# Internal Rate of Return and NPV

Suppose that for a sequence of cash flows, the first cash flow in the sequence is negative and that the cash flows have a unique Internal Rate of Return of 15% per year. Is the following statement true or false?

What happens to the NPV of cashflows if you discount the cash flows using a rate of 15% per period? Is it positive, 0, or negative?

Now, I have read that the IRR equates the inflows and outflows - i.e., the NPV becomes 0. I’m just confused with the first part of the question wherein they have mentioned about the 1st CF to be negative.

Can someone explain please?

Thanks,
Giggsy!

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I think they mean CF0 is negative rather than CF1. So if CF0 is negative it is the same as paying out cash for an investment, which you later receive positive returns…CF1 and beyond.

If there is no initial negative cash flow (investment) then wouldn’t any positive cash flow received result in a positive IRR no matter what rate youre discounting it at?

For the IRR to be zero you need that initial CF0 to be negative.

Lets make it simple:

Suppose CF0 or first cash flow CF1 are only two things in series:

CF0= -100

CF1 = 115

Then, IRR will be 15% || Put in MS Excel function: =IRR(Values,[guess]) — Dont feed anything in [guess]

Now come to NPV:

Rate is 15% (IRR)

CF0 = -100

CF1 = 115

Now NPV = 0

Put above all data in MS Excel Function: =NPV(Rate,Value1,Value2…….)

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If CF0 is negative value then put CF1 as positive number in above case

or one can put either way if putting CF0 as positive number value then put CF1 as negative number

CF0= 100

CF1= -115

IRR and NPV will be the same.

NPV is comparitive thingy. You compare CF0 with all PV of future cash flow.

Suppose you have invested 100 means negative 100 then you are expecting to receive 115 (positive) @15% at least

Means,  is -100 and PV of 115 is added it should be zero. =115/1.15 = 100

-100 (CF0 invested) + 100 (Discounted CF1) = 0