Download Term Structure

Corporate Finance
Long Term Debt
Government Bond Analysis
FINA 4330
Lecture 5
Ronald F. Singer
Fall, 2010
Topics Covered
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Real and Nominal Rates of Interest
The Term Structure and YTM
How Interest Rate Changes Affect Bond Prices
Explaining the Term Structure
Real and Nominal Rates of Interest
• Classical Theory of Interest Rates
– Developed by Irving Fisher
• The real interest rate (r) tends to be relatively
stable over time
• That means that the nominal interest rate (R)
tends to move with the rate of inflation.
Term Structure and Yields
The Return on US Treasury Bills and the Inflation rate (1953-2003)
16
14
Treasury Bills
Inflation
12
8
6
4
2
2003
1998
1993
1988
1983
1978
1973
1968
1963
-2
1958
0
1953
Percent
10
Real and Nominal Interest Rates
Nominal R = (1+Real r) (1 + expected inflation) -1
Real r is theoretically somewhat stable
Inflation is an important variable in determining the
level and movement of the Nominal Rate
This theory allows us to understand the Term
Structure of Interest Rates.
The Term Structure tells us the cost of debt.
Last Year Yield Curve
Current Yield Curve
Present Value of a Loan
1
PV 
1  r1
The Term Structure can be
reflected in using various “r” terms
for different time periods, where
“r’s” are nominal rates.
1
1
PV 

2
1  r1 1  r2 
Empirical Term Structure
WSJ Yield on “Strips”
A Strip is a government bond that has had the
coupon or the Principal “stripped from its
payments, so the “Principal strips” is the
annualized yield for a government bond that
makes only one payment at maturity.
Bond valuation
XYZ 5s 2010: Interest paid semiannually each May 15 and
October 15
Term Structure From “Strips”
Maturity
YTM
5/09
5%
11/09
6%
5/10
7%
11/10
8%
Value:
YTM?
Six Month Rate
2.5%
3.0%
3.5%
4.0%
Periods
1
2
3
4
Bond Valuation
• What Is the “Value” of this bond
• Cash Flow:
50
50
50
1050
Bond Valuation
• What is the Value of this Bond?
Given the Term Structure by “strips”, the Bond is valued
as follows:
Present Value of first coupon: PV(2.5%,1,50)
= 49.90
Present Value of second coupon: PV(3%,2,50)
= 49.75
Present Value of third Coupon
= 49.57
Present Value of Principal + Last Coupon = 1036.12
1,185.34
Bond Valuation
• Yield to Maturity:
• Find that annualized interest rate which makes
the present value of its payments equal to its
market value
• N = 4, PV = -1185.34, PMT = 50, FV = 1000
• Compute I%/YR = 3 times 2 = 6%.
•
Yield to Maturity
Example
• A treasury bond expires in 5 years. It pays a
coupon rate of 10.5%. If the market price of
this bond is 107.88, what is the YTM?
Yield to Maturity
Example
• A $1000 treasury bond matures in 5 years. It pays a
coupon rate of 10.5%. If the market price of this
bond is 107.88, what is the YTM?
C0
-1078.80
C1
C2
C3
C4
C5
105
105
105
105
1105
Calculate IRR = YTM = 8.5%
Procedure for a Public Debt Offering
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Approval from Board of Directors
Registration Statement
SEC studies for 20-days
Final prospectus is issued
Securities are sold
Indentures
• Registration material must include a indenture
• The indenture is an agreement between the
issuer (firm) and a bondholders’ trustee (trust
company) which is the representative of the
Bondholders.
• Trustee’s duties
– Make sure indenture is obeyed
– Manage the “Sinking Fund”
– Represent Bondholders in general
Bond Indenture Provisions
1. The basic terms of the bond
2. Property used as security if any
3. Details of protections Bondholders have
– Protective Covenants
4. The Sinking Fund arrangements
5. The call provisions
The Basic Terms
• Timing and the amount of the payments to the
bondholders:
“The bond will pay interest at a rate of 16% of par,
semiannually on each October 15 and April 15
from April 15, 2009 through April 15, 2024. The
annual interest rate is 16%. On April 15, 2024 the
bond will make its final interest payment and also
pay the holder the par value of $1,000.
Security of the Bond
• Collateral Trust Bonds: Common Stock held by
the company is used to pledge against the bonds.
– If the firms does not pay the Bondholder, they can
take the stock instead.
• Mortgage Securities: Bonds that have specific
long term assets or property as collateral
• Unsecured Bonds: Bonds that don’t have any
specific security are called unsecured or
Debentures
– The bondholders become a general obligation of the
firm in default.
Protective Covenants
• Negative Covenants: Prohibits certain actions
that the firm may take that could harm
bondholders
– Limit dividend payments, sale of assets or mergers
(without bondholders’ permission), issue additional
debt of a certain class
• Positive Covenants: Company agrees to take
certain actions
– Maintain working capital
– Furnish financial statements
Sinking Fund Agreements
• Firm agrees to periodically repurchase the
bonds at a given price (usually par), or at the
market price whichever is lower.
– Provides additional protection to bondholders by
providing an early warning system to bondholders
if the firm is in trouble
– Firm has the choice of retiring the debt at market
prices or at the fixed price set in the contract.
Call Provision
• Allows the firm to repurchase (Call) the bond
at a predetermined price (the call price) prior
to its maturity
– The call premium is the difference between the
call price and the par value of the debt
– Call premium generally starts at par plus one
year’s coupon and declines to zero near maturity
– Call protection give the bondholder protection
from a call over the early years of the Bond