Question

What is the price of a Verismo Company’s bond that has a 7.50 percent coupon and a face value of $1,000, pays interest semiannually, and has 15 years to maturity, if the required rate of return is 5 percent? (Points : 3.5)

       $1051.87.
       $1,134.21.
       $1,261.63.
       $997.25.
       $950.08.

Answer 1

Correct option is C

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Price of the bond could be calculated using below formula.

P = C/ 2 [1 - {(1 + YTM/2) ^2*n}/ (YTM/2)] + [F/ (1 + YTM/2) ^2*n]

Where,

                Face value (F) = $1000

                Coupon rate = 7.5%

                YTM or Required rate = 5%

                Time to maturity (n) = 15 years

                Annual coupon C = $75

Let's put all the values in the formula to find the bond current value

P = 75/ 2 [{1 - (1 + 0.05/2) ^-2*15}/ (0.05/ 2)] + [1000/ (1 + 0.05/2) ^2*15]

    = 37.5 [{1 - (1 + 0.025) ^ -30}/ (0.025)] + [1000/ (1 + 0.025) ^30]

    = 37.5 [{1 - (1.025) ^ -30}/ (0.025)] + [1000/ (1.025) ^30]

    = 37.5 [{1 - 0.47674}/ (0.025)] + [1000/ 2.09757]

    = 37.5 [0.52326/ 0.025] + [476.74213]

    = 37.5 [20.9304] + [476.74213]

    = 784.89 + 476.74213

    = 1261.63213

So price of the bond is $1261.63

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