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6-17. What is the price today of a two-year, default-free security with a face value of $1000 and an annual coupon rate of 6%? Does this bond trade at a discount, at par, or at a premium? P 60 60 1000 $1, 018.81 (1 0.046) (1 0.05)2 This bond trades at a premium. The coupon of the bond is greater than each of the zero-coupon yields, so the coupon will also be greater than the yield to maturity on this bond. Therefore, it trades at a premium 6-23. Prices of zero-coupon, default-free securities with face values of $1000 are summarized in the following table: Suppose you observe that a three-year, default-free security with an annual coupon rate of 10% and a face value of $1000 has a price today of $1183.95. Is there an arbitrage opportunity? If so, show specifically how you would take advantage of this opportunity. If not, why not? First, figure out if the price of the coupon bond is consistent with the zero-coupon yields implied by the other securities. 972.14 1,000 (1 YTM1 )1 YTM1 2.87% 939.62 1,000 (1 YTM 2 )2 YTM 3 3.16% 906.24 1, 000 (1 YTM 3 )3 YTM 3 3.34% According to these zero-coupon yields, the price of the coupon bond should be: P 100 100 100 1, 000 $1,188.04. 2 (1 0.0287) (1 0.0316) (1 0.0334)3 The price of the coupon bond is too low, so there is an arbitrage opportunity. To take advantage of it: Buy 10 Coupon Bonds Short Sell 1 One-Year Zero Short Sell 1 Two-Year Zero Short Sell 11 Three-Year Zeros Net Cash Flow Today –11839.50 +972.14 +939.62 +9968.64 40.90 1 Year +1000 –1000 2 Years +1000 3 Years +11,000 –1000 0 0 –11,000 0 9-6. Summit Systems will pay a dividend of $1.46 this year. If you expect Summit’s dividend to grow by 5.1% per year, what is its price per share if its equity cost of capital is 11.2%? P = 1.46 / (11.2% – 5.1%) = $23.93 9-8. Canadian-based mining company El Dorado Gold (EGO) suspended its dividend in March 2016 as a result of declining gold prices and delays in obtaining permits for its mines in Greece. Suppose you expect EGO to resume paying annual dividends in two years time, with a dividend of $0.25 per share, growing by 2% per year. If EGO’s equity cost of capital is 10%, what is the value of a share of EGO today? The price in one year is P(t+1) = Div(t+2)/(r – g) = 0.25/(.10 – .02) = $3.125 The price today is P(t) = P(t+1)/(1+r) = $3.125/1.1 = $2.84 9-11. Cooperton Mining just announced it will cut its dividend from $4.07 to $2.47 per share and use the extra funds to expand. Prior to the announcement, Cooperton’s dividends were expected to grow at a 2.8% rate, and its share price was $50.31. With the new expansion, Cooperton’s dividends are expected to grow at a 4.9% rate. What share price would you expect after the announcement? (Assume Cooperton’s risk is unchanged by the new expansion.) Is the expansion a positive NPV investment? Estimate rE: rE = Div Yield + g = 4.07 / 50.31 + 2.8% = 10.89% New Price: P = 2.47/(10.89% – 4.9%) = $41.24 In this case, cutting the dividend to expand is not a positive NPV investment. 9-15. Halliford Corporation expects to have earnings this coming year of $2.77 per share. Halliford plans to retain all of its earnings for the next two years. For the subsequent two years, the firm will retain 48% of its earnings. It will then retain 19% of its earnings from that point onward. Each year, retained earnings will be invested in new projects with an expected return of 27.21% per year. Any earnings that are not retained will be paid out as dividends. Assume Halliford’s share count remains constant and all earnings growth comes from the investment of retained earnings. If Halliford’s equity cost of capital is 9.5%, what price would you estimate for Halliford stock? See the spreadsheet for Halliford’s dividend forecast (g = retention rate × return on new investment): Year Earnings 1 EPS Growth Rate (vs. prior yr) 2 EPS Dividends 3 Retention Ratio 4 Dividend Payout Ratio 5 Div (2 × 4) 0 1 2 3 4 5 6 27% 27% 13% 13% 5% $2.77 $3.52 $4.48 $5.07 $5.73 $6.03 100% 100% 48% 48% 19% 19% 0% 0% 52% 52% 81% 81% $0.00 $0.00 $2.33 $2.64 $4.64 $4.88 From year 5 on, dividends grow at constant rate of 5%. Therefore, P(5) = 4.88/(9.5% – 5%) = $108.54 Then P(0) = 2.33 / 1.0953 + 2.64 / 1.0954 + (4.64+108.54) / 1.0955= $75.51 9-19. Heavy Metal Corporation is expected to generate the following free cash flows over the next five years: After then, the free cash flows are expected to grow at the industry average of 4.3% per year. Using the discounted free cash flow model and a weighted average cost of capital of 14.4%: a. Estimate the enterprise value of Heavy Metal. b. If Heavy Metal has no excess cash, debt of $280 million, and 35 million shares outstanding, estimate its share price. a. V(4) = 82.7 / (14.4% – 4.3%) = $818.81 V(0) = 51.3 / 1.144 + 69.7 / 1.144 2 + 79.5 / 1.1443 + (74.3 + 818.81) / 1.1444 = $672.64 b. 9-27. P = (V + C – D)/N = (672.64 + 0 – 280)/35 = $11.22 In addition to footwear, Kenneth Cole Productions designs and sells handbags, apparel, and other accessories. You decide, therefore, to consider comparables for KCP outside the footwear industry. a. Suppose that Fossil, Inc., has an enterprise value to EBITDA multiple of 11.08 and a P/E multiple of 17.09. What share price would you estimate for KCP using each of these multiples, based on the data for KCP in Problems 25 and 26? b. Suppose that Tommy Hilfiger Corporation has an enterprise value to EBITDA multiple of 7.07 and a P/E multiple of 17.36. What share price would you estimate for KCP using each of these multiples, based on the data for KCP in Problems 25 and 26? a. Using EV/EBITDA: EV = 51.3 × 11.08 = 568.4 million, P = (568.4 + 107 – 3.3) / 23 = $29.22 Using P/E: P = 1.67 × 17.09 = $28.54 b. Using EV/EBITDA: EV = 51.3 × 7.19 = 368.85 million, P = (368.85 + 107 – 3.3) / 23 = $20.55 Using P/E: P = 1.67 × 17.36 = $28.99.