# Understanding the Difference Between NPV vs IRR

Understanding the difference between the net present value (NPV) versus the internal rate of return (IRR) is critical for anyone making investment decisions using a discounted cash flow analysis. Yet, this is one of the most commonly misunderstood concepts in finance and real estate. This post will help you understand the difference between NPV vs IRR, and clear up some common misconceptions.

First, let’s go over some definitions of NPV and IRR, then we’ll walk through an example and some common pitfalls.

### Net Present Value (NPV) Definition

Net present value (NPV) is an investment measure that tells an investor whether the investment is achieving a target yield at a given initial investment. NPV also quantifies the adjustment to the initial investment needed to achieve the target yield assuming everything else remains the same. Formally, the net present value is simply the summation of cash flows (C) for each period (n) in the holding period (N), discounted at the investor’s required rate of return (r):

### Internal Rate of Return (IRR) Definition

Internal rate of return (IRR) for an investment is the percentage rate earned on each dollar invested for each period it is invested. IRR is also another term people use for interest. Ultimately, IRR gives an investor the means to compare alternative investments based on their yield. Mathematically, the IRR can be found by setting the above NPV equation equal to zero (0) and solving for the rate of return (IRR).

### Distinction Between NPV vs IRR

So, what’s the difference between NPV and IRR? As shown in the formulas above, the NPV formula solves for the present value of a stream of cash flows, given a discount rate. The IRR on the other hand, solves for a rate of return when setting the NPV equal to zero (0).

In other words, the IRR answers the question “what rate of return will I achieve, given the following stream of cash flows?”, while the NPV answers the question “what is the following stream of cash flows worth at a particular discount rate, in today’s dollars? To dive deeper into a more intuitive explanation of IRR and NPV, check out the Intuition Behind the NPV and IRR.

### Quantitative Example of NPV vs IRR

Consider a property with expected future net cash flows of \$30,000 per year for the next five years (starting one year from now). If you expect to sell the property 5 years from now for a price 10 times the net cash flow at that time, what is the value of the property if the required return is 12%?

Plugging in the \$30,000 net cash flows for five years into the NPV equation above along with the 12% discount rate, you’ll find that the net present value is \$278,371. You can also find all of the formulas and answers to these questions in this spreadsheet we put together:

Where should we send your NPV vs IRR solutions file?

Now, let’s extend this example with a few more questions:

• Suppose the seller of the above building wants \$300,000. Should you do the deal still assuming your required rate of return is 12%?
• What is the IRR if you pay \$260,000 and how does this compare to the required return of 12%?

Plugging into the equations above (or using the above linked spreadsheet), if the owner insists on getting \$300,000 for the building, it drives down the IRR to 10% and generates an NPV of -\$21,629.  This means you should not do the deal if your required return is 12% and you would instead need to pay \$21,629 less for the property in order to achieve your target yield.

Assuming you are able to negotiate the price down to \$260,000, then your IRR becomes much more attractive at 13.87%. Also, at a \$260,000 acquisition price, the NPV becomes a positive \$18,371, which means that you could pay roughly \$18,000 more for the property and still achieve your target yield of 12%.

### Limitations of the Internal Rate of Return (IRR)

One problem with the IRR is that it ignores the initial investment amount. If you’re comparing two alternative investments and your only decision criteria is the IRR, then which is better – a 50% return on \$1,000 investment, or a 10% return on a \$50,000 investment?  If IRR was your only decision criteria, then you’d choose the first option, ignoring the the size of your initial investment, and therefore the actual cash you’re able receive as a result of your investment.

Another limitation of the IRR is that it doesn’t always equal the return on your initial investment over the holding period. When periodic cash flows exist in an investment that results in capital recovery, the IRR makes no assumptions about what you do with these interim cash flows. For example, you might put that cash flow into a bank account with a much lower yield than the IRR, which can be problematic when evaluating the true return for an investment.

### Limitations of the Net Present Value (NPV)

One limitation of the NPV is that it doesn’t take into account the timing or variability of cash flows.  For example, which is better, a project that returns one lump sum in 10 years, or instead a project with even cash flows every year for ten years? These are two different investments and, depending on your needs, you might prefer one over the other, even if the NPV for both projects is the same.

Another limitation of the NPV is that it’s often difficult to accurately estimate the discount rate. Because of this, it might also be difficult to accurately account for the riskiness of projected cash flows. For example, if you’re evaluating a building with short term leases, then you might consider bumping up your discount rate to account for this rollover risk.  But exactly how much higher should your discount rate be?  This is often a subjective decision that an objective measure, like the NPV, can’t easily account for.

### No Silver Bullet for Investment Analysis

Understanding the difference between NPV vs IRR is important, but perhaps more important is understanding that there is no silver bullet for making an investment decision.  Both NPV and IRR should be taken into account, along with other investment decision indicators such as the payback period and the capital accumulation method, as well as a solid understanding of your own investment needs, risk aversion, and available options.

• Joel Gabelman

Your IRR calculations appear incorrect in your excel sheet. You rare including TWO columns, when you should only be including the series of cash flows. As an example, your IRR for question 3 on your Excel sheet is 6.71%, when the correct answer should be 13.87%.

• Rob

Joel, thanks for pointing this out. This file was recently converted from an open office sheet to an Excel sheet and it appears that during the conversion process the formula picked up the periods column instead of the cash flows column. This has been corrected and uploaded to the post. Thank you.

• IK

Hi, thanks for explaining this so clearly. So if I was looking at an expansion for a business that had an IRR of only 2.13% but an NPV of just over \$900,000 would it be worth going ahead with the investment even if there was a required rate of return of 8.2%? Thanks!

• Rob

When you calculated your NPV of \$900,000, what discount rate did you use?

• IK

Hi, 8.2% was used as the discount rate. Thanks!

• Rob

So if 8.2% is what you want (discount rate), but 2.13% is what you get (IRR), then I’m not seeing how you are getting a positive NPV of \$900,000. Can you post your cash flows?

• IK

Thanks so much for your help but it is probably a bit complex for this forum… I have had a chat to someone in person and I think I’m across where I went wrong now. Thanks again for the advice – great article! 🙂

• I don’t understand your comment: “One problem with the IRR is that it ignores the initial investment amount.” The initial investment is right there in your examples at T0; #2 and #3 illustrate the results of 10% IRR if the initial investment was \$300K, or 13.87% if the initial investment was \$260K. This is consistent with how I’ve been using it for years and also with the examples in XL and other places.

• Rob

Yea, you got it.

• What threw me off is that the Excel function for NPV does NOT account for the initial T0 outflow (since that value doesn’t need to be discounted), and, unlike IRR, needs to be added back in manually, so I was thinking about the actual equations.

• kikib

I am a residential underwriter and I am interested in getting into commercial. Could anyone suggest any materials or books that will help get at least the basic knowledge so that I can hopefully one day be given the opportunity to cross over.

• Sanjay Minni

You can try a free online calculator at uxfin.com that accepts multiple receipts and payments with varying amounts and date intervals. you can also force compounding intervals

• shamal

does anyone know about VOI( value of information) spreadsheet?pls i need some help i am a petroleum student ???

• Shekhar

When calculating the Project IRR, we take the residual value and residual value is a notional value (speculative). IRR with residual value is three times the Interest cost while without the residual value, IRR is less than the Interest cost. How do we read that?

• Shekhar

When calculating the Project IRR, we take the residual value and residual value is a notional value (speculative). IRR with residual value is three times the Interest cost while without the residual value, IRR is less than the Interest cost. How do we read that?

• Richard Bird

hi – we are working on a investment present net value calculation for uni and debating if initial investment always gos on year 0 – as it is farm equipment finaced over 4 yrs??? anyone??

• Don Issac

the initial investment usually goes in as year0. and then the cashflows (interim or other) start at periods greater than year0. However if you need to pump in more cash/investment into the project at a later stage those amounts will need to put into their corresponding time periods. eg 2ys later maintenance for farm equipment costs etc. However please note that in such cases IRR may not work if the net cashflow for that period changes from positive to negative