NPV and IRR calculator (with MIRR and payback)

Q: How do you calculate NPV?

Divide each cash flow by (1 + r)^t, where t is its period, and add the results, counting the initial outlay at t = 0. At 10%, the flows −10,000, 3,000, 4,200 and 6,800 are worth −10,000 + 2,727.27 + 3,471.07 + 5,108.94 = 1,307.29. A positive NPV means the project earns more than the discount rate.

Q: Why does Excel's NPV function give a different answer?

Excel's NPV treats the first value in its range as arriving at the end of period 1, not at period 0. Putting all four default flows into =NPV(10%, …) returns 1,188.44, which is 1,307.29 ÷ 1.1. To get the usual NPV, leave the initial outlay out of the function and add it separately: =NPV(10%, 3000, 4200, 6800) − 10000.

Q: How is IRR calculated?

IRR is the rate that makes NPV zero, and it has to be found by trial: there is no general formula beyond four periods. For the default flows it is 16.34%. Excel's IRR starts from a 10% guess and returns #NUM! if it has not converged after 20 tries; here the search scans rates from −99.9% to 1,000% and then refines the root.

Q: What is the difference between IRR and MIRR?

IRR implicitly assumes every inflow is reinvested at the IRR itself; MIRR uses a stated reinvestment rate and finance rate, and it always has a single answer. In Microsoft's example, −120,000 followed by 39,000, 30,000, 21,000, 37,000 and 46,000 has an IRR of 13.07% but an MIRR of 12.61% at a 10% finance rate and 12% reinvestment rate.

Q: What is the difference between payback and discounted payback?

Payback counts plain cash; discounted payback counts present values, so it is always longer when the rate is positive. For the default flows, cumulative cash is −2,800 after two periods and the third period's 6,800 covers it in 0.41 of a period, a payback of 2.41. At 10% the discounted payback is 2.74 periods. Neither measure counts cash after the payback point.

Q: 「NPV and IRR calculator (with MIRR and payback)」の精度はどのくらいですか？

精度は入力値と計算方法の前提に依存します。十進演算には有効数字50桁を使いますが、推定、数値計算手法、元データの精度はそれより低い場合があります。表示の丸め処理でこれらの制約がなくなるわけではありません。 独立した出典の解答と照合した計算例：6。 例えば、「Four-year project at 10%」はPython decimal (prec 50) script: textbook NPV, IRR by 300-step bisection, Excel MIRR definition. Microsoft's NPV example gives 1,188.44 for these flows with the first at t = 1; ×1.1 = 1,307.28と照合しています。

Q: この計算方法の出典は何ですか？

Microsoft Excel IRR function; Microsoft Excel MIRR function; Microsoft Excel NPV function; Brealey, Myers & Allen — Principles of Corporate Finance, ch. 5 (NPV and other investment criteria).

Calculate NPV, IRR, modified IRR, payback and discounted payback for a series of periodic cash flows, with the NPV profile across rates.

更新日 2026年9月28日検証済みの例：6

Net present value

小数点以下の桁数：2；最も近い値へ、等距離なら末尾が偶数の値へ

Internal rate of return: 16.34%
Modified IRR: 15.15%
Payback period: 2.41periods
Discounted payback period: 2.74periods
Profitability index: 1.1307

The project is worth $1,307.29 more than it costs in today's money at a 10% discount rate. Its IRR is 16.34% and it pays back after 2.41 periods.

NPV profile

Cumulative cash flow

Cumulative (payback 2.41)Cumulative present value (payback 2.74)

Cash flows and discounting 行数：4

Period	Cash flow	Discount factor	Present value	Cumulative	Cumulative PV
0	−$10,000.00	1	−$10,000.00	−$10,000.00	−$10,000.00
1	$3,000.00	0.9091	$2,727.27	−$7,000.00	−$7,272.73
2	$4,200.00	0.8264	$3,471.07	−$2,800.00	−$3,801.65
3	$6,800.00	0.7513	$5,108.94	$4,000.00	$1,307.29

計算方法 S

Discount every flow to period 0
$NPV = \frac{-10{,}000}{(1+0.1)^{0}} + \frac{3{,}000}{(1+0.1)^{1}} + \frac{4{,}200}{(1+0.1)^{2}} + \frac{6{,}800}{(1+0.1)^{3}} = 1{,}307.29$
CF₀ sits at t = 0 and is not discounted. Excel's NPV() treats its first value as arriving at t = 1, so Excel returns this NPV divided by (1 + r).
Internal rate of return
$\sum_{t=0}^{3} \frac{CF_t}{(1+IRR)^t} = 0 \;\Rightarrow\; IRR = 16.340560\%$
Bracketed on a rate grid, narrowed by bisection, then refined with Newton's method: 16 steps, |NPV| = 8 × 10⁻⁴⁶ at the root.
Modified IRR
$FV_{\text{in}} = \sum_{CF_t>0} CF_t(1+0.12)^{3-t} = 15{,}267.20,\quad PV_{\text{out}} = \sum_{CF_t<0} \frac{CF_t}{(1+0.1)^t} = -10{,}000.00$
MIRR
$MIRR = \left(\frac{15{,}267.20}{10{,}000.00}\right)^{1/3} - 1 = 15.1471\%$
Payback
Cumulative cash turns non-negative after 2.4118 periods, and cumulative present value after 2.7441.
Within the crossing period, cash is assumed to arrive evenly (linear interpolation).

NPV and IRR calculator (with MIRR and payback)について

NPV discounts each period's cash flow back to the start and adds them up: NPV = Σ CF_t ÷ (1 + r)^t, with the first flow at period 0. IRR is the discount rate at which NPV is exactly zero. MIRR instead assumes outflows are funded at a finance rate and inflows reinvested at a reinvestment rate. Payback counts the periods until cumulative cash turns positive, and discounted payback does the same with present values.

With the defaults, an outlay of 10,000 followed by 3,000, 4,200 and 6,800, discounted at 10%, the NPV is 1,307.29 and the IRR is 16.34%. The money comes back after 2.41 periods, or 2.74 periods counting the time value of money. MIRR, at a 10% finance rate and 12% reinvestment rate, is 15.15%.

A period can be a year, a quarter or a month, as long as the rate is for the same period. Flows that change sign more than once can have several IRRs; the result then warns you and MIRR is the better guide.

計算例

Four-year project at 10%

Cash flows, period 0 first: -10000, 3000, 4200, 6800
Discount rate (per period): 10%
Finance rate for MIRR: 10%
Reinvestment rate for MIRR: 12%

Net present value: 1,307.29
Internal rate of return: 16.34056%
Modified IRR: 15.147134%
Payback period: 2.41 periods
Discounted payback period: 2.74 periods

照合元：Python decimal (prec 50) script: textbook NPV, IRR by 300-step bisection, Excel MIRR definition. Microsoft's NPV example gives 1,188.44 for these flows with the first at t = 1; ×1.1 = 1,307.28

Microsoft MIRR example, five years

Cash flows, period 0 first: -120000 39000 30000 21000 37000 46000
Discount rate (per period): 10%
Finance rate for MIRR: 10%
Reinvestment rate for MIRR: 12%

Modified IRR: 12.609413%
Internal rate of return: 13.073554%
Payback period: 3.81 periods

照合元：Microsoft MIRR documentation: 12.61% (five years); Python decimal gives 12.6094130366 and IRR 13.0735539471

Microsoft MIRR example, three years

Cash flows, period 0 first: -120000 39000 30000 21000
Discount rate (per period): 10%
Finance rate for MIRR: 10%
Reinvestment rate for MIRR: 12%

Modified IRR: -4.804466%
Internal rate of return: -14.405951%

照合元：Microsoft MIRR documentation: −4.80% after three years; Python decimal gives −4.8044655250

Microsoft IRR example, five years

Cash flows, period 0 first: -70000 12000 15000 18000 21000 26000
Discount rate (per period): 10%
Finance rate for MIRR: 10%
Reinvestment rate for MIRR: 12%

Internal rate of return: 8.663095%
Net present value: -2,683.31

照合元：Microsoft IRR documentation: 8.7% after five years; Python decimal bisection gives 8.6630948037

よくある質問

How do you calculate NPV?

Divide each cash flow by (1 + r)^t, where t is its period, and add the results, counting the initial outlay at t = 0. At 10%, the flows −10,000, 3,000, 4,200 and 6,800 are worth −10,000 + 2,727.27 + 3,471.07 + 5,108.94 = 1,307.29. A positive NPV means the project earns more than the discount rate.

Why does Excel's NPV function give a different answer?

Excel's NPV treats the first value in its range as arriving at the end of period 1, not at period 0. Putting all four default flows into =NPV(10%, …) returns 1,188.44, which is 1,307.29 ÷ 1.1. To get the usual NPV, leave the initial outlay out of the function and add it separately: =NPV(10%, 3000, 4200, 6800) − 10000.

How is IRR calculated?

IRR is the rate that makes NPV zero, and it has to be found by trial: there is no general formula beyond four periods. For the default flows it is 16.34%. Excel's IRR starts from a 10% guess and returns #NUM! if it has not converged after 20 tries; here the search scans rates from −99.9% to 1,000% and then refines the root.

What is the difference between IRR and MIRR?

IRR implicitly assumes every inflow is reinvested at the IRR itself; MIRR uses a stated reinvestment rate and finance rate, and it always has a single answer. In Microsoft's example, −120,000 followed by 39,000, 30,000, 21,000, 37,000 and 46,000 has an IRR of 13.07% but an MIRR of 12.61% at a 10% finance rate and 12% reinvestment rate.

What is the difference between payback and discounted payback?

Payback counts plain cash; discounted payback counts present values, so it is always longer when the rate is positive. For the default flows, cumulative cash is −2,800 after two periods and the third period's 6,800 covers it in 0.41 of a period, a payback of 2.41. At 10% the discounted payback is 2.74 periods. Neither measure counts cash after the payback point.

「NPV and IRR calculator (with MIRR and payback)」の精度はどのくらいですか？

精度は入力値と計算方法の前提に依存します。十進演算には有効数字50桁を使いますが、推定、数値計算手法、元データの精度はそれより低い場合があります。表示の丸め処理でこれらの制約がなくなるわけではありません。独立した出典の解答と照合した計算例：6。例えば、「Four-year project at 10%」はPython decimal (prec 50) script: textbook NPV, IRR by 300-step bisection, Excel MIRR definition. Microsoft's NPV example gives 1,188.44 for these flows with the first at t = 1; ×1.1 = 1,307.28と照合しています。

この計算方法の出典は何ですか？

Microsoft Excel IRR function; Microsoft Excel MIRR function; Microsoft Excel NPV function; Brealey, Myers & Allen — Principles of Corporate Finance, ch. 5 (NPV and other investment criteria).

この計算機について

NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t},\qquad \sum_{t=0}^{n} \frac{CF_t}{(1+IRR)^t} = 0,\qquad MIRR = \left(\frac{FV_{\text{inflows}}}{-PV_{\text{outflows}}}\right)^{1/n} - 1

出典

Microsoft Excel IRR function
Microsoft Excel MIRR function
Microsoft Excel NPV function
Brealey, Myers & Allen — Principles of Corporate Finance, ch. 5 (NPV and other investment criteria)

計画の参考用です。金融機関、税務当局、市場は独自の丸め方、手数料、規則を適用します。契約などの前に該当機関へ金額を確認してください。

出典と照合済み

この計算機には、独立した出典の解答を使った計算例が 6 件あります。テストに組み込まれており、ここでも実行できます。

NPV profile

Cumulative cash flow

Discount every flow to period 0

Internal rate of return

Modified IRR

MIRR

Payback