IRR non-discounted payback period /discounted payback

I am sorry but either you have copied the question wrong, or the question in whatever book you found it is nonsense. The payback period is measured in years - a payback period cannot possibly be a NPV.

The question did asked what is the payback period and discounted payback period: My working Payback Cost 270,000 Year 1 50,000 Year 2 180,000 Year 3 100,000 Year 4 50,000 Year 4 scrap value 20,000 130,000 positive Non payback period ( costs of capital 12% pa ) Cost 270,000 Year 1 44650 Year 2 143460 Year 3 71200 Year 4 31800 21110 positive Please advice asking another question : what is the internal rate of return to the nearest % ? the answer is 18% , please explain .

The 130,000 and the 21,110 are the net present values at 0% (when no discounting) and at 12%. They are NOT the payback periods - the payback period is always measured in years as I wrote before. The NPV of 21,110 is not correct - you have forgotten to discount the scrap of 20,000 by 4 years. The correct NPV is 33,830 To calculate the IRR you need to guess at a rate higher than 12% - any rate, but I would try 20%. Then you approximate between the two rates in the way that I do in the lecture.