Present Value of a Note - Posted by Char

Posted by Char on May 17, 2000 at 11:49:57:


Present Value of a Note - Posted by Char

Posted by Char on May 12, 2000 at 07:16:37:

Though I understand the general concept of Present Value I am having trouble with and have four questions involving the following scenario:

A seller takes back a $68,000 2nd mortgage and agrees to accept 60 monthly principal only payments of $1133.33. In effect, it is a zero interest loan.

Question 1: What is the present value; that is, what would be the equivalent cash at close offer to that $68,000 interest free loan paid over 5 years?

On a financial calculator, if you put n = 60, i = 0, FV = 0, and pmt = 1133.33 (-1133.33 for 12C, etc.) and solve for PV you get $68000 (actually real close to it).

If you leave all the numbers the same but impute an interest rate and solve for PV you do get a “discount.”

Question 2: Is it that you have to factor how much interest per year you would save? For example, if you assume the zero interest seller financing would be in place of you having to get a loan with 10% as the interest rate you get $53,340.60 as the PV for the 5 year term (and $35,155.03 for $68000 interest free over 180 payments of $377.79 - just another example I was playing with).

Question 3: If you must impute an interest rate, what is considered appropriate when you are the buyer? What are some reasonable approaches to consider other than what the cost of financing might be at a bank?

Question 4: Is there a way to do this calculation using FV?

Thanks in advance for your replies.

Re: Present Value of a Note - Posted by Carol

Posted by Carol on May 14, 2000 at 08:35:51:

I think the responses were what they were because it was assumed that this was a practical as opposed to a theoretical question.

What are you really trying to figure out - what problem are you trying to solve? It was assumed that you were a note buyer (or perhaps seller).

Maybe I missed it. Or maybe you are just having fun working through the mysteries of the financial calculator.

Anyway, i hope you end up with a satisfactory answer to whatever the real qtn is!

I Think Was Unclear (long) - Posted by Char

Posted by Char on May 13, 2000 at 06:47:21:

Thanks Dave and Sean for the two replies. Unfortunately both of the answers suggest that I didn’t make the premise of my questions clear enough.

The original statement in my post read:
“A seller takes back a $68,000 2nd mortgage and agrees to accept 60 monthly principal only payments of $1133.33. In effect, it is a zero interest loan.”

That statement and the questions that followed it were written from the perspective of me being a BUYER of REAL ESTATE (not a note buyer or note broker) who was purchasing a property from a seller of real estate (not a seller of the note). The seller of the real estate had the intention to hold the note as it was created and receive all of the monthly payments. I wanted to be able to accurately determine the present value of that zero interest loan.

Dave, I’m ashamed to admit that I do have Jon Richards book (Calculator Power! - good book, by the way) and have recently read it and worked all of the examples completely from start to finish and should, therefore, have a better understanding of this. However, being a novice with these matters I’m not ashamed to admit that while the basic concepts are firm in my mind, some of the subtleties (at least subtleties to me) and issues not directly covered in the book are still, in some cases, at least a little fuzzy.

I purposely didn’t get into my particular lengthy logic because I didn’t want to influence the course or direction of the discussion any more than necessary. I was hoping I might learn some things that I wasn’t aware of - perhaps approaches or logic not covered in Mr. Richard’s book.

For example, I am very clear on the concept of present value. I understand it very well in the context of purchasing a note at a discount to achieve a required yield. I clearly understand how to calculate the PV of a balloon note and one that has a series of payments to achieve a particular yield. Although I am reasonably certain the example above is directly on point for the “series of payments” calculation I am not 100% certain that there isn’t some other twist to understanding the example above that true pros in this arena may be aware of and that I would like to learn.

If the only way to determine PV is to assign a yield of some sort then I understand the value of the note in the example above to be potentially different for the buyer and the seller.

The seller will/should view it in the context of what they would get for their typical investments, perhaps discounting it based on the current 6.5% of a CD from their bank, for example, and arrive at a value of PV being $57,923 in that context (I = 6.5/12, N = 60, PMT = 1133.33).

I, as the buyer would need to use a figure that the money would otherwise cost me (or some other standard I hope someone will suggest). So the present value for me might be $54,596.33 (I = 9.0/12, N = 60, PMT = 1133.33) assuming that an alternative form of financing would cost me 9.0%. On the exact same note, my PV will be over $3000 lower than the PV of the seller of the property.

In neither example is the $68,000 figure pertinent except to figure what the monthly, interest only payment should be ($68,000 / 60). So again, my basic questions are:

  1. Is there some other way I should be looking at the problem of determining the PV of a zero interest loan with a series of regular payments?

  2. As a buyer of real estate is there a better “I” to use than what financing would cost me? My current thought process is telling me that using the financing interest rate (perhaps 9.0%) would be the more conservative, realistic number than perhaps how much I normally get as a return on my investments (a higher number that would result in a lower PV).

  3. Is there any way to calculate the PV using FV for this particular example where a series of payments (not a balloon) is involved?

Thanks again in advance for your time and knowledge.

Re: Present Value of a Note - Posted by David Butler America’s Note Network

Posted by David Butler America’s Note Network on May 13, 2000 at 01:08:15:

Hello Char,

You might want to get some real conceptual experience with your questions in addition to what Sean explained. There is an excellent little book, Invest In Debt, by Jimmy Napier that I have always thought was one of the best start-up primers. Russ Dalbey’s Winning In The Note Business also covers a lot of time value of money explanations. For sheer practice at running the numbers and easy to follow explanations, Jon Richard’s Calculator Power is another excellent publication. All of these guides are very inexpensive, and will help you absorb the reasoning behind the numbers.

Hope this helps, and best of luck.

David P. Butler Vice President, Broker Relations

Interest - Posted by Sean

Posted by Sean on May 12, 2000 at 08:28:07:

I don’t think there’s anyone here on this board who wants to make an interest-free loan. We’re all here to make some money while buying/brokering notes.

Accordingly when we would determine the PV of a note we’re all going to put in some kind of an i% and accordingly the note will sell at a discount.

What kind of i% are people going to use? Well the water is muddied by you saying that it’s a second trust deed. Let’s instead assume that it’s a first and that we’re using First National Acceptance Corp of North America as our source of funds.

Let’s further say that we assign your note an AA rating (see Accordingly we know we’re going to be paying 11.5 percent to borrow the money we need to buy the note.

Accordingly we’re going to put in an i% of not less than 12 percent. This is because pricing it at 11.5% isn’t going to give us any profit since fnac’s rates may go up (Alan Greenspan being a busy guy) and fnac has other fees like origination costs and a $6 fee for every payment they collect for you (and they insist upon doing that).

As for FV that’s pretty simple. Let’s stick with your no-interest scenario for ease of calculation. Let’s say you loan someone $68,000 on a first trust deed at no interest with 60 payments of $100 and the balance of $62,000 is due at the end of 60 payments (5 year balloon).

n 60
i% 0
pv 68000
pmt 100
fv 62000

and let’s say we’re going to price this at 15%

15 divided by 12 = 1.25 [i%]

Re: I Think Was Unclear (long) - Posted by MDonovan

Posted by MDonovan on May 16, 2000 at 16:35:03:

You are correct in your logic. The cash flow is just a series of payments. What that flow is worth is directly related to 1) your usual cost of funds, which is different for each investor. And 2) the risk factors involved which can be quite subjective.

The interest rate on the note is not a determining factor, whether it be 18% or 0%. But keep in mind that the note may pay off at any time, so the current balance may play a factor in the pv computation.

Look at the bond market. A bond may have a face interest rate of X%, but due to market interest rate fluctuations, the actual yield will track the prevailing rates by adjusting the bid and ask price for the bonds. The yield will be a safe current market rate (say T-Bonds) plus a risk factor for the bond payer. The X% rate does not enter into the valuation. Its no different with a note.