A MATHCAD ELECTRONIC BOOK

Personal Finance: Lease Versus Buy Analysis: General Theory

Reprinted from Marc Vandenplas, Personal Finance, MathSoft, Inc. Copyright © 1997.

The lease versus buy decision is based on a comparison between the net present value of the buy alternative with the net present value of the cash flows associated with leasing. In the model below, explicit financing costs are excluded, because capital decisions are not necessarily made in isolation of one another, and the purchase is assumed to be an outright purchase for cash.

Formula

The variables are defined in the example below.

This formula returns the difference in the net present values of the lease and buy alternatives. If the number returned is positive, a purchase for cash instead of leasing is indicated. If the number returned is negative, a lease is more desirable than a purchase.

Example

You are faced with the option of either leasing a new office machine or buying it outright for cash and you wish to analyze a lease without respect to any additional opportunities for investment. The office machine can be purchased for $3,000 and has an economic life of 6 years after which it will retain a value of $1,500. In the case of a purchase, its residual book value at the end of its economic life after depreciation will be zero; the applicable tax rate on gain issuing from the sale of the asset is 35%; and its operation will cost $400 yearly. If leased, the annual lease payment will be $850. The income tax rate is 40%; cost of capital is 12% and the after-tax rate for borrowing is 5%.

economic life or term of the lease, in years

cash purchase price, in dollars

salvage value, in dollars

applicable tax rate on gain

residual book value

lease payments

operational cost

income tax rate

cost of capital

after-tax rate for borrowing

Depreciation Schedule

A depreciation schedule for the asset must be used. The sum-of-the-years’ digits method is used below. The formula below is modified to omit the salvage value (SV ), as that is used elsewhere in the NPV lease-buy calculation:

yearly depreciation schedule

Result

The net present value difference is computed:

difference in net present value, in dollars

A negative result indicates that leasing is preferable to an outright cash purchase. In this particular case, very little difference exists between leasing and buying outright this office equipment.