# wayne lippman present s bonds and their valuation

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1 Wayne Lippman Walnut Creek, CA

Post on 17-Feb-2017

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Wayne LippmanWalnut Creek, CA

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Bonds are simply long-term IOUs that represent claims against a firm’s assets.

Bonds are a form of debtBonds are often referred to as fixed-

income investments.

Bond Basics

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Key Features of a BondDebt instrument issued by a corp. or

government.

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Key Features of a BondPar value = face amount of the bond, which

is paid at maturity (assume \$1,000).

=

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Key Features of a BondCoupon rate – stated interest rate

(generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest.

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Key Features of a BondMaturity date – when the bond must be

repaid.Yield to maturity - rate of return earned on a

bond held until maturity.

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What is interest rate risk?Interest rate risk is the concern that interest

rates will change, and therefore, a reduction in the value/price of a security.

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Suppose you just inherited \$500,000. You intend to invest the money and live off the interest.

Interest rate risk example

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Interest rate risk exampleYou may invest in either a:

10-year bond series of ten 1-year bonds

Both bonds currently yield 5%.

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If you choose the 1-year bond strategy:After year 1, you receive \$25,000 in income and have \$500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to \$15,000.

If you choose the 10-year bond strategy:You can lock in a 5% interest rate, and \$25,000 annual income.

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Interest Rate RiskPrice Risk

Change in price due to changes in interest rates

Long-term bonds have more price risk than short-term bonds

Low coupon rate bonds have more price risk than high coupon rate bonds

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Bond ValueBond Value = PV(coupons) + PV(par)Bond Value = PV(annuity) + PV(lump sum)Remember:

As interest rates increase present values decrease

( r → PV )As interest rates increase, bond prices decrease

and vice versa

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Bond ValuationBond Valuation

Compute the value for an IBM Bond with a 6.375% coupon that will mature in 5 years given that you require an 8% return on your investment.

What are the annual interest payments (\$)?

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0 1 2 3 4 5

2009 2010 2011 2012 2013

63.75 63.75 63.75 63.75 63.751,000.00

IBM Bond Timeline:IBM Bond Timeline:

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\$63.75 Annuity for 5 years \$1000 Lump Sum in 5 years

0 1 2 3 4 5

2009 2010 2011 2012 2013

63.75 63.75 63.75 63.75 63.751000.00

IBM Bond Timeline:IBM Bond Timeline:

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= 63.75 PMT 1000 FV 8% I 5 N

= PV = 935.12

\$63.75 Annuity for 5 years \$1000 Lump Sum in 5 years

0 1 2 3 4 5

2009 2010 2011 2012 2013

63.75 63.75 63.75 63.75 63.751000.00

IBM Bond Timeline:IBM Bond Timeline:

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Most Bonds Pay Interest Semi-Annually:Most Bonds Pay Interest Semi-Annually:

What is the value of a bond with a semi-annual coupon with 5 years to maturity, 9% (nominal) coupon rate if an investor desires a 10% (nominal) return?

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Most Bonds Pay Interest Semi-Annually:Most Bonds Pay Interest Semi-Annually:

e.g. semiannual coupon bond with 5 years to maturity, 9% annual coupon rate.

Instead of 5 annual payments of \$90, the bondholderreceives 10 semiannual payments of \$45.

0 1 2 3 4 5

2013 2014 2015 2016 2017

45 45.001000.00

45 45 45 45 45 45 45 45

2020

Compute the value of the bond given that you require a 10% s-a. return on your investment.

Since interest is received every 6 months, we need to usesemiannual compounding

VB = 45 - PMT 1000 - FV 5% - I 10 - N

Most Bonds Pay Interest Semi-Annually:Most Bonds Pay Interest Semi-Annually:

0 1 2 3 4 5

2013 2014 2015 2016 2017

45 45.001000.00

45 45 45 45 45 45 45 45

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Most Bonds Pay Interest Semi-Annually:Most Bonds Pay Interest Semi-Annually:

= PV = 961.39

Compute the value of the bond given that you require a 10% s-a. return on your investment.

Since interest is received every 6 months, we need to usesemiannual compounding

0 1 2 3 4 5

2013 2014 2015 2016 2017

45 451,000

45 45 45 45 45 45 45 45

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Semiannual Bonds

Coupon rate = 14% - SemiannualYTM = 16% (APR)Maturity = 7 yearsValue of bond?

Number of coupon payments? (2t or N)14 = 2 x 7 years

Semiannual coupon payment? (C/2 or PMT)\$70 = (14% x Face Value)/2

Semiannual yield? (YTM/2 or I/Y)8% = 16%/2

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Semiannual BondsSemiannual coupon =

\$70Semiannual yield =

8%Periods to maturity =

14

Bond value = 70[1 – 1/(1.08)14] / .08 +

1000 / (1.08)14 = 917.56

2t

2t

2YTM1

F

2YTM

2YTM1

1-1

2C Value Bond

14

14

)08.1(1000

08.0)08.1(11

70B

Using the calculator:14 N8 I/Y70 PMT1000 FVCPT PV = -917.56

Using Excel: =PV(0.08, 14, 70, 1000, 0)

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If bond Sells at a DISCOUNT (less than \$1,000) then YTM > Coupon Rate

If bond Sells at a PREMIUM (more than \$1,000) then YTM < Coupon Rate

Yield to Maturity

-1,000

0 1 2 3 4 5

2013 2014 2015 2016 2017

80 80 80 80 801,000

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Valuing a Discount Bond with Annual Coupons

Coupon rate = 10%Annual couponsPar = \$1,000Maturity = 5 yearsYTM = 11%Price= ?

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Valuing a Discount Bond with Annual Coupons

Coupon rate = 10%Annual couponsPar = \$1,000Maturity = 5 yearsYTM = 11%

5

5

)11.1(1000

11.0)11.1(

11100B

Using the formula:B = PV(annuity) + PV(lump sum)B = 369.59 + 593.45 = 963.04

Using the calculator:5 N11 I/Y100PMT1000 FVCPT PV = -963.04

Note: When YTM > Coupon rate Price < Par = “Discount Bond”

Using Excel: =PV(0.11, 5, 100, 1000, 0)

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Valuing a Premium Bond with Annual CouponsCoupon rate = 10%Annual couponsPar = \$1,000Maturity = 20 yearsYTM = 8%Price = ?

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Valuing a Premium Bond with Annual CouponsCoupon rate = 10%Annual couponsPar = \$1,000Maturity = 20 yearsYTM = 8%

20

20

)08.1(1000

08.0)08.1(11

100

B

Using the formula:B = PV(annuity) + PV(lump sum)B = 981.81 + 214.55 = 1196.36

Note: When YTM < Coupon rate Price > Par = “Premium Bond”

Using the calculator:20 N8 I/Y100PMT1000 FVCPT PV = -1196.36

Using Excel: =PV(0.08, 20, 100, 1000, 0)

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Yield to MaturityIf an investor purchases a 6.375% annual

coupon bond today for \$900 and holds it until maturity (5 years), what is the expected annual rate of return (YTM)?

-900

??

0 1 2 3 4 5

2013 2014 2015 2016 2017

63.75 63.75 63.75 63.75 63.75

1000.00

+ ??

900900

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Yield to Maturity

YTMB = 63.75 PMT 1000 FV 5 N -900 PVI = ?

• If an investor purchases a 6.375% annual coupon bond today for \$900 and holds it until maturity (5 years), what is the expected annual rate of return ? Will it be >< than 6.375%?

-900

??

0 1 2 3 4 5

2013 2014 2015 2016 2017

63.75 63.75 63.75 63.75 63.75

1000.00

+ ??

900900

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90 90 90

0 1 9 10rd=?

1,000PV1 . . .PV10PVM887 Find rd that “works”!

...

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10 -887 90 1000N I/YR PV PMT FV

10.91

INPUTS

OUTPUT

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Types of BondsVanilla – fixed coupons, repaid at maturityZero Coupon – pay no explicit interest but

instead, sell at a deep discountConvertible – can be converted into to stock

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Types of BondsJunk Bonds – below investment grade

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Government BondsTreasury Securities = Federal

government debtTreasury Bills (T-bills)

Pure discount bonds Original maturity of one year or less

Treasury notes (T-notes) Coupon debt Original maturity between one and ten years

Treasury bonds (T-bonds) Coupon debt Original maturity greater than ten years

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Tax ConsequencesA taxable bond has a yield of 8% and amunicipal bond has a yield of 6%If you are in a 40% tax bracket, which

bond do you prefer?8%(1 - .4) = 4.8%The after-tax return on the corporate bond is

4.8%, compared to a 6% return on the municipal

At what tax rate would you be indifferent between the two bonds?8%(1 – T) = 6%T = 25%

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Bond RatingsMoody’s , Standard & Poor’s and Fitch

regularly monitor issuer’s financial condition and assign a rating to the debt

AAA Best QualityAA High QualityA Upper Medium GradeBBB Medium GradeBB SpeculativeB Very SpeculativeCCC Very Very SpeculativeCCC No Interest Being PaidD Currently in Default

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Bond Ratings – Investment QualityHigh Grade

Moody’s Aaa and S&P AAA – capacity to pay is extremely strong

Moody’s Aa and S&P AA – capacity to pay is very strong

Medium GradeMoody’s A and S&P A – capacity to pay is strong,

but more susceptible to changes in circumstances

Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay

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Moody’s Ba, B, Caa and CaS&P BB, B, CCC, CCConsidered speculative with respect to

capacity to pay. The “B” ratings are the lowest degree of speculation.

Very Low GradeMoody’s C and S&P C – income bonds

with no interest being paidMoody’s D and S&P D – in default with

principal and interest in arrears

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What affects Bond prices?RiskInterest rates

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What is the “term structure of interest rates”? What is a “yield curve”?

Term structure: the relationship between interest rates (or yields) and maturities.

A graph of the term structure is called the yield curve.

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Draw a normal yield curve

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Hypothetical Treasury Yield Curve

0

5

10

15

1 10 20Years to Maturity

InterestRate (%) 1 yr 8.0%

10 yr 11.4%20 yr 12.65%

Real risk-free rate

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What factors can explain the shape of this yield curve?

This constructed yield curve is upward sloping.

This is due to increasing expected inflation and an increasing maturity risk premium.

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Current Yield CurveBloomberg

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Default riskIf an issuer defaults, investors receive

less than the promised return. Influenced by the issuer’s financial

strength and the terms of the bond contract.

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