Solutions-Chapter9

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Anle Corporation has a current price of $20, is expected to pay a dividend of $1 in one year, and its expected price right after paying that dividend is $22.
a. What is Anle’s expected dividend yield?
b. What is Anle’s expected capital gain rate?
c. What is Anle’s equity cost of capital?
a. Divyld=1/20=5%
b. Cap gain rate = (22 – 20)/20 = 10%
c. Equity cost of capital = 5% + 10% = 15%
9-3. Suppose Acap Corporation will pay a dividend of $2.80 per share at the end of this year and $3 per share next year. You expect Acap’s stock price to be $52 in two years. If Acap’s equity cost of capital is 10%:
a. What price would you be willing to pay for a share of Acap stock today, if you planned to hold the stock for two years?
b. Suppose instead you plan to hold the stock for one year. What price would you expect to be able to sell a share of Acap stock for in one year?
c. Given your answer in part (b), what price would you be willing to pay for a share of Acap stock today, if you planned to hold the stock for one year? How does this compare to your answer in part (a)?
a. P0 = 2.80 / 1.10 + (3.00 + 52.00) / 1.102 = $48.00
b. P1 = (3.00 + 52.00) / 1.10 = $50.00
c. P0 = (2.80 + 50.00) / 1.10 = $48.00
9-5. NoGrowth Corporation currently pays a dividend of $2 per year, and it will continue to pay this dividend forever. What is the price per share if its equity cost of capital is 15% per year?
With the simplifying assumption (as was made in the chapter) that dividends are paid at the end of the year, then the stock pays a total of $2.00 in dividends per year. Valuing this dividend as a perpetuity, we have, P 􏰃 $2.00 / 0.15 􏰃 $13.33 .
9-6. Summit Systems will pay a dividend of $1.50 this year. If you expect Summit’s dividend to grow by 6% per year, what is its price per share if its equity cost of capital is 11%?
P = 1.50 / (11% – 6%) = $30
9-7. Dorpac Corporation has a dividend yield of 1.5%. Dorpac’s equity cost of capital is 8%, and its dividends are expected to grow at a constant rate.
a. What is the expected growth rate of Dorpac’s dividends?
b. What is the expected growth rate of Dorpac’s share price?
a. Eq9.7(intheeText)impliesrE =DivYld+g,so8%–1.5%=g=6.5%.
b. With constant dividend growth, share price is also expected to grow at rate g = 6.5% (or we can solve this from Eq 9.2).
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 [at (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
9-12. Proctor and Gamble paid an annual dividend of $1.72 in 2009. You expect P&G to increase its dividends by 8% per year for the next five years (through 2014), and thereafter by 3% per year. If the appropriate equity cost of capital for Proctor and Gamble is 8% per year, use the dividend- discount model to estimate its value per share at the end of 2009.