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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#5. Growth rate g = retention ratio x ROE = .50 x .12 = 6.0% Next year earnings = $40 million x 1.06 = $42.40 million #6. g = retention ratio x ROE = 0.75 x 0.12 = 0.09 = 9% Current Dividend per share = $20 million (1 - 0.75) / 1.25 million = $4 Next year’s expected dividend = $4 x (1 + g) = $4 x 1.09 = $4.36 (a) r = D 1 /P 0 + g = $4.36/$60 + 0.09 = 0.1627 =
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Problem Set 2 Solutions - FI 311H- Financial Management-...

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