Solution to Practice Problems for the Midterm Examination

Solution to Practice Problems for the Midterm Examination -...

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S OLUTION TO P RACTICE P ROBLEMS FOR THE M IDTERM 1. Given r 1 = 0.25%, r 2 = 0.5%, r 3 = 1%, and r 4 = 1.1%, the price of a 4-year 3 7/16% coupon bond is P 0 = $3.4375/1.0025 + $3.4375/1.005 2 + $3.4375/1.01 3 + $103.4375/1.011 4 = $109.1774. 2 (i). Given that y, the yield to maturity on a 25-year 3.75% bond is 7.5%, we can work out its price as P 0 = $3.75*AF(7.5%, 25) + $100 = $58.19895. 2 (ii). The value of your investment at t=25 is $58.19895*1.075 25 = $354.91698. 2 (iii). The profit you make is $354.91698 – $58.19895 = $296.71803. 2 (iv). The amount you earned as coupons is 25*$3.75 = $93.75. It forms $93.75/$296.71803 = 31.59565% of the total profit. 2 (v). The amount you earned as capital gains is $100 – $58.19895 = $41.80105. It forms
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Unformatted text preview: $41.80105/$296.71803 = 14.087802% of the total profit. 2 (vi). The amount you earned as reinvestment income is $296.71803 $93.75 $41.80105 = $161.16698. It forms $161.16698/$296.71803 = 54.316545% of the total profit. 3 (i). Given that D 1 = $2, r = 13.5% = 0.135, and g = 9.5% = 0.095, we can work out that P = $2/(0.135 0.095) = $50. 3 (ii). Given that P = $100, D 1 = $4, and r = 0.15, we can work out that g = r D 1 /P = 0.15 $4/$100 = 0.11 = 11%. 3 (iii). Given that P = $120, r = 20% = 0.2,and g = 16% = 0.16, we can work out that D 1 = P *(r g) = $120*(0.2 0.16) = $4.80....
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This note was uploaded on 07/27/2011 for the course BUS 106 taught by Professor Li,c. during the Winter '08 term at UC Riverside.

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