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)” எவ்வளவு துல்லியமானது?

துல்லியம் உங்கள் உள்ளீடுகளையும் முறையின் அனுமானங்களையும் சார்ந்தது. தசமக் கணக்கீடு 50 முக்கிய இலக்கங்களைப் பயன்படுத்துகிறது. ஆனால் மதிப்பீடுகள், எண் முறைகள், மூலத் தரவுகள் குறைந்த துல்லியத்தைக் கொண்டிருக்கலாம்; காட்டப்படும் மதிப்பை வட்டமிடுவது இந்த வரம்புகளை நீக்காது. சுயாதீன மூலங்களின் தீர்வுகளுடன் சரிபார்க்கப்பட்ட எடுத்துக்காட்டுகள்: 6. எடுத்துக்காட்டாக, “Four-year project at 10%” என்பது 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 உடன் சரிபார்க்கப்படுகிறது.

Q: இந்த முறையின் மூலம் என்ன?

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.

புதுப்பிக்கப்பட்டது 28 செப்டம்பர், 2026சரிபார்க்கப்பட்ட எடுத்துக்காட்டுகள்: 6

Net present value

தசம இடங்கள்: 2; அருகிலுள்ள மதிப்பு; சம தூரத்தில் இரட்டைப்படை இலக்கை நோக்கி

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 வரிசைகள்: 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

கணக்கிடும் முறை 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) பற்றி

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.

தீர்க்கப்பட்ட எடுத்துக்காட்டுகள்

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

சரிபார்ப்பின் மூலம்: 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

சரிபார்ப்பின் மூலம்: 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%

சரிபார்ப்பின் மூலம்: 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

சரிபார்ப்பின் மூலம்: Microsoft IRR documentation: 8.7% after five years; Python decimal bisection gives 8.6630948037

கேள்விகள்

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)” எவ்வளவு துல்லியமானது?

துல்லியம் உங்கள் உள்ளீடுகளையும் முறையின் அனுமானங்களையும் சார்ந்தது. தசமக் கணக்கீடு 50 முக்கிய இலக்கங்களைப் பயன்படுத்துகிறது. ஆனால் மதிப்பீடுகள், எண் முறைகள், மூலத் தரவுகள் குறைந்த துல்லியத்தைக் கொண்டிருக்கலாம்; காட்டப்படும் மதிப்பை வட்டமிடுவது இந்த வரம்புகளை நீக்காது. சுயாதீன மூலங்களின் தீர்வுகளுடன் சரிபார்க்கப்பட்ட எடுத்துக்காட்டுகள்: 6. எடுத்துக்காட்டாக, “Four-year project at 10%” என்பது 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 உடன் சரிபார்க்கப்படுகிறது.

இந்த முறையின் மூலம் என்ன?

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).

இந்தக் கணிப்பான் பற்றி

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

ஆதாரங்கள்

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)

திட்டமிடலுக்கு மட்டும். கடன் வழங்குநர்கள், வரி அமைப்புகள், சந்தைகள் தங்களின் வட்டமிடல் முறைகள், கட்டணங்கள், விதிகளைப் பயன்படுத்துகின்றன; உறுதியளிக்கும் முன் அவர்களிடம் தொகைகளைச் சரிபார்க்கவும்.

ஆதாரங்களுடன் சரிபார்க்கப்பட்டது

இந்தக் கணிப்பானில் சுயாதீன ஆதாரங்களிலிருந்து பதில்கள் பெறப்பட்ட 6 தீர்க்கப்பட்ட எடுத்துக்காட்டுகள் உள்ளன. இவை சோதனைத் தொகுப்பில் இயங்குகின்றன; இங்கேயும் அவற்றை இயக்கலாம்.

NPV profile

Cumulative cash flow

Discount every flow to period 0

Internal rate of return

Modified IRR

MIRR

Payback