1 SECURITY VALUATION BOND VALUATION When a corporation (or the government) wants to borrow money, it often sells a bond. An investor gives the corporation money for the bond, and the corporation promises to give the investor: 1. Regular coupon payments every period until the bond matures. 2. The face value of the bond when it matures. Additional Features: 1. Payments are a legal obligation. In case of default, bondholders can force firm into bankruptcy. 2. “Senior” or “Junior” debt pertains to who gets paid first in case of bankruptcy. In some cases “junior” debtholders can get partially paid before senior debtholders are fully paid. 3. Call provisions: A call provision gives the corporation the right to buy back an outstanding bond (usually at face value). 4. Put provisions: A put provision gives the bondholder the right to sell the bond back to the corporation. 5. Convertible bonds. Questions: • What is the market price of a U.S. Treasury Bond? • What is the relation between U.S. Treasury Bond prices and interest rates? • Are U.S. interest rates expected to rise or fall? • How should you pick a Certificate of Deposit? Terminology Bond: Loan made by numerous individuals and/or institutions (the bond holders) to a firm/state/country. Par Value: Principal amount to be paid at maturity, usually $1000, also known as Face Value. Maturity: Amount of time that will pass until par value is paid. Coupon: Percentage of par value that is paid every year (usually semi-annually so divide by two to determine the payment amount). Current Yield: Coupon amount divided by a bond’s current price.
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SECURITY VALUATION
BOND VALUATION
When a corporation (or the government) wants to borrow money, it often sells a bond. An
investor gives the corporation money for the bond, and the corporation promises to give the
investor:
1. Regular coupon payments every period until the bond matures.
2. The face value of the bond when it matures.
Additional Features:
1. Payments are a legal obligation. In case of default, bondholders can force firm into
bankruptcy.
2. “Senior” or “Junior” debt pertains to who gets paid first in case of bankruptcy. In some cases
“junior” debtholders can get partially paid before senior debtholders are fully paid.
3. Call provisions: A call provision gives the corporation the right to buy back an outstanding
bond (usually at face value).
4. Put provisions: A put provision gives the bondholder the right to sell the bond back to the
corporation.
5. Convertible bonds.
Questions:
• What is the market price of a U.S. Treasury Bond?
• What is the relation between U.S. Treasury Bond prices and interest rates?
• Are U.S. interest rates expected to rise or fall?
• How should you pick a Certificate of Deposit?
Terminology
Bond: Loan made by numerous individuals and/or institutions (the bond holders) to a
firm/state/country.
Par Value: Principal amount to be paid at maturity, usually $1000, also known as Face Value.
Maturity: Amount of time that will pass until par value is paid.
Coupon: Percentage of par value that is paid every year (usually semi-annually so divide by two
to determine the payment amount).
Current Yield: Coupon amount divided by a bond’s current price.
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Zero Coupon Bonds: Bonds which return par value at maturity but pay no coupons along the
way. (We’ll talk about Treasury STRIPS.)
Yield to Maturity: Single, constant discount rate that equates the bond’s current price to the
present value of its cash flows.
Bond Valuation
Economic value of a bond is present value of its cash flows:
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Three pieces of information needed to value a bond:
1. What are the expected cash flows?
2. When and how frequently do the cash flows arrive?
3. What is the appropriate discount rate?
II. The Basic Bond Valuation Model
Value = PV(stream of interest payments) + PV(maturity value).
Case 1: Zero Coupon Bond
Example: What is the value of a zero coupon bond with a face value of $1000 and maturity of
10 years? Assume an annual interest rate of 8%, compounded semiannually.
0 1 2 20
$0 $0 $1000
Price of the zero bond = $1000(1/1.04)20= $ 456.39
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Case 2: Coupon Bonds
Example
. What is the value of a bond that pays 8% coupon rate annually and matures in 10
years from today when the appropriate discount rate for similar bonds today is 8%?
Example
. Suppose all the factors in the economy and company remain constant. What
would be the value of the same bond a year from today?
Rule 1: The value of a bond remains constant as long as
the interest rate in the economy remains constant.
Example
. Suppose the interest rate in the economy rises to 10% after the bond was issued.
What is the value of the bond after one year?
Rule 2: The bond will sell at discount.
Example
. Suppose the interest rate in the economy fell to 6% a year after the bond was
issued. What is the value of the bond after one year?
Rule 3: The bond will sell at premium over its face value.
General Rules:
1- if the Interest Rate=Coupon Rate then Price=Face Value=
1000
2- if the Interest Rate> Coupon Rate then Price<Face Value
- the bond is selling at discount
3- if the Interest Rate< Coupon Rate then Price> Face Value
- the bond is selling at premium
4- as the interest rate goes up, the price of the bond goes down
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Example of Bond Valuation
Consider a 3-year, 10% coupon bond with a face value of $1000. The
bond pays coupons annually. If appropriate annual discount rate
is 8%, what is the highest price that are you willing to pay for the