[William_777]

Here’s a question I used to know , but cant remember exactly.

If a bond sells at a premium, the Coupon Rate > Market Rate.

If a bond sells at a discount, the Coupon Rate < Market Rate.

But I get lost in the above explanation because it sounds so abstract and relative, so I’ll ask it in more human terms.

I go to a bank selling a bond to buy one from them. The bond sells at a premium. The coupon rate is 7%, but the market rate is only 5%.

Now here’s the rub…

Because the bond sold at a premium – it seems like (with respect to the coupon rate) someone came out 2% ahead and someone came out 2% behind.

If I recall correctly, which I may not be doing, then I think the bank is the one who suffered the 2% loss below par because the market would only be willing to 3% for the bond. Therefore, the client would be getting the best bargain.

But then I might be wrong. If the bank pays only 3% on the bond, when it was expecting to pay 5% par, then I am actually the one suffering the 2% loss. In this interpretation, the bond would be selling at a premium (i.e. a higher price to me due to less ROI) to me the buyer, and the bank would be making out better because they would only have to pay me the buyer 3% interest instead of five.

A discount situation would be the opposite, of course.

But I need to grasp this thing with who benefits the most under at least one of the situations (discount or premium) to understand the concept like I used to recall it.

I think it is the latter. The logic seems more sound.

Any validation confirmation here?

Ty.

wm

[William_777]

I hope all that made sense.

I feel like I end up chasing my tail even trying to explain it.

[William_777]

Grrrr…

In a nutshell, is it correct to say, if a bond sells at a premium, the issuer (i.e. the bank in the example above), is the one to come out better off because they don't have to pay as much interest on the bond issue? And, on the flip side, if a person in the market pays a premium, then they get less ROI on their investment.

I think that's it.

Maybe I just needed to rehash it a few times.

[Anonymous]

I don't think it's a matter of who benefits from the discount or premium but whether or not the seller can actually sell the bonds. If a company has a 5% bond and the market rate of interest is 3%, then the bank is going to get more money up front but they have to pay a higher interest rate every year. The bonds will sell quick and the company will get the cash they need quickly. The bond holder probably isn't looking for a “deal”. They are probably looking for the highest return per month. Typically bond holders are insurance companies, large banks, and mutual funds. They don't mind paying more in the beginning because they have a guaranteed income for the life of the bond. Does that make sense?

[William_777]

Kricket. With all due respect – no… as per my third post in this thread…

You said —> If a company has a 5% bond and the market rate of interest is 3%, then the bank is going to get more money up front but they have to pay a higher interest rate every year. —

Such a bond would be selling at a premium, and premium payments go down as they mature.

Again, I think my third post in this thread says it right, the issuer pays less interest on a premium, so it's like the investor's demand creates a lower ROI…

I could be wrong, but I'm still a bit confused.

Thank you for trying though.

[Anonymous]

The bond issuer will pay the same every year, principle times the stated rate. The amortization is the only thing that goes down. Do you know the JEs that need to be made for a bond? If not send me an email, kricket0513@gmail.com.

[Katydid]

HI William. I'm not sure that I can help but I'd like to try.

The market rate on a bond determines what an investor can expect to receive on a bond based on the type and risk factors associated with it. The stated coupon rate is the rate at which the company issuing the bond believes they should have to pay for the bond. So it's like getting a loan. You decide (your the company issuing the bond) that you should be able to get a 5% car loan based on your credit score and employment status, etc. You walk into a bank (the investors in the market) and they decide that you should be paying 7%. Well lucky you, you're paying 7% whether you like it or not because that's the current market rate for a car loan with your credit status. Bonds are the same way. A company issues bonds for 5%, investors in the market place decide with that level of risk that they really should be getting 7% or they are not going to invest. The company can't change the coupon rate, so the purchase price of the bond has to go below par to make up for it, which creates a discount. The company doesn't receive as much money as they were hoping up front because they are now expected to pay 7% on this bond instead of 5%. So in this case, it is more advantageous for the investor. They are receiving 7% instead of the 5% offered by way of the discount. But keep in mind that the investor is not going to receive 7% of par annually, they are still going to be receiving 5%. The 2% difference in the interest rates is accounted for by the initial discount in the purchase price of the bond. The investor's ROI is higher and the company's cost of capital is higher than they were anticipating.

I hope this helps.

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[jfreelov]

I find it's easiest to relate to if you just envision yourself as the investor and think in the first person. You can take your cash any time you want and get the market rate of return. Someone offers you a bond that pays X percent. Would you rather take the bond or the market rate? If you'd rather the bond, then it's too attractive and you ought to pay a premium. If you think to yourself, “Why would I invest in THAT when it's less than what I could get anywhere else?” then you ought to be getting a discount.

I like this problem because I think it personifies the difference between memorizing rules vs understanding why the rules work.

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[William_777]

Well, jfreelov, I am glad it is helpful to you. Really. When I would ask “personalized” questions in the classrooms, I swear, someone once said – “Kill him!”

~LOL~

I think the problem I was (or am) having is how we look at the matter when we calculate the price of the bond, amortize the premium/discount, etc? Do we look at it from the investor's perspective, or do we look at it from the issuer's perspective? Who is the one who walks away from the deal with the discount or premium?

When we form a journal entry like this:

Dr Cash $4,120,000

Cr Bond premium $120,000

Cr Bonds payable $4,000,000

Who's “side” (perspective) are we considering when we form the above journal entry? We are looking at it from the issuer's side, no? The issuer sold a bond, and they got cash out of it.

And, if I am following the logic correctly, the bond issue was sold at a premium because… grrr… this is the hard part… the investor…

Ack! Forget it… I still dont get it…

In the case of a premium, the market is paying less interest on the bond than the issuer expected, but the cash debit in the journal entry seems to indicate just the opposite because the issuer got more money out of the sale of the bond than they had anticipated. Maybe it is because they have to pay the investor less interest, and, therefore, the lower than expected interest rate boosts the issuer's…… ugh….. ROI? After all, the issuer is selling debt…

So, I hate to be a stickler, but how can a premium (more money) be achieved by a lower market interest rate?

I hope this makes sense. I think the conversation is becoming more confusing than helpful at times.

If this is so, then dont kill me… just let me know, and I'll hush up… It's just I feel like I have half an understanding, and half an understanding can be worse than none at all sometimes…

Ty.

wm

[jfreelov]

I admire your tenacity to stick with this until you really grasp it.

“In the case of a premium, the market is paying less interest on the bond than the issuer expected, but the cash debit in the journal entry seems to indicate just the opposite because the issuer got more money out of the sale of the bond than they had anticipated.”

Remember the market is not directly involved in the transaction. The market is only used as a reference to determine whether a stated interest rate is high, low, or just right. In the case above, the market is paying less interest than the bond you are offering. Because you are paying more interest to the investor over the course of the loan, they have to pay a higher price for that stream of interest. Hence, the cash is you receive is higher (premium) and and interest that you will be paying out is also higher.

Maybe a different type of metaphor could work. Instead of a bond issue, let's pretend I'm renting a chicken. Most chickens lay 2 eggs per day, but the chicken you are offering will lay 3 eggs per day. Your chicken will therefore receive more money in rent compared to the average 2 egg/day chicken (the market).

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[William_777]

Thanks, jfreelov.

I hate to ask you to check my thinking, but – in all humility – does this follow accordingly… If any sections are wrong, then please let me know…

---

Bond Discounts and Premiums Table

---

If a bond sells at a premium, the Coupon Rate > Market Rate.

I.E., the issuer'S “ANTICIPATED” Rate > Investor's “ACTUAL” Rate.

We look at things from the issuer's, i.e. the seller of debt's, perspective, like so…

Dr Cash $4,120,000 ($4m x 103%)

Cr Bond premium $120,000 (amortized over 20 periods)

Cr Bonds payable $4,000,000 (always face value)

In a premium

Issuer receives MORE BC THEY PAY A LOWER INT RATE THAN ANTICIPATED… ?

Investor RECEIVES Less ROI… ?

---

If a bond sells at a discount, the Coupon Rate < Market Rate.

I.E., the issuer'S “ANTICIPATED” rate < investor's “ACTUAL” rate.

We look at things from the issuer's, i.e. the seller of debt's, perspective, like so…

Dr Cash $3,800,000 ($4m x 95%)

Dr Bond discount $200,000

Cr Bonds payable $4,000,000 (always face value)

In a discount

Issuer receives less BC THEY PAY A HIGHER INT RATE THAN ANTICIPATED… ?

Investor receives MORE ROI… ?

---

[William_777]

I'm posting that info because I am trying to figure out where I am going wrong… I think the table above has mistakes in it, but I cant tell where the mistake is occurring…

[jfreelov]

Let's use a different word than anticipated, that isn't really reflective of reality. The issuer can set the interest rate to whatever rate they want, it's completely arbitrary and doesn't have to do with expectations.

“In a premium

Issuer receives MORE BC THEY PAY A LOWER INT RATE THAN ANTICIPATED… ?

Investor RECEIVES Less ROI… ?”

Should be:

In a premium

Issuer receive MORE BC THEY PAY A HIGHER INT RATE THAN THE MARKET.

Investor RECEIVES Exactly the Same ROI

Maybe that last part is where you are stuck. A premium or discount is calculated such that the ROI will match what the market rate is. For FAR related questions, this is always true. Let that sink in. The price of a bond, whether it ends up being a premium or discount, is the price that results in the EFFECTIVE interest rate being equal to the market interest rate.

“In a discount

Issuer receives less BC THEY PAY A HIGHER INT RATE THAN ANTICIPATED… ?

Investor receives MORE ROI… ?”

Should be

In a discount

Issuer receives less BC THEY PAY A LOWER INT RATE THAN THE MARKET

Investor receives EXACTLY SAME ROI.

FAR - 71, 94
BEC - 91
REG - 51, 88
AUD - 89

[William_777]

Got it!

Tyvm, jfreelov!!!

[Author]

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