NPV (Net Present Value)

Key takeaways

NPV = sum of discounted future cash flows − initial investment. Positive NPV creates value; negative destroys it; zero is indifferent.
The discount rate is your cost of capital (WACC) or hurdle rate — what you'd earn on an alternative investment of similar risk.
NPV beats IRR when comparing mutually exclusive projects of different scale or duration. IRR can rank wrongly; NPV can't.
Highly sensitive to the discount rate. Sensitise NPV against discount rate ± 200 bps and across plausible cash-flow scenarios.
Use Excel =NPV() for evenly-spaced cash flows; use =XNPV() with actual dates for irregular timing.

The formula

NPV = Σ_t=1ⁿ [ CF_t / (1 + r)^t ] − Initial Investment

Where:

CF_t — cash flow in year t (positive for inflows, negative for outflows)
r — discount rate (WACC for corporate projects, hurdle rate for project finance)
Initial investment — upfront capital deployed (typically at t = 0, expressed as positive)

The decision rule

NPV > 0 — accept the project. It creates value above the cost of capital.
NPV = 0 — indifferent. The project earns exactly the cost of capital.
NPV < 0 — reject. It destroys value relative to the alternative use of the capital.

For mutually exclusive projects (you can do A or B but not both), pick the one with the higher NPV. For independent projects with capital constraints, rank by profitability index (NPV per dollar invested) and select the top-ranked until the capital budget is exhausted.

Worked example

A factory upgrade requires $1,000K upfront. Expected after-tax cash flows: $300K, $400K, $500K, $400K over four years. Hurdle rate is 10%.

Year	Cash flow ($K)	Discount factor	PV ($K)
0	(1,000)	1.000	(1,000)
1	300	0.909	273
2	400	0.826	331
3	500	0.751	376
4	400	0.683	273
Sum (NPV)	$253K

Positive $253K NPV — accept the project. At a 15% hurdle rate, NPV would drop to $111K (still positive). At 20%, NPV is roughly $0 — that's the project's IRR.

NPV vs IRR — when they disagree

For a single conventional project (one initial outflow followed by inflows), NPV and IRR give the same accept/reject answer. For ranking mutually exclusive projects, they can disagree. Two scenarios where NPV is right and IRR is misleading:

Scale. Project A: invest $100, get $130 in year 1 (IRR 30%, NPV $18 at 10%). Project B: invest $1,000, get $1,200 in year 1 (IRR 20%, NPV $91). IRR ranks A higher; NPV ranks B higher; B creates more value.
Timing. Project A: $1,000 in year 1. Project B: spread over 5 years totalling $1,500. Different IRRs but NPV captures the time pattern correctly.

The rule of thumb: NPV is the canonical decision rule. Use IRR as a communication shorthand and a sanity check, not as the primary ranking metric for mutually exclusive choices.

Common NPV errors

Wrong discount rate. Using a corporate WACC for a project with materially different risk gives a wrong NPV. Use a project-specific hurdle if the project's risk profile differs from the firm's.
Mixing nominal and real. Nominal cash flows must be discounted at a nominal rate; real cash flows at a real rate. Mixing produces wrong answers.
Forgetting working-capital recovery. Working capital invested at the start should be recovered at project end as a cash inflow. Many models forget this.
Excel =NPV() bug. Excel's NPV function assumes the first cash flow is at t=1, not t=0. If your initial investment is in the function range, you've undercounted by one year. Fix: =NPV(rate, year1:yearN) − initial_investment.
Hardcoded NPV. If you change a cash-flow input and NPV doesn't recompute, the model is decorative.

How Smalt AI builds it

For project finance and capital-budgeting decisions, Smalt AI builds NPV alongside IRR, payback, and a sensitivity table on discount rate × revenue (or cost) assumption. The Excel formula uses =XNPV(rate, cash_flows, dates) with actual dates so irregular cash flow timing is handled correctly. Outputs include the project's break-even discount rate (the IRR) and a tornado chart of input sensitivities.