Finance Exercises 5 - Valuing the Firm and Stocks - LBS, Solutions, Exercises of Finance

Download Finance Exercises 5 - Valuing the Firm and Stocks - LBS, Solutions and more Exercises Finance in PDF only on Docsity! Session 5: Valuing the Firm Read: Chapter 9: Valuing Stocks 1. Consider the following three stocks: a. Stock A is expected to provide a dividend of $10 a share forever. b. Stock B is expected to pay a dividend of $5 at the end of first year. Thereafter, dividend growth is expected to be 4 percent a year forever. c. Stock C is expected to pay a dividend of $5 at the end of first year. Thereafter, dividend growth is expected to be 20 percent a year for 5 years (i.e. until the end of year 5) and zero thereafter. If the market capitalization rate for each stock is 10 percent, which stock is the most valuable? What if the capitalization rate is 7 percent? Solution a. . $100.00 0.10 $10 r DIVP 1A  $83.33 .0400.10 $5 gr DIVP 1B     b.        6 7 6 6 5 5 4 4 3 3 2 2 1 1 C 1.10 1 0.10 DIV 1.10 DIV 1.10 DIV 1.10 DIV 1.10 DIV 1.10 DIV 1.10 DIVP c. $104.50 1.10 1 0.10 12.44 1.10 12.44 1.10 10.37 1.10 8.64 1.10 7.20 1.10 6.00 1.10 5.00P 6654321C       At a capitalization rate of 10 percent, Stock C is the most valuable. For a capitalization rate of 7 percent, the calculations are similar. The results are: PA = $142.86 PB = $166.67 PC = $156.48 Therefore, Stock B is the most valuable. 2. Crecimiento s.a. currently plows back 30 percent of its earnings and earns a return of 25 percent on this investment. The dividend yield on the stock is 5 percent. a. Assuming that Crecimiento can continue to plow back this proportion of earnings and earn a return of 25 percent on the investment, how rapidly will earnings and dividends grow? What is the expected return on Crecimiento stock? b. Suppose that management suddenly announces that future investment opportunities have dried up. Now Crecimiento intends to pay out all its earnings. How will the stock price change? c. Suppose that management simply announces that the expected return on new investment will in the future be the same as the cost of capital. Now what is Crecimiento’s stock price? Solution a. We know that g, the growth rate of dividends and earnings, is given by: g = plowback ratio  ROE = 0.30  0.25 = 0.075 = 7.5% We know that: r = (DIV1/P0) + g = dividend yield + growth rate Therefore: r = 0.05 + 0.075 = 0.125 = 12.5% b. Dividend yield = 5%. Therefore: DIV1/P0 = 0.05 DIV1 = 0.05  P0 A plowback ratio of 0.3 implies a payout ratio of 0.7, and hence: DIV1/EPS1 = 0.7 DIV1 = 0.7  EPS1 Equating these two expressions for DIV1 gives a relationship between price and earnings per share: 0.05  P0 = 0.7  EPS1 P0/EPS1 = 14 Also, we know that:        00 1 P PVGO1r P EPS With (P0/EPS1) = 14 and r = 0.125, the ratio of the present value of growth opportunities to price is 42.86 percent. Thus, if there are suddenly no future investments opportunities, the stock price will decrease by 42.86 percent. c. In Part (b), all future investment opportunities are assumed to have a net present value of zero. If all future investment opportunities have a rate of return equal to the capitalization rate, this is equivalent to the statement that the net present value of these investment opportunities is zero. Hence, the impact on share price is the same as in Part (b). 3. Year 1 2 3 4 Book equity 10.00 Earnings per share, EPS Return on equity, ROE .25 .25 .16 .16 Payout ratio .20 .20 .50 .50 Dividends per share Growth rate of dividends - a. Complete the table above. b. Assume that the opportunity cost of capital is 12%. Calculate the value of the company’s stock. c. What part of that value reflects the discounted value of P3, the price forecasted for year 3? d. What part of P3 reflects the present value of growth opportunities (PVGO) after year 3?