NPV: Lease vs. Buy
A lease vs buy decision compares two ways of getting the same asset. You turn each option's cash outflows into today's money and pick the one with the lower present value cost. Because the asset is the same either way, only the cash flows that differ matter: payments, purchase price, resale value and, in fuller versions, taxes.
What you will learn
- How to frame a lease or buy decision as an NPV problem
- How to find the present value of lease payments
- Why the asset's resale (salvage) value matters when buying
- How taxes and depreciation enter the full exam version
- How to state the final lease or buy recommendation
The formulas
- L
- lease payment per year, paid at year end
- r
- discount rate per year
- n
- number of lease payments
- P
- purchase price paid today
- S
- salvage (resale) value at the end of year n
- r
- discount rate
Worked example
A machine costs $10,000 to buy and can be sold for $1,000 after 3 years. Or you can lease it for $3,800 a year, paid at the end of each year for 3 years. Use an 8% discount rate and ignore taxes. Lease or buy?
- Annuity factor: [1 − 1.08⁻³] ÷ 0.08 ≈ 2.577097
- PV of lease: 3,800 × 2.577097 ≈ 9,792.97
- PV of salvage: 1,000 ÷ 1.08³ = 793.83
- PV of buying: 10,000 − 793.83 = 9,206.17
- Compare: buying costs about 586.80 less in today's money
Answer: Buy. Its present value cost is about $9,206 vs $9,793 for leasing (rounded to the dollar). Without the $1,000 resale value, leasing would have been cheaper.
Common questions
How do you do a lease vs buy analysis?
List the cash outflows for each option, discount them to today at the same rate, and compare. Leasing is the sum of discounted lease payments. Buying is the purchase price minus the discounted resale value. Choose the option with the lower present value cost.
What discount rate should be used in a lease vs buy decision?
Textbooks usually use the after-tax cost of borrowing, because a lease is a lot like a loan. If your course or exam gives a single discount rate, use that. The key is to use the same rate for both options.
How do taxes affect lease vs buy?
Lease payments are usually tax-deductible, so each payment's after-tax cost is lower. Buying gives you depreciation tax shields instead. Full exam versions include both, plus tax on any gain from selling the asset, so check what your question asks.
Is it better to lease or buy equipment?
There is no universal answer. It depends on the price, lease payments, how long you need the asset, its resale value, taxes and your borrowing cost. Run the present value comparison and pick the cheaper option for that specific case.