THE CPA AND THE COMPUTER

July 2001

Lease or Purchase? A Spreadsheet Analysis

By Craig G. White

Leases constitute approximately 30% of the overall new vehicle market; however, leases constitute 60–70% of the luxury vehicle market. For many consumers, the decision to lease or to buy can have a significant financial impact and tax implications.

The level of information available on automobile leases has increased with the growth of the Internet, but many web resources take a narrow view of the topic, ignoring important issues such as tax implications and the option nature of the lease. The spreadsheet described below allows deeper analysis of lease arrangements. It is available for download from the author’s website, located at www.Tax-Ideas.com.

The Basic Lease Payment Calculation

The basic lease payment consists of a depreciation component and a rent charge for the use of the vehicle:

The capitalized cost in the formula is the agreed-upon value of the vehicle plus any amounts paid over the lease term (such as service contracts, insurance, and any outstanding loan balances) and minus any net trade-in allowance, rebate, noncash credit, or cash paid to reduce the capitalized cost.

The residual value is the projected value of the vehicle at the end of the lease term. The lessee usually has the option to purchase the vehicle for this price. The residual value, which probably will not equal the actual value of the vehicle at the end of the lease term, is an important part of the lease versus purchase decision.

The money factor is the annual percentage rate (APR) divided by 24. The money factor applies the monthly APR to the average value of the vehicle financed over the lease term.

The Underlying Economics of the Lease Calculation

The lease payment can be analyzed similar to a purchase amortization schedule. In a purchase transaction, the purchaser is shouldering the burden of the entire value of the vehicle. The purchaser either pays outright for the vehicle with current dollars, finances the vehicle, or uses a combination of down payment and financing. In a lease transaction, the lessee finances only a portion of the value of the vehicle. The lessee must either pay the residual value of the vehicle at the end of the lease term or transfer the vehicle back to the lessor. In a sense, a lease is like a balloon note: The capitalized cost is the principal amount of the debt, and the residual value is the balloon amount at the end of the financing term. However, with a lease, the lessee has the option to walk away from the balloon amount (vehicle) at the end of the term.

In order to compare the purchase and lease transactions, the residual value must be discounted back to the present to determine the true portion of the value of the vehicle financed by the lessee. Once the residual value is discounted to the present value, the lease payment can be compared to the purchase payment.

Example 1. A client can either lease the vehicle over 48 months at an APR of 8.5% (money factor = .003542) with a capitalized cost of $25,000 and a residual value of $13,750, or purchase the vehicle for $25,000 financed over 48 months at an APR of 8.5%.

Using the basic lease payment calculation, the monthly depreciation charge is $235 [($25,000 – 13,750) / 48] and the monthly rent charge is $137 [($25,000 + 13,750) 5 (.085 / 24)], making the total monthly payment approximately $372.

An alternate means of determining the lease payment is by first determining the present value of the residual value of the vehicle. The $13,750 discounted back to the present at an APR of 8.5% is $9,922. The lessee is in effect using $15,078 of the value of the vehicle in present value terms ($25,000 – $9,922). The monthly payment for financing $15,078 over four years at an APR of 8.5% results in the $372 payment. The monthly payment for purchasing the vehicle is $616. The $244 difference in the monthly payment stems from the additional $9,922 the purchaser must amortize over the four years at 8.5%.

If the lessee purchases the vehicle and sells it at the end of the finance term for $13,750, the lease and the purchase are equivalent. The lessee receives $9,922 in sales proceeds in present value terms at the end of the four years (discounted back to the present at the rate of 8.5%) and will have spent $15,078 in current dollars for the use of the vehicle over the four years. In nominal dollars, the lease would cost the client $17,389 over the lease term, while the purchase (assuming a sale at the end of the fourth year) would cost the client $15,818 over this period.

Using the same APR for both a purchase and a lease, however, is somewhat unrealistic (unless the manufacturer is offering lease incentives) because of the option value of the lease described below. If the lessee has investment opportunities that exceed the 8.5% rate, the analysis could tilt toward the lease because the current cash saved on a lease could be invested for higher return. In addition, if the lessee has other loans at a higher interest rate than the automobile financing, the cash flow difference could be better used to pay down the other debt.

Example 2. Assume the same facts as Example 1 except the lessee also has credit card debt with a 15% interest rate. Discounting the payment streams of the lease and the purchase at the 15% rate, the lease becomes more attractive, with a cash outflow present value of $13,354 versus $14,280 for the purchase.

The Lease as a Call Option

A lease offers an added feature over a purchase because the lessee has a call option on the vehicle. In a closed-end lease, the lessor is shouldering the risk of a greater than expected decrease in the value of the vehicle over the term of the lease. If the vehicle decreases in value beyond the residual value, the lessee can simply walk away from the vehicle at the end of the lease, net of any disposition fees. If the vehicle is worth more than the residual value at the end of the lease, the lessee can exercise the purchase option for the residual value and sell the vehicle for the higher fair market value. Conversely, a purchaser retains the risk of a greater-than-expected decrease in the fair market value of the vehicle.

Example 3. Assume the same facts as Example 1, except that the fair market value of the car is $13,000 rather than $13,750 at the end of the four-year term. A lease locks the lessee into paying the cost of the lease only down to the originally agreed upon residual value. Assuming a closed-end lease, the lessee could simply return the vehicle and pay any disposition fee at the end of the lease term. The lessor bears the economic burden of the additional $750 decrease in value, unless caused by excessive use by the lessee. The $750 decline in value decreases the sales proceeds available to a purchaser at the end of the fourth year. The lease still costs the lessee $15,078; however, a purchase now costs $15,620 in present value terms.

This price protection feature of a lease has value. All else being equal, the APR for a lease should be higher than that for a purchase—in effect, an option premium. Alternatively, the lessee may be charged the premium for price protection in the disposition fee. A lessee should not reject a lease just because the APR is higher than for a purchase; the expected resale may more than offset the difference. Of course, the expected resale market may also be more favorable for the lessor than the lessee. The lessee may consider the trade-in value of the vehicle, whereas the lessor may realize the retail value, decreasing the value of the option to the lessee.

The Tax Elements

Tax implications change the ultimate cash flow paid for a vehicle when used for a trade or business. The tax rules allow two different methods for deducting the costs of a vehicle used for trade or business purposes: 1) deducting actual costs or 2) using a standard mileage rate. These methods are available whether the taxpayer purchases or leases.

Purchased vehicle: Actual cost method. A taxpayer can deduct the actual costs of ownership for trade or business use of a vehicle (i.e., the nonpersonal usage of the vehicle). These costs include depreciation, interest, registration fees, licenses, insurance, repairs, gas, oil, tires, garage rent, parking fees, and tolls.

Under IRC section 168, depreciation can be calculated under a variety of different methods over a five-year life. The vehicle can be depreciated using an accelerated method, using either a 200% or 150% declining balance (assuming the vehicle is used more than 50% for a trade or business), or it can be recovered ratably over its life. The vehicle may even qualify as a section 179 expense. However, the luxury auto deduction limitation rules under section 280F limit both the annual deduction amount and the amount that can be claimed under section 179. Interest is deductible for trade or business usage; however, interest on the financing of a vehicle is not available for unreimbursed employee usage. This consideration may favor a lease, as discussed below, where interest is a component of the overall lease payment.

Purchased vehicle: Standard mileage rate. A second option is the standard mileage rate. This set deduction amount per mile estimates the actual costs of depreciation, registration fees, licenses, insurance, repairs, gas, oil, and tires. Interest expense and payments for other costs external to the vehicle (e.g., garage rent, parking fees, and tolls) are deductible in addition to the standard mileage rate. The 2000 standard mileage rate is 32.5 cents per mile. The component of this rate considered for depreciation is 14 cents per mile.

If the taxpayer uses an accelerated depreciation method in the first tax year, the standard mileage method cannot be used in later tax years, and vice versa. These rules are less restrictive than they appear: The luxury auto depreciation rules restrict the benefits of accelerated depreciation. A taxpayer may want to choose straight-line depreciation in order to retain the option of the standard mileage rate.

Leased vehicle: Actual cost method. The actual cost method for a leased vehicle is similar to that for a purchased vehicle. The primary differences between a lease and a purchase are in the areas of depreciation and interest expense.

A lessee does not deduct depreciation because she does not own the vehicle (The IRS has argued that a long-term lease is really a conditional sales agreement. See Revenue Ruling 55-540, 1955-2 C.B. 39). However, cost recovery is included in the lease payment because the lease payment covers both the decrease in the value of the vehicle and a rent charge for the use of money.

Example 4. Assume the same facts as Example 1. The taxpayer uses the vehicle 100% for a trade or business. Over the term of the lease, the taxpayer can deduct $15,078 of the value of the vehicle in present value terms.

In contrast, a purchaser of a vehicle can deduct only $12,685 in cost recovery over this same period ($3,060 + 4,900 + 2,950 + 1,775). The lease inclusion rules are meant to mitigate this difference. The tax code requires a lessee of vehicles over a certain dollar value to include set amounts in income based on the percentage of the use of the vehicle the taxpayer is deducting (IRC section 280F, Revenue Procedure 2000-18, IRB No. 9,722).

Example 5. Assume the same facts as Example 1. The lessee is required to include lease inclusion amounts of $77, $168, $249, and $298 in income in each of the tax years.

A lease presents a distinct tax advantage for individuals that incur unreimbursed vehicle expenses as employees. The lease payment includes a charge for the cost of money; therefore, the employee can effectively deduct interest for the unreimbursed portion of usage. An employee cannot deduct the interest on a purchased vehicle.

Leased vehicle: Standard mileage rate. The standard mileage rate is also available for leased vehicles, at the same 32.5 cents per mile. However, it holds a distinct disadvantage for leases. The standard mileage rate substitutes for both the direct operating expenses of the vehicle and the lease payment amount. This precludes the deduction of the interest equivalent. As demonstrated below, this inherent limitation generally results in the actual cost method being far superior to the standard mileage method for leases. Furthermore, use of the standard mileage rate in the first tax year precludes the use of the actual cost method in later years.

Numerical Analysis of Tax and Non-Tax Factors

A numerical example of the cash flow differences for a given set of circumstances illustrates the situational sensitivity of lease analysis. Exhibit 1 presents the present value of cost of ownership when the vehicle is not used in a trade or business. Given that there is no deductible usage, if the APR is the same for both and the projected residual value equals the actual residual value, the lease and the purchase are equivalent.

Exhibit 2 provides the results for the same fact situation except, in this case, the actual value is assumed to be 50% of the original value while the projected residual value remains 55% of the original value. Finally, Exhibit 3 details the after-tax cash flows of a purchase and a lease when the vehicle is used exclusively for business purposes. The lease–actual cost method produces the most advantageous outcome because the lease deduction amount, even with the lease inclusion amount, is greater than the luxury auto limited depreciation deduction.

Spreadsheet Analysis

The spreadsheet described below (available from www.Tax-Ideas.com) consists of four main sections entitled payment calculation, tax analysis–leasing, tax analysis–purchase, and summary of after-tax cash flow. It also includes an amortization schedule for both a lease or a purchase based on the information input in the payment calculation section. The lease inclusion section provides the inclusion amounts for various vehicle fair market values for calendar year 2000.

Payment calculation. The payment calculation is the beginning point of the cash-flow analysis. The user enters the requested information in the black boxes. The necessary inputs for the lease payment calculation are capitalized cost, capitalized cost reduction, residual value, sales/use tax rate, lease term in months, and the money factor (the APR divided by 24). The necessary inputs for the purchase calculation are the purchase price, amount of down payment, financing term, and APR. Once these parameters are entered, the spreadsheet reports each option’s monthly payment.

Tax analysis–leasing. The leasing analysis requires the input of the following additional variables:

The spreadsheet calculates the approximate deduction under both the actual cost and standard mileage method.

Tax analysis–purchase. The purchase analysis requires the input of the same variables as the lease analysis. The spreadsheet calculates the approximate deduction under the 200% declining balance depreciation.

Summary of after-tax cash flows. This section of the spreadsheet brings together the elements calculated in the first three sections. The user must input the taxpayer’s estimated marginal tax rate, the assumed sales price of the vehicle at the end of the finance term, and the cash flow discount rate. The bottom-line present value of after-tax cash outflow is calculated with the assumption that a purchased vehicle is sold at the end of the financing term for the assumed sales price. This amount is split into a tax portion based upon the business use percentage input in the tax analysis–purchase worksheet.


Craig G. White PhD, CPA, is an assistant professor of accounting at the Anderson Schools of Management, University of New Mexico, Albuquerque.

Editors:
Paul D. Warner, PhD, CPA
Hofstra University

L. Murphy Smith, DBA, CPA
Texas A&M University


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