A “century” bond has a 6 percent coupon rate and makes semiannual payments ($30

Question

A “century” bond has a 6 percent coupon rate and makes semiannual payments ($30 every six months). The yield to maturity is 4 percent and the maturity date is December 11, 2115. You should assume that today is December 11, 2015.

1. What is the estimated market value of the stream of promised coupon payments?

2. What is the estimated market value of the promised payment at maturity?

3. Compute the modified duration of the century bond described above, using the short-cut formula described in Fabozzi.

Explanation / Answer

Answer: the bond gives 6% annual coupons The coupons paid semi-annually and has amount = $30 Face value of bond= $1,000 Tenure of bond = 100 years Yield to maturity = 4% Answer-1 Estimated market value of coupon payments = present value of $30 for 100 years Estimated market value = $1,471.42 Answer-2 Promised payment at maturity = $1,000 Market value of $1000 today = $19.05 Answer-3 Modified Macaulay Duration: Period Cash Flow Present value @4% PV x Period 1 $30 $29.41 $29.41 2 $30 $28.84 $57.67 3 $30 $28.27 $84.81 4 $30 $27.72 $110.86 5 $30 $27.17 $135.86 6 $30 $26.64 $159.83 7 $30 $26.12 $182.82 8 $30 $25.60 $204.84 9 $30 $25.10 $225.92 10 $30 $24.61 $246.10 11 $30 $24.13 $265.41 12 $30 $23.65 $283.86 13 $30 $23.19 $301.48 14 $30 $22.74 $318.31 15 $30 $22.29 $334.36 16 $30 $21.85 $349.65 17 $30 $21.42 $364.22 18 $30 $21.00 $378.09 19 $30 $20.59 $391.27 20 $30 $20.19 $403.78 21 $30 $19.79 $415.66 22 $30 $19.41 $426.91 23 $30 $19.02 $437.57 24 $30 $18.65 $447.64 25 $30 $18.29 $457.15 26 $30 $17.93 $466.11 27 $30 $17.58 $474.55 28 $30 $17.23 $482.47 29 $30 $16.89 $489.91 30 $30 $16.56 $496.86 31 $30 $16.24 $503.36 32 $30 $15.92 $509.41 33 $30 $15.61 $515.03 34 $30 $15.30 $520.23 35 $30 $15.00 $525.03 36 $30 $14.71 $529.44 37 $30 $14.42 $533.48 38 $30 $14.14 $537.15 39 $30 $13.86 $540.48 40 $30 $13.59 $543.47 41 $30 $13.32 $546.13 42 $30 $13.06 $548.48 43 $30 $12.80 $550.53 44 $30 $12.55 $552.29 45 $30 $12.31 $553.77 46 $30 $12.06 $554.97 47 $30 $11.83 $555.92 48 $30 $11.60 $556.61 49 $30 $11.37 $557.07 50 $30 $11.15 $557.29 51 $30 $10.93 $557.29 52 $30 $10.71 $557.08 53 $30 $10.50 $556.66 54 $30 $10.30 $556.04 55 $30 $10.10 $555.23 56 $30 $9.90 $554.24 57 $30 $9.70 $553.08 58 $30 $9.51 $551.75 59 $30 $9.33 $550.25 60 $30 $9.14 $548.61 61 $30 $8.96 $546.82 62 $30 $8.79 $544.88 63 $30 $8.62 $542.81 64 $30 $8.45 $540.62 65 $30 $8.28 $538.30 66 $30 $8.12 $535.86 67 $30 $7.96 $533.32 68 $30 $7.80 $530.66 69 $30 $7.65 $527.91 70 $30 $7.50 $525.06 71 $30 $7.35 $522.12 72 $30 $7.21 $519.09 73 $30 $7.07 $515.98 74 $30 $6.93 $512.79 75 $30 $6.79 $509.53 76 $30 $6.66 $506.20 77 $30 $6.53 $502.80 78 $30 $6.40 $499.35 79 $30 $6.28 $495.83 80 $30 $6.15 $492.26 81 $30 $6.03 $488.64 82 $30 $5.91 $484.98 83 $30 $5.80 $481.27 84 $30 $5.68 $477.51 85 $30 $5.57 $473.72 86 $30 $5.46 $469.90 87 $30 $5.36 $466.04 88 $30 $5.25 $462.16 89 $30 $5.15 $458.24 90 $30 $5.05 $454.31 91 $30 $4.95 $450.35 92 $30 $4.85 $446.37 93 $30 $4.76 $442.37 94 $30 $4.66 $438.36 95 $30 $4.57 $434.34 96 $30 $4.48 $430.30 97 $30 $4.39 $426.26 98 $30 $4.31 $422.21 99 $30 $4.22 $418.16 100 $30 $4.14 $414.10 101 $30 $4.06 $410.04 102 $30 $3.98 $405.98 103 $30 $3.90 $401.92 104 $30 $3.83 $397.87 105 $30 $3.75 $393.82 106 $30 $3.68 $389.77 107 $30 $3.60 $385.73 108 $30 $3.53 $381.70 109 $30 $3.46 $377.68 110 $30 $3.40 $373.68 111 $30 $3.33 $369.68 112 $30 $3.27 $365.70 113 $30 $3.20 $361.73 114 $30 $3.14 $357.77 115 $30 $3.08 $353.83 116 $30 $3.02 $349.91 117 $30 $2.96 $346.01 118 $30 $2.90 $342.12 119 $30 $2.84 $338.26 120 $30 $2.79 $334.41 121 $30 $2.73 $330.59 122 $30 $2.68 $326.78 123 $30 $2.63 $323.00 124 $30 $2.57 $319.24 125 $30 $2.52 $315.51 126 $30 $2.47 $311.80 127 $30 $2.43 $308.11 128 $30 $2.38 $304.45 129 $30 $2.33 $300.81 130 $30 $2.29 $297.20 131 $30 $2.24 $293.61 132 $30 $2.20 $290.05 133 $30 $2.15 $286.52 134 $30 $2.11 $283.01 135 $30 $2.07 $279.53 136 $30 $2.03 $276.08 137 $30 $1.99 $272.66 138 $30 $1.95 $269.26 139 $30 $1.91 $265.90 140 $30 $1.88 $262.56 141 $30 $1.84 $259.25 142 $30 $1.80 $255.97 143 $30 $1.77 $252.72 144 $30 $1.73 $249.49 145 $30 $1.70 $246.30 146 $30 $1.67 $243.14 147 $30 $1.63 $240.00 148 $30 $1.60 $236.90 149 $30 $1.57 $233.82 150 $30 $1.54 $230.77 151 $30 $1.51 $227.76 152 $30 $1.48 $224.77 153 $30 $1.45 $221.81 154 $30 $1.42 $218.88 155 $30 $1.39 $215.99 156 $30 $1.37 $213.12 157 $30 $1.34 $210.28 158 $30 $1.31 $207.47 159 $30 $1.29 $204.69 160 $30 $1.26 $201.94 161 $30 $1.24 $199.21 162 $30 $1.21 $196.52 163 $30 $1.19 $193.86 164 $30 $1.17 $191.22 165 $30 $1.14 $188.62 166 $30 $1.12 $186.04 167 $30 $1.10 $183.49 168 $30 $1.08 $180.97 169 $30 $1.06 $178.48 170 $30 $1.04 $176.01 171 $30 $1.02 $173.58 172 $30 $1.00 $171.17 173 $30 $0.98 $168.79 174 $30 $0.96 $166.43 175 $30 $0.94 $164.11 176 $30 $0.92 $161.81 177 $30 $0.90 $159.54 178 $30 $0.88 $157.29 179 $30 $0.87 $155.08 180 $30 $0.85 $152.88 181 $30 $0.83 $150.72 182 $30 $0.82 $148.58 183 $30 $0.80 $146.47 184 $30 $0.78 $144.38 185 $30 $0.77 $142.32 186 $30 $0.75 $140.28 187 $30 $0.74 $138.27 188 $30 $0.72 $136.28 189 $30 $0.71 $134.32 190 $30 $0.70 $132.39 191 $30 $0.68 $130.47 192 $30 $0.67 $128.58 193 $30 $0.66 $126.72 194 $30 $0.64 $124.88 195 $30 $0.63 $123.06 196 $30 $0.62 $121.27 197 $30 $0.61 $119.50 198 $30 $0.59 $117.75 199 $30 $0.58 $116.02 200 $1,030 $19.62 $3,924.94 Total = $1,490.47 $73,137.13 Modified macaulay duration = 24.535

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