Financial Economics ECON 136
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This 2 page Class Notes was uploaded by Dr. Janiya Bernier on Thursday October 22, 2015. The Class Notes belongs to ECON 136 at University of California - Berkeley taught by Staff in Fall. Since its upload, it has received 19 views. For similar materials see /class/226716/econ-136-university-of-california-berkeley in Economcs at University of California - Berkeley.
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Date Created: 10/22/15
Econ 136 Section Notes VII Eguig Valuation Oct 8 2008 Rachita Gullapalli I EQUITY VALUATION MODELS Dividend Discount Model This says that the price of a stock today is the present value of its future dividend payments Similar to price of bon Pt HEm DHi1R39 I Gordon Growth Model Assumes that dividends grow at a constant rate G and the discount rate remains constant R Thus DH1Dt1G and with this assumption the dividend discount model reduces to PE DMRG Some De nitions For now all assume 100 equity financing of the firm meaning the firm has no debt Return on Equity ROE Amount of money earned on each dollar invested in the firm Earnings E 7 Total amount of money earned on the total amount of money invested in the firm Retention ratio or Plowback Ratio B 7 amount of money reinvested in the company for each dollar earned39 Earnings growth rate GROEB in steady state 0 Dt 1BEt Dt also has growth rate of GROEB in steady state 0 Plugging these definitions into the Gordon Growth Model produces the more detailed formula Pt 1BEmR CROEB o EH1 Kt ROE K is firm s capital stock 0 KHI Kt EH1B Kt 1ROEB Present value of growth opportunities PVGO PVGO tells us how much value the company s management is creating by reinvesting some of its earnings as opposed to paying more out as dividends When ROE gt R PVGO gt 0 When ROER PVGO 0 When ROE lt R PVGO lt 0 Pt PV of Earnings from Today s Assets PVGOt PVGOt Pt PV of Earnings from Today s Assets PVGO D E E m 39 Em R R R OEB R 11 EXAMPLES 1 Similar to PS4 2006 Consider company CBA whose stock pays an initial dividend per share next year of 100 and has expected dividend growth rate of 6 per year when the discount rate is 8 per year a What is the price of a share of CBA 100 08 06 35 000 b If expected dividend growth falls to 4 what would happen to the share price 100 08 04 32 500 c Now go back to the assumption of 6 dividend growth CBA has the expected dividend growth of 6 because its return on equity is 10 and management retains threefifths of earnings What is the earnings per share of CBA next period What is the present value of growth opportunities per share of CBA EM DMIB 100I6250 PVGO 100 0806 7 250105531375 e Would you advise the firm to retain a smaller or larger fraction of its earnings Note thatPVGOgt0 ROEgtR Every reinvested in the rm earns a higher return ROE than alternative investments with similar risk This implies that shareholder value is higher through reinvestment in the rm So to increase shareholder value I would advise the rm to retain more ofits earnings i e raise B Can B be increased to I note that in this model when E I P 0 Also when R lt ROE B Plt0 indicating that the Gordon Growth Model doesn t apply As G ROE 3 increases and gets closer and closer to 8 share price approaches in nity 2 Imagine that you have a technology company with current earnings per share of 55 The company reinvests all of these earnings into its own capital and with this reinvestment the company has capital 39875 per share This company s ROE for the next 10 years is 16 and it retains all earnings for the next 10 years Suppose that after these 10 years ROE falls to 10 and the company starts to pay out all dividends starting year 11 The annual discount rate is 10 Our goal is to value this company a If the price of one share of this company in year 10 is P10 what is the price today ie express P0 using P10 Pg PmIIm b What is the rate of earnings growth during the first ten years of the company Express E10 as a function oon and ROE 16 Calculate E10 G ROEB 16I I6 EmEgIG1 55 1161 242 63 c What is the rate of capital growth during the first ten years of the company Express K10 as a function of K0 and ROE 16 Calculate K10 G ROEB 16I 16 Km Kg 1Gm398 75 1161 1 75906 d Calculate E11 keeping in mind that ROE falls to 10 after year 10 Hint use K10 in your calculation E11 K10ROE 1759061 17591 e Calculate D11 using the fact that the company pays out all earnings starting year 11 Given that all earnings are paid out what is the growth rate of dividends from year 11 on D11E11 17591 G ROEBI0 0 f Calculate P10 the price in period 10 using the magical Gordon growth formula recall you need to use dividends a period ahead in the Gordon model Pm DuRG 3175911 1 75906 g Calculate Po the stock price today Pg Pimp 175906111 67819 g What is the dividendprice ratio in period 10 DuPm RiG 0170 01 The expected dividend payment per share next year is 10 of today s share price
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