Problem 71 Bond valuation Callaghan Motors bonds have 7 year

Problem 7-1 Bond valuation Callaghan Motors bonds have 7 years remaining to maturity. Interest is paid annually, they have a $1,000 par value, the coupon interest rate is 7%, and the yield to maturity is 10%, what is the bond\'s current market price? Round your answer to the nearest cent.

Solution

So the current price of the bond is 853.95

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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%

                YTM or Required rate = 10%

                Time to maturity (n) = 7 years

                Annual coupon C = $70

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

P = 70* [{1 - (1 + 0.1) ^ -7}/ (0.1)] + [1000/ (1 + 0.1) ^7]

P = 70* [{1 - (1.1) ^ -7}/ (0.1)] + [1000/ (1.1) ^7]

P = 70* [{1 - 0.51316}/ 0.1] + [1000/ 1.94872]

P = 70* [0.48684/ 0.1] + [513.15735]

P = 70* 4.8684 + 513.15735

P = 340.788 + 513.15735

P = 853.94535

So price of the bond is $853.95

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