1 valuation and characteristics of bonds chapter 7
TRANSCRIPT
1
Valuation and Valuation and Characteristics of BondsCharacteristics of Bonds
Chapter 7Chapter 7
3General Valuation: The following comments are valid for all kind of assets.
General Valuation: The following comments are valid for all kind of assets.Book ValueBook Value
Stated value from the firm’s Balance SheetMarket ValueMarket Value
The price for the asset at any given time--determined by supply and demand in the marketplace. Asset can be bought or sold at this price.
Intrinsic ValueIntrinsic ValuePresent value of the asset’s expected cash flow
Investor estimates cash flowsInvestor determines required rate based on risk of asset and market conditions.
4
In a perfect market where all investors have the In a perfect market where all investors have the same expectations & risk aversion:same expectations & risk aversion:
Market Value = Intrinsic Value
In a perfect market where all investors have the In a perfect market where all investors have the same expectations & risk aversion:same expectations & risk aversion:
Market Value = Intrinsic Value
5BondsBonds Debt InstrumentsDebt Instruments
Bondholders are lending to the corporation (or, governments) money for some stated period of time.
Liquid AssetLiquid AssetCorporate Bonds can be traded in the secondary market.Price at which a given bond trades is determined by market
conditions and terms of the bond.
6Bond TerminologyBond TerminologyPar ValuePar Value
Usually $1,000. Also called the Face ValueCoupon Interest RateCoupon Interest Rate
Borrowers (firms) typically make periodic payments to the bondholders. Coupon rate is the percent of face value paid every year.
MaturityMaturityTime at which the maturity value (Par Value) is paid to the bondholder.
IndentureIndentureDocument which details the legal obligation of the corporation to the bondholders. The indenture lists all
the terms and conditions of the bond.
7Types of BondsTypes of BondsDebenturesDebenturesSubordinated DebentureSubordinated DebentureMortgage BondMortgage BondEurobondEurobondConvertible BondConvertible BondZero Coupon BondsZero Coupon BondsJunk BondJunk Bond
8Bond RatingsBond Ratings Moody’s and Standard & Poors regularly monitor issuers’ Moody’s and Standard & Poors regularly monitor issuers’
financial conditions and assign a rating to the debt. Bond financial conditions and assign a rating to the debt. Bond rating shows the relative probability of default.rating shows the relative probability of default.similar to a personal credit report
AAA Top QualityAAABBBBBBCCCCC Low QualityC No interest being paidD Currently in Default
Investment Investment GradeGrade
JunkJunk
9Bond RatingsBond Ratings
Bond Ratings can change due to many factors.Bond Ratings can change due to many factors.Caterpillar Corp debt was recently upgraded due to
fact that it appears that current 10 month strike has not affected prospects of firm in any significant manner.
Corporate Bond RatingsCiticorp A-GMAC BBB+Bell South AAADuPont AA-Phillip Morris AKroger BB+Unisys BB-Bethlehem Steel B+Grand Union D
10Bond QuotesBond Quotes
Cur Net Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Company Issuing the BondCompany Issuing the Bond
11Bond QuotesBond Quotes
Cur Net Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Coupon Interest RateCoupon Interest Rate
12Bond QuotesBond Quotes
Cur Net Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Coupon Interest RateCoupon Interest Rate
Determines the Investor’s Periodic Cash Flow
13Bond QuotesBond Quotes
Cur Net Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Coupon Interest RateCoupon Interest Rate
Determines the Investor’s Periodic Cash Flow
Cash Flow = Interest Payment = Coupon Rate x Par
= .06375 x 1000 = $63.75/Year
14Bond QuotesBond Quotes
Cur Net Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Year of MaturityYear of Maturity
15Bond QuotesBond Quotes
Cur Net Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Year of MaturityYear of Maturity
Determines the Time frame for the Investment
00 = year 2000, therefore in 1995 this is a 5 year investment
16Bond QuotesBond Quotes
Cur Net Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Current Yield (%)Current Yield (%)
17Bond QuotesBond Quotes
Cur Net Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Current Yield (%)Current Yield (%)
Current Yield = Anuual $ Coupon
Market Price= .066 = 6.6% 63.75
966.25=
18Bond QuotesBond Quotes
Cur Net Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Daily Trading Volume Daily Trading Volume
19Bond QuotesBond Quotes
Cur Net Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Daily Closing Market PriceDaily Closing Market Price
20Bond QuotesBond Quotes
Cur Net Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Daily Closing Market PriceDaily Closing Market Price
Expressed as a % of Par
21Bond QuotesBond Quotes
Cur Net Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Daily Closing Market PriceDaily Closing Market Price
$Price = 965/8 x 10 = $966.25
Expressed as a % of Par
22Bond QuotesBond Quotes
Cur Net Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Change from Previous Day’s Closing PriceChange from Previous Day’s Closing Price
23Bond Valuation ModelBond Valuation Model
Bond Valuation is an application of Present Value.Bond Valuation is an application of Present Value.The Value of the bond is the present value of all the The Value of the bond is the present value of all the
cash flows the investor receives as a result of cash flows the investor receives as a result of holding the bond.holding the bond.
3 Cash Flows3 Cash FlowsAmount that is paid to purchase the bond (PV)Periodic Interest Payments made to the bondholders
(PMT)Payment of maturity value at end of Bond’s life.
Other TerminologyOther TerminologyTime frame for cash flows (N) = Bond’s Maturity Interest Rate for Time Value is the rate at which
future cash flows are being discounted to present.
24Bond Valuation ModelBond Valuation Model
IBM Bond Timeline:IBM Bond Timeline:Cur Net
Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
Investor that purchases bond today (1995) for $966.25 will receive 5 annual interest payments of $63.75 and a $1,000 payment in 5 years.
Investor that purchases bond today (1995) for $966.25 will receive 5 annual interest payments of $63.75 and a $1,000 payment in 5 years.
25Bond Valuation ModelBond Valuation Model
IBM Bond Timeline:IBM Bond Timeline:Cur Net
Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
Investor that purchases bond today (1995) for $966.25 will receive 5 annual interest payments of $63.75 and a $1,000 payment in 5 years.
Investor that purchases bond today (1995) for $966.25 will receive 5 annual interest payments of $63.75 and a $1,000 payment in 5 years.
26Bond Valuation ModelBond Valuation Model
Compute Bond’s Intrinsic ValueCompute Bond’s Intrinsic Value
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
27Bond Valuation ModelBond Valuation Model
Compute Bond’s Intrinsic ValueCompute Bond’s Intrinsic Value
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
$59.03 $63.75 (1.08)
28Bond Valuation ModelBond Valuation Model
Compute Bond’s Intrinsic ValueCompute Bond’s Intrinsic Value
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
$59.03 $63.75 (1.08)2
$54.66
29Bond Valuation ModelBond Valuation Model
Compute Bond’s Intrinsic ValueCompute Bond’s Intrinsic Value
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
$59.03$54.66$50.61
$63.75 (1.08)3
30Bond Valuation ModelBond Valuation Model
Compute Bond’s Intrinsic ValueCompute Bond’s Intrinsic Value
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
$59.03$54.66$50.61$46.86
$63.75 (1.08)4
31Bond Valuation ModelBond Valuation Model
Compute Bond’s Intrinsic ValueCompute Bond’s Intrinsic Value
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
$59.03$54.66$50.61$46.86
$43.39
$63.75 (1.08) 5
32Bond Valuation ModelBond Valuation Model
Compute Bond’s Intrinsic ValueCompute Bond’s Intrinsic Value
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
Compute the Intrinsic Value for the IBM Bond given that you require a 8% return on your investment.
$59.03$54.66$50.61$46.86
$43.39
$935.12
$1000 (1.08) 5
$680.58
33Bond Valuation ModelBond Valuation Model
Compute Bond’s Intrinsic ValueCompute Bond’s Intrinsic Value
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
$63.75 Annuity for 5 years$63.75 Annuity for 5 years
34Bond Valuation ModelBond Valuation Model
Compute Bond’s Intrinsic ValueCompute Bond’s Intrinsic Value
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
$63.75 Annuity for 5 years$63.75 Annuity for 5 years
$1000 Lump Sum in 5 years$1000 Lump Sum in 5 years
35Bond Valuation ModelBond Valuation Model
Compute Bond’s Intrinsic ValueCompute Bond’s Intrinsic Value
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
$63.75 Annuity for 5 years$63.75 Annuity for 5 years
Vb = I(PV of Annuity) + PV of Par$1000 Lump Sum in 5 years$1000 Lump Sum in 5 years
37Bond Valuation ModelBond Valuation Model
Compute Bond’s Intrinsic ValueCompute Bond’s Intrinsic Value
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
$63.75 Annuity for 5 years$63.75 Annuity for 5 years
Vb = I(PV of Annuity) + PV of Par$1000 Lump Sum in 5 years$1000 Lump Sum in 5 years
1 .08(1+.08)5
1 .08
= 63.75( ) + 1000 (1+.08)5
38Bond Valuation ModelBond Valuation Model
Compute Bond’s Intrinsic ValueCompute Bond’s Intrinsic Value
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
$63.75 Annuity for 5 years$63.75 Annuity for 5 years
Vb = I(PV of Annuity) + PV of Par$1000 Lump Sum in 5 years$1000 Lump Sum in 5 years
1 .08(1+.08)5
1 .08
= 63.75( ) +
= 63.75(3.9927) + 680.58
1000 (1+.08)5
39Bond Valuation ModelBond Valuation Model
Compute Bond’s Intrinsic ValueCompute Bond’s Intrinsic Value
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
$63.75 Annuity for 5 years$63.75 Annuity for 5 years
Vb = I(PV of Annuity) + PV of Par$1000 Lump Sum in 5 years$1000 Lump Sum in 5 years
1 .08(1+.08)5
1 .08
= 63.75( ) +
= 63.75(3.9927) + 680.58
1000 (1+.08)5
= 254.54 + 680.58 = 935.12
40Bond Valuation ModelBond Valuation Model
Some Bonds Pay Interest Semi-Annually:Some Bonds Pay Interest Semi-Annually:Cur Net
Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
45 45.001000.00
45 45 45 45 45 45
41Bond Valuation ModelBond Valuation Model
Some Bonds Pay Interest Semi-Annually:Some Bonds Pay Interest Semi-Annually:Cur Net
Bonds Yld Vol Close ChgAMR6¼24 cv 6 91¼ -1½ATT 8.35s25 8.3 110 102¾ +¼IBM 63/8 00 6.6 228 965/8 -1/8
Kroger 9s99 8.8 74 1017/8 -¼
Source: Wall Street Journal
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
45 45.001000.00
45 45 45 45 45 45
Rather than receiving 4 annual payments of $90, the bondholder will receive 4x2 = 8 semiannual payments of 90÷2=$45.
Rather than receiving 4 annual payments of $90, the bondholder will receive 4x2 = 8 semiannual payments of 90÷2=$45.
42Bond Valuation ModelBond Valuation Model
Some Bonds Pay Interest Semi-Annually:Some Bonds Pay Interest Semi-Annually:
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
45 45.001000.00
45 45 45 45 45 45
Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment.
Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment.
43Bond Valuation ModelBond Valuation Model
Some Bonds Pay Interest Semi-Annually:Some Bonds Pay Interest Semi-Annually:
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
45 45.001000.00
45 45 45 45 45 45
Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment.
Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment.
Since interest is received every 6 months, need to usesemi-annual compounding
44Bond Valuation ModelBond Valuation Model
Some Bonds Pay Interest Semi-Annually:Some Bonds Pay Interest Semi-Annually:
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
45 45.001000.00
45 45 45 45 45 45
Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment.
Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment.
Since interest is received every 6 months, need to usesemi-annual compounding
1 .05(1+.05)8
1 .05Vb = 45( ) +
1000 (1+.05)8
10%2
10%2
Semi-AnnualCompounding
45Bond Valuation ModelBond Valuation Model
Some Bonds Pay Interest Semi-Annually:Some Bonds Pay Interest Semi-Annually:
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
45 45.001000.00
45 45 45 45 45 45
Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment.
Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment.
Since interest is received every 6 months, need to usesemi-annual compounding
1 .05(1+.05)8
1 .05Vb = 45( ) +
=45(6.4632) + 676.84
1000 (1+.05)8
46Bond Valuation ModelBond Valuation Model
Some Bonds Pay Interest Semi-Annually:Some Bonds Pay Interest Semi-Annually:
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
45 45.001000.00
45 45 45 45 45 45
Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment.
Compute the Intrinsic Value for the Kroger Bond given that you require a 10% return on your investment.
Since interest is received every 6 months, need to usesemi-annual compounding
1 .05(1+.05)8
1 .05Vb = 45( ) +
=45(6.4632) + 676.84
1000 (1+.05)8
= 290.85 + 676.84 = 967.68
47Yield to MaturityYield to Maturity
Bondholder’s Expected Rate of Return.Bondholder’s Expected Rate of Return.If an investor purchases bond at today’s price and
hold it until maturity, what is the annual rate of return that is earned?
48Yield to MaturityYield to Maturity
Bondholder’s Expected Rate of Return.Bondholder’s Expected Rate of Return.If an investor purchases bond at today’s price and
hold it until maturity, what is the annual rate of return that is earned?
Substitute the Market Price (P0) for Vb and solve for kb where kb = Annual YTM
Substitute the Market Price (P0) for Vb and solve for kb where kb = Annual YTM
Pk k k
Par
kb b bn
bn0
1 1
1 1
( ) ( )
49Yield to MaturityYield to Maturity
Bondholder’s Expected Rate of Return.Bondholder’s Expected Rate of Return.If an investor purchases bond at today’s price and
hold it until maturity, what is the annual rate of return that is earned?
Pk k k
Par
kb b bn
bn0
1 1
1 1
( ) ( )
Substitute the Market Price (P0) for Vb and solve for kb where kb = Annual YTM
Substitute the Market Price (P0) for Vb and solve for kb where kb = Annual YTM
Cannot Solve Directly
Cannot Solve Directly
50Yield to MaturityYield to Maturity
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
Bondholder’s Expected Rate of Return.Bondholder’s Expected Rate of Return.If an investor purchases bond at today’s price and
hold it until maturity, what is the annual rate of return that is earned?
-966.25
IBM Corporate Bond:IBM Corporate Bond:
51Yield to MaturityYield to Maturity
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
Bondholder’s Expected Rate of Return.Bondholder’s Expected Rate of Return.If an investor purchases bond at today’s price and
hold it until maturity, what is the annual rate of return that is earned?
-966.25
?? + ??966.25
IBM Corporate Bond:IBM Corporate Bond:
52Yield to MaturityYield to Maturity
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
Bondholder’s Expected Rate of Return.Bondholder’s Expected Rate of Return.If an investor purchases bond at today’s price and
hold it until maturity, what is the annual rate of return that is earned?
-966.25
?? + ??966.25
IBM Corporate Bond:IBM Corporate Bond:
53Yield to MaturityYield to Maturity
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
Bondholder’s Expected Rate of Return.Bondholder’s Expected Rate of Return.If an investor purchases bond at today’s price and
hold it until maturity, what is the annual rate of return that is earned?
-966.25
?? + ??966.25
IBM Corporate Bond:IBM Corporate Bond:
966 25 63 751 1
1
1000
15 5. .
( ) ( )
k k kb b b
54Yield to MaturityYield to Maturity
Cannot Solve directly, must use a Financial Calculator or the following Approximation Formula for YTM:
Cannot Solve directly, must use a Financial Calculator or the following Approximation Formula for YTM:
966 25 63 751 1
1
1000
15 5. .
( ) ( )
k k kb b b
55Yield to MaturityYield to Maturity
Cannot Solve directly, must use a Financial Calculator or the following Approximation Formula for YTM:
Cannot Solve directly, must use a Financial Calculator or the following Approximation Formula for YTM:
YTM Approximation Formula
k
P
nPb
o
1000
1000 2
30
966 25 63 751 1
1
1000
15 5. .
( ) ( )
k k kb b b
56Yield to MaturityYield to Maturity
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
-966.25
IBM Corporate Bond:IBM Corporate Bond:
YTM Approximation Formula
k
P
nPb
o
1000
1000 2
30
57Yield to MaturityYield to Maturity
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
-966.25
IBM Corporate Bond:IBM Corporate Bond:
YTM Approximation Formula
63 751000 966 25
51000 2 966 25
3
..
( . )k
P
nPb
o
1000
1000 2
30
58Yield to MaturityYield to Maturity
63 751000 966 25
51000 2 966 25
3
..
( . )
0 1 2 3 4 5
1995 1996 1997 1998 1999 2000
63.75 63.75 63.75 63.75 63.751000.00
-966.25
IBM Corporate Bond:IBM Corporate Bond:
70.50 977.50
7.21%
k
P
nPb
o
1000
1000 2
30
YTM Approximation Formula
59Interest Rate RiskInterest Rate Risk
Bond Prices fluctuate over TimeBond Prices fluctuate over TimeAs interest rates in the economy change, required
rates on bonds will also change resulting in investor’s intrinsic values changing and market prices changing.
Interest Interest RatesRates VVbb
60Interest Rate RiskInterest Rate Risk
Bond Prices fluctuate over TimeBond Prices fluctuate over TimeAs interest rates in the economy change, required
rates on bonds will also change resulting in investor’s intrinsic values changing and market prices changing.
Interest Interest RatesRates VVbb
Interest Interest RatesRates VVbb
61Interest Rate RiskInterest Rate Risk
Bond Prices fluctuate over TimeBond Prices fluctuate over Time
62Interest Rate RiskInterest Rate Risk
Bond Prices fluctuate over TimeBond Prices fluctuate over TimeWhen bonds are originally issued, the coupon rate is
set to match current prevailing rates.
63Interest Rate RiskInterest Rate RiskBond Prices fluctuate over TimeBond Prices fluctuate over Time
When bonds are originally issued, the coupon rate is set to match current prevailing rates.
Over time, the prevailing rates may change, but the coupon rate is fixed.
64Interest Rate RiskInterest Rate RiskBond Prices fluctuate over TimeBond Prices fluctuate over Time
When bonds are originally issued, the coupon rate is set to match current prevailing rates.
Over time, the prevailing rates may change, but the coupon rate is fixed.Resulting in the actual price of the bond changing.
65Interest Rate RiskInterest Rate RiskBond Prices fluctuate over TimeBond Prices fluctuate over Time
When bonds are originally issued, the coupon rate is set to match current prevailing rates.
Over time, the prevailing rates may change, but the coupon rate is fixed.Resulting in the actual price of the bond changing.
1995
Purchase ATT 6s2015 Bond for $1000.00
AAA Bonds are currently yielding 6%
66Interest Rate RiskInterest Rate RiskBond Prices fluctuate over TimeBond Prices fluctuate over Time
When bonds are originally issued, the coupon rate is set to match current prevailing rates.
Over time, the prevailing rates may change, but the coupon rate is fixed.Resulting in the actual price of the bond changing.
1995
Purchase ATT 6s2015 Bond for $1000.00
AAA Bonds are currently yielding 6%
1 .06(1+.06)20
1 .06Vb = 60( ) +
1000 (1+.06)20
= $1,000
67Interest Rate RiskInterest Rate Risk
1995
Purchase ATT 6s2015 Bond for $1000.00
AAA Bonds are currently yielding 6%
1998
If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 9%)
AAA Bonds are currently yielding 9%
68Interest Rate RiskInterest Rate Risk
1995
Purchase ATT 6s2015 Bond for $1000.00
AAA Bonds are currently yielding 6%
1998 AAA Bonds are currently yielding 9%
1 .09(1+.09)17
1 .09Vb = 60( ) +
1000 (1+.09)17
= $743.69
If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 9%)
69Interest Rate RiskInterest Rate Risk
1995
Purchase ATT 6s2015 Bond for $1000.00
AAA Bonds are currently yielding 6%
1998 AAA Bonds are currently yielding 9%
Market Price for ATT6s2015 is now $743.69
2001
If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 5%)
AAA Bonds are currently yielding 5%
If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 9%)
70Interest Rate RiskInterest Rate Risk
1995
Purchase ATT 6s2015 Bond for $1000.00
AAA Bonds are currently yielding 6%
1998 AAA Bonds are currently yielding 9%
Market Price for ATT6s2015 is now $743.69
2001
If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 5%)
AAA Bonds are currently yielding 5%
1 .05(1+.05)14
1 .05Vb = 60( ) +
1000 (1+.05)14 = $1,098.99
If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 9%)
71Interest Rate RiskInterest Rate Risk
1995
Purchase ATT 6s2015 Bond for $1000.00
AAA Bonds are currently yielding 6%
1998 AAA Bonds are currently yielding 9%
Market Price for ATT6s2015 is now $743.69
2001 AAA Bonds are currently yielding 5%
Market Price for ATT6s2015 is now $1,098.99
If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 9%)
If you want to sell the the ATT 6s2015 Bond, it must be priced to earn the purchaser a competitive rate (required rate = 5%)
Bond Prices fall during periods of rising interest rates and rise during periods of falling interest rates.
73Bond RelationshipsBond Relationships
Bond Price changes in the opposite direction of the Bond Price changes in the opposite direction of the interest rate changesinterest rate changes
74Bond RelationshipsBond Relationships
Bond Price changes in the opposite direction of the Bond Price changes in the opposite direction of the interest rate changesinterest rate changes
If the coupon rate of a bond is less than the required rate If the coupon rate of a bond is less than the required rate of investors, the bond will sell at a discount. Fig. 7-3.of investors, the bond will sell at a discount. Fig. 7-3.
As the maturity date approaches, the market value of the As the maturity date approaches, the market value of the bond approaches its par value. Fig 7-4, Table 7-2. bond approaches its par value. Fig 7-4, Table 7-2.
Everything else being equal, a bond with longer maturity Everything else being equal, a bond with longer maturity is more price sensitive to changes in interest rates than is more price sensitive to changes in interest rates than a bond with shorter maturity. a bond with shorter maturity.
75Bond RelationshipsBond Relationships
Bond Price changes in the opposite direction of the Bond Price changes in the opposite direction of the interest rate changes.interest rate changes.
If the coupon rate of a bond is less than the required If the coupon rate of a bond is less than the required rate of investors, the bond will sell at a discount. Fig. rate of investors, the bond will sell at a discount. Fig. 7-3.7-3.
As the maturity date approaches, the market value of As the maturity date approaches, the market value of the bond approaches its par value. Fig 7-4, Table 7-the bond approaches its par value. Fig 7-4, Table 7-2.2.
Everything else being equal, a bond with longer Everything else being equal, a bond with longer maturity is more price sensitive to changes in interest maturity is more price sensitive to changes in interest rates than a bond with shorter maturity. rates than a bond with shorter maturity.
Everything else being equal, a bond with higher Everything else being equal, a bond with higher coupon is less price sensitive to changes in interest coupon is less price sensitive to changes in interest rates than a bond with lower coupon.rates than a bond with lower coupon.
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