Question

Suppose that General Motors Acceptance Corporation issued a bond with 10 years until​ maturity, a face value of $ 1000​, and a coupon rate of 7.7 % ​(annual payments). The yield to maturity on this bond when it was issued was 5.9 %. What was the price of this bond when it was​ issued?

When it was​ issued, the price of the bond was ​? ​ (Round to the nearest​ cent.)

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 = 7.7%

                YTM or Required rate = 5.9%

                Time to maturity (n) = 10 years

                Annual coupon C = $77

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

P = 77* [{1 - (1 + 0.059) ^ -10}/ (0.059)] + [1000/ (1 + 0.059) ^10]

P = 77* [{1 - (1.059) ^ -10}/ (0.059)] + [1000/ (1.059) ^10]

P = 77* [{1 - 0.56369}/ 0.059] + [1000/ 1.77402]

P = 77* [0.43631/ 0.059] + [563.6915]

P = 77* 7.39508 + 563.6915

P = 569.42116 + 563.6915

P = 1133.11266

So price of the bond is $1133.11

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