Let’s continue exploring some of the concepts basic to an understanding of discounted notes (aka discounted paper). This article explains the difference between interest and yield and how the time value of money affects yield.
Interest vs. yield
Interest and yield are not the same. Sometimes, though, the numbers may be the same. Interest is a percentage lenders charge for the use of their money. Yield is the amount of the profit divided by the amount of money invested. Yield is also called “return on investment.” The next two examples demonstrate the difference between interest and yield.
Example 1. We have a $10,000 note with a 10% annual interest rate, all due in one year. Ten percent annual interest on a $10,000 loan earns the investor $1,000 in interest when the note is due in one year.
The formula for calculating yield is the amount of profit divided by the amount invested. The $1,000 profit divided by the $10,000 investment equals 10%. Therefore, the investor’s return on investment or yield is also 10% in this example.
Example 2. Suppose we need money now for an emergency and cannot wait for a year to collect on our $10,000 note. To attract a buyer right now, we offer to sell the note for $9,000. That means we discount the note by $1,000. By selling the note for $9,000, what is the buyer’s return on investment or yield?
To compute the yield, add up the profit the buyer will earn. Then divide the amount of profit by the cost of the note. The buyer paid $9,000 for the note even though the face value is $10,000. So the $1,000 discount is part of the profit.
In addition to the discount, the buyer will receive $1,000 in interest when the note matures one year from now. The $1,000 discount and $1,000 in interest total to $2,000 in profit. Dividing the profit ($2,000) by the amount invested ($9,000) produces a return on investment of 22.2% in one year. The return on investment is called the yield.
Even though the interest rate is the same 10% in each example, the yield jumps from 10% to 22% when we discount the note. This simple illustration shows that yield is a much more accurate way to compute the profit realized from investing in a note or mortgage.
Term
The term of a mortgage is the length of time the mortgage lasts before it must be paid in full. Most conventional, FHA, and VA mortgages have a term of fifteen or thirty years. A long mortgage keeps the monthly payments lower than a shorter mortgage. That’s why most home buyers prefer thirty-year mortgages. They want lower monthly payments.
Here’s an example of how the monthly payment amount changes according to the term of the mortgage. All other elements remain the same; the only thing we are changing is the term. This is a fully amortized $100,000 mortgage with a 10% interest rate.
Loan Amount |
$100,000 |
$100,000 |
$100,000 |
Interest Rate |
10% |
10% |
10% |
Term |
30 years |
15 years |
5 years |
Payment |
$ 877.57 |
$1,074.61 |
$2,124.70 |
As you can see from this example, payments on a thirty-year mortgage are much lower than payments on a fifteen-year or five-year mortgage. The term of the mortgages we create is very short, usually 12 or 18 months.
We create short-term mortgages for two reasons. First, a short-term mortgage is much more attractive to investors. Most investors prefer short-term mortgages. They would rather get their money back within one to three years than have it tied up for ten or fifteen years.
Second, because of the time value of money, a short mortgage is worth more than a long mortgage. Therefore, the faster the mortgage pays off, the less you will have to discount it to produce an attractive yield. A long-term mortgage requires a much larger discount to provide the same yield.
Let’s use the same example mortgage to demonstrate how the time value of money affects yield. Again, the only thing we are changing is the term of the loan. The “Amount Funded” is the amount of money the investor will pay for the mortgage after we discount it to produce a 15% yield.
Loan Amount |
$100,000 |
$100,000 |
$100,000 |
Interest Rate |
10% |
10% |
10% |
Term |
30 years |
15 years |
5 years |
Yield |
15% |
15% |
15% |
Amt Funded |
$69,404 |
$76,780 |
$89,311 |
Discount |
$30,596 |
$23,220 |
$10,689 |
As you can see from this example, you must discount a thirty-year mortgage by more than $30,000 to produce a yield of 15%. A five-year mortgage needs only a $10,689 discount to produce the same yield. The time value of money dramatically affects the discount amount.
By the way, don’t be intimidated by these calculations. I used a very simple real estate calculator that costs about fifty dollars. It makes these calculations fast and easy, even for those of us who shy away from math.
Discounted paper is a very powerful investment tool that all serious real estate investors should master. I hope this two-part “Crash Course On Discounted Paper” helps clarify the topic for you. For more information, look under real estate notes in our Online Bookstore.