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What Is The Value of Your Note?
| | Thursday, November 06, 2003 @ 05:00 PM EST
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Contributed by: Ed Meyer
Ed Meyer Properties
Read more archived articles about Paper and Mortgage Investing
If you have a room full of people and you were to ask them, “Would you prefer to have $5 today or $5 one year from now?” Almost everyone will answer, “$5 today”. If you ask why, you will hear “uncertainty in the future”, “I can invest the $5 and have more than $5 in a year”, etc. Now, if you ask “Would you prefer to have $4.50 today or $5 one year from now?”, you will find that some will prefer $5 in a year. My experience (I have done this several times) has been that asking “Would you prefer to have $4 today or $5 one year from now?” will produce about 50% for each preference. At this point I declare that we have market equilibrium and the fun begins. I tell those who prefer $5 in a year find someone who
prefers $4 today then take $4 from purse or wallet and give it to him/her and be sure to receive back a promissory note for $5 payable in a year.
Two things to observe.
1) The value of a future payment is worth less today than the day it is due.
2) This transaction will scale proportionally (within limits) meaning that if I have $8 to invest I can likely find someone who will give me a one year note for $10 or I can find two people who each will give one year notes in the amount of $5
We can look at any such transaction two ways.
1) The investor gets annual return of 25%.
2) The investor gets a 20% discount on the $5 note. (5 times (1-.2) = 5 times .8 = 4.)
If anyone has trouble relating the two numbers, send me a private message with an e-mail address and I will return an MS Word document with an explanation. For now, the number .8 which is 1 minus discount rate expressed as a fraction is going to be key.
Now, I know you are ready to ask this question. “If I prefer $5 in two years to money today, what should I pay today?” Here is the reasoning. We first ask ourselves, “What would be the value of the two year $5 note one year from today?” Assuming preferences are the same as today, we know that the answer is $4. This assumes that in a year in our room full of people we could find someone who will pay $4 for the note. So now we need to determine what we should pay today for a note worth $4 one year from now. Using proportional scaling we see that we should pay 4 times (1 - .2) = 4 times .8 = 3.2, so we should pay $3.20 today for the $5 note due in two years. We can look at this and see that we pay 5 times .8 times .8 = 3.2 or $3.20. We can easily see what a three year $5 note is worth today. It is 5 times .8 times .8 times .8 = 2.56 or $2.56. We can also see that we have the recipe for determining the value of any single payment note providing we know a discount rate.
If we have a note that has an income stream , that is to say, it promises multiple future payments, we would use the ideas above to calculate today’s value for each future payment and add them up. This value, of course, depends on an assumed discount rate or equivalently, return on investment.
The harder calculation is to determine the return on investment given the price paid today for a given stream of future income. Fortunately, for this we have financial calculators!
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