Bonds - (financial)

In Finance , a bond is a promise from a company (or government) to pay interest and principal in the future.  A bond is simply a loan, but in the form of a security.

The purpose of bonds is to raise money for a company or government, to enable them to finance long-term investments with external funds.

In addition to public debt issued as bonds, others may be privately held with a private lending institution. 

Most public -issued bonds have a face value of $1000 (principal, par value)

Maturities

Bonds are generally issued for a fixed term (the maturity) longer than ten years.  The Maturity is simply the length of time of the bond.

Bond:  10+ years

Note:  1-10 years

Bill:  less than 1 year

U.S Treasury securities issue debt with life of ten years or more, which is a bond. New debt between one year and ten years is a "note", and new debt less than a year is a "bill".  Note: CDs (certificates of deposit) or commercial paper are considered money market instruments, and not bonds.

When comparing bonds, you can either look at the "time to maturity", or (preferably) at the "duration", which is like a weighted average that tells you how long until the bond comes due.  Duration is important in comparing two bonds, or mortgages against each other.  It is also very important when hedging interest rate risk, and for matching the maturities of assets and liabilities on the balance sheet. 

Types of Bonds

1. Pure "Discount" bonds = "zero coupon" bonds = bullet bond.......all names for the same thing - a bond that pays no cash payments until maturity (all payments at end, in one lump sum).  For this type of bond, the PV = Future payment / (1+r) ^t, where r is the market interest rate, and t is the number of periods (years) of the life of the bond.

2. Coupon bonds - pay off some of the principal (denomination) + interest during the life of the bond.  The present value of this bond can be figured out either (a) by considering it as a whole bunch of individual "discount" bonds, in which case you just make many individual PV calculations, and add them up., or (b) using an excel spreadsheet, or financial table...find the annuity factor for time = T, and rate = r, and plug into this formula:  PV = C * annuity factor + Future payment / (1+r)^t.

3.  Consols:  a unique type of bond that pays a coupon payment forever, but never pays back the face value (no lump sum at the end).  You can value this just like a perpetuity (PV = C/r). 

Yield to Maturity on a Bond

The YTM of a bond is simply the IRR of its expected future cash flows.  It is the discount rate that will make the present value of all of its future cash flows equal to the bond price.  Think about the IRR as the discount rate when NPV is =0, and realize that all stocks and bonds are NPV=0, so the yield to maturity of a bond is just that...the IRR of the bond when NPV = 0. 

Example:

During the Credit Crisis, the "yield" on Treasuries dropped to record lows.  This happens when everyone wants to buy these assets, which drives up the price, and has an inverse effect of driving down the "yield to maturity".

Example:

If a bond is selling at  $1050.00, and the face value is $1000, with a 2 year life, and a coupon rate of 10%, then what is the YTM on this bond?

$1050 = $100  +  $1000 + $100

               1 + y         (1+y) ^2

the YTM is the yield (the discount) rate that makes this true.  So, if you solve for y, you find that the YTM of this bond is approximately 7.23%.  And since it is selling for more than its face value, then it is selling at a premium.  The offered coupon rate is more than the going market rate of just 7.23%, so the price of the bond gets bid upward from $1000 to $1050.

Current Yield

Current Yield = current coupon / current price

Be careful, this is not the same thing as the YTM (which is more important) listed above. 

The "current yield" is often quoted, but is not as useful as the YTM.

Market Price of bond

Bonds are traded publicly in exchanges.  The market price of the bond will not be solely based upon the PV of the future cash flows (plus the coupon interest rates).  It is not that simple.  Because in the market of trading, there are other factors that might bid up or down the market price of the bond, such as:

1.  Expectations about future interest rate changes

2.  Expectations about the future ability of the firm to pay fixed income (bond) payments

3.  Expectations about the possibility of bankruptcy in the future.

4.  Expectations about potential future competition .....etc, etc.....

The key point is that if a firm issues a 30 year bond...will they still be around in 30 years to pay off their principal value?  For many newer companies, investors can not say for certain if they will...so, they often demand a higher coupon payment every 6 months.

Also, this explains why people pay such close attention to the bond ratings agencies.  (AAA, AA, A, BBB, BB, B, CCC,CC,C, D).  If a bond gets rated as D, it means that they are in default, and that they will not pay.  The safest bonds have an AAA rating.   But, with safety comes lower returns.  With risk comes higher expected returns.

Sensitivity to Interest rates

Bond values have an inverse relationship with market interest rates.  If market interest rates go down, then the value of existing bonds will go up.   If market interest rates go up, then the value of existing bonds goes down.  

Why?

There are two ways to look at it.  (1)  think of a bond as a series of future cash flows.  In order to find the present value of those cash flows (and the price of the bond), you first need to discount the cash flows to the PV.  To do so, you must divide the expected cash flow by the discount rate....so, the higher the interest rate, the lower the expected present value of the bond.

Another way to think about it (2):  Think about the coupon % offered on the bond.  If the bond is offering 10% interest (fixed over 30 years)...what do you think will happen to the value of that bond if the market interest rates jumped up to 15%?  That means that normal investors could invest in other investments that could result in 15% interest rates...so, do you think they will value a bond that only pays out 10%? Of course not, and so the value of the bond will fall if market interest rates rises.  If, on the other hand, the market interest rates were to fall to just 5%, then the 10% interest being paid by this bond will suddenly look very attractive, so investors will want it, and that demand will bid up the price. 

Result:  Either way you look at it....bond values have an inverse relationship with interest rates.

Thinking of Stocks and Bonds as Call options

The stock (equity) of a company can be thought of as a "call option" on the firm.  The value of the call option increases with volatility, and a rise in volatility will increase the value of the stock of the firm.  This means that the value of the stock equity will increase as the firm selects riskier projects.  But, on the other hand, the value of the bond holders will decrease as riskier projects are selected.  This can also be seen in terms of Options.   The value of a risky bond can be seen as the difference between the value of the firm and the value of the call option on the firm.  So, as the value of the call option increases (value of the stock increases), this means that the value of the bonds decreases.  The bondholders are therefore hurt when the firm selects riskier projects. 

How to issue a bond

for a public offering, first need an indenture (a written agreement) between the company and a trust company.  The trust company will represent the bondholders.   They will make sure that the terms of the indenture are obeyed by the company.  this document will outline the terms of the bond, if the bond has any securitization (asset-backed?), if there are any covenents to protect the bondholders (see discussion above), how the "sinking fund" will be set up, and any notes about call provisions. 

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External Links

Wikipedia article for more info