# NPV v IRR:Question

Is it necessary that a project with a higher NPV will have a higher IRR??

No.

That’s why, when you can afford to do several projects, you should rank them according to NPV, not according to IRR.

K. Can you give an example where a project having a higher NPV had a lower IRR? In what scenario this might be possible?

All that IRR does is to equate the value of the inflows to the outflows. One possible example where the NPV is high but the IRR is still low is when the cashflows are uncolventional. Lets say, you received majority of your cash at the end of the period. In such instances, there can be multiple IRRs. There are also cases when you may have no IRR at all, i.e. there is simply no such value that can discount all the cash flows to make the NPV zero.

Now that you know that it’s possible, you should open up Excel and play with it to come up with your own example; you’ll learn a lot more doing that than merely reading something that someone here writes.

Two projects cost \$100,000 each. The first has cash flows of \$30,000 at the end of each year for four years. The second has these cash flows at the end of each year (in order): \$20,350, \$40,350, \$20,350, and \$40,350. The cost of capital is 7%.

I’ll leave it to you to compute the NPV and IRR for each. Report back when you’re done.

Cool! No IRR at all…That’s a new addition. When is it possible? Can you give an example?

It’s 6:00 in the morning here. I’ll do it once I wake up and I’ll report back.

The two problems with IRR – no IRR, or multiple IRRs – occur only with nonstandard cash flows. (Standard cash flows are: outflow at inception, all other cash flows are inflows. Nonstandard means that there are (net) outflows during the project, not just at inception.)

With that knowledge, you should be able to come up with a simple example of each, though it will take a bit of fiddling. The thing to do is create a set of cash flows in Excel – you can get an example with only 2 or 3 years, so don’t go wild – create a table of discount rates and use Excel’s NPV function to calculate the NPV for each discount rate, then plot NPV vs. discount rate. Finally, fiddle with the cash flows until the graph crosses 0 twice, and fiddle with the cash flows until the graph misses 0 completely.

If you have access to a copy of Schweser’s Mind Maps for Level I, they have examples in there.

Got it! Didn’t go for excel (but I’ll do that exercise also). I was just wondering about the equation for NPV and then suddenly the eureka moment- an IRR can be a quadratic with two values or with no soln also…That way, I related to this… Thank God there is Math in this world. Things make so much sense when you interpret math.

No. But NPV will always be positive if IRR is greater than cost of capital. In other words NPV can never be positive if IRR is lesser than the cost of capital

Obviously No , NPV is dependent on the project size but IRR is not.

I am not sure I understand the context in which you’ve answered this. I assume it is for the question that I had put up initially.

First off, thank you for reverting back.

Second off, where does “project size” come in? I am not sure, but can’t a small project also have a high NPV?

Thanks

Another way of viewing this is that NPV and IRR will _ always give you the same decision on a single project_: if NPV says do it (NPV is positive), then IRR will say do it (IRR is greater than WACC); if NPV says don’t do it (NPV is negative), then IRR will say don’t do it (IRR is less than WACC).

Yes. Thank you all So blackjack21 here we take short example to explain this, Let say you have 2 projects with size.

Project 1 - Investment = 10000 , NPV = 1000 , IRR = 8%, cost of capital = 6%

Project 2 - Investment = 1000 , NPV = 400 , IRR = 14%, cost of capital = 6%

Here in example Project 1 has greater NPV but has smaller IRR because of large investment amount needed.

So, it is not necessary that a project with a higher NPV will have a higher IRR

Ok. I got it now. Thanks.

In a way, isn’t IRR too dependent on project size then? Like in this case, project size is small and IRR is large because the return is higher because of a smaller base.

You can say that, but it’s a poor way to look at it.

If you invest \$1,000,000 in a stock and make a 1-year profit of \$100,000 (and cost of capital is 5%), then your NPV is \$47,619, and the IRR is 10%. If you invest only \$1,000 in that stock (for a 1-year profit of \$100), the NPV is \$476, and the IRR is 10%. To say that the IRR depends on the profit versus the initial investment is true, but silly: you aren’t going to earn \$100,000 on a \$1,000 investment in this stock.

The first project has NPV of (\$11,964.42) and the second project has NPV of

(\$12,097.02)

Both have an IRR of 8%