# Intuition Behind IRR and NPV

What’s the intuition behind Internal Rate of Return (IRR) and Net Present Value (NPV)? Discounted cash flow analysis is an essential tool in the commercial real estate practitioner’s toolbelt, but unfortunately for many people, there is still a lot of mystery surrounding this concept.

First of all let’s get some definitions out of the way and then we’ll walk through an example.

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.

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.

What does all this mean? Consider the following discounted cash flow analysis for a small office building:

The IRR is simply the rate of return an investor would expect to achieve on this property, given its projected cash flows over the holding period. In this case it would be 7.51% without leverage and 10.71% with debt added to the property.

The NPV, on the other hand, depends on the discount rate, which in this case is 12.00%. What is a discount rate? The discount rate is simply the investor’s desired rate of return. Normally the discount rate used is the investor’s opportunity cost of capital or, in the case of an institutional investor, the weighted average cost of capital.

What the NPV tells us is how far off the mark we are from the investor’s desired rate of return. In this case, the NPV is (\$50,225) in the levered example and (\$402,421) in the unlevered example. This means that in order to achieve our desired 12.00% return we’d have to reduce our initial investment in the property (acquisition price, fees, etc.) by \$50,225 or \$402,421, depending on whether or not we place debt on the property.

Notice that the IRR calculated above told us the return on our projected cash flows was 10.71% (levered) and 7.51% (unlevered). So, intuitively, we’d expect to reduce our initial cash outlay in order to improve our rate of return. The NPV simply quantifies how much we need to adjust our initial investment in order to achieve our target yield.

• mo

I don’t think this is right

• Shane

Could you define “Levered” and “Unlevered” better? I am guessing that “Levered” is leveraged using an interest bearing loan of some sort and “Unlevered” is Cash Equity 100% down.

When I google the terms it comes up with “levered and unlevered betas” and basic methods for evaluating companies to make sure they are solvent minus the capitalization structure.

I could not find much information on it in regards to Commercial Real-estate specific evaluations.

• Shane

Excellent article by the way. Other than my ability to fully understand Levered vs. Unlevered. I can see how it would be useful.

• Rob

Hi Shane,

Levered means that you are using debt to finance your acquisition. Unlevered means that you are not using any debt. Using debt is leverage in that it can improve the return your receive on the cash you have invested. On the other hand, leverage also increases the downside risk should the project not work out as planned.

• Steve

Great article, simple and to the point!

• Tara Piantanida-Kelly

I’m still trying to wrap my head around this. In the example above, is the property purchased for \$1,515,000 initially (with \$515,000 cash in and a \$1,000,000 mortgage for the levered side and all cash for the unlevered side)? And then sold after a 10-year holding period for \$1,823,915? And are the EOY increments showing the projected cash flow (NOI – debt service) for each year?

• Rob

Hi Tara, yes that is correct. The levered example is with debt service and the unlevered example is without any debt on the property. The dollar figures for each year are the cash flow before tax numbers determined on the proforma.

• Kevin

graet article. Is the property sold for the same price in lvered and unlevered? this confuses me a bit

• Robby

Yes it’s sold for the same price, but the net proceeds are less in the levered example because you have to pay off the loan balance.

• Arkansas_Red

Is there a “rule of thumb” discount rate that people use for quick analysis?

• Rob

For an individual investor the discount rate is usually the investor’s required rate of return.

• Arkansas_Red

So, what would you do if you were deciding to purchase a property with “Bridgewater Industrial” numbers? Would you only purchase the property if you could reduce the price by either \$50,225 or \$402,421 (for levered or unlevered, respectively)?

• Rob

As always, it depends. If I had alternative investments I could make with my capital that would yield 12% (my discount rate), then I’d probably look closer at those alternatives. On the other hand, I may be willing to accept a lower return in exchange for some other benefit, such as a solid credit tenant. It really depends on your own investment objectives, time horizon, available alternatives, etc. IRR and NPV are tools that allow you to quantify and compare potential investments, but the decision ultimately comes down to what you want to achieve.

• Arkansas_Red

Thanks – this is a good blog ðŸ™‚

• Arkansas_Red

And one other question:

1. The firm that I work for likes to hold on to its properties forever — meaning: they don’t really consider a holding period or disposition. Instead, they simply apply a cap rate to the NOI (along with other mundane things like location, location, and location). What’s wrong with doing that? What do you miss out by not doing a discounted cash flow?

• Rob

When properly applied to a stabilized NOI projection, the simple cap rate can produce a valuation approximately equal to what could be generated using a more complex DCF analysis. However, if the propertyâ€™s net operating income stream is complex and irregular, with substantial variations in cash flow, only a full DCF analysis will yield a credible and reliable valuation. More on the cap rate here:

http://www.propertymetrics.com/blog/2013/06/03/cap-rate/

• Andrew

Nice article, but I’m confused.

You state:

“The discount rate is simply the investorâ€™s desired rate of return. Normally the discount rate used is the investorâ€™s opportunity cost of capital or, in the case of an institutional investor, the weighted average cost of capital.”

However I seem to be missing something. If my cost of capital (loan) is 12%, and my desired rate of return is 12%, I have made zero profit. Shouldn’t my desired rate of return be greater than my cost of capital?

In other words, if I borrow the full amount of the purchase price at 12% (call it \$1 to keep the math simple), then at the end of 1 year I will owe \$1.12. Clearly I need to earn greater than \$1.12 to make a profit, otherwise I have merely broken even. So what am I not understanding? Thank you

• Rob

Assuming you are approaching the discount rate through the lens the the weighted average cost of capital (WACC), then any investment that the company makes must at least achieve your 12% return in order to satisfy debt and equity investors. Any return greater than 12% will create additional value for the shareholders.

In practice your capital structure will include some equity component (not 100% debt like your example). If your property was financed 100% by debt investors and 0% by equity investors, then that means you don’t require any return to equity investors. This scenario seems unlikely.

• mike

Wait, you are getting confused Andrew. OPPORTUNITY cost of capital (discount rate) is NOT the cost of borrowed funds (e.g., mortgage interest rate).The opportunity cost of capital (discount rate) is the rate you could expect to earn from similar investments of similar risk. Your understanding of the opportunity cost of capital was confusing you.

• herkshire

Hi Rob, in order to calculate the IRR, do I need to discount the cash flows back to today first?

• Rob

Yes. IRR is determined through a process of trial and error by trying different discount rates, checking the resulting NPV, and then iterating until NPV is 0.

• herkshire

Hi Rob, thanks for helping. Perhaps I should clarify my question. Let’s say my initial cash outflow is -\$100, & my cash inflow at the end of years 1-5 is \$100. In order to calculate the IRR, would I simply solve the equation:

0 = -100 + 100/r + 100/r2 + 100/r3 + 100/r4 + 100/r5 ???

Or would I need to discount the cash flows first by the WACC, and then solve the equation for the IRR??? i.e.

0 = -100 + 100/r + 98/r + 96/r + 94/r + 92/r

And from the above follows, do I need a discount rate before I calculate the IRR?

Hope that makes sense…

• Rob

The IRR is the interest rate that makes the NPV zero.

You wouldn’t discount the cash flows by the WACC and then try to solve for IRR. This would be assuming what you are trying to solve, which wouldn’t make sense.

You could discount the cash flows by your WACC, check what the resulting NPV is, then adjust the discount rate rate up or down until you can make the NPV equal zero. Once you do this you will have found your IRR through a process of trial and error.

• mike

I am not sure I agree. I think the answer is no. if you want to calculate the IRR in excel you simply put in the formula =IRR(-100,100,100,100,100,100,.1) and you will get your IRR which comes out to IRR = 97%. (best investment ever lol). and then you can put in the formula =NPV(.97,100,100,100,100,100)-100 and you will get NPV=0.

In short, the answer to your question is NO you do not need to discount the cash flows back to today first. All you gotta do is use the IRR formula in excel. And you can check yourself by putting in the IRR you just got as the discount rate when using the NPV formula and it will come out to 0.

• Based on the IRR rule,an investment is acceptable if the IRR exceeds the required rate return.It should be rejected otherwise.

• Mike

IRR must be > Cost of Capital or WACC (if it comes from debt and equity), and NPV must be at least positive or > 0 to make that project feasible.

• IRR,its the discount rate that makes the NPV of investment zero.Its internal rate that only depends on the cash flows of particular investment,not on rates offered elsewhere.
NPV,signifies the difference between an investment’s market value and its initial outlay investment cost.Means how much value is created by undertaking an investment by discounted its future cash flow at the appropriate cost of capital(discount rate)

• Kevin

sorry but based on what you say is this statement true

If the IRR is greater than the cost of capital, accept the project. If the IRR is less than the cost of capital, reject the project.

would appreciate if you could clarify.

e.g. this silly example in excel =IRR(-100,100,100,100,100,100,.1) and you will get your IRR which comes out to IRR = 97%. Therefore as long as 97% is greater than cost of capital it is acceptable?

• Mike

hi Rob, if we assume at the end of year 10 the company will sell the asset (tangible (fixed asset) and intangible ( the business) as also), how to estimate the salvage value (terminal value) from our asset to be added in the last cash flow to be discounted back to today ? thanks.

• Rob

For the real estate you can estimate sale price based on a terminal cap rate or by simply applying an annual rate of appreciation to the purchase price. With owner-occupied real estate the building value would likely be based on a third-party appraisal, which would be separate from the value of the business based on free cash flow.

• Hi Rob,
Thanks for the article it was to the point and spot on from other articles I have read about IRR and NPV.
Cheers,
Chris

• NPV is the current value of future cash flows discounted at rhe appropriate discount rate.

• Michael

Why would do you use the same discount rate for levered and unlevered cash flow? Shouldn’t we use different rates?

• Rob

If you require a higher rate of return to compensate for the additional risk when using leverage, then yes, you would increase your discount rate. Also, keep in mind that as long as it’s a positive leverage situation your IRR will also increase when using debt.

• Bob

The additional cost of capital (for leverage) is already included in the cash flow calculations.

• Yvonne

I wish i can understand the importance of using the IRR if we have already the NPV which i found more strong in decision making. Does the IRR really matter? it’s calculation i found it funny. If possible please make me understand the necessity of IRR in project decision making…

• malourdes barangan

I think it is important. To compare it with the discount rate that you used to get the NPV. If the IRR is lesser than the discount rate it ‘s not ideal.. Thats my opinion, correct me if I’m wrong.

• Mat Tallon

Great article. I have 2 questions which have been nagging me for a few weeks!
Am I correct in thinking that the following rules apply in validating a project:

Project gets green light if:
Unlevered IRR > WACC (becasue neither cost of equity or debt are factored into cash flows)
Levered IRR > cost of equity (because cost of debt is already factored in cash flows)

Assuming above rules are correct, should I be able to derive levered IRR if I know unlevered IRR and cost of debt?

• P

Hi there, how can we derive unlevered IRR from a levered IRR? I have the cost of debt, the debt-equity ratio and the levered IRR. Many thanks

• Frank

Hi, I’m not sure if I’m being stupid but using the figures above I get an NPV of (39,513) using excel?

• Kevin

maybe this is my lack of understanding in terminology but I would appreciate if you could clarify

With this silly example in excel =IRR(-100,100,100,100,100,100,.1) and you will get your IRR which comes out to IRR = 97%.

Am I right to say:
97% is the IRR (and this makes the npv=0)?
is this 97% the actual return to the investor using discount cash flow?
In other words is it the same as spending 100 in year 1 and then getting 197 back in year 2, effectively giving you 97% return?

IRR does not take into account interest rates for borrowing, would this have to be factored in somewhere else? Or does IRR just look at unleveraged examples?

• Robby

You are correct in that it’s the discount rate that sets the NPV equal to 0. However, the IRR isn’t always a rate of return on the initial investment amount. It only measures the return on what remains in the investment, which can change if there are interim cash flows (or interim equity injections). Take a look at this article for a more detailed explanation of IRR:

http://www.propertymetrics.com/blog/2014/06/09/what-is-irr/

Also, in terms of leverage, this would change the cash flows, which would in turn change the inputs into the IRR calculation. But, the IRR math itself wouldn’t change.

• Bandit

I read through the myriad discussions pertaining to IRR and NPV. Happy to stick with mathematics and physics. Business math always confused me. Too many interpretations.

• Useful article thanks… scanning the comments two fundamentals stand out as not being totally understood:
1. Required return and WACC or cost of capital involve “opportunity cost”… the alternative comparable (including risk) investment. What is being given up by investing in “this”. Crucial.
2. When using debt there is still no free lunch. A bit of debt may bring down WACC but it drives up equity risk (and thus cost) – its all wonderfully symmetrical.

• Mauricio

For the following exercise, complete the calculations below. Evaluate different capital investment appraisal techniques by completing the calculations shown below:

Bongo Ltd. is considering the selection of one of two mutually exclusive projects. Both would involve purchasing machinery with an estimated useful life of 5 years.

Project 1 would generate annual cash flows (receipts less payments) of Â£200,000; the machinery would cost Â£556,000 with a scrap value of Â£56,000.

Project 2 would generate cash flows of Â£500,000 per annum; the machinery would cost Â£1,616,000 with a scrap value of Â£301,000.

Bongo uses straight-line depreciation. Its cost of capital is 15% per annum.

Assume that all cash flows arise on the anniversaries of the initial outlay, that there are no price changes over the project lives, and that accepting either project will have no impact on working capital requirements.

Assess the choice using the following methods by completing the calculations shown below:

ARR?

NPV?

IRR?

Payback period?

• Toussaint

How does weighted average cost of capital work when debt is being used and the debt has partial interest only features? Would you use the interest rate of the debt or a weighted mortgage constant (e.g. 7 year debt with 2 years IO @ 4% but a fully amortizing mortgage of 5.6 for the remaining 5 years)?

• Stan Lake

I was looking for a way to figure out the true cost of a Merchant Cash Advance.

The NPV formula explanation is helpful – and now I see why I kept getting the wrong answers in previous attempts to use it!

That being said, the NPV formula doesn’t seem to be the proper tool to figure the actual cost of the loan offer that my friend is considering.

The face amount of the agreement is \$500,500 (minus a \$500 handling fee)
The daily payment (21 per month) is \$2,581.94
The total contract amount is for \$650,648.88

It seems I should be able to plug the data into a formula to solve for APR, but my poor addled brain is too many years from grad school to remember which one!

Another piece of information – the agreement calls for 4% of sales up to the repayment amount…

I sure would appreciate any help someone might be interested in offering.