Understanding NPV - A Real Life Scenario

[J Scott]

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:

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:

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…

[Kelvin Hamilton]

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