Buy-Lease Decision (1)


Introduction.  This sample problem illustrates the relationship between Discounted Cash Flow (DCF) in a public sector Cost-Benefit Analysis (CBA) with no revenue stream and a private sector decision.  Some private sector capital equipment expenditures are not the ones envisioned in finance texts in that they lack a measurable revenue stream following the expenditure.  Expenditure decisions, some quite large, present this way: similar costs, unmeasurable revenues, equal or similar benefits, and substantially different risks.  DCF analysis accommodates the difficulties while IRR provides useful risk insight.  DCF also accounts for the time value of money, a significant shortcoming in some lease-buy algorithms.

Problem or Opportunity.  This is a buy-lease comparison.  You need a replacement computer in order to remain in business. You have a choice of purchasing (buying) it for $12,500 installed or leasing the same system for $370 per month payable in advance annual $4,440 installments.  If you purchase, repairs, insurance, etc. are estimated at 10 percent of the purchase price ($1,250/year).  You estimate you can get 20 cents on the dollar ($2,500) for the computer in five years. Your cost of capital is 14.5 percent.

Simplifying Assumptions. Tax implications are excluded for simplification although they could be an overriding consideration in practice.  An investment tax credit alone could sway the decision in favor of purchasing.

Discussion.  Although the computer is capital equipment, this is not the capital investment decision envisioned in finance texts.  This problem lacks a readily measurable revenue stream following the expenditure.(2)  It could be quite difficult to estimate the revenue or cash inflows, if any, resulting from replacing any equipment necessary to remain in business.  But estimating inflows is unnecessary in this case because the benefits are the same for both alternatives--a wash.  The financial part of the decision is straightforward and can be made using discounted cash flows only.  The tougher part of the decision is evaluating relative risk.

Calculations.  See S29ALL.TXT.  S29A.TXT models the purchase; S29B.TXT models the lease.  Compare total discounted cash flow for each.  (If you find S29A1.TXT confusing, use S29A2.TXT instead.  Results are the same.)(3)  The purchased system is least expensive with a total discounted cash flow (present value) of $15,469 versus $17,245 for leasing.  S29C.TXT is the delta or difference between the two streams.  The positive total discounted cash flow (NPV) reflects leasing as more costly.  IRR (24.23 percent) does the same.

Risk. .If you purchase, you accrue risks that go with ownership.  With similar total discounted cash flows and equal benefits, risk is an overriding consideration.  One risk factor is estimating error.  The decision is sensitive to changes in the estimated terminal value--difficult to determine five years in advance.  And terminal value could go either way.  While computer equipment can become obsolete in less than five years and have to be replaced, it may satisfy the need beyond its anticipated five-year "useful life."(4)  The magnitude IRR-discount rate differential (9.73 percent in S29C.TXT) is indicative of  relative risk. While this differential is attractive, it can evaporate quickly with changes in TV and other factors.

Decision.  If you have plenty of cash and readily accept risk, then purchase.  If you are short on cash or risk averse, then lease.

Notes

  1. This is Sample Problem 29, Lease-Make-Buy Analysis. It illustrates the relationship between Discounted Cash Flow (DCF) and Cost-Benefit Analysis (CBA).  DCF accounts for the time value of money, a significant shortcoming in some lease-make-buy algorithms.
  2. It is commonplace in the private sector to have financial problems in which the time value of money is an important consideration but lack a measurable revenue stream following the expenditure.  Many purchases, some quite large, present this way: similar NPVs and IRRs; equal, similar or at least comparable benefits; and substantially different risks.  Substantially different risks might be those in which changing a single risk factor would reverse the decision using NPV/IRR.  This makes them akin to Cost-Benefit Analyses (CBAs), Economic Analysis (EA) and the like used in the public sector.  Analysis is the same in both sectors and DCF works equally well in the both.  IRR helps assess risk, which is key in these decisions.
  3. Terminal value (TV) is always discounted at the end of the last study period regardless of the discounting method (equation) used.  With end-of-year discounting, the discount factor for TV is the same as it is for the last period.  This is illustrated in S29A2.TXT and S29C2.TXT, included in S29ALL.TXT.  A2 and C2 are included primarily because they are easier to read.  It would be different using continuous or middle-of-(period) discounting.  TV would have to be calculated separately.  TV is also called economic life.
  4. Please contact me, Ray Martin, Ray_Martin@AltaVista.net if you see a problem with one of my working papers. Especially with problems. Really.

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