2. Discounts and Premiums

I want to talk some more theory before we actually get into some of the technical bond stuff. So when you're selling a bond, you can sell it at a discount, you can sell it at a premium, or the third option is you can sell it at face value. And I want to talk about the difference between discount and premium and how you can remember it very easily. If you watched the last video, you know that a bond is a promise of two things. One, it's a promise to pay back the face value, and two, it's a promise to pay some ordinary stream of payments. Let's say it's 10% and it's semiannual.

So this bond promises 100,000 at maturity, which is, doesn't matter, and it promises 10% APR paid semiannually. So that's 5% twice a year. And in the last video, we discussed that this 10% is the coupon rate. It is printed on the bond, and it is never going to change. So our market rate can go up and down, but our coupon rate was printed on the bond, therefore it can never change. Now the question is: how much would this bond sell for? How much would this $100,000, 10% bond sell for? Well, we would expect it would be somewhere near 100,000, wouldn't we?

'Cause if you're gonna get $100,000 back, you would expect you would have to pay close to $100,000. We can't answer that question, how much is it gonna sell for, without some more information. And for this high-level example, the information that we're missing is the market interest rate. Let's take three different scenarios.

So if the market interest rate is 10%, then this bond is doing just as well as the market is doing. You could earn 10% somewhere else in the market through some other financial instrument, or you could earn 10% here with our bond that's marked 10%. Our bond is no better than the market rate. Our bond is also no worse than the market rate. So when it comes to how much are we gonna sell this bond for, it's gonna be the face value. That's not very interesting. What if the market rate was 8%?

Now we're getting somewhere. If the market rate is 8%, so if market is here in the black and our coupon rate we know is 10%, then what we're saying is our bond is earning 2% more than you could find anywhere else in the market. Our bond is better than the market by 2%. You could go out, and you could find some other financial instrument, and you would only earn 8%. Or you could buy our shiny, fancy bond and get 10%. Do you think that's gonna make our bond more expensive or less expensive?

If everyone else gets 8 and we're given 10, do you think that makes our bond more valuable, more desirable, or less desirable? Obviously more. So our sales price is going to be something more than face value. And what do we call that? We call that a premium. We get to sell our bond at a premium because our coupon rate is higher than the market. People want 10% versus 8%, so that pushes the price up. So it's conceivable that our schedule could look like this. We could sell it for 110,000, and then the face value is still 100,000.

This never changes because it's printed on the bond. We promised $100,000. And of course, you've still got the payments here in the middle. But it's conceivable that we could get 110,000 and then pay back 100,000. And the reason is because these payments are at 10%, whereas the market payments are at 8%. So people are willing to pay more for these higher payments.

What if the market rate was at 12%? Well, now the market rate is up here. So the market rate is at 12, and our stupid little bond is only at 10. So our bond sucks compared to the market. People could go out anywhere in the market and get 12%. Why would they get our bond for 10%? Well, they would only buy our bond for 10% if they had to pay less than the face value or if they got some sort of discount. So what if our schedule looks like this? What if they paid 90,000 and they got back the face value, which never changes, it's a promise, and then they got these payments here in the middle?

Well, these payments are 10%, which is lower than the 12% they could get elsewhere. But hey, they only paid 90 grand, and they're gonna get 100 back. So the only reason that somebody would buy our dumb little 10% bond when the market is giving back 12 is if they don't have to pay as much upfront. So if you paid 90,000 and you got 100,000 back, you'd be pretty happy. And I'll show you in some of the other videos that follow this how paying 110,000 for a 100,000 bond actually makes the return come out to 8%.

And paying 90,000 for a 100,000 bond actually makes the return come out to 12%. So what we end up doing is if the market rate is the same as the coupon rate, well, then we just pay face value. We just pay the 100,000. But if the market is 8 and the coupon is 10, we're gonna pay more than face value, and that's gonna decrease our effective return down to 8%.

And if the market is 12, we're gonna pay less than face value, which is gonna bring our effective return up to the 12. So I'll show you in the next videos how the bond price adjusts based on the interest rate, such that you're always earning the market rate. That's how these bonds get priced, is by the market rate. It has on there printed, here's what you're gonna get back, here's what you're gonna get in the middle, but it does not have on there how much it sells for. So how much it sells for fluctuates based on the prevailing market interest rate. And it always works out mathematically such that you end up earning the 12% market rate.