chapter 5 fundamentals of corporate finance fourth edition valuing bonds slides by matthew will...
TRANSCRIPT
Chapter 5Fundamentals of
Corporate FinanceFourth Edition
Valuing Bonds
Slides by
Matthew Will
McGraw Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved
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Topics Covered
Bond Characteristics reading the financial pages
Bond Prices and Yields Bond prices and interest rates YTM vs. current yield Rate of Return Interest Rate Risk The Yield Curve Nominal and Real Rates of Interest Default Risk Variations in Corporate Bonds
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BondsTerminologyBond - Security that obligates the issuer to
make specified payments to the bondholder.Coupon - The interest payments made to the
bondholder.Face Value (Par Value or Maturity Value) - Payment
at the maturity of the bond.Coupon Rate - Annual interest payment, as a
percentage of face value.
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Bonds
WARNINGWARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations.
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Bonds
WARNINGWARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations.
The coupon rate merely tells us what cash flow the bond will produce.
Since the coupon rate is listed as a %, this misconception is quite common.
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Bond Pricing
The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.
PVcpn
r
cpn
r
cpn par
r t
( ) ( )
....( )
( )1 1 11 2
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Bond Pricing
Example
What is the price of a 6.5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 3.9%.
29.072,1$
)039.1(
065,1
)039.1(
65
)039.1(
65321
PV
PV
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Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 6.5 %?
000,1$
)065.1(
065,1
)065.1(
65
)065.1(
65321
PV
PV
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Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 15 %?
93.805$
)15.1(
065,1
)15.1(
65
)15.1(
65321
PV
PV
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Bond Pricing
Example (continued)
What is the price of the bond if the required rate of return is 6.0% AND the coupons are paid semi-annually?
94.072,1$
)0195.1(
50.032,1
)0195.1(
50.32...
)0195.1(
50.32
)0195.1(
50.326521
PV
PV
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Bond Pricing
Example (continued)
Q: How did the calculation change, given semi-annual coupons versus annual coupon payments?
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Bond Pricing
Example (continued)
Q: How did the calculation change, given semi-annual coupons versus annual coupon payments?
Time Periods
Paying coupons twice a year, instead of once
doubles the total number of cash flows to be discounted
in the PV formula.
Discount Rate
Since the time periods are now half years, the discount rate is also
changed from the annual rate to the half year rate.
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Bond Yields
Current Yield - Annual coupon payments divided by bond price.
Yield To Maturity - Interest rate for which the present value of the bond’s payments equal the price.
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Bond Yields
Calculating Yield to Maturity (YTM=r)
If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r.
PVcpn
r
cpn
r
cpn par
r t
( ) ( )
....( )
( )1 1 11 2
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Bond Yields
Example
What is the YTM of a 6.5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,072.29.
29.072,1$
)1(
065,1
)1(
65
)1(
65321
PV
rrrPV
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Bond Yields
WARNINGWARNINGCalculating YTM by hand can be very tedious.
It is highly recommended that you learn to use the “IRR” or “YTM” or “i” functions on a financial calculator.
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Bond Yields
Rate of Return - Earnings per period per dollar invested.
Rate of return =total income
investment
Rate of return =Coupon income + price change
investment
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Bond Valuation Spreadsheet
Valuing bonds using a spreadsheet
6.5 % coupon 6% couponmaturing May 2005 10-year maturity
Settlement date 5/15/02 1/1/00Maturity date 5/15/05 1/1/10Annual coupon rate 0.065 0.06Yield to maturity 0.039 0.07Redemption value (% of face value) 100 100Coupon payments per year 1 1
Bond price (% of par) 107.229 92.976
=PRICE(B7,B8,B9,B10,B11,B12)
Esc and Double click on spreadsheet to access
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Bond Yield Spreadsheet
Finding yield to maturity using a spreadsheetMay 2005 maturity bond, coupon rate = 6.5%, maturity = 3 years
Annual coupons Semiannual coupons
Settlement date 5/15/02 5/15/02Maturity date 5/15/05 5/15/05Annual coupon rate 0.065 0.065Bond price 107.229 107.229Redemption value (% of face value) 100 100Coupon payments per year 1 2
Yield to maturity (decimal) 0.04 0.0392
=YIELD(B7,B8,B9,B10,B11,B12)
Esc and Double click on spreadsheet to access
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Interest Rate Risk
880
900
920
940
960
980
1,000
1,020
1,040
1,060
1,080
0 5 10 15 20 25 30
Time to Maturity
Bo
nd
Pri
ce
Price path for Premium Bond
Price path for Discount BondToday
Maturity
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Interest Rate Risk
-
500
1,000
1,500
2,000
2,500
3,000
0 2 4 6 8 10
YTM
$ B
on
d P
ric
e
30 yr bond
3 yr bond
When the interest rate equals the 6.5% coupon rate, both
bonds sell at face value
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Nominal and Real rates
0
2
4
6
8
10
12
14
1682 85 88 91 94 97
2000
Year
Pe
rce
nt
Yield on UK nominal bonds
Yield on UK indexed bonds
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Default Risk
Credit riskDefault premiumInvestment gradeJunk bonds
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Default RiskStandard
Moody' s & Poor's Safety
Aaa AAA The strongest rating; ability to repay interest and principalis very strong.
Aa AA Very strong likelihood that interest and principal will berepaid
A A Strong ability to repay, but some vulnerability to changes incircumstances
Baa BBB Adequate capacity to repay; more vulnerability to changesin economic circumstances
Ba BB Considerable uncertainty about ability to repay.B B Likelihood of interest and principal payments over
sustained periods is questionable.Caa CCC Bonds in the Caa/CCC and Ca/CC classes may already beCa CC in default or in danger of imminent defaultC C C-rated bonds offer little prospect for interest or principal
on the debt ever to be repaid.
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Corporate Bonds
Zero couponsFloating rate bondsConvertible bonds
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The Yield Curve
Term Structure of Interest Rates - A listing of bond maturity dates and the interest rates that correspond with each date.
Yield Curve - Graph of the term structure.
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Web Resources
www.investinginbonds.com
www.moodys.com/cust/default.asp
www.standardandpoor.com
http://gozips.uakron.edu/~drd/ratings.html
www.smartmoney.com/bonds
www.ustreas.gov
www.ustreas.gov/offices/domestic-finance/debt-management/interest-rate/index.html
www.bondmarkets.com
www.publicdebt.treas.gov/sec/sec.htm
www.bondsonline.com/asp/research/glossary.asp
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