chapter 7a- bonds valuation

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    BOND VALUATION

    From: Basic Financial Management

    Seventh EditionChapter 7

    Chapter

    7A

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    Terminology and Characteristics of Bonds

    Bonds a type of debt or long-term promissory note,

    issued by the borrower, promising to pay its holder a

    predetermined and fixed amount of interest each year.

    Types of Bonds:

    Debenture- any unsecured long-term debt.

    Subordinated Debentures a debenture that is

    subordinated to other debentures in being paid in case of

    insolvency.

    Mortgage Bonda bond secured by a lien on real property.

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    Terminology and Characteristics of Bonds

    (Continued)

    Zero and Very Low Coupon Bondsbonds issued

    at a substantial discount from their $1,000 face

    value that pay no or little interest.

    Junk or Low-Rated Bonds bonds rated BB or

    below.Eurobonds bonds issued in a country different

    from the one in whose currency the bond is

    denominated for instance, a bond issued inEurope or Asia by an American company that

    pays interest and principal in U.S. dollars.

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    Features or Characteristics of Bonds

    Claim on Assets and Income in case of

    insolvency, claims of debt in general, includingbonds, are honored before those of the

    preferred and ordinary shares of stock. Bonds also

    have claim on income that comes ahead ofcommon and preferred stocks.

    Par Value bonds face value that is returned to

    the bondholder at maturity, usually $1,000.Coupon Interest Rateindicates what percentage

    of the par value of the bond will be paid out

    annually in the form of interest.

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    Features or Characteristics of Bonds (Continued)

    Indenture the legal agreement or

    contract between the firm issuing the

    bonds and the bond trustee who

    represents the bondholders.Current Yield the ratio of the interest

    payment to the bonds market price.

    Maturity the length of time until thebond issuer returns the par value to the

    bondholder and terminates the bond.

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    Valuation is an important issue if we are to manage acompany effectively. And understanding of theconcepts and how to compute the value of asecurity underlie much that we do in finance andin making correct decisions for the firm as a

    whole. Only if we know what matters to ourinvestors can we maximize the firms value.

    Value is defined differently depending on the context.But for us, value is the present value of futurecash flows expected to be received from aninvestment discounted at the investors requiredrate of return.

    Definitions of Value

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    Definitions of Value (Continued)

    Book Valuethe value of an asset as shown on a

    firms balance sheet. It represents the historicalcost of the asset rather than its current market

    value or replacement cost.

    Liquidation Valuethe amount that could be

    realized if an asset were sold individually and not

    as a part of the going concern.

    Market Valuethe observed value for an asset in

    the market place.

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    Intrinsic or Economic Valuethe present

    value of the assets expected future cashflows. This value is the amount the

    investor considers to be a fair value, given

    the amount, timing, and riskiness of futurecash flows.

    Efficient Marketa market in which the

    values of securities at any instant in time

    fully reflect all available information,

    which results in the market value and the

    Definitions of Value (Continued)

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    Valuation: Understanding the Process

    Valuation process can be described as follows:It is assigning value to an asset by calculating

    the present value of its expected future cash

    flows using the investors required rate ofreturn as the discount rate.

    The investors required rate of return, k, equals

    the risk-free rate of interest plus a risk

    premium to compensate the investor for

    assuming risk.

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    Elements that affect the value of an asset:

    1. The amount and timing of the assets expected

    cash flows;

    2. The riskiness of these cash flows; and

    3. The investors required rate of return for

    undertaking the investment.

    Valuation: Understanding the Process

    (Continued)

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    *Bond Valuation*

    The value of a BOND is the present value

    both of future interest to be received

    and the par or maturity value of thebond.

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    Bondholders Expected Rates of Return

    Expected Rate of Return the discount rate that equates the

    present value of the future cash flows (interest and maturity

    value) with the current market price of the bond. It is the rate of

    return an investor will earn if a bond is held to maturity.

    Yield to Maturity the same as the expected rate of return.

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    Bond Valuation:

    Five Important Relationships

    1. A decrease in interest rates (required rates of

    return) will cause the value of the bond to

    increase; an interest rate increase will cause a

    decrease in value. The change in value causedby changing interest rates is calledInterest Rate

    Risk.

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    Bond Valuation: (Continued)

    Five Important Relationships

    2. If the bondholders required rate of return

    (current interest rate):

    a.) Equals the coupon interest rate, the bond

    will sell at par, or maturity value.

    b.) Exceeds the bonds coupon rate, the bond

    will sell below par value, or at a discount.

    c.) Is less than the bonds coupon rate, the

    bond will sell above par value, or at a

    premium.

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    3. As a bond approaches maturity, the market

    price of the bond approaches the par value.

    4. A bondholder owning a long-term bond isexposed to greater interest rate risk than

    one owning a short-term bond.

    Bond Valuation: (Continued)

    Five Important Relationships

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    Bond Valuation: (Continued)

    Five Important Relationships

    5. The sensitivity of a bonds value to interest

    rate changes is not only affected by the time

    to maturity, but also by the time pattern ofinterim cash flows, or its duration.

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    Bond Valuation:

    Exercise Problems

    Ex. #1- Wapoco bonds have a coupon rate of 8%, apar value of P 1,000, and will mature in 20 years.

    If you require a return of 7%, what price would

    you be willing to pay for the bond? Whathappens if you pay more for the bond? What

    happens if you pay less for the bond?

    B d V l ti

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    Value (Vb) = +

    Bond Valuation:

    Solution to Exercise#1

    20

    t=1(1.07) t

    $80 $1,000

    20(1.07)

    Thus,

    Present value of interest: $80(10.594) =$ 847.52

    Present value of par value: $1,000(0.258) =$ 258.00

    Value of the Bond (Vb) =$1,105.52

    ========

    If you pay more for the bond, your required rate of return will not be

    satisfied. In other words, by paying an amount for the bond that exceeds

    $1,105.52, the expected rate of return for the bond is less than the

    required rate of return. If you have the opportunity to pay less for the

    bond, the expected rate of return exceeds the 7% required rate of return.

    B d V l i

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    Ex. #2-Gandania Co.s bonds, maturing in 7 years

    , pay 8% on a $1,000 face value. However,

    interest is paid semiannually. If your required

    rate of return is 10%, what is the value of thebond? How would your answer change if the

    interest were paid annually?

    Bond Valuation:

    Exercise Problems

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    Bond Valuation:

    Solution toExercise#2

    If interest is paid semiannually:

    Value (Vb) =

    Thus,

    $40(9.899) = $ 395.96

    $1,000(0.505) = $ 505.00

    Value (Vb) = $ 900.96

    =======

    If interest is paid annually:

    Value (Vb) =

    Value (Vb) = $80(4.868) + $1,000(0.513)

    Value (Vb) = $902.44

    =======

    14t=1

    (1+0.05)

    $40 $1,000

    t (1+0.05)14

    7

    t=1

    $80

    ( 1.10)

    t

    $1,000

    ( 1.10)

    7

    +

    +

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    Ex. #3 (Expected Rate of Return)

    Ganansia Co.s bonds are selling in the market

    for $1,045. These 15-year bonds pay 7%

    interest annually on a $1,000 par value. If

    they are purchased at the market price, what

    is the expected rate of return?

    Bond Valuation:

    Exercise Problems

    B d V l ti

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    $1,045 =

    At 6%: $70(9.712) + $1,000(0.417)=$1,096.84

    At 7%: Value must equal $1,000.Interpolation:

    Expected Rate of Return:

    = 6% + (1%) = 6.54%

    $1,096.84-$1,000 = $ 96.84

    $1,096.84-$1,045 = $ 51.84

    Bond Valuation:

    Solution toExercise#3

    15$70( 1+k )

    $1,000t

    t=1+

    ( 1+k )

    15

    $51.84

    $96.84k