **lessor**) holds title, but the firm (the **lessee**) uses the asset.
Textbook Link: Ross, Chapter 27, Section 27.1 (Page 901)
Operating vs. Financial Leases
| Characteristic | Operating Lease | Financial Lease |
|---|---|---|
| **Lease Term** | Short-term, shorter than asset's economic life | Long-term, for a major part of asset's life |
| **Amortization** | Partially amortized | Fully amortized (payments cover asset cost) |
| **Maintenance** | Typically lessor's responsibility | Typically lessee's responsibility (triple net) |
| **Cancellation** | Often includes a cancellation option | Generally cannot be canceled without penalty |
Textbook Link: Ross, Chapter 27, Section 27.1 (Pages 902-903)
Exam Hint: Be able to distinguish between these two lease types and understand the rationale behind each. Financial leases are often referred to as **capital leases** in accounting.
Taxes and IRS Guidelines
For lease payments to be tax deductible, the IRS requires the lease to be a **true lease**, not a disguised secured loan. The primary concern of the IRS is to prevent firms from using leases solely for tax avoidance by accelerating deductions.
Textbook Link: Ross, Chapter 27, Section 27.3 (Page 905)
Exam Hint: This concept is vital. Differential tax rates between lessor and lessee can create value. Profitable firms (high tax bracket) are more likely to be lessors, while less profitable firms (low tax bracket) are more likely to be lessees. This was tested in **Question 2 from the May 2023 exam**.
2. Lease-Versus-Buy Analysis
Incremental Cash Flows
The decision to lease or buy should be based on the **incremental after-tax cash flows**. We compare the cash flows if we lease to the cash flows if we buy. **Textbook Link:** Ross, Chapter 27, Section 27.4 (Page 906)
The 3 Key Differences:
- **Initial Cost:** A positive cash flow today from **avoiding** the purchase price.
- **After-Tax Lease Payments:** Negative cash flows for each lease payment.
- **Lost Depreciation Tax Shield:** A negative cash flow for each year's lost tax shield.
Net Advantage to Leasing (NAL)
The **Net Advantage to Leasing (NAL)** is the NPV of the cash flows from leasing instead of buying. The relevant discount rate for this analysis is the firm's **after-tax borrowing rate**. **Textbook Link:** Ross, Chapter 27, Section 27.5 (Page 908)
If NAL > 0, the firm should lease. If NAL < 0, the firm should buy.
Exam Hint:
The after-tax cost of debt is the correct discount rate. The WACC is **not** appropriate for this type of specific financing decision. This concept was tested in **Question 2(b) from the May 2024 exam**.
3. Problems & Solutions
Problem Statement: A diagnostic scanner costs $75,000 and is obsolete in 3 years. You can borrow at 10% or lease for $27,000/year (end of year). Depreciation is straight-line to zero over 3 years. The tax rate is 21%. Should you lease or buy?
Solution:
1. Calculate After-Tax Borrowing Rate:
$r_{after-tax} = 10\% \times (1 - 0.21) = 7.9\%$
2. Calculate Incremental Cash Flows from Leasing vs. Buying:
- Year 0: Avoid purchase cost = +$75,000
- Years 1-3: After-tax lease payment = -$27,000 * (1-0.21) = -$21,330
- Years 1-3: Lost depreciation tax shield = -$25,000 * 0.21 = -$5,250
- Net Cash Flow (Y1-3) = -$21,330 - $5,250 = -$26,580
3. Calculate NAL:
PV of annuity at 7.9% = $26,580 \times 2.551 = $67,798
$NAL = \$75,000 - \$67,798 = +\$7,202
Since the NAL is positive, **you should lease** the scanner.
Problem Statement: In the previous question, what is the NPV of the lease to the lessor? At what lease payment will the lessee and the lessor both break even?
Solution:
NPV to Lessor:
The cash flows to the lessor are the exact opposite of the lessee's cash flows, assuming the same tax rate. From the solution to 27.1, the NPV is **-$7,202**.
Break-Even Lease Payment:
The lessee and lessor will break even when NAL = 0. We need to find the lease payment (LP) that makes the present value of the after-tax lease payments plus the lost depreciation tax shield equal to the initial cost.
PV of After-tax Lease Payments = $LP \times (1-0.21) \times 2.551 = 2.015 \times LP$
PV of Lost Depreciation Tax Shield = $5,250 \times 2.551 = $13,408
Initial Cost = $75,000
We need $75,000 = (2.015 \times LP) + 13,408 \implies 2.015 \times LP = 61,592 \implies LP = $30,567
The break-even lease payment is $30,567 per year.
Problem Statement: An asset costs $745,000 and will be depreciated straight-line over its three-year life. It has no salvage value. The lessor can borrow at 6% and the lessee at 9%. The corporate tax rate is 21% for both.
a. How do different borrowing rates affect the NAL calculation?
b. What set of lease payments will make the lessee and the lessor equally well off?
c. Assume the lessee pays no taxes and the lessor is in the 21% tax bracket. For what range of lease payments does the lease have a positive NPV for both parties?
Solution:
a. Different Borrowing Rates:
The NAL calculation uses the lessee's after-tax borrowing rate as the discount rate. The lessor's NPV calculation uses the lessor's after-tax borrowing rate. The difference in rates can create a mutually beneficial situation where the lessor's gain is greater than the lessee's cost, allowing both parties to benefit by splitting the surplus value.
b. Break-Even Lease Payments:
After-tax borrowing rate for lessee = $9\% \times (1-0.21) = 7.11\%$
After-tax borrowing rate for lessor = $6\% \times (1-0.21) = 4.74\%$
For the **lessee** to break even, the PV of leasing costs must equal the initial cost avoided. We solve for the after-tax lease payment (ATLP).
PV = $745,000$. PV of lost tax shield = $(745,000/3) \times 0.21 \times PVIFA(7.11\%, 3yrs) = 52,150 \times 2.62 = 136,603$.
$745,000 = ATLP \times 2.62 + 136,603 \implies ATLP = \$232,976 \implies LP = \$294,900$
For the **lessor** to break even, the PV of cash flows must equal the initial cost. ATLP = $LP \times 0.79$. PV of Depr. Tax Shield = $52,150 \times PVIFA(4.74\%, 3yrs) = 52,150 \times 2.72 = 141,894$.
PV of cash flows = $ATLP \times 2.72 + 141,894 = 745,000 \implies ATLP = \$221,061 \implies LP = \$279,824$
Any lease payment between $279,824 and $294,900 will make both parties better off. Let's assume there is a typo in the question and a simpler way to solve is needed.
c. Tax Asymmetry:
Since the lessee pays no taxes, their after-tax borrowing rate is the same as their pre-tax rate (9%). The after-tax cost of leasing for the lessee is the lease payment itself, which must be less than the cost of borrowing and buying. The lessor still gets the tax shield from depreciation. The range of lease payments that benefits both parties is between the PV of the cost of owning for the lessee and the PV of the cash flows for the lessor.
4. Minicase: Warf Computers
Warf Computers needs to obtain equipment costing $7.93 million. It can buy it or lease it from Hendrix Leasing for four annual payments of $1.924 million (beginning of year) with a $520,000 security deposit.
Solution:
We calculate the NAL to find which option is cheaper.
Step 1: Calculate After-Tax Borrowing Rate
$r_{after-tax} = 11\% \times (1 - 0.21) = 8.69\%$
Step 2: Calculate Incremental Cash Flows
Initial Cost Avoided = +$7,930,000
Depreciation Tax Shield: MACRS 3-year property rates are 33.33%, 44.45%, 14.81%, 7.41%. The depreciation tax shields for years 1-4 are calculated by multiplying the depreciation by the tax rate (21%).
After-tax Lease Payment (Beginning of year): -$1.924M * (1-0.21) = -$1.52M
Security Deposit: -$520,000 at Year 0, +$520,000 at Year 4
Step 3: Calculate NAL
NPV of lost depreciation tax shield at 8.69% = -$1,154,677
NPV of after-tax lease payments at 8.69% = -$5,394,360
NPV of security deposit = -$520,000 + $520,000 / (1.0869)4 = -$130,528
$NAL = \$7,930,000 - \$1,154,677 - \$5,394,360 - \$130,528 = +\$1,250,435
Since the NAL is positive, **Warf should lease** the equipment.