Financial Planning Problems
Problems A.1–A.4 refer to the following table:
A.1. What is the forward rate for year 2 (the forward rate quoted today for an investment that begins in one year and matures in two years)?
A.2. What is the forward rate for year 3 (the forward rate quoted today for an investment that begins in two years and matures in three years)? What can you conclude about forward rates when the yield curve is flat?
When the yield curve is flat (spot rates are equal), the forward rate is equal to the spot rate.
A.3. What is the forward rate for year 5 (the forward rate quoted today for an investment that begins in four years and matures in five years)?
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A.4. Suppose you wanted to lock in an interest rate for an investment that begins in one year and matures in five years. What rate would you obtain if there are no arbitrage opportunities?
A.5. Suppose the yield on a oneyear, zerocoupon bond is 5%. The forward rate for year 2 is 4%, and the forward rate for year 3 is 3%. What is the yield to maturity of a zerocoupon bond that matures in three years?
Lecture Seven  Valuing Stocks
91. Assume Evco, Inc., has a current price of $50 and will pay a $2 dividend in one year, and its equity cost of capital is 15%. What price must you expect it to sell for right after paying the dividend in one year in order to justify its current price?
92. 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?
93. 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 you answer in part (a)?
94. Krell Industries has a share price of $22 today. If Krell is expected to pay a dividend of $0.88 this year, and its stock price is expected to grow to $23.54 at the end of the year, what is Krell’s dividend yield and equity cost of capital?
95. 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?
96. 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%?
97. 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
98. Kenneth Cole Productions (KCP), suspended its dividend at the start of 2009. Suppose you do not expect KCP to resume paying dividends until 2011.You expect KCP’s dividend in 2011 to be $0.40 per year (paid at the end of the year), and you expect it to grow by 5% per year thereafter. If KCP’s equity cost of capital is 11%, what is the value of a share of KCP at the start of 2009?
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99. DFB, Inc., expects earnings this year of $5 per share, and it plans to pay a $3 dividend to shareholders. DFB will retain $2 per share of its earnings to reinvest in new projects with an expected return of 15% per year. Suppose DFB will maintain the same dividend payout rate, retention rate, and return on new investments in the future and will not change its number of outstanding shares.
a. What growth rate of earnings would you forecast for DFB?
b. If DFB’s equity cost of capital is 12%, what price would you estimate for DFB stock?
c. Suppose DFB instead paid a dividend of $4 per share this year and retained only $1 per share in earnings. If DFB maintains this higher payout rate in the future, what stock price would you estimate now? Should DFB raise its dividend?
910. Cooperton Mining just announced it will cut its dividend from $4 to $2.50 per share and use the extra funds to expand. Prior to the announcement, Cooperton’s dividends were expected to grow at a 3% rate, and its share price was $50. With the new expansion, Cooperton’s dividends are expected to grow at a 5% 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?
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911. Gillette Corporation will pay an annual dividend of $0.65 one year from now. Analysts expect this dividend to grow at 12% per year thereafter until the fifth year. After then, growth will level off at 2% per year. According to the dividenddiscount model, what is the value of a share of Gillette stock if the firm’s equity cost of capital is 8%?
912. ColgatePalmolive Company has just paid an annual dividend of $0.96. Analysts are predicting an 11% per year growth rate in earnings over the next five years. After then, Colgate’s earnings are expected to grow at the current industry average of 5.2% per year. If Colgate’s equity cost of capital is 8.5% per year and its dividend payout ratio remains constant, what price does the dividenddiscount model predict Colgate stock should sell for?
913. What is the value of a firm with initial dividend Div, growing for nyears (i.e., until year n+ 1) at rate g_{1} and after that at rate g_{2} forever, when the equity cost of capital is r?
914. Halliford Corporation expects to have earnings this coming year of $3 per share. Halliford plans to retain all of its earnings for the next two years. For the subsequent two years, the firm will retain 50% of its earnings. It will then retain 20% of its earnings from that point onward. Each year, retained earnings will be invested in new projects with an expected return of 25% 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 10%, what price would you estimate for Halliford stock?
915. Suppose Cisco Systems pays no dividends but spent $5 billion on share repurchases last year. If Cisco’s equity cost of capital is 12%, and if the amount spent on repurchases is expected to grow by 8% per year, estimate Cisco’s market capitalization. If Cisco has 6 billion shares outstanding, what stock price does this correspond to?

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Solution: Financial Planning Problems