Wayne lippman present s bonds and their valuation

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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


1717

= 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


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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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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


0 1 2 3 4 5

2013 2014 2015 2016 2017

45 45.001000.00

45 45 45 45 45 45 45 45

2121


= 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

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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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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Bond Ratings - SpeculativeLow Grade

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

Inflation premium

Maturity risk premium

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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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About Wayne Lippman

https://www.facebook.com/lippman.associates.CPAs

https://www.youtube.com/waynelippman

http://lippmancpas.com

https://twitter.com/waynelippman

Wayne Lippman has forty years of experience in public accounting including twenty years with Price Waterhouse, where he served as a tax partner in the San Francisco and Oakland offices. He was previously Managing Tax Partner of the Walnut Creek office of Price Waterhouse.

http://Waynelippman.wordpress.com

Wayne lippman present s bonds and their valuation

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