# Lease or Buy / Make

Joachim Kuczynski, 03 April 2023

A rental agreement that extends for a year or more by a series of fixed payments is called a lease. Firms lease as an alternative to buying capital equipment. Cars, aircraft, ships, farm equipment and trucks are leased many times. In principal every kind of asset can be leased. In this post I want to describe the valuation of a lease contract and how you can analyse whether to prefer buying / making or leasing an asset from the financial point of view.

## The correct way

At first you have to figure out all free cash flows that are different between buying an asset in comparison to leasing it. Usually this concerns cash flows from purchasing, tax shield because of EBIT reduction caused by depreciation or leasing payments, tax shields because of debt interest deduction, maintenance costs and salvage value of the asset. After that you have to discount all cash flows with the appropriate risk adjusted discount factor ( for the buying and for the leasing scenario). Adding up all present values you get a net present value (NPV) of the buying case and a NPV of the leasing case.

The case with the higher NPV is the better one from financial point of view. That means leasing is better than buying, if .

Many firms do not value this way because they are not familiar with risk appropriate discounting of cash flows. Therefore they use simplified formulas described in many corporate finance books. But in general that can lead to false results if the premises of the simplifications do not fit reality. So take care and do not use the simplified formulas without checking the concrete situation.

## Simplified ways

The short ways are characterized by unifying discount factors for cash flows. This assumes that the cash flows have the same risk adjustment. In general that is not the case obviously. Each cash flow has its own risk in principle. In my calculation I consider each cash flow and calculate its specific risk. That is not much additional work. But I can be sure that I get the correct result.

In some cases you can assume the same discount factor. Tax shield because of EBIT reduction, caused by depreciation and leasing payments, and debt interest deduction can be considered as fixed cash flows in most cases. They have no market dependency. Hence you can discount their cash flows with the company’s debt interest rate. Depending on the debt interest deductibility of the cash flows you have to take the before or after interest tax rate (operating and financial lease).

If some cash flows have market dependency (e.g. salvage value) or are realised in different currencies, the discount factors might not be the same. Additionally, the changing capital structure and the dependency of tax deductibility on the market development can lead to different discount rates. In all these cases you cannot use the simplifies formulas. Then you have to apply the APV method and calculate all NPV contributions seperately. This is the procedure of the previous section.

## Debt-equivalent cash flows

The authors of many books about corporate finance use the term debt-equivalent cash flows. That are the additional cash flows that occur when financing a free cash flow stream by an equivalent loan. At leasing vs buying the free cash flow stream is leasing FCF minus buying FCF. After that you calculate interests of the loan and the interest tax shields with APV or with simplified adjusted discount rates (as described before). But take care! This simplified version is only valid, if leasing and buying cash flows have the same discount factor (risks) in each period. Otherwise the calculation with debt-equivalent cash flows provides false results!

## Options in leasing contracts

Many leasing contracts include options like buying the assets at the end of the leasing time or cancelling the leasing contract before expiration. Any option can be valued with Real Options Analysis. The analysis is problem-specific. But in general each option in a leasing contract has a specific, well defined value.

## Conclusion

The analysis of leasing contracts (and their comparion to buying / making) is completely the standard analysis of asset valuation. But you should do that in the basic accurate way. That means DCF analysis with appropriate risk-adjusted discount rates (Component Cash Flow Procedure) including the adjusted present value (APV) approach. It is not much additional work to do. But you can be sure, that your results are right.

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