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16 October, 01:11

Both Bond Bill and Bond Ted have 12.6 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 6 years to maturity, whereas Bond Ted has 23 years to maturity. Both bonds have a par value of 1,000. a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?

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  1. 16 October, 02:33
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    The correct answer is - 7.817 % and - 13.163%.

    Explanation:

    According to the scenario, the computation of the given data are as follows:

    Par value = $1,000

    Coupon rate = 12.6%

    So, Semi-annual coupon rate = 6.3%

    Semi annual coupon payment = 6.3% * $1,000 = $63

    If interest rate rise by 2%

    Then, the discount rate = 12.6% + 2% = 14.6% p. a.

    Discount rate (i) semiannual = 7.3%

    PV of Annuity = C * [ (1 + i) ^t - 1) ] : ((1 + i) * i)

    Where, t = Time period semiannual

    C = Coupon payment semiannual

    By putting the value,

    Price of Bill Bond = $63 * (1.073^12-1) : ((1.073^12) * 0.073) + $1,000 : (1.073^12)

    = $921.83

    So, Percentage change in Bill Bond = (($921.83 - $1,000) : $1,000) * 100

    = - 7.817 %

    Price of Ted Bond = $63 * (1.073^46 - 1) : ((1.073^46) * 0.073) + $1,000 : (1.073^46)

    = $868.37

    So, Percentage change in Ted Bond = (($868.37 - $1,000) : $1,000) * 100

    = - 13.163%
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