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Math Help - Raising Capital

  1. #1
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    Raising Capital

    A company needs to raise $10 million to finance an investment. How many bonds would the firm need to sell (ignoring transaction costs)? Assume the company decides to issue 10-year maturity bonds with a 5% coupon rate, paying coupons semi-annually. The yield to maturity is currently 4%.

    My finance teacher gave us this problem and never went over it. Does anyone know the formula or what to do to find the answer to this problem.
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  2. #2
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    Quote Originally Posted by johnkw87 View Post
    A company needs to raise $10 million to finance an investment. How many bonds would the firm need to sell (ignoring transaction costs)? Assume the company decides to issue 10-year maturity bonds with a 5% coupon rate, paying coupons semi-annually. The yield to maturity is currently 4%.
    I guess the bonds would be $1000 bonds.

    k = PV @ 4% of a 10year $1000 bond with annual coupons of $50

    Number of bonds = 10000000 / k
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  3. #3
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    Quote Originally Posted by Wilmer View Post
    I guess the bonds would be $1000 bonds.

    k = PV @ 4% of a 10year $1000 bond with annual coupons of $50

    Number of bonds = 10000000 / k
    With my online tool that shows calculation for price of non zero coupon bonds I get the following results

    http://finance.thinkanddone.com/onli...lculation.html

    Compounding = semi annually
    Par Value = 1000
    Coupon Rate = 0.025
    Market Rate = 0.02
    N = 20

    Non Zero Bond Price Formula
    Coupon Rate x Par Value x PVIFA(ytm%, n) + Par Value x PVIF(ytm%, n)

    PVIFA Formula
    PVIFA(ytm%, n) = [1 - v] / ytm%
    v = 1 / (1 + ytm%)^n
    PVIFA(ytm%, n) = [1 - { 1 / (1 + ytm%)^n }] / ytm%

    PVIFA Calculation
    v = 1 / (1+0.02)^20
    v = 0.67297133310806
    PVIFA(0.02, 20) = [1 - 0.67297133310806] / 0.02
    PVIFA(0.02, 20) = 0.32702866689194 / 0.02
    PVIFA(0.02, 20) = 16.351433344597

    PVIF Formula
    PVIF(ytm%, n) = 1 / (1 + ytm%)^n

    PVIF Calculation
    PVIF(0.02, 20) = 1 / (1+0.02)^20
    PVIF(0.02, 20) = 1 / 1.4859473959784
    PVIF(0.02, 20) = 0.67297133310806

    Non Zero Bond Price Calculation
    Price = 0.025 x 1000 x 16.351433344597 + 1000 x 0.67297133310806
    Price = 408.78583361493 + 672.97133310806
    Price = 1081.76

    One could have used MS Excel PV function to find the price of the bond with the following formula
    =PV(rate,nper,pmt,fv,type)
    =PV(4%/2,10*2,1000*5%/2,1000,0)
    Last edited by dexteronline; October 31st 2010 at 07:08 AM.
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  4. #4
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    Quote Originally Posted by dexteronline View Post
    Compounding = semi annually
    Par Value = 1000
    Coupon Rate = 0.025
    Market Rate = 0.02
    N = 20
    Not sure why you're going through all those unnecessary steps, Dexter.
    The coupon being $25, this is all you need to do:

    [PV of $1000] + [PV of 20 payments of $25] =
    [1000 / 1.02^20] + [25(1 - 1/1.02^20) / .02] = 1081.76
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  5. #5
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    Bond price calculation

    Quote Originally Posted by Wilmer View Post
    Not sure why you're going through all those unnecessary steps, Dexter.
    The coupon being $25, this is all you need to do:

    [PV of $1000] + [PV of 20 payments of $25] =
    [1000 / 1.02^20] + [25(1 - 1/1.02^20) / .02] = 1081.76
    Hi Wilmer

    I was awaiting your reply

    I am doing exactly what you just explained, I am just throwing in the details so someone who is not familiar with the formulas for finding the price of the bond can see the workout. It may seem confusing but what do you suggest?

    Should I just show the formula for bond price and plug in the number without explaining what is going on?
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  6. #6
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    Depends, I guess; the poster requested:
    "Does anyone know the formula or what to do to find the answer to this problem."

    What you did is nice and kind-hearted, but is more what he'd be shown in a classroom...
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  7. #7
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    Quote Originally Posted by Wilmer View Post
    Depends, I guess; the poster requested:
    "Does anyone know the formula or what to do to find the answer to this problem."

    What you did is nice and kind-hearted, but is more what he'd be shown in a classroom...
    Yes that was my intention for visitors to the bond price calculation page that went live today. I think you missed the link in my first post, here it is again http://finance.thinkanddone.com/onli...lculation.html

    I can use your feedback on this one, if you think showing work for PVIFA and PVIF is redundant then I can remove that from the calculation shown and instead plug in the values in the bond price formula
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  8. #8
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    Quote Originally Posted by dexteronline View Post
    I can use your feedback on this one, if you think showing work for PVIFA and PVIF is redundant then I can remove that from the calculation shown and instead plug in the values in the bond price formula
    Use PayPal? My consulting fees are $567.50 per hour or part thereof.
    Discount of .00001% if paid within 30 minutes
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  9. #9
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    Quote Originally Posted by Wilmer View Post
    Use PayPal? My consulting fees are $567.50 per hour or part thereof.
    Discount of .00001% if paid within 30 minutes
    With 1491 posts on this forum and at the rate you charge, you must be a rich man
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