Net Present Value (Uniform Cash Flow)
Discount an initial cost plus a level annual cash flow to present value and get the NPV of the project.
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The engineering
NPV brings every future dollar back to today using the discount rate that represents your minimum acceptable rate of return (MARR). This card assumes a single up-front investment, a level annual net cash flow, and an optional salvage in the final year — the classic textbook lifecycle case. A positive NPV means the project clears the hurdle rate; between two competing projects the higher NPV wins.
The result swings hard on the discount rate and horizon, so treat both as assumptions, not facts: an 8% vs 12% rate on a 20-year annuity moves the P/A factor by roughly a third. If your cash flows are uneven, this uniform-series shortcut won't hold — discount each year individually. And never compare NPVs computed at different discount rates.
Where this math comes from
Discounting future money is old — merchants and moneylenders priced deferred payments for centuries — but the formal engineering-economy treatment traces to Eugene Grant's 1930 Principles of Engineering Economy, which pulled interest-factor tables and equipment-replacement logic into a discipline engineers could apply on the shop floor.
Irving Fisher's 1930 The Theory of Interest gave the present-value idea its rigorous economic footing, and by mid-century NPV had displaced payback-period rules of thumb in capital budgeting. The modern classroom form — the (P/A) and (P/F) factor notation used here — is the version standardized in Blank and Tarquin's Engineering Economy, the text most Tennessee-Valley PE candidates cut their teeth on.
- 1930Irving FisherThe Theory of Interest formalizes present value and the rate of return.
- 1930Eugene L. GrantPrinciples of Engineering Economy establishes interest-factor methods for engineers.
- 1951Joel DeanCapital Budgeting argues for discounted cash flow over payback rules.
- 1976Leland Blank & Anthony TarquinEngineering Economy codifies the (P/A, i, n) factor notation used in FE/PE prep.
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