Question

Calculate the value of a bond that matures in 13 years and has a $1,000 par value. The annual coupon interest rate is 9 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 11 percent. The value of the bond is

Answer 1

Price of the bond could be calculated using below formula.

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

Where,

                Face value = $1000

                Coupon rate = 0.09

                YTM or Required rate = 0.11

                Time to maturity (n) = 13 years

                Annual coupon C = $90

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

P = 90* [{1 - (1 + 0.11) ^ -13}/ (0.11)] + [1000/ (1 + 0.11) ^13]

P = 90* [{1 - (1.11) ^ -13}/ (0.11)] + [1000/ (1.11) ^13]

P = 90* [{1 - 0.25751}/ 0.11] + [1000/ 3.88328]

P = 90* [0.74249/ 0.11] + [257.51427]

P = 90* 6.74991 + 257.51427

P = 607.4919 + 257.51427

P = 865.00617

So price of the bond is $865.01

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