A bond is long term debt normally issued by the government or corporations. Most bonds pay:

• A fixed annual or semi-annual coupon.
• A final lump sum (face value) at maturity.

Bonds can be sold on the secondary market. The price at which they sell is determined by their current yield to maturity. Below is a list of relevant definitions:

-  Issuer: The party who issues (sells) the bond (i.e. government or corporations).

-  Bondholder: The party or investor who buys (holds) the bond (i.e. funds, individual investors).

-   Face or par value: The amount of money we will receive on maturity (normally 100 or 1000).

-   Maturity: The due date of the bond.

-  Yield to Maturity (YTM): The current return on investment for a bondholder – Changes as the bond price changes.

-  Coupon rate: Fixed payment of the bond. It is the amount of money that will be received each period.

YTM v Coupon rate:

In finance 251 you must understand the difference between YTM and coupon rate.

YTM: The current implied interest rate. Changes constantly – Used as the discount rate

Coupon rate: The amount paid to the bondholder at the end of each period. Used as “C” – the annuity payment.

There is a direct relationship between the difference in YTM and coupon rate and the current bond price. Below is a simple explanation to understand this concept:

-          If the current YTM = coupon rate, bond price = par/face value

-          If the current YTM < coupon rate, bond price > par/face value

-          If the current YTM > coupon rate, bond price < par/face value 

Valuing Bonds

The value of a bond can be calculated like any present value calculation. It is simply the present value of the future cash flows. It is the present value of:

• The annual coupon payment (This is an annuity where “t” is the time to maturity).
• The single one off payment (Face value).
• The discount rate is the YTM

Formula:

PV = PVA + PV (par/face value)

Example: Value the following bond:

-          4 year bond

-          Coupon rate = 5.2%

-          Begin 1.1.09

-          Current date 1.1.10

-          Current YTM = 6%

-          Face value 1000

-          Coupon semi annually

Answer:

PV = PVA + PV(1000) 

Important Note: The YTM of a bond is given as an annual amount. If coupon payments are semi-annual you must determine the semi annual rate. When valuing bonds all we do is divide the annual rate by 2

This entry was posted on Sunday, May 10th, 2009 at 3:39 am and is filed under Finance. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.