FIN 365 Business Finance
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Transcript FIN 365 Business Finance
FIN 365 Business Finance
Topic 13: Bonds and their Valuation
Larry Schrenk, Instructor
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Bond Valuation
• Bond Basics
• Valuing Bonds
• The Comparative Statics of Bonds
• Interest Rate Risk
• Technical Features of Bonds
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Bond Basics
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What is a Bond?
• A long-term debt instrument in
which a borrower agrees to make
payments of principal and
interest, on specific dates, to the
holders of the bond.
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Bond Markets
• Primarily traded in the over-the-counter
(OTC) market.
• Most bonds are owned by and traded
among large financial institutions.
• Full information on bond trades in the OTC
market is not published, but a representative
group of bonds is listed and traded on the
bond division of the NYSE.
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Bond Basics
•
•
•
•
•
–
–
–
Coupons
Coupon Rate (cr)
Fixed Payment
Bankruptcy Trigger
Par Value/Face Value/Principal
Period (typically semi-annual)
Maturity
Interest Rate
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Features of a May Department
Stores Bond
Terms
Explanations
Amount of issue
$125 million
Date of issue
Maturity
Annual coupon
2/28/86
3/1/16
9.25
Offer price
face value).
100
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The company will issue $125 million worth
of bonds.
The bonds were sold on 2/28/86.
The principal will be paid in 30 years.
The denomination of the bonds is
$1,000. Each bondholder will receive
$92.50 per bond per year (9.25% of the
The offer price will be 100% of the
$1,000 face value per bond.
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Features of a May Department
Stores Bond (concluded)
Terms
Explanations
Coupon payment dates
3/1, 9/31
Coupons of $92.50/2 = $46.25 will be
paid on these dates.
Security
None
The bonds are debentures.
Sinking fund
the sinking fund.
Annual, toward
beginning 3/1/97
The firm will make annual payments
Call Provision
Not callable
before 2/28/93
The bonds have a deferred call
Call price
106.48 initially,
declining to 100
After 2/28/93, the company can buy
back the bonds for $1,064.80 per bond,
declining to $1,000 on 2/28/05.
Rating
Moody’s A2
This is one of Moody’s higher ratings.
The bonds have a low probability
of default.
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Bond Types
• Consols
• Zero-Coupon Bonds
• Fixed-Coupon Bonds
• Variable Rate Coupon Bonds
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Issuers of Bonds
• Government
–
–
U.S. Treasury Securities
•
Treasury Inflation-Protected Securities (TIPS)
State and Local (‘Muni’s’)
• Corporate
–
–
•
Corporate Bonds
Short-Term Debt
Commercial Paper
• Home Mortgages
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Bond Rating Agencies
• Agencies
–
–
–
Standard & Poor's
Moody's
Fitch Ratings
• Distinction
–
–
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Investment Grade Bonds
Junk Bonds
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Bond Ratings
• Standard & Poor's System
– Investment Grade
• AAA: the best quality companies, reliable and stable
• AA: quality companies, a bit higher risk than AAA
• A: economic situation can affect finance
• BBB: medium class companies, which are satisfactory at the
moment
– Non-Investment Grade (also known as junk bonds)
• BB: more prone to changes in the economy
• B: financial situation varies noticeably
• CCC: currently vulnerable and dependent on favorable
economic conditions to meet its commitments
• CC: highly vulnerable, very speculative bonds
• C: highly vulnerable, perhaps in bankruptcy or in arrears but
still continuing to pay out on obligations
• CI: past due on interest
• R: under regulatory supervision due to its financial situation
• SD: has selectively defaulted on some obligations
• D: has defaulted on obligations and S&P believes that it will
generally default on most or all obligations
• NR: not rated
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Valuing Bonds
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Valuing Bonds
• Bond Value = PV(cash flows)
• Two cash flows:
– (semi-annual) fixed coupons
– Par value at maturity.
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Valuing Bonds
• Bond Value
= PV(coupons) + PV(par value)
– Coupons are an annuity
– Par value is one time payment
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Valuing Bonds
• Formula for Bond Valuation
PVbond
C
1
Par Value
1
Tm
Tm
r
r
r
m 1 m 1 m
PV(Coupons) PV(Par Value)
PVBond = Value/Price of Bond; C = Period Cash Flow; r = Discount Rate; m = Periods per Year
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Valuing Bonds
• EXAMPLE
– What is the present value of a four year,
semi-annual bond with a par value of
$1,000.00 and a coupon rate of 8% if the
discount rate is 6%?
PVbond
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40
1
1,000
1
$1,070.20
42
42
0.06 0.06 0.06
2 1 2 1 2
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Valuing Bonds: Calculator
• EXAMPLE
– What is the present value of a four year, semiannual bond with a par value of $1,000.00 and
a coupon rate of 8% if the discount rate is 6%?
P/Y = 2; N = 8; I/Y = 6;
PV = $1,070.20; PMT = -40; FV = -1000
–
–
–
–
P/Y = 2 (semi-annual bond)
N = 8 (= 4 x 2)
PMT = 40 (= (1,000 x 0.08)/2) PMT = Period Cash Flow
Why these negative signs?
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Yield to Maturity (YTM)
• Discount rate such that
Price = PV(cash flows).
T
YTM s.t. 0
t 1
T
Ct
1 YTM
t
Investment
t 0
Ct
1 YTM
t
YTM = Yield to Maturity; Ct = Cash Flow in Year t
• Expected return if the bond purchased
at a fair value.
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Yield to Maturity: Calculator
• EXAMPLE
– What is the YTM of a five year, semi-annual bond
with a par value of $1,000 and a coupon rate of
9% if the bond is selling for $990?
P/Y = 2; N = 10; I/Y = 9.25%;
PV = 990; PMT = -45; FV = -1000
–
–
–
–
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P/Y = 2 (semi-annual bond)
N = 10 (= 5 x 2)
PMT = 45 (= (1,000 x 0.09)/2) PMT = Period Cash Flow
Why these negative signs?
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Valuing Bonds
• Two Notes on Yield to Maturity
– YTM = expected return only when just
purchased.
– YTM versus realized/actual yield
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Definitions
Annual coupon payment
Current yield (CY)
Current price
Change in price
Capital gains yield (CGY)
Beginning price
Expected Expected
Expectedtotalreturn YTM
CY
CGY
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An Example: CY
Find the current yield and the capital
gains yield for a 10-year, 9% annual
coupon bond that sells for $887, and
has a face value of $1,000.
Current Yield = $90 / $887
= 0.1015 = 10.15%
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An Example: CGY
YTM = Current Yield + Capital Gains
Yield
CGY = YTM – CY
= 10.91% - 10.15%
= 0.76%
Could also find the expected price one year from
now and divide the change in price by the
beginning price, which gives the same answer.
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Yield to Call (YTC)
• The yield of a bond if you were to
buy and hold the security until the
call date.
• Calculation─Same as YTM but:
– Use the periods to the call date (not
maturity) for N
– Use the call price (not par value) for FV
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Yield to Call: Calculator
• EXAMPLE
– What is the YTC of a five year, semi-annual bond
with a par value of $1,000 and a coupon rate of
9% if the bond is selling for $990, the call price is
$1,100 and the call date is two years?
P/Y = 2; N = 4; I/Y = 14.09%;
PV = 990; PMT = -45; FV = -1100
–
–
–
–
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P/Y = 2 (semi-annual bond)
N = 4 (= 2 x 2)
PMT = 45 (= (1,000 x 0.09)/2) PMT = Period Cash Flow
Why these negative signs?
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The Comparative Statics of
Bonds
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T-P-S
You have two identical zero coupon
bonds─except that the maturity of one
is twice the maturity of the other. Will
the price of the shorter bond…
1.
2.
3.
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More sensitive to changes in interest rates
than the longer bond
As sensitive to changes in interest rates
than the longer bond
Less sensitive to changes in interest rates
than the longer bond
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Price versus Interest Rate
Price-Yield Relationship
$2,500
Price
$2,000
$1,500
$1,000
$500
.5
%
12
.5
%
14
.5
%
16
.5
%
18
.5
%
10
5%
8.
5%
6.
5%
4.
5%
2.
0.
5%
$0
Yield
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T-P-S
You have two identical zero coupon
bonds─except that the maturity of one is
twice the maturity of the other. Will the
price of the shorter bond be…
1.
More than half the price of the longer bond
2.
Half the price of the longer bond
3.
Less than half the price of the longer bond
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Price versus Coupon Rate
Price-Yield Relationship
1.00
0.80
0.60
0.40
0.20
0.00
Zero
5% Coupon
18.5%
15.5%
12.5%
9.5%
6.5%
3.5%
10% Coupon
0.5%
Ratio
(normalized by dollar value)
Yield
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Price versus Time to Maturity
$1,600
$1,400
$1,200
$1,000
$800
$600
$400
$200
$0
3
6
9
12
15
18
21
24
27
discount
par
premium
30
Price
Price-Maturity Relationship
Years to Maturity
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Factors Affecting Default Risk
and Bond Ratings
• Financial performance
– Debt ratio
– TIE ratio
– Current ratio
• Bond contract provisions
–
–
–
–
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Secured vs. Unsecured debt
Senior vs. subordinated debt
Guarantee and sinking fund provisions
Debt maturity
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Interest Rate Risk
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Interest Rate Risk
• Interest Rate Risk
– Value changes due to interest rate
• Components
– Price Risk
– Reinvestment Risk
Note: Different from Textbook
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Interest Rate Risk
• Price Risk
– Interest rates up/down ??
• Reinvestment Risk
– Interest rates up/down ??
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Technical Features of Bonds
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Features of Bonds
• Examples
– Bond Covenant
– Sinking Fund
– Technical Default
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Premium versus Discount Bonds
• Premium: cr > r
– Price > par value
• At par: cr = r
– Price = par value
• Discount: cr < r
– Price < par value
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Premium versus Discount Bonds
• EXAMPLE
– Consider a ten year, semi-annual, bond
with a par value of $1,000 and a coupon
rate of 8%:
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• r = 6%
price = $1,148.77.
• r = 8%
price = $1,000.00.
• r = 10%
price = $875.38.
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Types of Bond Values
•
Book Value
•
Liquidation Value
•
Market Value
•
–
For Prices,
http://cxa.marketwatch.com/finra/BondCenter/Default.aspx
Intrinsic/Economic Value
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Embedded Options
• Like derivatives securities, e.g.,
call or put options
• Types of Embedded Options
–
Call Provision
–
Conversion Provision
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T-P-S
A bond with a call option is worth…
1.
More than a straight bond
2.
The same as a straight bond
3.
Less than a straight bond
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Other Types (Features) of Bonds
• Warrant – long-term option to buy a stated
number of shares of common stock at a
specified price.
• Putable bond – allows holder to sell the bond
back to the company prior to maturity.
• Income bond – pays interest only when interest
is earned by the firm.
• Indexed bond – interest rate paid is based
upon the rate of inflation.
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Protective Covenants
• Agreements to Protect Bondholders
• Negative Covenants (Thou shalt not…):
– Pay dividends beyond specified amount
– Sell more senior debt and amount of new debt is
limited
– Refund existing bond issue with new bonds paying
lower interest rate
– Buy another company’s bonds
• Positive Covenants (Thou shalt…):
– Use proceeds from sale of assets for other assets
– Allow redemption in event of merger or spinoff
– Maintain good condition of assets
– Provide audited financial information
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Bond Investment Strategies
• Interest Rate Strategy: Select bonds
for investment based on interest rate
expectations
– Purchase long-term bonds if you expect interest rates to fall
• Passive Strategy: Invest in a diversified
portfolio of bonds that are held for a long
period of time
• Maturity Matching Strategy: Invest in bonds
that will generate payments to match future
expenses
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