hasanzulfiqar@yahoo.co.uk 1

Bond Valuation

Zulfiqar Hasan 2

Contents

Bonds-its definition and types, Value a straight bond and a zero-coupon bond using present discounted value techniques; relationship between interest rates and bond prices; Determine the yield to maturity for a straight bond; relationships between zero coupon bonds and coupon bonds; Analyze bond price dynamics and predict how bond prices respond to changes in interest rates; Explain why coupon bonds and zero coupon bonds react differently to changes in interest rates; Explain the relationship between real and nominal interest rates

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How does corporation raise capital?Corporations raise capital in two Forms:1. Debt: A type of Financing through the selling of a debt instrument is

called Debt Financing.

2. Equity: Raising money for company activities by selling common or preferred stock to individual or institutional investors.

No YesLiquidation will result if not paid

No YesProvides a tax Shield/Deduction

YesNoGrants ownership of the firm

NoYesRepayment is an obligation of the firm

EQUITY

FINANCINGDEBT

FINANCING

Issues

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Definition of Bond

• In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest (the coupon) and/or to repay the principal at a later date, termed maturity. A bond is a formal contract to repay borrowed money with interest at fixed intervals.

• Bonds are long-term debt instruments sold by a company or government to raise money. It is a long-term promissory note.

• A Bond is an instrument which pays fixed amounts (usually) of interest (called a coupon) on a regular basis, over its life and is redeemed at par value (usually) at maturity, by the issuer .

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Basics Terms of Bond/ Features of Bonds

• Par or Face Value: The par or face value of a bond is the amount of money that is paid to the bondholders at maturity.

• Coupon Interest Rates: The stated annual rate of interest paid on a bond.

• Coupon Payment: The coupon payments represent the periodic interest payments from the bond issuer to the bondholder.

• Maturity Date: The maturity date represents the date on which the bond matures, i.e. the date on which the face value is repaid. The last coupon payment is also paid on the maturity date.

• Original Maturity: The time remaining until the maturity date when the bond was issued.

• Call Provision: A provision in a bond contract that gives the issuer the right to “recall” the bond and pay it off under specified terms prior to the stated maturity date.

• Indenture: A legal document contains the details of the bond issue called the indenture.

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1.0 Classification of Bonds: By Issuer

a. Government: Government issued treasury bondb. Corporation: industrial, utility, financial, transportationc. Foreign Bond: e.g. foreign government, foreign

corporation, World Bank2.0 Classification of Bonds: By security

1. Unsecured Bonds - backed by faith in the taxing power of the government, or the good name of the company (debenture)

2. Secured Bonds e.g. revenue bond, assessment bond, mortgage, collateral trust bond, equipment trust certificate Bond security sometimes comes from non-traditional sources. Some rock stars floated bonds using their future earnings as backing.

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3.0 Classification of Bonds: By Term

a. short-term ( a year) e.g. US Treasury bills

b. intermediate-term e.g. US Treasury notes (2 to 10 years )

c. long-term e.g. US Treasury bonds ( 10 years)

d. open-ended e.g. corporate line of credit

e. serial bond - a portfolio of bonds with staggered terms

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ni)(1

M

ni)(1

INT ..............

2i)(1

INT

1i)(1

INT Vd

Or

nii 1

1 - 1

di 1

M INT V

n

• Vd = Bond Value/Present Value of the Bond/ Current Price of the Bond

• i = Kd = r =The average rate of return • n = The number of years before the bond matures.• INT=Amount of interest paid each year (Coupon payment) =

Coupon rate X Par value• M = The par or face value of the bond.• NB: Some books use PMT or Cr instead of INT.

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Problem 01: Bond price or Current Value

A bond has a coupon interest rate of 10% per year, a $1,000 par value, and 3 years remaining until maturity. The market rate of interest for this bond is 9%. If interest is paid annually, what is the current value of the bond?

$1,025.33

9%)3(1

100039%)(1

10029%)(1

10019%)(1

100

ni)(1

Mni)(1

INT.........

2i)(1

INT1i)(1

INTVd

$1,025.33

$772.20 $253.13

22)$1,000(.77 3)$100(2.531

39% 1

10009%

39% 1

1 - 1

$100

i 1

M INT V ni

i 1

1 - 1

d

n

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Problem 02: Multiple Compounding

A bond has a coupon interest rate of 10% per year, a $1,000 par value, and 3 years remaining until maturity. The market rate of interest for this bond is 8%. If interest is paid semi-annually, what is the current value & yield of the bond?

mnm

im

i 1

1 - 1

d

m

i 1

M

m

INT V

mn

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Practice 01

What’s the value of a 10-year, 10% coupon bond if i = 10% and Face value is $1000?

n = Your Age

n = Your Age

$1000

100.10% 1

10000.10%

100.10% 1

1 - 1

$100

n

Mn

i 1 INT V i

i 1

1 - 1

d

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Practice 01

mnm

im

i 1

1 - 1

d

m

i 1

M

m

INT V

mn

You have a chance to buy a BB-rated bond that has a face value of $1,000. The bond has a 5% coupon rate of interest and matures in four years. Interest is paid semi-annually. The market rate of interest is currently 6% per year for similar bonds.

a. How much should you be willing to pay for the bonds?

90.964$

41.78949.175

41.7897.0196666 25

41.789 251.26677

1000 25

03.1

1000

2

50 V

0.030.21059

0.03430.78940923 - 1

80.031.03

1 - 1

d

8

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Practice 02: Current Value of Bond

A bond has a coupon interest rate of 10% per year, a $1,000 par value, and 2 years remaining until maturity. The market rate of interest for this bond is 9%. If interest is paid annually, what is the current value of the bond?

$1017.61

Practice 03: Current Value of BondComplex Systems has an outstanding issue of $1000 par value bond with a 12% coupon interest rate. The issue pays interest annually and has 16 years remaining to its maturity date. If bonds of similar risk are currently earning a 10% rate of return, how much should the Complex System bond sell for today?

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It is the annual interest payment on a bond divided by its current market value.

dVINT

ValueMarket Current Payment Coupon YieldCurrent

Example: A bond has a coupon interest rate of 10% per year, a $1,000 par value, and 3 years remaining until maturity. The market rate of interest for this bond is 9%. If interest is paid annually, what is the current Yield of the bond?

9.75%$1025.33

$100

)Value(VMarket Current

T)Payment(INCoupon YieldCurrent

d

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It is the average rate of return earned on a bond if it is held to maturity. The rate of return anticipated on a bond if it is held until the maturity date. YTM is considered a long-term bond yield expressed as an annual rate. The calculation of YTM takes into account the current market price, par value, coupon interest rate and time to maturity. It is also assumed that all coupons are reinvested at the same rate. Sometimes this is simply referred to as "yield" for short.

3

M)d2(V

)n

dVM(INT

YTM

An approximate YTM can be found by using a bond yield table. However, because calculating a bond's YTM is complex and involves trial and error, it is usually done by using a programmable business calculator.

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Finding the YTM

YTM 01: A bond has a coupon interest rate of 15% per year, a $1,000 par value, and 14 years remaining until maturity. The current value of this bond is $1368.31. What is the approximate YTM of the bond?

10% 0.0993$1245.54

$26.31)($150

3$1000)2($1368.31

14$1368.31$1000

$150

3

M)d

2(V

)n

dVM

(INTYTM

YTM 02: The Seven Company’s bonds have four years remaining to maturity. Interest is paid annually, the bonds have a $1000 par value, and the coupon interest rate is 9 percent.

Compute the Approximate yield to maturity for the bonds if the current market price is either $829 or $1104.

YTM at $829 is 15%

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Practice: Lahey Industries has outstanding a $1000 par value bond with an 8% coupon interest rate. The bond has 12 years remaining to its maturity date.

1.If interest is paid annually, find the value of the bond when the required return is 7%, 8% and 10%.

2.Indicate for each case in part a whether the bond is selling at a discount, at a premium, or at its par value.

3.Using the 10% required return, find the bond’s value when interest is paid semiannually.

Result $1079.43, $1000, $863.73 Sells at premium, par value, Discount $862.01

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Duration is the average time to maturity of the bond i.e. the average time after which the cash flows on the bond will be received.

A bond with a YTM of 8% and a 10% coupon to be redeemed at par after 3 years.

Present value:

PV= 10/ (1.08) + 10/ (1.08) 2 +110/ (1.08) 3

105.13 = 9.26 + 8.57 + 87.3

Duration: 9.26 x 1 + 8.57 x 2 + 87.3 x 3

105.13= 2.74 years

Duration 02: A bond with a YTM of 10% and a 10% coupon to be redeemed at par ($100) after 3 years. Find out the duration of this bond.

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Factors that Affect Bond Prices Over Time

• Factors that Affect the Risk-Free Rate

– The Central Bank’s monetary policy

– Impact of inflation

– Impact of economic growth

• Factors that Affect the Default Risk Premium:

– Change in economic conditions

– Change in a firm’s financial conditions

• Bond Market Indicators

– Indicators of inflation

– Indicators of economic growth

– Indicators of a firm’s financial condition

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• A passive strategy is a strategy in which investors establish a diversified portfolio of bonds and maintain the portfolio for a long period of time.

• A matching strategy is a strategy in which investors estimate future cash outflows and choose bonds whose coupon or principal payments will cover the projected cash outflows.

• A laddered strategy is a strategy in which investors evenly allocate funds invested in bonds in each of several different maturity classes to minimize interest rate sensitivity.

• A barbell strategy is a strategy in which investors allocate funds into bonds with short-term and long-term, but few or no intermediate-term maturities.

• An interest rate strategy is a strategy in which investors allocate funds to capitalize on interest rate forecasts and revise their portfolio in response to changes in interest rate expectations.

Bond Investment Strategies

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Terms of Repayment on Bond

1. Interest Only: the periodic payments are entirely interest

2. Sinking Fund: periodically, a portion of the debt principal is set aside or certain number of the bonds is retired

3. Balloon Loan: the debt may be partially amortized with each payment

4. Income Bond: interest is payable only if it is earned

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Bond Principles: Bond Cash Flows

1. Annuities: most bonds are annuities plus an ultimate repayment of principal

2. Zero Coupon: only the par value is returned at maturity

3. Variable (Adjustable) Rate: the rate fluctuates in accordance with some market index or predetermined schedule

4. Consols: a level rate of interest is paid perpetually

5. Inflation-indexed Treasury Bonds: the principal value is adjusted based on the consumer price index

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Bond Options

Convertible Bond : may be exchanged for common stock in the company that issued the bond

Exchangeable Bond : may be exchanged for shares in another firm

Bond Registration

1. Bearer (Coupon) Bonds - belong to whomever legally hold them; no longer issued in the United States because of tax considerations

Registered Bonds : the bonds show the bondholder’s name

Book Entry Bonds : bond ownership is reflected only in the accounting records

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Bond Risks: Convenience Risks call risk: the possibility that the company will exercise a bond’s call feature reinvestment rate risk: the chance that the interest received cannot be reinvested to earn as much as the bond’s original yield to maturity. The higher the coupon on a bond, the higher its reinvestment rate risk marketability risk: The difficulty of selling a bond in the secondary market

Bond Risks: Price Risks default risk - the possibility that the issue of the bond is unable to pay; rated by agencies like Moody’s and Standard & Poor’sinterest rate risk - the chance of loss due to changing interest rates