Pricing the Discounted Note

Well the other day somebody on TCI posted a question about how to price a note for purchase. Essentially they asked whether such pricing was regulated by law.



No, you can pay whatever you want for a note. You can even pay a premium to the face value if the note was written at a high rate and you are willing to take a lower rate of return.



And that little Interchange reminded me of this wonderful bit of comic business writing by Sidney Homer in The Bond Buyer's Primer, the Chapter is entitled "How (Not) To Explain The Bond Market To Your Wife" It was written in 1968 and is full of the assist stereotypes of the day. But in spite of that I still find it hillarious.
"It was close to your dinner hour and you found yourself at home with your wife, Florence. Each was poised on the brink of a martini. You were stroking the chilly side of your glass. She was dipping her little finger into the clear liquid and tasting it -- a trick her mother taught her. The conversation proceeded as follows:

The First Martini

She: How was the bond market today, George?

You: Down again.

She: Goodness, again? Hasn't it been going down for a long time? I hope that isn't bad for you.

You: Bad and good. Of course, prices are down and we have some losses, but the interest rates on bonds are getting better and better -- they are really going through the roof -- haven't been so high in 30 years.

Pause

She: Now, George, I just don't understand and I wish you would explain. You say that bond prices are going down and at the same time that the interest rates bonds pay are going up. That doesn't make sense. If they pay more interest certainly they would go up in price; at least that couldn't possibly put them down. Don't people want more interest? Of course they do. I am sure I keep misunderstanding you. I wish you would explain.

There you have it. Easy? Elementary? Just try.

You: Very well Florence, I'm glad to have you so interested in my work. The thing is that the rates bonds pay don't ever go up or down --

She: George! You keep say-

You: Yes, I know the rates bond buyers get are almost always going up or down, but the rates a bond pays never changes.

She: George how is that possible? If somebody gets more interest, somebody else pays more interest and if somebody gets less interest somebody pays less interest. And if somebody pays more interest I am sure the buyer would pay a higher price than if they didn't. Why did you raise your interest rates at the bank last month? You said to get more deposits from the Clayton. If those 4 percent bonds you bought me last year began paying 5 percent would that make them go down in price? I'll never believe it.

You: Of course you are right, Florence. But those bonds won't ever pay a cent more than 4 percent. That's just it. It is not the rate they pay that changes, it's their yield that keeps changing.

She: Yield ... What is that?

You: That is the rate of interest the buyer gets from the bonds. If the price goes down, naturally the yield goes up.

She: George, don't keep saying that! It makes you sound so foolish. I don't think of you that way. If the rate of interest the buyer gets goes up, why in the world does the price go down? Men aren't dumb. I know Mr. Cortley doesn't know much about bonds but ...

You: Flo, please don't bring Felix into this. I know he doesn't like bonds, but he is a wonderful president and he knows that when bond yields go up bond prices go down.

She: I will ask HIM why.

You: Please don't. That is my job. I'll start over again in just a minute.

The Second Martini

You: I still think that nail polish will poison you some day. Anyway, let's take a 4 percent bond, any 4 percent bond, and let's suppose it is selling at 100. You buy it at 100, or sell it at 100, either way it yields 4 percent -- are you with me?

She: Yes, George I am. Am I buying or am I selling it?

You: Either ...

She: You mean I get the same interest whether I buy it or sell it? George, why would I ever buy it?

You: All right, you're right, to get the interest you have to buy it.

She: I thought so. I knew you were mixed up. So, I buy a 4 percent bond for $100?

You: Yes -- No, It really costs you $1,000.

She: Well, that's different! Why didn't you say so? Why should anybody ever pay $1,000 for a bond selling for $100? Do you?

You: Of course not. That's just the way bonds are quoted. 100 is not what you pay for a bond; it is the price it is selling at.

She: Georgie, say that again. I know the Government has laws about stocks and bonds, but I never realized ...

You: No, Flo, I am not talking about monkey business. I am talking about par value. Almost all bonds are $1,000 par value.

She: Oh, yes, I know about par value. That is what goes down when they split. I am beginning to understand.

You: No, Flo they don't split bonds.

She: Why not?

You: Why would they? Nobody would gain anything; 10 bonds of $100 par would sell at exactly the same price as one bond of $1,000 par.

She: Oh, no! Take my AT&T. I've worked it all out. Just let me show you.

You: Flo, bonds are different: They are more mathematical and logical. They never split. Par value is always $1,000. The price they sell at is a ratio to par determined scientifically by the interest rate they pay which we call the coupon and which is also a percentage of par, and the market rate of interest for all bonds of that kind which we call the yield. If the rate they pay is low, of course, the bonds have to sell at a lower price, but if ...

She: Georgie, that's just what I said. If the rate goes down, the bonds go down.

You: No, Fluff, the rate never changes, but on some bonds it's low and on other bonds it's high. Just let me give you an example and you'll understand everything. Take a 4 percent bond selling at 100. That means a $1,000 par value bond paying $40 a year and selling at $1,000. The price is the only thing that changes; the $40 never changes, and the bond will be paid off at maturity for $1,000 in exactly one year. So you buy it for $1,000 and you get in one year $1,040 and you have made $40 interest which is just 4 percent on your investment. How am I doing?

She: I think that is all right, Georgie, but just go ahead.

You: OK. Now suppose the bond goes down to 99. That means it is selling at $990 for a $1,000 bond, due in one year. All right. So you get $40 interest plus the $10 profit. Add those up and you get $50, which is just a little over 5 percent on a price of $990. So you see, Fluff, if the price goes down from 100 to 99, the yield goes up from 4 percent to 5 percent. There we have it. How about a dividend?

The Third Martini

She: Georgie dear, I don't like to be a pest and perhaps we'd better talk about this another time. The trouble is -- well -- the trouble is that you're wrong.

You: But, Fluff --

She: You said the bond goes down from 100 to 99.

You: Yes, from a dollar price of $1,000 to $990.

She: And it still pays the same old $40.

You: Yes, dear.

She: All right then. I see you still get the $40 but at $99 you've lost $10 and so you must take the $10 away from the $40. Your mistake was that you added it -- $40 interest less $10 loss is $30 not $50. That is just what I suspected all along. Of course, the more the market goes down the less you get.

You: But dearest, you're not selling it at $99; you're buying it at $99.

She: But Georgie, you said the yield was all the same at a price whether I bought it or sold, I'm sure you did.

You: Let's eat!"