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    Bond Valuation Practice Solution

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    XDkillua45

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    Bond Valuation Practice Solution

    Uploaded by

    XDkillua45
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    Original Title

    Bond-Valuation-Practice-Solution (1)

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    16 views5 pages

    Bond Valuation Practice Solution

    Uploaded by

    XDkillua45

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    © All Rights Reserved
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    of 5

    Practice Problems

    AEC 23 Financial Markets


    Bond Valuation

    1. The bond has a face value of ₱1,000,000. The bond pays interest of 5% every year. The bond
    matures in 5 years. The prevailing market rate is 6%.

    How much is the present value of the bond?

    Present value of face value:

    1,000,000 1,000,000
    = = 747,258.17
    (1 + 0.06)5 1.338226

    Present value of interest payments:


    Face value ₱1,000,000
    Multiply: nominal interest rate 5%
    Annual interest payment ₱50,000

    1 − (1 + 𝑟)−𝑛
    𝑃
    𝑟
    First, solve what is called the present value factor:

    1 − (1 + 𝑟)−𝑛 1 − (1 + 0.06)−5 1 − 0.7472582 0.2527418


    = = = = 4.212364
    𝑟 0.06 0.06 0.06
    Note:
    1
    (1 + 0.06)−5 =
    (1 + 0.06)5

    Second, multiply the PV Factor to the annuity payment:


    Annual interest payment ₱50,000
    Multiply: PV factor 4.212364
    PV of interest payments ₱210,618.19

    The value of the bond is:


    PV of face value ₱747,258.17
    PV of interest payments 210,618.19
    Value of bonds ₱957,876.36

    CVGCastro 1S 2022-2023
    When performing the computation, it is important not to do any rounding during the
    computation. If that is unavoidable, make sure to round somewhere up to 6 decimal places to be
    as accurate as possible.

    2. The bonds have a face value of ₱1,000,000. They pay interest of 10% every year. The bond
    matures in 10 years. The prevailing market rate is 12%. How much is the value of the bonds?

    Present value of face value:

    1,000,000 1,000,000
    = = 321,973.24
    (1 + 0.12)10 3.1058482

    Present value of interest payments:


    Face value ₱1,000,000
    Multiply: nominal interest rate 10%
    Annual interest payment ₱100,000

    1 − (1 + 𝑟)−𝑛
    𝑃
    𝑟

    1
    1 − (1 + 𝑟) −𝑛 1−
    (1 + 0.12)10
    = = 5.6502230
    𝑟 0.12

    Annual interest payment ₱100,000


    Multiply: PV factor 5.6502230
    PV of interest payments ₱565,022.30

    PV of face value ₱321,973.24


    PV of interest payments 565,022.30
    Value of bonds ₱886,995.54

    CVGCastro 1S 2022-2023
    3. The bonds have a face value of ₱1,000,000. They pay interest of 10% every year. The bond
    matures in 10 years. The prevailing market rate is 8%. How much is the value of the bonds?

    Present value of face value:

    1,000,000 1,000,000
    = = 463,193.49
    (1 + 0.08)10 2.158925000

    Present value of interest payments:


    Face value ₱1,000,000
    Multiply: nominal interest rate 10%
    Annual interest payment ₱100,000

    1 − (1 + 𝑟)−𝑛
    𝑃
    𝑟

    1
    1 − (1 + 𝑟)−𝑛 1−
    (1 + 0.08)10
    = 100,000 = 6.7100814
    𝑟 0.08

    Annual interest payment ₱100,000


    Multiply: PV factor 6.7100814
    PV of interest payments ₱671,008.14

    PV of face value ₱463,193.49


    PV of interest payments 671,008.14
    Value of bonds ₱1,134,201.63

    The value is higher which means that the bonds are valued at a premium.
    The bonds are more valuable compared to the prevailing market conditions.

    4. The bonds have a face value of ₱5,000,000. They pay interest of 10% every year. The bond
    matures in 5 years. The prevailing market rate is 12%. How much is the value of the bonds?

    PV of face value ₱2,837,134.28


    PV of interest payments 1,802,388.10
    Value of bonds ₱4,639,522.38

    CVGCastro 1S 2022-2023
    5. The bonds have a face value of ₱3,000,000. They pay interest of 6% every year. The bond
    matures in 7 years. The prevailing market rate is 7%. How much is the value of the bonds?

    PV of face value ₱1,868,249.23


    PV of interest payments 970,072.09
    Value of bonds ₱2,838,321.32

    6. The bonds have a face value of ₱5,000,000. They pay interest semi-annually of 10% every year.
    The bond matures in 5 years. The prevailing market rate is 12%. How much is the value of the
    bonds?

    The present value of the face value is as follows:

    𝑃
    𝑟
    (1 + )𝑡𝑛
    𝑡
    r = yield rate or effective rate
    t = number of payments each year
    n = number of years to maturity

    Interest is paid semi-annually. As such, there are 2 payments each year.

    𝑃 5,000,000 5,000,000
    𝑟 = = = 2,791,973.88
    (1 + )𝑡𝑛 (1 + 0.12)5(2) (1 + 0.06)
    10
    𝑡 2
    The present value of the interest annuity is as follows:

    𝑟 0.12 −5(2) 1
    1 − (1 + )−𝑛𝑡 1 − (1 + ) 1−
    𝑡 2 (1 + 0.06)10
    𝑃 𝑟 = 𝑃 = 𝑃
    0.12 0.06
    𝑡 2
    Each interest payment in this case is computed as follows:
    P = Nominal rate x Face value x Time elapsed in years
    = 10% x 5,000,000 x 1/2 (because payments are made semi-annually)
    = 250,000

    CVGCastro 1S 2022-2023
    1
    1−
    (1 + 0.06)10
    250,000 = 1,840,021.76
    0.06

    7. The bonds have a face value of ₱5,000,000 and have a term of 5 years. The bonds contain a
    sinking fund provision, where the issuer must pay ₱1,000,000 worth of bonds each year. Interest
    is paid at 10% annually. The prevailing market rate is 12%. How much is the value of the bonds?

    1,000,000 is paid every year. Thus, the face value has become an annuity of 1,000,000 each year.

    1
    −𝑛 1−
    1 − (1 + 𝑟) (1 + 0.12)5
    𝑃 = 1,000,000 = 3,604,776.20
    𝑟 0.12
    On the other hand, the interest cannot be computed as an annuity. Because the principal
    decreases each year, the interest to be paid will also decrease and is no longer uniform:

    1st year: 5,000,000 x 10% = 500,000


    2nd year: 4,000,000 x 10% = 400,000
    3rd year: 3,000,000 x 10% = 300,000
    4th year: 2,000,000 x 10% = 200,000
    5th year: 1,000,000 x 10% = 100,000

    The PV of each individual payment must be computed separately:

    CVGCastro 1S 2022-2023

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