NPV vs IRR: Net Present Value and Internal Rate of…

Q: What is NPV in simple terms?

Net Present Value converts all future cash flows into today's money, then subtracts what you pay today. NPV > 0: the project earns MORE than your required return — accept. NPV < 0: you'd do better putting the money elsewhere. Example: pay ¥100k, receive ¥25k/year for 5 years, discount at 8% → NPV ≈ −¥182 → decline.

Q: What is IRR and how is it different from NPV?

IRR is the discount rate that makes NPV exactly zero — the project's built-in rate of return. Compare it to your cost of capital: IRR 12% vs 8% financing → accept; vs 15% → decline. NPV gives an absolute money figure; IRR gives a percentage. Use IRR for quick screening, NPV for final decisions.

Q: What discount rate should I use for NPV?

Your opportunity cost: (1) personal investing — your reliable alternative return (5–8%); (2) borrowed money — the actual loan rate plus risk premium; (3) business — WACC, typically 8–12%. When unsure, run the model at 8% and then stress-test at ±2% to see if the decision flips.

Q: How do I calculate NPV and IRR in Excel?

=NPV(rate, cashflows_yr1_onward) + initial_investment (the initial outlay stays OUTSIDE the NPV function, entered as a negative). =IRR(all_cashflows) including the negative initial value. For irregular dates use =XNPV and =XIRR with a date column.

Q: When NPV and IRR disagree, which do I trust?

Trust NPV. Conflicts arise with different project scales or cash-flow timing: a tiny project can show 40% IRR yet add less wealth than a big project at 12% IRR. IRR also assumes interim cash flows reinvest AT the IRR — often unrealistic. NPV assumes reinvestment at the cost of capital, the safer assumption.

Q: Is a fast payback period enough to approve a project?

No. Payback ignores everything after the cutoff and ignores discounting entirely. Two projects can both "pay back in 3 years" while one stops generating cash in year 4 and the other runs for 15. Use payback only as a liquidity screen; let NPV make the call.

Metric

Accept when

Meaning

NPV

> 0

Value created after cost of capital

IRR

> hurdle rate

Break-even discount rate

Payback

< expected horizon

Time to recover principal (ignores discounting)

Key Takeaways

NPV: discounted future cash flows minus initial cost — positive = creates value

IRR: the discount rate where NPV = 0 — accept if IRR > your cost of capital

Discount rate = opportunity cost: your loan rate or reliable investment return

Mutually exclusive projects: pick the higher NPV, not the higher IRR

Core answer: NPV = the sum of all future cash flows discounted back to today, minus the initial investment — a project is worth doing only if NPV > 0. IRR is the rate that makes NPV exactly zero — acceptable only when IRR exceeds your cost of capital (e.g., a 5% loan). When the two conflict, NPV wins.

Why discount at all

¥100 today ≠ ¥100 next year: at 8% returns, today's 100 becomes 108; conversely, next year's 100 is worth only 92.6 today (100 ÷ 1.08).

Discounting converts all future money into "what is it worth today" so it can be weighed against the investment on the same scale.

NPV formula and example

NPV = −initial investment + Σ [year-t cash flow ÷ (1+r)^t]

Example 1: invest ¥100k in a small shop, receiving ¥25k net per year for 5 years, discount rate 8%:

Year	Cash flow	Discount factor (8%)	Present value
0	−100,000	1	−100,000
1	25,000	0.926	23,148
2	25,000	0.857	21,433
3	25,000	0.794	19,846
4	25,000	0.735	18,376
5	25,000	0.681	17,015
NPV	−182

NPV ≈ −¥182 < 0: the project cannot beat an 8% cost of capital — don't do it.

How to find IRR

IRR solves −investment + Σ CF_t/(1+IRR)^t = 0 — no closed-form solution, so trial and error:

For the example above: at 7.9% NPV is still slightly negative; at 7% NPV turns positive → IRR ≈ 7.9%, below the 8% cost of capital. Same conclusion: pass.

Rule: IRR > cost of capital → accept; IRR < cost of capital → reject.

Three Excel functions

Function	Usage	Note
=NPV(rate, v1, v2…)	=NPV(8%, 25000 ×5 yrs) − 100000	Subtract the initial outlay separately — it is not in the arguments
=IRR(all cash flows)	=IRR({-100000,25000,…})	Includes the initial investment, returns IRR directly
=XNPV / XIRR	With actual dates	For irregular cash flows

Example: choosing between two projects

Example 2 (mutually exclusive) — you can only fund one:

Project	Outlay	5-yr inflow	NPV (8%)	IRR
A: corner store	¥100k	30k/yr	+19.8k	15.2%
B: parcel-station franchise	¥400k	100k/yr	−0.7k	7.9%

Choose A: NPV is positive and IRR beats the cost of capital; B is 4× bigger yet creates no value.

When NPV and IRR disagree

Occasionally project A has the higher IRR but lower NPV than B (scale or timing differences):

Mutually exclusive projects: always pick the larger NPV — maximizing owner wealth is the goal
IRR's reinvestment assumption: IRR implicitly reinvests interim cash at the IRR itself; the higher the IRR, the more distorted the assumption; NPV discounts at the cost of capital — more conservative and reliable
Non-conventional cash flows (positive, then negative, then positive) can produce multiple IRRs — look only at NPV

Common mistakes and myths

"Fast payback means a good project" — payback ignores post-payback cash flows and discounting; two 3-year-payback projects can have wildly different NPVs.
"High IRR always means profit" — IRR is relative: 10% on ¥10k earns ¥1k, while 7% on ¥1M earns ¥70k. Absolute wealth is measured by NPV.
"Any discount rate will do" — the discount rate is your opportunity cost; individuals should use the return they can reliably earn (e.g., 5%–8%). A wrong rate invalidates everything.
"Forgetting terminal salvage value" — equipment salvage and store transfer fees are year-N cash flows; omitting them understates NPV.

Use the [NPV/IRR Calculator](/c/finance/npv-irr) to compute from cash flows directly, and the [ROI Calculator](/c/finance/roi) for simple projects.

Frequently Asked Questions

What is NPV in simple terms?

Net Present Value converts all future cash flows into today's money, then subtracts what you pay today. NPV > 0: the project earns MORE than your required return — accept. NPV < 0: you'd do better putting the money elsewhere. Example: pay ¥100k, receive ¥25k/year for 5 years, discount at 8% → NPV ≈ −¥182 → decline.

What is IRR and how is it different from NPV?

IRR is the discount rate that makes NPV exactly zero — the project's built-in rate of return. Compare it to your cost of capital: IRR 12% vs 8% financing → accept; vs 15% → decline. NPV gives an absolute money figure; IRR gives a percentage. Use IRR for quick screening, NPV for final decisions.

What discount rate should I use for NPV?

Your opportunity cost: (1) personal investing — your reliable alternative return (5–8%); (2) borrowed money — the actual loan rate plus risk premium; (3) business — WACC, typically 8–12%. When unsure, run the model at 8% and then stress-test at ±2% to see if the decision flips.

How do I calculate NPV and IRR in Excel?

=NPV(rate, cashflows_yr1_onward) + initial_investment (the initial outlay stays OUTSIDE the NPV function, entered as a negative). =IRR(all_cashflows) including the negative initial value. For irregular dates use =XNPV and =XIRR with a date column.

When NPV and IRR disagree, which do I trust?

Trust NPV. Conflicts arise with different project scales or cash-flow timing: a tiny project can show 40% IRR yet add less wealth than a big project at 12% IRR. IRR also assumes interim cash flows reinvest AT the IRR — often unrealistic. NPV assumes reinvestment at the cost of capital, the safer assumption.

Is a fast payback period enough to approve a project?

No. Payback ignores everything after the cutoff and ignores discounting entirely. Two projects can both "pay back in 3 years" while one stops generating cash in year 4 and the other runs for 15. Use payback only as a liquidity screen; let NPV make the call.