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ECON 310: Problem Set #3 Please submit through Canvas Due Date: October 23, 2020 For all of the questions in this problem set, amume there is no tax at all. Stocks Consider stock A with a dividend yield equal to 2.5% (based on its dividend payments over the past year). The dividends are expected to grow at 8% per year. Stock A is currently traded at $52 per share. 1. According to Gordon's model, what would be the expected return on the stock? Answer: The Gordon's model states that 1+9 P = DI TE - 9 Rearrange the terms we get Pi(1+g) +9 = 2.5% . (1 +8%) + 8% = 10.7%% 2. Suppose the total dividends paid over the next year is $1.4 per share, leading to a downward revision of the expected dividend growth rate to 7.5%%, Assume the expected rate of return remains the same for this stock, what would be the actual rate of return from holding this stock over the next year? Answer: The price of stock A a year from now, according to Gordon's model, is 1+4 -14- 1+7.5% 10.7% -7:5%% =$47.03/share The rate of return is Rut - De + An -A 14+ 47.03-52 52 =-6.87% 3. Consider stock B which just paid $6 in dividends over the past year. The expected return on the stock is 12.5% and the stock is currently traded at $120 per share. At what rate are the dividends expected to grow for this stock according to Gordon's model? Answer: Again, starting with the Gordon's model 1+9 PEDITE - 9 and rearrange the terms we have Pi(TE - 9) = Di(1+ 9)DFB, Inc. expects earnings next year of $5.00 per share, and it plans to pay a $3.00 dividend to shareholders (assume that is one year from now). DFB will retain $2.00 per share of its earnings to reinvest in new projects that have an expected return of 15.0%% 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. Assume next dividend is due in one year. a. What growth rate of earnings would you forecast for DFB? b. If OFB's equity cost of capital is 12.0%, what price would you estimate for DFB stock? c. Suppose Instead that DFB paid a dividend of $4.00 per share at the end of this year and retained only $1.00 per share in earnings. That is, it chose to pay a higher dividend instead of reinvesting in as many new projects. If DFB maintains this higher payout rate in the future, what stock price would you estimate for the firm now? Should DFB raise its dividend? a. What growth rate of earnings would you forecast for DFB? DFB's growth rate of eamings is |%. (Round to one decimal place.) b. If DFB's equity cost of capital is 12.0%, what price would you estimate for DFB stock? If OFB's equity cost of capital is 12.0%, then DFB's stock price will be $. (Round to the nearest cent) c. Suppose instead that DFB paid a dividend of $4.00 per share at the end of this year and retained only $1.00 per share in earnings. That is, it chose to pay a higher dividend instead of reinvesting in as many new projects. If DFB maintains this higher payout rate in the future, what stock price would you estimate for the firm now? If DFB paid a dividend of $4.00 per share next year and retained only $1.00 per share in earnings, then OFB's stock price would be $ . (Round to the nearest cent.) Should DFB raise its dividend? (Select the best choice below.) O A. Yes, DFB should raise dividends because, according to the dividend-discount model, doing so will always improve the share price. Q B. No. DFB should not raise dividends because the projects are positive NPV. O C. Yes, DFB should raise dividends because the return on now investments is lower than the cost of capital. D. No, DFB should not raise dividends because companies should always reinvest as much as possible, Click to select your answer(s).Q4. Use the semiannually compounded yield curve in the following table to price some xed income securities: Maturity T Yield r2 (0, T) 0-50 (a) 1.5year zero coupon bond (b) 2-year coupon bond paying 15% semiannually (d) 15year coupon bond paying 9% annually (e) 2-year oating rate bond with zero spread and semiannual payments (1") 15-year oating rate bond with zero spread and annual payments. For this question, assume r1 (0.5,0.5) = 6%. (h) 1.5-year oating rate bond with 40 basis point spread with annual payments. For this question, assume T1 (0.5, 0.5) = 6%. 3. Forward rate. Suppose the following spot rates are available: 5.0% for one year, 6.0% for two years, 6.5% for three years, and 7.0% for four years. Suppose you want to borrow $20 million for two year, starting one years from today, what would be a fair rate for the forward contract? 4. Dividend discount model. The common stock of XYZ is selling for $17.00. The firm pays dividends that are expected to grow at a rate of 3.60% indefinitely. (a) If the current dividend is $1/share, what is the implied required rate of return of XYZ's equity? (b) If the expected next year dividend is $1/share, what is the implied required rate of return of XYZ's equity? (c) What do you estimate the price of XYZ stock to be after 10 years (at t = 10)? 5. Growth opportunities. The firm XYZ has projected earnings per share (EPS) for the next three years as listed in the following table. The firm plan to payout a fraction of EPS as dividend, with the payout ratio listed in the table. Starting from year 4, the firm will maintain a constant payout ratio of 80%. Suppose the firm XYZ's return on equity is 15%, and the required rate of return is 10%. Year 1 2 3 4 EPS/$ 2.1 3.5 5.0 ? Grow at 9 =7% Payout ratio 20% 40% 60% 80% Constant 80% Dividend ? ? ? Grow at g =7% (a) What are the expected dividend payments in the first three years? (b) What is the expected EPS and expected dividend in year 4? (c) What is the growth rate of expected dividend after year 4? (d) What is your estimation of current stock price using DDM