Understanding NPV - A Real Life Scenario

25 Replies

Note: I wrote this post pretty quickly, so I’m sure there will be some questions and perhaps even some confusion…if so, feel free to ask, and I have some additional disclaimers at the bottom...

I’ve written a bunch of blog and forum posts about analyzing deals and understanding various metrics and terminology, and people seem to find them useful.  So, that’s why I’m writing this one post.  I personally had to go through an analysis exercise today, and I figured I’d share it here, just to provide another example of how some basic mathematical concepts can govern our investment decisions.

Here was the situation that I found myself in today:

I bought a property a couple weeks ago with the intent of doing some trash out and minor repairs, and reselling to another investor.  I’m all-in on the property (purchase, closing costs and rehab) for $77,000.I recently marketed the property for resale, and received an offer for $100,000.  But, the offer was contingent on owner financing – nothing down and payments of $800 per month for the next 125 months.

Is this a good deal?  If so, how good?  If not, how bad (and how could we make it good)?

The first thing you may notice is that $800 per month for the next 125 months is essentially $100,000 paid over 10.5 years.  Now, some of you are probably thinking, “He’s offering you $100K, but he wants an interest-free loan for 10 years!”  

While that may be true, you don’t want to get hung up on interest rates and time frames.  Here's why...

If he had offered me $300,000 for the property, with 125 payments of $2400 per month, that would also be an interest-free loan – but I think we all agree it would be a much better deal.  Also keep in mind that if he had offered me $80,000 with 125 payments of $800 per month, that would be equivalent to him paying 5% interest on the seller financing, but I’d ultimately make the exact same amount of money in the exact same amount of time.

For this reason, we shouldn’t get caught up on the interest rate being offered with the payment.  That, by itself, doesn’t tell us anything.

So, what will give us the information we need?

To get there, let’s revisit a concept most of you are probably familiar with, but also probably don’t think about very much.  It’s called “the time value of money,” and it basically says that $1 today is worth more than $1 tomorrow (or next month or next year). That’s because a dollar today can be invested and in a day, month or year will be worth more than a dollar.  Also, assuming inflation, a dollar tomorrow will have less buying power than it does today.

Given that, the fact that this buyer was offering me $100,000 over the next 10 years means that the value of that $100,000 is LESS than if I were getting it all at once, TODAY.  But, exactly how much less? If that $100,000 over 10 years is equivalent to getting $95,000 today, and if I’d be happy getting a $95,000 cash offer today, then that’s not too bad. But, if that $100,000 over 10 years is equivalent to getting $50,000 today, then I’d essentially be losing money making this deal (remember, I’m into the property for $77,000).

The mathematical idea of figuring out what future cash flows would be worth today is called Net Present Value (NPV).  Basically, using NPV, we can determine what any number of future payments of specific amounts would be valued at today.  If you recall, I mentioned that the reason a dollar today is worth more than a dollar tomorrow is because you can invest it today and make it worth more tomorrow.  How much more a dollar is worth today than tomorrow is going to be dependent on how much you’d be able to earn if you invested it.  If you could earn 1% annual returns on your investment, a dollar today isn’t going to be worth much more than that same dollar invested (at 1%) for the next year or two.  But, if you could earn 50% returns on your investment of that dollar, having it today versus in a year or two could mean having the opportunity to double your money in that time period.

This rate of return that you’d be getting on your money if you had it sooner rather than later is typically referred to as the “discount rate.”  I’m going to assume that if I got my $100,000 today, I could put it into a rental property generating 12% annual returns.So, for this analysis, I’m going to use a discount rate of 12%.

Okay, we have the information we need to perform our NPV analysis – we have the payment information (list of cash flows and payment periods) and the discount rate.  

Microsoft Excel will do the work for us if we plug the numbers in:

The fact that the NPV result is a negative number tells us that, if we were to make this investment (if we were to accept this deal), the value of the all the payments over the next 10.5 years in today’s dollars would be worth less than our $77,000 investment.  In other words, we’d be losing money by accepting this deal.

Further, the fact that our NPV was about -$21,608 tells us that the total value of the sum of all the payments in today’s dollars is about ($77,000 - $21,608) = $55,392.  In other words, that's about what the value of all those payments would be in today's dollars.  If we were all in to our deal for $55,392 (instead of $77,000) and were offered the same seller financing deal, we’d essentially be breaking even by taking it.

Just to verify that, we can plug the numbers back into our Excel spreadsheet, using the Initial Cost of $55,392:

And we see that the NPV goes to 0.  As we suspected.

If you’re still with me, we can actually do some even more interesting calculations now.You may have read the article I wrote a while back about Internal Rate of Return (IRR).  In that article, I made the following comment:

(For the other hard-core finance geeks out there, IRR is most specifically defined as the discount rate that makes an investment’s net present value (NPV) equal to 0.)

You may not have understood what that meant before, but now you can.  Let me explain it another way…

In our example above, we assumed that our Discount Rate was 12% (the amount we could invest our money for if we had it all today).  And in our example above, with a Discount Rate of 12%, the seller financing deal didn’t make sense – we would lose money.  

But, what if we couldn’t invest our money today at 12%?  What if we could only generate 8%?  Or 5%?  Or 2%?  

If we didn’t have the ability to generate high returns, would there be a point where accepting the seller financed deal made sense?  Presumably there is a point where, if our other investment return options were low enough, it would make sense to take the seller financing deal.

But, what is the ROI point where it starts to make sense? This is exactly what IRR tells us – it gives us the exact point where the NPV is $0…our breakeven point.

Let's plug the numbers into the spreadsheet to get the IRR of this deal:

It looks like our IRR is 4.86%.You can interpret that in a couple ways:

  1. 1.  First, as we discussed, this is the Discount Rate that makes our NPV = $0.In other words, if we only had the ability to invest money today at 4.86% returns, taking the seller financing deal would be a wash.
  2. 2.  If we did decide to take the seller financing deal, our compounded return on the deal over the 10.5 years would be 4.86%.

Now, just to round out the post, let’s go back to our spreadsheet, and rerun the NPV equation using the 4.86% Discount Rate:

As we now suspected, using the IRR percentage as our discount rate, our NPV went to $0 (again, this is the formal definition of IRR).

In summary, what we found was that the seller financed deal wasn’t a good one, given that I could be generating 12% returns if I had my $77,000 back in hand today.  But, if I could only be generating about 5% returns, it might be a reasonable deal, especially if doing the seller financing was a lot less work than my alternatives.  

By playing with the numbers (monthly payments, number of payments, upfront downpayment, balloon payment at the end, etc.), I could start to get a better feel for what would actually make this seller financed deal worthwhile.  In real life, it turns out I already have a full-priced cash offer, so there wasn’t much need to put together other scenarios, but I’m happy to touch on that if anyone is interested.

A few more things to round this post out:

  • First, there are a lot of nuances I didn't touch on around NPV and IRR in this post.It wasn't meant to be a formal math lesson.
  • I talked about our Discount Rate being the return I could get if I invested the initial capital elsewhere.  But, the Discount Rate can also be the interest rate at which your initial capital is borrowed.  If that $77,000 was money I borrowed at 8% interest, the Discount Rate we'd want to use in our equation is 8%, as that would be the amount we'd need to earn just to break even on the deal.
  • Based on the above point, Discount Rate is often referred to as your "hurdle" rate.  That's because this is the Discount Rate you need to achieve in order to surpass your financing hurdle.
  • For more accurate results, I should have listed monthly cash flows of $800 instead of yearly cash flows of $9600 – the year 11 number throws things off a tad bit
  • I didn’t include any of the Excel formulas in this post, but if anyone is interested, I’m happy to go into that as well
  • I should probably have discussed the difference between Net Present Value and Present Value a bit more.I have a feeling there will be some questions where I need to clarify points around this…I guess we’ll see…
Originally posted by @Sharad M. :

This would be a good concept to grasp for people who do or want to do lease options.

@J Scott I don't know if you do any lease options, but if you do, what's a minimum spread you look for?

Hey Sharad,

Agreed that this is something anyone doing lease options needs to understand (or notes or any other type of investment that generates an annuity or cash flow).  I've never done a lease option, so I can't answer your question about spread.

good stuff! I wonder to myself how "quick" you typed this up. Thanks for the knowledge!

@J Scott 

A few years ago when I was still working at an accounting firm, I was looking to invest in my 401k and that time there was a lot of discussion between 401k vs Roth 401k and Roth 401k was a hot item and a lot of financial gurus were talking about the great benefit of tax free returns.

So I put together a spreadsheet to see what the difference would be in my net ROI between traditional 401k vs Roth 401k and what I found was if there is no difference in tax rate between the time when a person invests and the time the person withdraws and also the traditional 401k and Roth 401k earns the same ROI, then there is no difference in ROI between the two.

Something along the lines of your calculation. It's interesting that once you start analyzing the returns and the reasoning behind them, how clearer the concept becomes.

@J Scott , @Sharad M.  

Not just for folks doing lease options.   Anyone who fancies themselves a buy-and-hold investor, once your first swat with the 50% rule (of thumb), cost/yield per unit, etc. indicates a property may be worth pursuing, this should be a next stop.

J.: For a top-of-mind narrative, it was easy to follow.

1(506) 471-4126

@J Scott Ok I'll bite, lets assume the discount rate is a more normal 8% how would you determine what payment amount on a ten year plan would then be a worthwhile deal for the seller? 

@J Scott 

  one of the more critical aspects of the note business of course.

It also helps with OREO resale's from a lender in possession perspective.

Playing around with NPV is when I came up with 0% financing for my OREO.. 30 months at 0% note has the same PV of 84 month note written at 15%... so which one is more palatable to the buyer.. well for my Saudi clients the 0%... And others that wanted to get very good deals and get their rentals paid off right quick.

Originally posted by @Jay Hinrichs :

@J Scott 

  one of the more critical aspects of the note business of course.

It also helps with OREO resale's from a lender in possession perspective.

Playing around with NPV is when I came up with 0% financing for my OREO.. 30 months at 0% note has the same PV of 84 month note written at 15%... so which one is more palatable to the buyer.. well for my Saudi clients the 0%... And others that wanted to get very good deals and get their rentals paid off right quick.

 That's a great way to be Sharia compliant.

@Cal C.  

  Exactly... and Exactly how I started selling property with no interest in the mid 80's I had Saudi clients that wanted to buy one of our properties .. and in those days it was down payment and 15 to 20% interest ( if you recall those days)... But we sold most of our paper that we took back.. so playing with NPV and having these clients tell me they could not pay interest for religious reasons. I just backed into the amount of months 0% would be to get the same yield as when I sold my 15% 84 month paper.

Did very very well with San Francisco based Saudi small business owners.. It was a trip.

Thanks J for providing this post... this all new to me, so I will read through again as I need to get my mind around the 12% and 4.86% scenario... but I will get there :)  Typically what I did was say $77k x 12% ut it came to $9250... $9600 was 12.5% over 10yrs, hence why I conclude I have to reread and understand the concept better.

I'm a novice so I aim to soak up the knowledge and move forward well armed with tools for success.

Again thanks for sharing.

Kelvin

Originally posted by @Cal C. :

@J Scott Ok I'll bite, lets assume the discount rate is a more normal 8% how would you determine what payment amount on a ten year plan would then be a worthwhile deal for the seller? 

You have multiple "knobs" you can play with here -- upfront payments, extra balloon payments at the end, more payments, higher payments, etc.

A couple simple scenarios:

Looks like about $930/month for those same 125 months accomplishes getting you to an 8% IRR. In this case, you're increasing each payment but keeping everything else the same.

Or, if the buyer put down $11,000 (taking your initial investment to $66,000) and paid the $800 for 125 months, that would also accomplish it.  That keeps the same number of payments and payment amount, but adds a downpayment, which reduces your initial investment.

In both scenarios, you could either look at it as $100K purchase price, but paying interest on the loan.  Or you could look at it as a higher purchase price, still interest free.  As Jay mentioned above, you can structure the deal in many ways (from the buyer's perspective) and still receive the same income benefits.

Of course, there are million additional ways to structure this deal to achieve that 8%, but all would require some form of upfront payment, a balloon at the end, more payments and/or higher payments.

Originally posted by @Kelvin Hamilton :

 Typically what I did was say $77k x 12% ut it came to $9250... $9600 was 12.5% over 10yrs, hence why I conclude I have to reread and understand the concept better.


Hey Kelvin,

Let me try to explain the piece I think you're missing...

Any payment from the buyer to the seller will include two parts:

- Interest

- Principal

In the scenario that I presented, the buyer essentially wanted a zero-interest loan, so that every penny that he paid to me over the 10.5 years was to pay down the principle. 

For example, the loan started at $100,000.  After one month, he paid $800, and now he owed $99,200.  After the second $800 payment, he owed $98,400.  Each payment reduced the principle amount owed by the full amount of the payment, as there was no interest being paid.

At the end of the 10.5 years, the principal he owed would be $0, and the loan is paid off.

Your example is exactly the opposite.  In your example, you'd be selling for $77,000, and you'd be charging 12.5% interest (12.467% to be more precise), and the $800 payment each month would just cover the interest amount owed, but none of the principal.  

So, in your example, after the first month, the buyer would pay $800 -- that $800 would fully go to paying interest, and since none of it went to paying down principal, the buyer would still owe $77,000 in principal after that first month.  After the second month, the exact same thing.

In fact, 10.5 years later, the buyer would still owe you $77,000, even though he had paid you $100,000 in interest the past 10.5 years!  In your example, the buyer would have to make an additional one-time $77,000 payment after 10.5 years to be done with the loan.  That final $77,000 payment takes you from a very negative NPV to a breakeven NPV at the 12.467% Discount Rate.  

In other words, the balloon payment at the end contributes greatly to your earning 12% return over the life of the loan. In my scenario, I don't get a bulk payment at the end. And if you didn't get a bulk payment at the end, you wouldn't be getting anywhere near 12% return (in fact, you'd be getting the 4.86% IRR that I was indicating in my original example).

Does that make sense?

I'm getting there...

$800 x 12 x 10 = $96,000

$800 x 5 = $4,000

So my slight confusion is the 12% figure you showed in the table above the $77k?

Sorry if I'm acting alittle simple... I just need to be completely clear on the maths. But to be truthful, I have not managed to reread as yet in depth, so maybe It will all make sense.

I'm always like this when I discover new ideas.

I'm totally green right now :/

Thanks for your patience.

Originally posted by @Kelvin Hamilton :

I'm getting there...

$800 x 12 x 10 = $96,000

$800 x 5 = $4,000

So my slight confusion is the 12% figure you showed in the table above the $77k?

The  $800 x 12 x 10 (and 5) is the 125 months of $800 monthly payments.  This is the "income stream" that the buyer offered me.  It totals $100,000, but isn't the same as him handing me $100,000 right this minute.  Remember "time value of money" -- the $100,000 this very minute is worth more than the $100,000 spread out over the 10.5 years (because if I had it right now, I could invest it for the next 10.5 years and earn more money!).

Good so far?  If not, go back and reread that last paragraph...

Okay, so the question is:  How much less is the $100,000 worth spread out over 10.5 years than it would be worth if I got it all at once right now?  

And the answer to that question will depend on what I would do with that $100,000 if handed to me right now.  More specifically, it will depend on how much I'd be able to earn on that $100,000 if I had it right now.  

If all I did was shove that $100,000 under my mattress for the next 10 years (i.e., invest it at 0% return), it would make no difference if I got the $100,000 now or got it in $800 monthly payments -- either way I have $100,000 in 10.5 years.  But, we assume I can get more than 0% return on that money if I had it (I'm a real estate investor, aren't I?).

If I could only earn a little bit of return on that money over the next 10 years, then having it all right now isn't much more valuable than getting it spread out in $800 payments.  But, if I could earn a LOT of return on that money, having it now would make it much more valuable.

With me so far?  If not, go back and reread those few paragraphs...

Okay, we now know that the difference in value of that $100,000 now versus later will be dependent on how much I can earn on that money if I have it now.  This return number is called the Discount Rate, and in my example, I assume it's 12%.

Where did I get 12%?  It's a guess of how much I'd earn annually on that $100,000 if I had it in my hand.  If I had it, I'd likely go buy a rental property with it, and the rental properties I purchase generally return about 12%.  So, that's why I chose that number.

Once I have that Discount Rate (12%), I know my initial cash investment (I spent $77,000 on the property) and I know my income stream ($800 per month for 125 months), I let the spreadsheet do the NPV calculation for me (using the "NPV" function in Excel).

What the NPV function will spit out is the answer to the question, "How much would that $100,000 -- given that it is delivered in $800 increments over the next 10.5 years -- be worth in today's dollars given our ability to invest it at our Discount Rate?"  

We know it's going to be worth less than $100,000, because future money is worth less than right-now money.  But how much less?  That's what NPV tells us.

In this case, NPV tells us that the $100,000 delivered over 10.5 years (when it could be invested at 12% if we had it all right now) is actually equivalent to about $55,400 today.  

In other words, the buyer wants to pay us the equivalent of $55,400 today for a property that we paid $77,000 for!!!

Clearly that's not a good deal.  

Let me know if that makes sense...and if you want me to clarify anything else...and don't feel bad if you don't get it for a while...it definitely takes some time and thought to truly "get it."

You are a patient Master J... the simple man now gets it completely :).

The NVP is determined by what you can do with your money to make it grow on an interest type basis.  So say I can make my money grow by 20% today, I should use the 20% to do my analysis to know what my money is worth in the future right?  Then I can confirm if I have a good deal or not over a period of time.

A method I have not used before, but one I will be using now as part of my analysis.  I guess there is a rule by thumb figure though that one should work to though... is it 10%, 15%, 20%?  Or is it purely unto the individual making the deal to decide what is worth the risk?

Thanks J

Originally posted by @Kelvin Hamilton :
The NVP is determined by what you can do with your money to make it grow on an interest type basis.  So say I can make my money grow by 20% today, I should use the 20% to do my analysis to know what my money is worth in the future right?  Then I can confirm if I have a good deal or not over a period of time.

Almost.  Instead of trying to figure out what your money is worth in the future, NPV allows you to figure out what future money would be worth today.

Here's another way to think about it...

In real estate, there are many occasions where you have the opportunity to pay a fixed amount today for a stream of income later.  For example, if you purchase a rental property -- you pay a fixed amount today (the purchase price) for monthly rent every month into the future.  Is the series of monthly rents into the future worth more than the fixed price you are paying for the property today?  Hopefully so.

Here's a good non-real estate example.  Let's say you win the lottery.  If it's a big win, you often have two options:

1.  Take a lump sum now

2.  Take an annual payout for 20-30 years

Here's an example with real numbers (based on a website I found):

If you won a $12 million jackpot in the multistate Mega Millions lottery game, you the option of getting a lump sum of $7,042,000 or getting an annual payout of $461,538 for 26 years.  

You notice that you get a good bit more by taking the annual payments over the lump sum ($12M vs $7M).  But, you have to wait much longer to get your money, and as we learned, money later is worth LESS than money today.  But, how much less?

If we stick that $12M (that we'd get over 26 years) into an NPV analysis, and plug in a discount rate that reflects how much we could be earning on that money if we had it today, we can figure out what all those $461,538 payments would be worth if we had them in one lump sum.  If they're worth more than $7M, that's probably the right choice; if they're worth less than $7M, then taking the $7M lump sum is probably right.

[Note that I'm ignoring all tax considerations and lots of other considerations here...this is just for example purposes.]

Let's assume that with that much money and receiving it that often, we'd have trouble making our 12% annual returns -- in fact, let's say that we could only make 5% returns on it.  Here's what the NPV analysis looks like:

Looks like the stream of $461K payments over the next 26 years would only be worth $6.6M if we had it today.  That's $407K less than the $7M they'd be offering us as a lump sum.  Better to take the lump sum and invest it at 5% annual returns...we'd end up making more than that $12M after 26 years.

But, what if that money was going to make us really lazy, and we couldn't even get the 5% annual returns (who needs to invest when you have millions of dollars! :).  Let's say you could only work hard enough to generate 4% returns on your new found money.  This is what the NPV would look like:

It appears that if we only have the ability to earn 4% on our money, that $461K per year is looking more valuable -- it's worth almost $7.4M in today's dollars, which is more than if we took the $7M lump sum and tried to invest it at our measly 4%.  Let's take the 26 annual payments and make more money!

So, using NPV, we can determine that if we have the ability to earn 5% on any money we have, we'd rather have the lump sum number and invest it at 5%.  But, if we only have the ability to earn 4% on our money, taking more money over long period of time is better than taking the lump sum now, since we're not skillful enough to make it worth more anyway.

The last question is, what if we can earn somewhere between 4-5%? Where is the cut off between it being worth taking the lump versus taking the annual payments? That crossover is where NPV is exactly $0. And, as we learned in the first post, the discount rate that makes NPV equal $0 is the same as the IRR.

If we do an IRR analysis of these cash flows, we find that the discount rate where things cross over is 4.43%:

Hope that helps!


Yep, that does J... It has sunk in clearly now.  Thanks for your time and effort to explain this to me; very much appreciated

Kind regards

Kelvin

Interesting topic, Do you look at an owner finance on your own purchase the same way. For example, if you purchase a property with owner financing using the same terms in your initial post do you consider the cost of the property to be $55,392?

Can you share the excel functions you use?

Thanks for taking the time to go deep on the details.

Originally posted by @Ben Leybovich :

@J Scott - you know nothing, but you are sexy!

 Ben, are you just kidding with J or do you  disagree with the post?   I can't  tell.  

Originally posted by Mark Forest:
Originally posted by @Ben Leybovich:

@J Scott - you know nothing, but you are sexy!

 Ben, are you just kidding with J or do you  disagree with the post?   I can't  tell.  

I was assuming it was a joke (just because he didn't mention anything specific he disagreed with), but I'm not positive...  :-)

Originally posted by @J Scott:
Originally posted by @Steve Might:
Originally posted by @Ben Leybovich:

@J Scott - you know nothing, but you are sexy!

 Ben, are you just kidding with J or do you  disagree with the post?   I can't  tell.  

I was assuming it was a joke (just because he didn't mention anything specific he disagreed with), but I'm not positive...  :-)

J thanks for getting back to me.  This is the thread.  Thank you for posting it.  

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