7-1. 7-2 a bond is simply a negotiable iou, or a loan. investors who buy bonds are lending a...

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CHAPTER 8Bonds and Their Valuation

7-2

A bond is simply a negotiable IOU, or a loan.

Investors who buy bonds are lending a specific sum of money to a corporation, government, or some other borrowing institution.

Bonds 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 reinvestment rate risk?Reinvestment rate risk is the concern

that interest rates will fall, and future money will have to be reinvested at lower rates, hence reducing income.

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

rates will rise, and therefore, a reduction in the value of a security.

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

Reinvestment rate risk example

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Reinvestment rate risk exampleYou may invest in either a 10-year bond or a

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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Long-term bonds: High interest rate risk, low reinvestment rate risk.

Short-term bonds: Low interest rate risk, high reinvestment rate risk.

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Bond 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.

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.

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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:

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

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= 63.75 PMT 1000 FV 8% I 5 N

= PV = 935.12

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

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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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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

2009 2010 2011 2012 2013

45 45.001000.00

45 45 45 45 45 45 45 45

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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 ?N


0 1 2 3 4 5

2009 2010 2011 2012 2013

45 45.001000.00

45 45 45 45 45 45 45 45

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= PV = 961.39



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

0 1 2 3 4 5

2009 2010 2011 2012 2013

45 451,000

45 45 45 45 45 45 45 45

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If YTM > Coupon Rate bond Sells at a DISCOUNT

If YTM < Coupon Rate bond Sells at a PREMIUM

Yield to Maturity

-1,000

0 1 2 3 4 5

2009 2010 2011 2012 2013

80 80 80 80 801,000

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Yield to MaturityIf an investor purchases a 6.375% annual

coupon bond today for $966.25 and holds it until maturity (5 years), what is the expected annual rate of return ?

-966.25

??

0 1 2 3 4 5

2009 2010 2011 2012 2013

63.75 63.75 63.75 63.75 63.75

1000.00

+ ??

966.25

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Yield to Maturity

YTMB = 63.75 PMT 1000 FV 5 N -966.25 PVI = ?

• If an investor purchases a 6.375% annual coupon bond today for $966.25 and holds it until maturity (5 years), what is the expected annual rate of return ? Will it be >< than 6.375%?

-966.25

??

0 1 2 3 4 5

2009 2010 2011 2012 2013

63.75 63.75 63.75 63.75 63.75

1000.00

+ ??

966.25

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What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887?

90 90 90

0 1 9 10rd=?

1,000PV1 . . .PV10

PVM

887 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 maturityConvertible – can be converted into to stockZero Coupon – pay no explicit interest but

instead, sell at a deep discount

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Types of BondsJunk Bonds – below investment grade

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Bond RatingsMoody’s and Standard & Poor’s

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

Investment Grade

Below Investment Grade (Junk)

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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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 20

Years to Maturity

InterestRate (%) 1 yr 8.0%

10 yr 11.4%20 yr 12.65%

Real risk-free rate

Inflation premium

Maturity risk premium

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Current RatesBloomberg

http://www.bloomberg.com/markets/rates/index.html

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What factors can explain the shape of this yield curve?

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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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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.

7-1. 7-2 a bond is simply a negotiable iou, or a loan. investors who buy bonds are lending a...

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