Basics of Bonds

8/7/2019 Basics of Bonds

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Bonds and Bond Valuation



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1. Understand basic bond terminology and apply the time value of money equation in pricingbonds.

2.Understand the difference between annual andsemiannual bonds and note the key features of zero-coupon bonds.

3. Explain the relationship between the coupon rate andthe yield to maturity.

4. Delineate bond ratings and why ratings affect bondprices.5. Appreciate bond history and understand the rights

and obligations of buyers and sellers of bonds.6. Price government bonds, notes, and bills.

LEARNING OBJECTIVES



6.1 Application of the Time Value of MoneyTool: Bond Pricing

y Bonds --Long-term debt instrumentsy

Provide periodic interest income annuity seriesy Return of the principal amount at maturity future lump sum

y Prices can be calculated by using present valuetechniques i.e. discounting of future cash f lows.

y Combination of present value of an annuity and of a lump sum

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6.1 Key Components of a Bond

Par value :Par value : Typically $1,000Coupon rate:Coupon rate: Annual rate of interest paid.Coupon:Coupon: Regular interestpayment received by holder per year.Maturity date:Maturity date: Expiration date of bond when par value is paid

back.Yield to maturity:Yield to maturity: Expected rateof return based on price of bond

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Table 6.1 Bond Information

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6.1 Key Components of a BondEx ample: Key components of a corporate bondLet s say you see the following price quote

for a corporate bond:I ssue Price Coupon(%) Maturity YTM% Current Yld. Rating

Hertz Corp. 91.50 6.35Hertz Corp. 91.50 6.35 1515--JunJun--2010 15.4382010 15.438 6.946.94 BB

Price = 91.5% of $1,000.00 =$915.00$915.00Annual coupon = 6.35% x $1,000.oo = $63.50$63.50Maturity date = June 15, 2010June 15, 2010If bought and held to maturity, yield (YTM) = 15.438%15.438%Current Yield = Annual Coupon / Price = $63.50 / $915.00 = 6.94%6.94%

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6.1 Pricing a Bond in StepsSince bonds involve a combination of an annuity (coupons) and a lump sum (par value) its price isbest calculated by using the following steps:

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6.1Pricing a Bond in Steps

Ex ample: Calculating the price of a corporate bond.Calculate the price of an AA-rated, 20-year, 8% coupon (paid annually)corporate bond (Par value = $1,000) which is expected to earn a yield tomaturity of 10%.

Annual coupon = PMT = Coupon rate x Par value = .08 * $1,000 = $80$80YTM =r = 10%10%Maturity = n = 2020Par Value = FV = $1,000.00$1,000.00Price of bond = Present Value of coupons + Present Value of par value

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Year 0 1

$80

2

$80

3

$80

20

$80$1,000

18 19

$80 $80«



6.1 Pricing a Bond in StepsEx ample: Calculating the price of a corporate bond

Present value of coupons =

Present Value of Par Value =

Present Value of Coupons = $80 x 8.51359 = $681.09$681.09Present Value of Par Value = $1,000 x 0.14864 = $148.64$148.64Price of bond = $681.09 + $148.64= $829.73$829.73

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6.1 Pricing a Bond in StepsMethod 2. Using a financial calculator

Mode: P/Y=1 C/Y = 1 (Because coupons are paid annually)

Key: N I/Y PV PMT FV Input: 20 10 ? 80 1000Compute --829.73829.73

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Most corporate and government bonds pay coupons ona semiannual basis.

Some companies pay no coupons, issuing zero-couponbonds by selling them at a deep discount.For computing price of these bonds, the values of theinputs have to be adjusted according to the frequency of the coupons (or absence thereof).

± For example, for semi-annual bonds, the annual coupon isdivided by 2, the number of years is multiplied by 2 fornumber of coupon payments and the YTM is divided by 2.

± The price of the bond can then be calculated by using theTVM equation, a financial calculator, or a spreadsheet.

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6.2 Semiannual Bonds and Zero-Coupon Bonds



6.2Semiannual Bonds

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6.2 Semiannual Bonds

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Using TVM Equation, YTM is 8.8%




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Using Financial Calculator, YTM is 8.8%




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6.2 Pricing Bonds after Original Issue

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The price of a bond is a function of the remaining cashflows (i.e. coupons and par value) that would be paid onit until expiration.

As of August 2008, the 8.5% semi annual 2022 Coca-Colabond has only 27 coupons left to be paid on it until itmatures on Feb. 1, 2022



6.2 Pricing Bonds after Original IssueEx ample: Pricing a semi-annual coupon bond afteroriginal issue:Sixteen and 1/2 years after issue, price the Coca-Cola bond

issued as an 8.5% coupon (paid semi-annually), 30-year, A-rated bond at its par value of $1000. Currently, the yield tomaturity on these bonds is 5.473%. Calculate the price of the bond today.

Remaining coupons, n = (60Remaining coupons, n = (60- -33) =33) = 2727SemiSemi--annual coupon = (.085 x 1000)/2 =annual coupon = (.085 x 1000)/2 = $42.50$42.50Par value =Par value = $1,000.00$1,000.00Annual YTM = 5.473%,Annual YTM = 5.473%, r =r = 5.473% / 2 =5.473% / 2 = 2.7365%2.7365%

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6.2Pricing Bonds after Original Issue

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Method 1: Using TVM equations

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ond Price = $1000 x 0.48243 + $42.50 x 18.91369ond Price = $482.43 + $803.83ond Price = $1,286.26



6.2 Pricing Bonds after Original Issue

Method 2: Using a financial calculator

Mode: P/Y=2; C/Y = 2

Key: N I/Y PV PMT FV Input: 27 5.473 ? 42.50 1,000Output --1,286.261,286.26

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6.2 Zero-Coupon BondsKnown as pure discount bonds and sold at a discountfrom face value

Does not pay any interest over the life of the bond.At maturity, the investor receives the par value, usually $1000 which reflects the original purchase price(principal) and accumulated interest.

Price of a zero-coupon bond is calculated by merely discounting its par value at the prevailing discount rateor yield to maturity.

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6.2 Amortization of a Zero-Coupon Bond

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Interest earned is calculated for each 6-month period, first period is:0.04 x 790.31 =$31.62$31.62Interest is added to price to compute ending price,

$790.31 + $31.62 =$821.93$821.93Zero-coupon bond investors have to pay tax on annual price appreciationeven though no cash is received.



6.2 Amortization of a Zero-Coupon BondEx ample: Price of and ta x es due on a zero-couponbond:

John wants to buy a 20-year, AAA-rated, $1000 par value,zero-coupon bond being sold by Diversified Industries Inc.The yield to maturity on the bonds is estimated to be 9%.A) How much would he have to pay for it?

B) How much will he be taxed on the investment after 1year, if his marginal tax rate is 30%?

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6.2 Amortization of a Zero-Coupon BondEx ample (Answer) First Price the Bond

Method 1: Using TVM equation

Bond Price = Par Value x [1/(1+r)n]Bond Price = $1000 x [1/(1.045)40]Bond Price = $1000 x 0.1719287 =$171.93$171.93

Method 2: Using a financial calculator

Mode: P/Y=2; C/Y = 2Key: N I/Y PV PMT FV Input: 40 9 ? 0 1000Compute --171.93171.93

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6.2Amortization of a Zero-Coupon Bond

Ex ample 4 (Answer continued)Calculate the price of the bond at the end of 1 year.

Mode: P/Y=2; C/Y = 2Key: N I/Y PV PMT FV Input: 3838 9 ? 0 1000Compute --187.75187.75

Taxable income = $187.75 - $171.93 =$15.82$15.82Taxes due = Tax rate * Taxable income = 0.30*$15.82 = $4.75$4.75

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6.3 Yields and Coupon RatesA Bond s coupon rate differs from its yield to maturity (YTM).

Coupon rate -- set by the company at the time of issueand is fixed (except for newer innovations which havevariable coupon rates)YTM is dependent on market, economic, and

company-specific factors.YTM varies across time as conditions of factorschange.

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6.3 The First Interest Rate: Yield to Maturity

Expected rate of return on a bond if held to maturity.The price that willing buyers and sellers settle at

determines a bond s YTM at any given point.Changes in economic conditions and risk factors willcause bond prices and their corresponding YTMs tochange.

YTM can be calculated by entering the coupon amount(PMT ), price ( PV ), remaining number of coupons ( n),and par value ( FV ) into the financial calculator orspreadsheet.

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6.3 The Other Interest Rate: Coupon RateThe coupon rate on a bond is set by the issuingcompany at the time of issue

It represents the annual rate of interest that the firm iscommitted to pay over the life of the bond.If the rate is set at 7%, the firm is committing to pay .07 x $1,000 = $70.00 per year on each bond,

It is usually paid either in a single check of $70.00(annual) or two checks of $35.00 (semi-annual).

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6.3Relationship of Yield to Maturity andCoupon Rate

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6.3 Relationship of Yield to Maturity andCoupon Rate

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6.3 Relationship of Yield to Maturity and CouponRate

Ex ample: Computing YTM

Last year, The A BC Corporation had issued 8% coupon(semi-annual), 20-year, AA-rated bonds (Par value =$1,000.00) to finance its business growth. If investors arecurrently offering $1,200.00 on each of these bonds, what istheir expected yield to maturity on the investment? If youare willing to pay no more than $980.00 for this bond, whatis your expected YTM ?

Remaining number of coupons = 19 x 2 = 38Semi-annual coupon amount =( .08 x $1,000)/2 = $40.00

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6.3 Relationship of Yield to Maturity and CouponRate

PV = $1,200.00Mode:P/Y=2; C/Y = 2

Key: N I/Y PV PMT FV Input: 38 ? -1200 40 1000Compute 6.196.19

Note: This is a premium bond, so it sYTM of 6.19% < Coupon rate of 8%

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6.3 Relationship of Yield to Maturity and CouponRatePV = $980.00Mode: P/Y=2; C/Y = 2

Key: N I/Y PV PMT FV Input: 38 ? -980 40 1000Compute 8.218.21

Note: This would be a discount bond so it sYTM of 8.21% > Coupon rate of 8%

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6.4Bond RatingsRatings are produced by Moody s, Standard and Poor s, and Fitch

Range from AAA ( top-rated) to C ( lowest-rated ) or D ( default).

Help investors gauge likelihood of default by issuer.

Assist issuing companies establish a yield on newly-issuedbonds.

J unk bonds : is the label given to bonds that are rated below BBB.These bonds are considered to be speculative in nature and carry higher yields than those rated BBBor above (investment grade).

Fallen angels: is the label given to bonds that have had theirratings lowered from investment to speculative grade.

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6.4 Bond Ratings

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6.5 Some Bond History and More Bond Features

Corporate bond features have gone through somemajor changes over the years.

± Bearer bonds:± Indenture or deed of trust :± Collateral :± Mortgaged security:± Debentures :± S enior debt :± S inking fund:± Protective covenants:

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6.5 Some Bond History and More BondFeatures

y Callable bond:y Yield to call:y Putable bond:y Convertible bond:y Floating-rate bond:y Prime rate:y Income bonds:y Exotic bonds:

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6.5 Some Bond History and More BondFeaturesEx ample: Calculating Yield to Call.

Two years ago, The Mid-Atlantic Corporation issued a

10% coupon (paid semi-annually), 20-year maturity,bond with a 5-year deferred call feature and a callpenalty of one coupon payment in addition to the parvalue ($1000) if exercised.

If the current price on these bonds is $1,080, what is itsyield to call?

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6.5 Some Bond History and More BondFeatures

Remaining number of coupons until first call date, n = 6Semi-annual coupon = $50.00 = PMT Call price = $1,050= FV Bond price = $1,080 = PV

Mode: P/Y=2; C/Y = 2Key: N I/Y PV PMT FV Input: 6 ? -1080 50 1050Compute 8.438.43

YTC YTC

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6.6 U. S. Government Bonds

Include bills, notes, and bonds sold by the Department of the Treasury State bonds, issued by state governmentsMunicipal bonds issued by county, city, or localgovernment agencies.Treasury bills, are zero-coupon, pure discount securitieswith maturities ranging from 1-, 3-, and 6-months up to 1year.Treasury notes have between two to 10 year maturities.Treasury bonds have greater than 10-year maturities, whenfirst issued.

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6.6 U. S. Government Bonds

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6.6 Pricing a U . S. Government Note or Bond

y Similar to the method used for pricing corporate bonds and can be done by using TVM equations, a financial calculator or a spreadsheet program.

y For example, let s assume you are pricing a 7-year, 6% coupon (semi-annual)$100,000 face value Treasury note, using an expected yield of 8%:

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6.6 Pricing a Treasury bill

Calculated by discounting the bill s face value for thenumber of days until maturity and at the prevailing bank discount yield.

Bank discount yield: is a special discount rate used inconjunction with treasury bills under a 360 day-per-yearconvention (commonly assumed by bankers).

Bond equivalent yield (BEY),is the APR equivalent of thebank discount yield calculated by adjusting it as follows:

BEY = 365 xBank discount yield360 - (days to maturity x discount yield)

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6.6 Pricing a Treasury bill (continued)

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6.6 Pricing a Treasury billEx ample : Calculating the price and B E Y of a Treasury bill.Calculate the price and BEY of a treasury bill which matures in105 days, has a face value of $10,000 and is currently being quotedat a bank discount yield of 2.62%.

Price of T-bill = Face value x [1-(discount yield * days until maturity/360)]

Price of T-bill = $10,000 x [ 1 - (.0262 x 105/360)] = $10,000 x 0.9923583

Price of T-bill = $9,923.58$9,923.58

BEY = 365 x Bank discount yield_________ = 365 x 0.0262360 - (days to maturity x discount yield) 360 - (105 x 0.0262)

BEY = .026768 = 2.68%2.68% (rounded to 2 decimals)

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Basics of Bonds

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