Valuation and Characteristics of Bonds

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.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

5Bonds 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 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 BondsDebenturesDebenturesSubordinated DebentureSubordinated DebentureMortgage BondMortgage BondEurobondEurobondConvertible BondConvertible BondZero Coupon BondsZero Coupon BondsJunk BondJunk Bond

8Bond 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 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 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 Quotes



Coupon Interest RateCoupon Interest Rate

12Bond Quotes




Determines the Investor’s Periodic Cash Flow

13Bond Quotes




Determines the Investor’s Periodic Cash Flow

Cash Flow = Interest Payment = Coupon Rate x Par

= .06375 x 1000 = $63.75/Year

14Bond Quotes



Year of MaturityYear of Maturity

15Bond Quotes



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 Quotes



Current Yield (%)Current Yield (%)

17Bond Quotes



Current Yield (%)Current Yield (%)

Current Yield = Anuual $ CouponMarket Price

= .066 = 6.6% 63.75 966.25

=

18Bond Quotes



Daily Trading Volume Daily Trading Volume

19Bond Quotes



Daily Closing Market PriceDaily Closing Market Price

20Bond Quotes




Expressed as a % of Par

21Bond Quotes




$Price = 965/8 x 10 = $966.25

Expressed as a % of Par

22Bond Quotes



Change from Previous Day’s Closing PriceChange from Previous Day’s Closing Price

23Bond 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.


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


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.


IBM Bond Timeline:IBM Bond Timeline:Cur Net



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.


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.



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

63.75 63.75 63.75 63.75 63.751000.00


$59.03 $63.75 (1.08)



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

63.75 63.75 63.75 63.75 63.751000.00


$59.03 $63.75 (1.08)2

$54.66



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

63.75 63.75 63.75 63.75 63.751000.00


$59.03$54.66$50.61

$63.75 (1.08)3



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

63.75 63.75 63.75 63.75 63.751000.00


$59.03$54.66$50.61$46.86

$63.75 (1.08)4



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

63.75 63.75 63.75 63.75 63.751000.00


$59.03$54.66$50.61$46.86$43.39

$63.75 (1.08) 5



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

63.75 63.75 63.75 63.75 63.751000.00


$59.03$54.66$50.61$46.86$43.39

$935.12

$1000 (1.08) 5

$680.58



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



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

63.75 63.75 63.75 63.75 63.751000.00


$1000 Lump Sum in 5 years



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

63.75 63.75 63.75 63.75 63.751000.00


Vb = I(PV of Annuity) + PV of Par$1000 Lump Sum in 5 years



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

63.75 63.75 63.75 63.75 63.751000.00



1 .08(1+.08)5

1 .08= 63.75( ) + 1000

(1+.08)5



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

63.75 63.75 63.75 63.75 63.751000.00



1 .08(1+.08)5

1 .08= 63.75( ) +

= 63.75(3.9927) + 680.58

1000 (1+.08)5



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

63.75 63.75 63.75 63.75 63.751000.00



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


Some Bonds Pay Interest Semi-Annually:Some Bonds Pay Interest Semi-Annually:Cur Net



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

45 45.001000.00

45 45 45 45 45 45


Some Bonds Pay Interest Semi-Annually:Some Bonds Pay Interest Semi-Annually:Cur Net



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.


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.



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

45 45.001000.00

45 45 45 45 45 45


Since interest is received every 6 months, need to usesemi-annual compounding



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

45 45.001000.00

45 45 45 45 45 45



1 .05(1+.05)8

1 .05Vb = 45( ) +

1000 (1+.05)8

10%2

Semi-AnnualCompounding



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

45 45.001000.00

45 45 45 45 45 45



1 .05(1+.05)8

1 .05Vb = 45( ) +

=45(6.4632) + 676.84

1000 (1+.05)8



0 1 2 3 4 5

1995 1996 1997 1998 1999 2000

45 45.001000.00

45 45 45 45 45 45



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 MaturityBondholder’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

Pk k k

Parkb b b

nbn0

1 11 1

( ) ( )



Pk k k

Parkb b b

nbn0

1 11 1

( ) ( )

Substitute the Market Price (P0) for Vb and solve for kb where kb = Annual YTM

Cannot Solve Directly

50Yield 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 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

?? + ??966.25


52Yield 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

?? + ??966.25


53Yield 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

?? + ??966.25


966 25 63 751 1

11000

15 5. .( ) ( )

k k kb b b

54Yield to Maturity

Cannot Solve directly, must use a Financial Calculator or the following Approximation Formula for YTM:

966 25 63 75 1 11

100015 5. .

( ) ( )

k k kb b b

55Yield to Maturity

Cannot Solve directly, must use a Financial Calculator or the following Approximation Formula for YTM:

YTM Approximation Formula

k

PnPb

o

1000

1000 23

0

966 25 63 75 1 11

100015 5. .

( ) ( )

k k kb b b

56Yield 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



k

PnPb

o

1000

1000 23

0

57Yield 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



63 751000 966 25

51000 2 966 25

3

..

( . )k

PnPb

o

1000

1000 23

0

58Yield 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


70.50 977.50 7.21%

k

PnPb

o

1000

1000 23

0


59Interest Rate RiskBond Prices fluctuate over TimeBond Prices fluctuate over Time

As 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


As interest rates in the economy change, required rates on bonds will also change resulting in investor’s intrinsic values changing and market prices changing.





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.



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%




1995



1 .06(1+.06)20

1 .06Vb = 60( ) +

1000 (1+.06)20

= $1,000

67Interest Rate Risk1995



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%)





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%)





Market Price for ATT6s2015 is now $743.69











1 .05(1+.05)14

1 .05Vb = 60( ) +

1000 (1+.05)14 = $1,098.99








Market Price for ATT6s2015 is now $1,098.99



Bond Prices fall during periods of rising interest rates and rise during periods of falling interest rates.

73Bond Relationships

Bond Price changes in the opposite direction of the Bond Price changes in the opposite direction of the interest rate changesinterest rate changes


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 is Everything else being equal, a bond with longer maturity is more price sensitive to changes in interest rates than a more price sensitive to changes in interest rates than a bond with shorter maturity. bond with shorter maturity.


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.

76

Documents

Valuation and Characteristics of Bonds