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31 October, 02:44

A bond has a par value of $1,000, a time to maturity of 10 years, and a coupon rate of 8.60% with interest paid annually. If the current market price is $860, what will be the approximate capital gain of this bond over the next year if its yield to maturity remains unchanged? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Capital gain

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  1. 31 October, 06:35
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    Capital Gain Yield = 0.94%

    Explanation:

    Par Value = $1,000

    Current Price = $860

    Annual Coupon Rate = 8.60%

    Annual Coupon = 8.60% * $1,000

    Annual Coupon = $86

    Time to Maturity = 10 years

    Let annual YTM be i%

    $860 = $86 * PVIFA (i%, 10) + $1,000 * PVIF (i%, 10)

    Using financial calculator:

    N = 10

    PV = - 860

    PMT = 86

    FV = 1000

    I/Y = 10.98%

    Annual YTM = 10.98%

    Price Next Year = $86 * PVIFA (10.98%, 9) + $1,000 * PVIF (10.98%, 9)

    Price Next Year = $86 * (1 - (1/1.1098) ^9) / 0.1098 + $1,000 / 1.1098

    Price Next Year = $868.12

    Capital Gain Yield = (Price Next Year - Current Price) / Current Price

    Capital Gain Yield = ($868.12 - $860) / $860

    Capital Gain Yield = 0.0094

    Capital Gain Yield = 0.94%
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