What is IRR? Why is it useful? How does it relate to NPV? If a project has a positive NPV, how can its IRR be calculated (the definition of IRR appears to suggest that IRR makes NPV = 0)?
Briefly (there are long chapters in text books about this):
The IRR is in fact the discount rate that makes the NPV zero. That is exactly its definition. If there is an initial investment and then all the remaining cash flows are positive receipts, there is exactly one positive IRR. In other cases there can be more than one IRR. For example, initial cost 40, year one +130, year two -100, you can see there are two IRRs 100% and 25%.
When there is a single IRR, the comparisions “is the NPV positive at discount rate r” is exactly the same as is the IRR > r. However even in this case it is not true that when comparing two projects the one with the higher NPV also has the higher IRR.
NPV is the generally preferred method for project selection.
I agree with OldGuy’s summary of the definitions, but I disagree with his last statement. Project selection criteria should use many measures in making a decision. IRR and NPV are just a few. The weighting of importance will depend upon the individual investor.
So what is the significance of the IRR standing on its own? Why is it important to look at the point where NPV = 0?
If you use a 10% discount rate in your cash flow model, and the NPV of your future cash flows is 0, then you know your IRR calculation is 10%. But if your NPV is > 0, then your IRR should be greater than 10%. Many firms have a hurdle rate for investments, say 15% unlevered. In order to see if your project’s IRR clears that hurdle rate, you need to know what the IRR on an unlevered basis is. You may then want to see how much return is added by adding leverage. IRR is a very useful calculation for decision making purposes.
It’s simply one easy way to compare different potential investments. Sure, you don’t need it, but then you don’t need NPV either. It’s all mathematically about the same as a practical matter, so most companies have their own favorite methods.
As an analogy…
Suppose you know 2 pieces of info: a car’s gas tank capacity and distance range (miles) on that one tank.
You can think of fuel efficiency in 3 different ways:
#1: miles-per-gallon.
#2: gallons-per-mile
#3: total miles on a full tank of gas
At one level, the 3 measurements are all mathematically related and could be considered redundant. (Similar to saying IRR and NPV are redundant.)
But sometimes it’s easier to frame decisions based on one measurement vs the other. If you’re making a cross country trip, you might be trying to minimize the # of gas station stops. In that case, you’d find it easier to think in terms of miles-per-tank even though the other 2 measurements can tell you the same answer.
NPV and IRR are related, but not redundant. IRR measures the performance of an investment. NPV measures both the performance and the magnitude. Doubling each of the cash flows associated with a project doubles the NPV, but leaves the IRR unchanged.
Context was NPV = 0.
Why must NPV = 0 for the internal rate of return to be calculated?
??? You may need to take some classes on reading comprehension or “how to phrase the question I really want to ask”.
Nowhere in any of the responses above has anyone said that NPV must = 0 in order to calculate an IRR.
The NPV of a project is the sum of the discounted cash flows
NPV = X[sub]0[/sub] + X[sub]1[/sub]/(1+r) + … + X[sub]n[/sub]/(1+r)[sup]n[/sup]
generally X[sub]0[/sub] is negative being the initial investment.
The IRR is DEFINED as that value of r for which the NPV is zero. Note that this is an “as if” question. It does not mean that the NPV is zero, just what discount rate would be required for teh NPV to be equal to zero.
And as I noted before there may be more than one value for which this is true. In general this problem is a polynomial of degree n and will have n solutions. If X[sub]0[/sub] is negative and all the others are not, then there will be exactly one value of r > -100%. (I misspoke before saying one positive r.)
The Net Present Value requires that you use a discount rate to determine it. The discount rate used usually matches your cost of capital. For example, if it costs you 5% to borrow money, you might use a 5% discount rate. Common rates used in the oil and gas industry are 9% or 10%. Let’s run through an example.
Let’s say you have a project that requires an initial cash out flow of $10 and then returns you $3 a year for 5 years. Let’s say you want to use a discount rate of 5%. The way you would calculate this is as follows.
NPV = (-10/(1.05^0)) + (3/(1.05^1))+(3/(1.05^2))+(3/(1.05^3))+(3/(1.05^4))+(3/(1.05^5))
In this case your NPV = $2.99. If you happened to choose a discount rate of 0%, your NPV would obviously simply be the sum of the cash flows or $5 in this case.
What the Internal Rate of Return is telling you is simply what is the actual rate of return of my investment. The math needed to determine this requires that you make the NPV = $0. In this case, the IRR would be 15.3% because if you made the discount rate equal to 15.3% then the NPV would equal $0.
I should also add that many times you will hear terms like PV10 or PV15. This simply means what is the present value using a discount rate of 10% or 15%.
Why does NPV = 0 when the IRR is being calculated? Shouldn’t the rate of return be analyzed based on a positive or negative NPV (i.e., whatever the NPV turns out to be)?
You don’t use NPV when calculating the IRR. They are separate calculations of the same cash flows.
The IRR calc. is traditionally based upon an initial negative cash out and then a stream of positive cash flows.
The NPV calc. is the present value of those same stream of cash flows discounted back using a discount rate.
Think about it this way. Consider the discount rate that you use as your required rate of return. Using my previous example, think of it as if I required a 15.3% rate of return, then there would be no excess value above that. If I required a 5% rate of return, then the value of the project would be $2.99.
The NPV is some what of a meaningless concept without stating the discount rate, right? I mean, you can’t just simply say that a project has an NPV of $50 or $0 or whatever. You have to state what discount rate you are using for that to have any meaning. It just so happens that the IRR is the unique rate calculated that makes the NPV equal to zero.
FIFY
IRR is also not a number handed down by God, but an estimate based on assumptions about the project. One should look at the variance of the expected IRR based on things like risk and market conditions. I know many cases where projects with IRRs well above that required by a company got rejected. I think a lot of this involves the discount rate required (perhaps unconsciously) by the decision maker being considerably higher then the corporate required IRR due to various factors.
But that involves its application, not its definition, of course.
Actually you didn’t fix anything. You made the statement redundant. The preceding sentence that you did not quote makes it exceedingly clear that the rate I was referencing is the discount rate.