Question

D Corporation has three bonds outstanding. All three have a coupon rate of 9 percent and a $1000 par value. The first bond has one year left to maturity. The second bond has 4 years left to maturity. The last bond has 8 years left to maturity. Assume for simplicity that the market rate for all three bonds is now 5 percent.

What is the value for the first bond with one year left to maturity? ___________

What is the value for the second bond with four years left to maturity? ______________

What is the value for the first bond with eight years left to maturity? ___________

Assuming the same stated interest rate, in an environment of increasing interest rates which bonds will decrease in value the most -- the one with a longer term (duration/maturity) or shorter term (duration/maturity)?

Answer 1

Assuming bonds are paying interest rate annually

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 = 9%

                YTM or Required rate = 5%

                Time to maturity (n) = 1 years

                Annual coupon C = $90

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

P = 90* [{1 - (1 + 0.05) ^ -1}/ (0.05)] + [1000/ (1 + 0.05) ^1]

P = 90* [{1 - (1.05) ^ -1}/ (0.05)] + [1000/ (1.05) ^1]

P = 90* [{1 - 0.95238}/ 0.05] + [1000/ 1.05]

P = 90* [0.04762/ 0.05] + [952.38095]

P = 90* 0.9524 + 952.38095

P = 85.716 + 952.38095

P = 1038.09695

So price of the bond is $1038.1

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                Face value = $1000

                Coupon rate = 9%

                YTM or Required rate = 5%

                Time to maturity (n) = 4 years

                Annual coupon C = $90

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

P = 90* [{1 - (1 + 0.05) ^ -4}/ (0.05)] + [1000/ (1 + 0.05) ^4]

P = 90* [{1 - (1.05) ^ -4}/ (0.05)] + [1000/ (1.05) ^4]

P = 90* [{1 - 0.8227}/ 0.05] + [1000/ 1.21551]

P = 90* [0.1773/ 0.05] + [822.69994]

P = 90* 3.546 + 822.69994

P = 319.14 + 822.69994

P = 1141.83994

So price of the bond is $1141.84

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                Face value = $1000

                Coupon rate = 9%

                YTM or Required rate = 5%

                Time to maturity (n) = 8 years

                Annual coupon C = $90

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

P = 90* [{1 - (1 + 0.05) ^ -8}/ (0.05)] + [1000/ (1 + 0.05) ^8]

P = 90* [{1 - (1.05) ^ -8}/ (0.05)] + [1000/ (1.05) ^8]

P = 90* [{1 - 0.67684}/ 0.05] + [1000/ 1.47746]

P = 90* [0.32316/ 0.05] + [676.83727]

P = 90* 6.4632 + 676.83727

P = 581.688 + 676.83727

P = 1258.52527

So price of the bond is $1258.53

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The bond with highest maturity date will decrease in value the most.

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