NPV

Net Present Value

Short definition

NPV discounts a project’s incremental cash flows at the hurdle rate and subtracts the initial outlay. A positive NPV says the project creates value at that rate; it does not by itself solve financing, collateral or intra-year cash timing.

Detailed explanation

NPV embeds time value and risk in the discount rate. The input is incremental cash, not accounting profit: after-tax operating cash, ΔNWC, maintenance and growth capex, salvage and tax effects. Sunk costs stay out; opportunity cost and cannibalisation come in.

When projects are mutually exclusive and differ in scale or life, IRR mis-ranks; NPV is the ranking rule. Under capital rationing, NPV is read with the profitability index so the scarce budget is allocated per unit of outlay. If r is WACC, a project whose risk differs from the firm average needs a beta or hurdle add-on.

Why it matters for the CFO

Capex, M&A and capacity decisions are taken on discounted incremental cash, not on “how many years to pay back”. A wrong hurdle or an inflated terminal value can make a value-destroying project look profitable.

How it is calculated

NPV = Σ CFₜ / (1+r)ᵗ − I₀

Sum incremental CFₜ discounted at r and subtract I₀. WACC embeds financing; if the debt is project-specific, APV books the tax shield separately.

Variables in the formula

• CFₜ: incremental free cash flow in period t
• r: discount rate (often WACC or a risk-adjusted hurdle)
• I₀: initial net investment

How to read it

NPV > 0 creates value at r; zero means the project earns exactly the hurdle. Absolute NPV rewards scale: a large low-margin project can beat a small high-IRR one. Keep cash flows and r in the same currency through FX, inflation and tax timing.

Numerical example

I₀ = 10 mn TL, CF = 4, 5 and 6 mn TL over three years, r = 20% → NPV ≈ 4/1.2 + 5/1.2² + 6/1.2³ − 10 ≈ 0.97 mn TL.

Definitions are educational. They are not investment, credit or tax advice.