Valuation, and Interest Rates
Key Concepts and Skills
What is a bond?
A bond is a security.
A bond is a long-term contract in which a borrower agrees to make payments of interest and principal, on specific dates, to the holders of the bond.
Cash Flows from Bonds
Bondholders normally expect to receive two different cash flows:
Periodic (usually semiannual) payments of interest during the bond life. These payments are often in the form of equal cash flows at periodic intervals, called an annuity.
Single payment of the face (principal) amount of the bond at maturity.
Cash Flows from Bonds
To illustrate, assume that investors wish to price a bond with a face amount of $1,000, an annual coupon rate of 6% payable semiannually and a maturity of 10 years.
Investors purchasing this issue will receive the following cash flows:
Number of Payments Dollars per Payment Total Cash Flows
Semi- annual interest payments Principal payment at maturity 10 years * 2 = 20
$1000 * 6%/2 = $30
Who Issues Bonds?
Treasury Bonds - Issued by U.S federal government
Corporate Bonds - Issued by corporations
No default-risk; Still have interest-rate risk
Default risk (or credit risk)
Municipal Bonds or “Munis” - Issued by state and local governments Default risk; interest earned is tax-exempt
Foreign Bonds - Issued by foreign governments or foreign corporations
Default risk; currency risk
Consider a taxable bond with a yield of 8% and a tax-exempt municipal bond with a yield of 6%. If you are in a 40% tax bracket, which bond do you prefer?
At what tax rate would you be indifferent between the two bonds?
Par or Face Value
The amount of money that is paid to the bondholders at maturity.
For most bonds this amount is $1,000. It also generally represents the amount of money borrowed by the bond issuer.
The default is $1,000, unless otherwise mentioned.
You will put $1,000 in FV.
This is the current market price of the bond.
You will put current market price or today’s price of the bond in
The coupon rate, which is generally fixed, determines the periodic coupon or interest payments. It is expressed as a percentage of the bond's face value.
The coupon rate does not normally change during the life of the bond, instead the price of the bond changes as the coupon rate becomes more or less attractive relative to other interest rates
The coupon payments represent the periodic interest payments from the bond issuer to the bondholder. The annual coupon payment is calculated by multiplying the coupon rate by the bond's face value ($1,000).
If nothing is mentioned, assume that the payments are made every six months. In that case, coupon payment = $1000 * coupon rate/2.
You will put coupon amount as PMT.
The maturity date represents the date on which the bond matures,
i.e., the date on which the face value is repaid. The last coupon payment is also paid on the maturity date.
The time currently remaining until the maturity date.
You will put remaining time to maturity as NPER.
Yield to maturity
The rate of return that an investor would earn if he bought the bond at its current market price and held it until maturity.
Alternatively, it represents the discount rate which equates the discounted value of a bond's future cash flows to its current market price.
It is also known as Yield, discount rate, required rate, nominal rate. The yield can change over the life of the bond based on the demand and supply of…