# Why would I not buy a bond for less than face value?

The way I understand it is that if you own a bond at maturity you will get the face value of the bond at that time.

So if you can purchase a bond at \$80 which has a face value of \$100 why would I not sell everything I own and put all that money into buying this bond? Is there not a guaranteed 20% profit to be made at maturity? Not to mention the coupon, that is to be made every year.

• The existing answers cover the details well. I'd just like to add, that if you ever feel "why would I not sell everything I own and put all that money into buying this thing", then you've probably missed something. Because the current price is roughly the level where people's desire to sell is roughly equivalent to people's desire to buy. If it were a ridiculously good opportunity, then basically everyone would buy everything they could (and push the price up), while no-one would be willing to sell a that price (which would also push the price up). Commented Jan 27, 2016 at 12:56
• Short version: If it sound too good to be true... Of course "what am I missing here" is a completely legitimate question. Commented Jan 27, 2016 at 14:22
• That would be a 25% profit. \$20 = \$80 * .25 Commented Jan 27, 2016 at 14:50
• You said in the comments to one of the answers that this particular bond that you have in mind matures in 2072. Consider how old you will be then. Consider how many companies were around in 1960 that aren't around now.
– user
Commented Jan 27, 2016 at 16:00
• I only see one answer below mentioning inflation. Is \$140 in 2072 going to be worth the \$100 you pay for it today? That's a 56-year difference. If we work the other way, imagine having paid \$100 for a bond in 1960, which is worth \$140 today. Seems like you could have gotten FAR MORE value from \$100 in 1960 than what \$140 would buy today. Am I misunderstanding inflation, and what a BAD thing it would be in this case? I'm not a financial expert AT ALL. I got my inflation numbers from here: data.bls.gov/cgi-bin/… Commented Jan 27, 2016 at 23:11

One reason that a bond can be significantly less than face value is that people are seeking better investments elsewhere, so for example if a bond doesn't mature for another 10 years, that 20% increase in face value isn't very attractive when compared to say leaving your money in the stock market for 10 years.

Another reason could be that the creditworthiness of the issuer has collapsed and people expect that there is a fairly good chance they are not going to make the payment. This could be what you would see if, for example, it was a one-year time until maturity, but it has a value of 40% of the face value.

There is a risk because they can simply not pay. For example, people who bought Greek bonds.

• the bond matures in 2072 Commented Jan 27, 2016 at 10:30
• 2072? As in the YEAR 2072? Even a savings account that accrues only 0.5% interest per year will turn 80 into 100 about 10 years earlier than this bond you are talking about Commented Jan 27, 2016 at 14:58
• @Aequitas massive companies go bankrupt all the time. If you look at sets of massive companies like S&P 500 some 50 years ago, then about half of those companies are now bankrupt. If you look at any perfectly healthy massive company now, then there may well be a 10% chance that it will be bankrupt in 10 years. Many of the current on-going long term massive brands have "survived" only as brands, having been through insolvency, restructuring and shedding of bonds multiple times. Commented Jan 27, 2016 at 15:25
• If the bond doesn't mature until 2072, it should be obvious that there are many reasons not to sell everything you own. Even if god himself gave his word of honor that he would pay you a trillion dollars in 2072, you still have to survive until 2072 to get it. Commented Jan 27, 2016 at 20:23
• @BrenBram the bond can be sold on earlier, so there is no need to wait until 2072. What the bond will be worth is another matter but that is addressed in the other answers. Commented Jan 28, 2016 at 7:06

As well as credit risk there's also interest risk. If a bond has a face value of \$100, pays 1% and matures in 20 years' time then you expect to receive a total of \$120 from buying it now -- \$1 per year for 20 years and \$100 at the end.

But if you can get a 3% return elsewhere, then if you invest your \$80 there instead you will get \$2.40 per year for 20 years and then \$80 at the end, making a total of \$128 (and you also get more of the money sooner). So even \$80 for the \$100 bond is a bad buy, and you should invest elsewhere.

A (very) simplified bond-pricing equation goes thus:

Fair_Price:
{Face_Value * (1 + Interest - Expected_Market_Return) ^ (Years_To_Maturity)}
* P(Company_Will_Default_Before_Maturity)

To reiterate, that is a very simplified model. But it allows us to demonstrate the 3 key factors that drive "Fair" Value:

1. The interest relative to the current market rate. If your AAA bond yields 1%, but an equally-good AAA bond currently sells at 3% in the market, then the "Equivalent" value is the face value minus 2% (1% - 3%) for every year to maturity.

2. Years to maturity. Because 1) is multiplied for every year to maturity, longer-dated bonds are more sensitive to changes in market rates. If your bond yields 2% less than market but matures in a year, then it's worth \$98, but if it matures in 56 years, then it's only worth 0.98^56 = \$32. Conversely, if your bond yields more than the market rate, then its' price will be greater than face value.

3. The company might default on the debt. If a Bond has a "Fair" Value of \$100, but you think there's a 50% chance that the company will default, then it's only worth \$50. In fact, it can be worth even less because getting paid on a defaulted bond can often take time and/or money and/or lawyers.

In your case, because your bond matures in 56 years but yields ~5% (well above the current market rate), for it to be below Face value implies a strong probability of default, or a strong belief that market returns will be above 5% over the next 56 years.

• RE "In fact, it's worth even less because getting paid on a defaulted bond..." I don't see how this follows, if there's a chance of getting paid even if the company defaults, then the value in the event of default is more than 0. You should also consider that you'll collect interest payments up until the date the company defaults. So just multiplying the value by P(default) is conservative --- it's at least slightly underestimating the value of the bond (but maybe not enough to make up for our optimism in estimating P(default) ). Commented Jan 28, 2016 at 0:22
• @ThePhoton Of course there are many considerations, how much of the face value you might receive in a default, seniority of the bond, length of time between default/bankruptcy/whatever and actually getting paid, whether you'll need to sue the company in bankruptcy court, how you expect market rates to change over time, how you expect probability of default to change over time, etc. I deliberately left all that out for the sake of simplicity in understanding the core factors.
– Kaz
Commented Jan 28, 2016 at 20:08

The time value of money is very important in understanding this issue. Money today is worth more than money next year, two years from now, etc. It's a well understood economics concept, and well worth reading about if you have some, well, time.

Not only is money literally worth more now than later due to inflation, but there is the simple fact that, assuming you have money for the purpose of doing something, being able to do that thing today is better than doing that same thing tomorrow. "A bird in the hand is worth two in the bush" gets to this rather directly; having it now is better than probably having it later. Would you rather have a nice meal tonight, or eat beans and rice tonight and then have the same nice meal next year?

That's why interest exists, in part: you're offered some money now, for more money later; or in the case of buying a bond, you're offered more money later for some money now. The fact that people have different discount rates for money later is why the loan market can exist: people with more money than they can use now have a lower discount for future money than people who really need money right now (to buy a house, to pay their rent, whatever).

So when choosing to buy a bond, you look at the money you're going to get, both over the short term (the coupon rate) and the long term (the face value), and you consider whether \$80 now is worth \$100 in 20 years, plus \$2 per year. For some people it is - for some people it isn't, and that's why the price is as it is (\$80). Odds are if you have a few thousand USD, you're probably not going to be interested in this - or if you have a very long term outlook; there are better ways to make money over that long term. But, if you're a bank needing a secure investment that won't lose value, or a trust that needs high stability, you might be willing to take that deal.