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Replacement Chain Analysis Calculator

Enter cost, cash flow, life and discount rate to analyze the replacement chain.

How it is calculated

The tool treats one machine or project as a level annuity. The present value of the inflows is PV = CF × (1 − (1 + i)−n) / i, where CF is the net cash inflow per year, i is the discount rate as a decimal (10% becomes 0.10) and n is the life in years. NPV of one cycle is NPV = PV − cost. The equivalent annual annuity is EAA = NPV / annuity factor, the annuity factor being the fraction in the PV formula. If the rate is 0, the factor is simply n. A negative rate, a life of zero or less, or any empty field gives no result. The calculation covers a single cycle; it does not stack repeated cycles up to a common life, so compare projects of different lengths by their EAA, not their raw NPV.

Worked example

Cost 50,000, cash inflow 18,000 a year, life 4 years, rate 10%. The annuity factor is (1 − 1.10−4) / 0.10 = 3.1699. The inflows are worth 18,000 × 3.1699 = $57,057.58. Subtracting the cost gives an NPV of $7,057.58. Dividing by the factor gives an EAA of $2,226.46 per year, which is the figure to set against another option with a different life.

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Common mistakes

  • Comparing the NPV of a 3-year machine with the NPV of a 6-year one. The longer life collects more cash and wins unfairly; compare the equivalent annual annuity instead.
  • Typing the rate as 0.10 instead of 10. The field expects a percentage, so 0.10 means a 0.1% rate and the NPV balloons.
  • Entering the cost as a negative number. The cost is entered as a positive outlay and the tool subtracts it itself.
  • Putting in profit after depreciation rather than the cash inflow; depreciation is not a cash flow.
  • Expecting the NPV shown to already cover several replacement cycles. It is the NPV of one cycle only.

Sources

About this calculator

Replacement chain analysis solves a problem plain NPV comparison gets wrong: when two mutually exclusive investment options have different useful lives, comparing their raw NPVs unfairly favors the longer-lived option just because it captures more years of cash flow. The method repeats each project hypothetically until both reach a common time horizon (the least common multiple of their lives), or equivalently converts each project's NPV into an equivalent annual annuity (EAA) — the constant yearly cash flow that would produce the same NPV over that project's own life — making the comparison apples-to-apples.

This calculator takes a project's initial cost, annual net cash inflow, useful life in years and discount rate, and computes the NPV of a single cycle, the present value of the inflows and the equivalent annual annuity. It does not repeat the project over a common horizon; instead, run it once for each option and compare the EAA figures, which ranks the options the same way a full chain would. Corporate finance analysts comparing equipment or machinery with different replacement cycles, capital budgeting committees evaluating competing projects, and finance students working through mutually-exclusive-project problems use it to avoid the common mistake of picking the higher-NPV option when it simply runs longer, not because it creates more value per year.

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  • Editorial team

    This also works for machines that only cost money. Enter the yearly running cost as a negative cash flow and read the EAA as an equivalent annual cost. A 20,000 machine lasting 5 years with 3,000 a year of running costs at 10 percent comes to about 8,276 a year, while a 30,000 one lasting 8 years with 2,500 a year comes to about 8,123, so the longer-lived one is cheaper per year. Are you comparing machines that earn money or only cost it?

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