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Negative NPV but finite payback period - how can this be?

If you are computing non discounted or regular payback period then it may happen to exists yet irr and npv may be negative
Take these cash flows
-100 50 50 10
You can see the project has a payback period (non discounted) of 2 years
Yet if the cost of capital or the discount rate is 10%, then the project has an NPV of -5.72 and irr doesn't exist or if does then it is negative
You would get a better view of payback period if you used discounted payback period which at 10% does not exist for this project

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The equation for the profitability index at a required return of 10 percent is: PI = [$7,300/1.1 + $6,900/1.1 2 +.If the discount rate is infinite, the NPV is $.

financeformulas.net/Perpetuity.html

www.wikihow.com/Calculate-NPV

www.investopedia.com/terms/n/npv.asp

financeformulas.net/Present_Value_of_Growing_Perpetuity.html

https://www.excelforum.com/./467891-how-to-calculate-npv-of-an-infinite-series.ht.

Say D is your discount rate, CF the annual constant cash flow. (note that D must be above 2% to estimate an "infinite" NPV) NPV = Sum CF* .