i can solve the npv thats no problem. I don’t understand how they managed to get 21.4% as the irr. this is the discount that should make = -$6million + 500k/(1+r) + 4mln/(1+r)^{2} +4mln/(1+r)^{3} + 4mln/(1+r)^{4} ±1mln/(1+r)^{5} = 0. in my financial calculator i plugged in cf_{0} as -6million and then cf_{1} as 500k and so on until i reach cf_{5} to plug in -$1 million in the end. the irr that should solve for npv of 0 should be 21.4% and its not. 21.4% irr gives me an npv of 192k. what am i doing wrong here?

If you put those numbers into Excel and use the built-in NPV function with 18% as the discount rate, you should get an NPV of 0.43.

Unfortunately, Excel’s NPV function is stupid: it assumes that the first cash flow (−6) occurs at time 0 1, not at time 1 0. So you have to multiply the answer by 1.18 (= 1 + 18%) to get the correct answer: 0.51 (or, to 6 decimal places, 0.509579).

" it assumes that the first cash flow (−6) occurs at time 0, not at time 1" but -6 is occurring at time 0 right? the question says “Investment outlays are $6 million immediately” - i.e. time 0? Do you mind telling me what keystrokes you used on your calculator please?

My mistake: I mistyped the numbers. The built-in NPV function in Excel assumes that the first cash flow is at time 1, not a time 0. When the initial cash flow is at time 0 (i.e., always!), the function will give an incorrect amount: too small by one period’s interest.

many thanks guys. final q (I promise). I was expecting to use the irr as the discount I and see an npv of 0 which I believe is what the irr is. does this work? I didn’t see that it did. that was actually the basis for this question. so the keystrokes would be.

CF_{0} = -6

CF_{1} = -0.5

CF_{2} = 4

CF_{3} = 4

CF_{4} = 4

CF_{5} = -1

and then i as 21.4% which should give 0 npv but it doesnt.

That’s cause you rounded it off to one decimal place. When you compute the IRR you should store the full numerical answer and use it for your NPV computation.

Fino you are on the money with that comment. I plugged in the numbers as millions and got around 0.16 as the npv which is close enough for me. Thanks very much and thanks to you too S2000.