Determine the price of a 1 million bond issue under each of

Determine the price of a $1 million bond issue under each of the following independent assumptions: E 14-2 Determine the price of bonds in various situations Maturity Interest Paid Stated Rate 10 years 10 years 10 years 20 years 20 years annually semiannually semiannually semiannually semiannually 10% 10% 12% 12% 12% 12% 12% 10% 10% 12% L014-2

Solution

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 = 0.1

                YTM or Required rate = 0.12

                Time to maturity (n) = 10 years

                Annual coupon C = $100

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

P = 100* [{1 - (1 + 0.12) ^ -10}/ (0.12)] + [1000/ (1 + 0.12) ^10]

P = 100* [{1 - (1.12) ^ -10}/ (0.12)] + [1000/ (1.12) ^10]

P = 100* [{1 - 0.32197}/ 0.12] + [1000/ 3.10585]

P = 100* [0.67803/ 0.12] + [321.97305]

P = 100* 5.65025 + 321.97305

P = 565.025 + 321.97305

P = 886.99805

So price of the bond is $887

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2.

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 = 0.1

                YTM or Required rate = 0.12

                Time to maturity (n) = 10 years

                Annual coupon C = $100

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

P = 100/ 2 [{1 - (1 + 0.12/2) ^-2*10}/ (0.12/ 2)] + [1000/ (1 + 0.12/2) ^2*10]

    = 50 [{1 - (1 + 0.06) ^ -20}/ (0.06)] + [1000/ (1 + 0.06) ^20]

    = 50 [{1 - (1.06) ^ -20}/ (0.06)] + [1000/ (1.06) ^20]

    = 50 [{1 - 0.3118}/ (0.06)] + [1000/ 3.20714]

    = 50 [0.6882/ 0.06] + [311.80429]

    = 50 [11.47] + [311.80429]

    = 573.5 + 311.80429

    = 885.30429

So price of the bond is $885.3

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3.

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 = 0.12

                YTM or Required rate = 0.1

                Time to maturity (n) = 10 years

                Annual coupon C = $120

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

P = 120/ 2 [{1 - (1 + 0.1/2) ^-2*10}/ (0.1/ 2)] + [1000/ (1 + 0.1/2) ^2*10]

    = 60 [{1 - (1 + 0.05) ^ -20}/ (0.05)] + [1000/ (1 + 0.05) ^20]

    = 60 [{1 - (1.05) ^ -20}/ (0.05)] + [1000/ (1.05) ^20]

    = 60 [{1 - 0.37689}/ (0.05)] + [1000/ 2.6533]

    = 60 [0.62311/ 0.05] + [376.88916]

    = 60 [12.4622] + [376.88916]

    = 747.732 + 376.88916

    = 1124.62116

So price of the bond is $1124.62

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4.

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 = 0.12

                YTM or Required rate = 0.1

                Time to maturity (n) = 20 years

                Annual coupon C = $120

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

P = 120/ 2 [{1 - (1 + 0.1/2) ^-2*20}/ (0.1/ 2)] + [1000/ (1 + 0.1/2) ^2*20]

    = 60 [{1 - (1 + 0.05) ^ -40}/ (0.05)] + [1000/ (1 + 0.05) ^40]

    = 60 [{1 - (1.05) ^ -40}/ (0.05)] + [1000/ (1.05) ^40]

    = 60 [{1 - 0.14205}/ (0.05)] + [1000/ 7.03999]

    = 60 [0.85795/ 0.05] + [142.04566]

    = 60 [17.159] + [142.04566]

    = 1029.54 + 142.04566

    = 1171.58566

So price of the bond is $1171.59

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5.

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 = 0.12

                YTM or Required rate = 0.12

                Time to maturity (n) = 20 years

                Annual coupon C = $120

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

P = 120/ 2 [{1 - (1 + 0.12/2) ^-2*20}/ (0.12/ 2)] + [1000/ (1 + 0.12/2) ^2*20]

    = 60 [{1 - (1 + 0.06) ^ -40}/ (0.06)] + [1000/ (1 + 0.06) ^40]

    = 60 [{1 - (1.06) ^ -40}/ (0.06)] + [1000/ (1.06) ^40]

    = 60 [{1 - 0.09722}/ (0.06)] + [1000/ 10.28572]

    = 60 [0.90278/ 0.06] + [97.22217]

    = 60 [15.04633] + [97.22217]

    = 902.7798 + 97.22217

    = 1000.00197

So price of the bond is $1000

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Hope that helps.

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