Problem Set 2 Solutions

# Problem Set 2 Solutions - FI 311H Financial Management...

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FI 311H- Financial Management- Professor Hadlock Problem Set #2 Answer Key Chapter 5 Problems #1. (a) PV = 1,000/ (1.06) 12 = 1,000/2.012 = \$496.97 (b) PV = 1,000/ (1.12) 12 = 1,000 /3.986 = \$256.68 (c) If the bond price equals \$256.68 then we know that 12% is the discount rate that equates this price with the present value. Thus, the answer is 12%. #2. The bond will pay 4% x 1,000 = \$40 every six months. Each of these \$40 payments should be discounted at 5%. There will be 20 such payments, along with the principal repayment at period 20. Using our formulas, the value of the bond is: (\$40/.05) x [1 – (1/(1.05) 20 )] + \$1,000/(1.05) 20 = \$498.49 + \$376.89 = \$875.38 #3. (a) Next year’s dividend (D 1 ) should be \$4 x (1.06) = \$4.24. Thus, the price of the stock given by our constant growth formula should be P = \$4.24/(r-g) = \$4.24/(.12-.06) = \$4.24/.06 = \$70.67. (b) The price in year five should be determined by the dividend one year thereafter (i.e., D 6 ) and the same constant growth formula. Note that D 6 = \$4 x (1.06) 6 = \$5.67 and thus P 5 = D 6 /(.12-06) = \$5.67/.06 = \$94.57 . #4. Dividend in year 1 \$1.00 x 1.12 = \$1.12, present value of 1.12/(1.10) = \$1.018 Dividend in year 2 \$1.12 x 1.12 = \$1.25, present value of 1.25/(1.10) 2 = \$1.037 Dividend in year 3 \$1.25 x 1.12 = \$1.40, present value of 1.40/(1.10) 3 = \$1.055 Dividend in year 4 \$1.40 x 1.12 = \$1.57, present value of 1.57/(1.10) 4 = \$1.075 Dividend in year 5 \$1.57 x 1.05 = \$1.65, grows at a 5% rate thereafter, this stream of dividends can be viewed as a growing perpetuity. Its value as of date 4 will be D 5 /(r-g) = \$1.65/(.10-.05) = \$33.04. Its value as of date 0 will then be \$33.04/(1.10) 4 = \$22.57. Total present value = \$1.018 + \$1.037 + \$1.055 + \$1.075 + \$22.569 = \$26.75

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