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NPV (net present value)

Also called: NPV, net present value

The sum of all of a project's cash flows, each converted to today's money, minus the investment. A positive NPV means the bet earns more than the discount rate.

NPV (net present value) adds up all of a project's cash flows in today's money: the investment now (negative) plus every later inflow, each divided by (1 + r)ᵗ. NPV = −investment + CF₁ ÷ (1 + r) + CF₂ ÷ (1 + r)² + … A positive NPV means the project returns more than the discount rate; a negative one means the money would do better elsewhere at a similar risk.

Unlike payback or IRR, NPV is in money and counts every year: it says how much value a bet adds, so it can rank options that compete for the same budget or the same developers. The rule is simple: among options of similar risk, prefer the higher NPV; reject a negative one unless something outside the numbers justifies it, and then say what.

The number is only as good as its inputs. Discount cash, not profit (no depreciation on top of the investment), count only cash that differs between doing and not doing the project, leave sunk costs out, and choose the rate by the bet's risk. Then test the assumptions the sign depends on, because a small change in volume or cost often turns a positive NPV negative.

Example

Klasna compares two product bets at its 25% rate. The maths mock-exam mode costs 1,200,000 UAH now and brings 300,000, 600,000, 800,000 and 800,000 over four years:

Year
0
1
2
3
4
Cash, UAH
−1,200,000
300,000
600,000
800,000
800,000
Factor
1
0.8
0.64
0.512
0.4096
Today's money
−1,200,000
240,000
384,000
409,600
327,680

NPV = −1,200,000 + 1,361,280 = +161,280 UAH.

A parent progress app costs 600,000 and brings 400,000 and 300,000: −600,000 + 320,000 + 192,000 = −88,000 UAH. The app pays back faster (1.67 years against 2.38) yet destroys value at 25%; the mock exams add it.

Common mistakes

  • Discounting profit instead of cash. Subtracting depreciation on top of the investment counts the build twice; in Klasna's build-or-buy case it turns +290,526.21 into −785,185.79.
  • Counting sunk costs. Money already spent is gone in both options; it belongs in neither.
  • Forgetting the cash that differs. Count the extra hosting, upkeep and lost sales of the option, not just the headline saving.
  • Treating NPV as precise. It inherits every assumption; show which change in volume or cost would flip its sign.
  • Comparing NPVs computed at different rates without saying so. State the rate and why it fits the bet's risk.

Learn it in the course