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24 January, 05:37

Leigh Delight Candy, Inc. is choosing between two bonds in which to invest their cash. One is being offered from Hershey's and will mature in 10 years and pay $30 each quarter. The other alternative is a Mars' bond that will mature in 20 years and pay $30 each quarter. What would be the present value of each bond if the discount rate is 10% compounded quarterly, and each bond pays $1,000 at maturity?

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  1. 24 January, 06:05
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    Hersey's bond = $1125.513

    Mars bond = $1172.259

    Explanation:

    Hersey bond;

    Period (t) = 10years = 40 (quartely)

    Coupon (C) = $30

    Rate (r) = 0.1 = 0.025 (quarterly)

    Pay at maturity (p) = $1000

    Using the both present value (PV) and compound interest formula;

    PV = [ C * (1 - (1+r) ^-t) : r] + [p : (1 + r) ^t]

    PV = [30 * (1 - (1.025) ^-40) : 0.025] + [1000: (1.025) ^40]

    PV = (753.083251562) + (372.4306236)

    PV = $1125.513

    Mars bond;

    Period (t) = 20years = 80 (quartely)

    Coupon (C) = $30

    Rate (r) = 0.1 = 0.025 (quarterly)

    Pay at maturity (p) = $1000

    PV = [ C * (1 - (1+r) ^-t) : r] + [p : (1 + r) ^t]

    PV = [30 * (1 - (1.025) ^-80) : 0.025] + [1000: (1.025) ^80]

    PV = (1033.55451663) + (138.704569467)

    PV = $1172.259
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