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    Bond pricing using zero coupon bonds

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    A 7% annual coupon bond (face value $1,000), with three years left till maturity is selling for $986.90. Zero-coupon bonds of 1, 2, 3 years maturity (all with face value of $1,000) sell for $950, $900, $820,respectively. Is this coupon bond properly priced? If not, show an arbitrage transaction to profit $2000 (today) from the mispricing.

    I'm not given the market interest rate, and struggling with BA2 plus on this one. Please help.

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    https://brainmass.com/business/bond-valuation/bond-pricing-using-zero-coupon-bonds-572783

    Solution Preview

    Please see the attached file:
    A 7% annual coupon bond (face value $1,000), with three years left till maturity is selling for $986.90.Zero-coupon bonds of 1, 2, 3 years maturity (all with face value of $1,000) sell for $950, $900, $820,respectively. Is this coupon bond properly priced? If not, show an arbitrage transaction to profit $2000(today) from the mispricin.

    We can price the coupon bond using the discount factor (present value factor) derived from the zero- coupon bonds

    Zero coupon bonds
    Face Value= $1,000
    Present value factor
    1 year $950 0.95 =$1,000 / $950
    2 year $900 0.90 =$1,000 / $900
    3 year $820 0.82 =$1,000 / $820

    Now that have got the discount factor we can price the coupon bond

    Face Value = $1,000
    Coupon = 7% = 7.% x $1,000
    Annual interest ...

    Solution Summary

    Prices a coupon bond using zero-coupon bonds and exploits an arbitrage opportunity because of mispricing.

    $2.19