A Model of the Forward PE Value of savings account Capitalized forward earnings

# A model of the forward pe value of savings account

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A Model of the Forward P/E Value of savings account = Capitalized forward earnings + No extra value Extra value is added if abnormal earnings growth is forecasted The model: Value of equity = Capitalized forward earnings + Extra value for abnormal earnings growth The intrinsic P/E is given by dividing through by Earn 1 6-44 3 4 2 3 2 1 0 1 1 1 E E E E E E AEG AEG AEG Earn V 3 4 2 3 2 1 1 1 E E E E AEG AEG AEG Earn 1 E 0 Earn V
Measuring Abnormal Earnings Growth for Equities: Dell and Nike, 2010 Abnormal earnings growth t (AEG t ) = Cum-dividend earn t - Normal earn t = [Earn t + (ρ E – 1) d t-1 ] – ρ Earn t-1 Dell: Required return = 9% Eps 2009 = \$1.25 Nike: Required return = 9% Eps 2009 = \$3.07 Dell Inc. Nike, Inc. Eps 2010 Dps 2009 Earnings on reinvested 2009 dividends Cum-dividend earnings 2010 Normal earnings from 2009: Dell: 1.25 x 1.09; Nike: 3.07 x 1.09 Abnormal earnings growth (AEG) 2010 \$0.00 \$0.73 \$0.00 0.73 1.363 -\$0.633 \$0.98 \$3.93 0.088 4.018 3.346 \$0.672 6-45 0.98*0.09
Cum-dividend Earnings Growth Rate Cum-dividend earnings growth rate (plus one): Note: This is not 6-46 1 t t t Earnings earnings dividend Cum G 1 t t earnings dividend Cum earnings divided Cum
Alternative Calculation of AEG Abnormal earnings growth t = [G t – ρ E ] x Earnings t-1 Where G t = Cum-dividend earnings growth rate (plus one) For Nike: G 2010 = 4.018/3.07 = 1.3088 (a 30.88% growth rate) AEG 2010 = [1.3088 – 1.09] x 3.07 = \$0.672 6-47 (Cum-dividend earnings 2010 / EPS 2009)
Steps in Applying the Model 1. Forecast earnings and dividends up to a forecast horizon. 2. Calculate AEG after the forward year from the forecasts of earnings and dividends. 3. Discount the AEG to present value at the end of the forward year. 4. Calculate a continuing value at the forecast horizon. 5. Discount the continuing value to present value at the end of the forward year. 6. Add 3, 5, and forward earnings 7. Capitalize this total at the required rate of return. 6-48 ) ( 1 1 1 1 3 4 2 3 2 1 0 g AEG AEG AEG AEG Earn V T T E E E E E
Applying the Model: A Simple Example and a Simple Model Forecast for a firm with expected earnings growth of 3 percent per year (in dollars). Required return is 10% per year. Residual earnings valuation: AEG valuation: 6-49 Normal Earnings = Earnings * 0.10 (Required rate of Return) = 12.36*(1+0.1) = 13.596 Cum Dividend Earning Growth 2002 = (13.667/12.36) -1 71 . 133 03 . 1 10 . 1 36 . 2 100 V E 2000 71 . 133 03 . 1 10 . 1 071 . 0 36 . 12 10 . 0 1 2000 E V
A Case 1 Valuation: General Electric Required return is 10% In this case, abnormal earnings growth is expected to be zero after 2004 Same as residual earnings valuation 6-50 13.07 0.017 1.29 10 0 1 V 1999 . E
A Case 2 Valuation: Nike, Inc. Required return is 9% In this case, abnormal earnings growth is expected to grow at a 4.5 percent rate after 2012 Same as residual earnings valuation 6-51 * 1.045 18 . 53 495 . 1 332 . 0 96 . 2 09 . 0 1 2006 E V
Converting Analysts’ Forecasts to a Valuation: Google Inc., 2010 Price, early 2011 = \$ 624 Required return = 11% Consensus eps forecasts: 2011 \$ 33.83 2012 \$ 39.47 5-year growth rate forecasted = 17.4% 6-52
Abnormal Earnings Growth is Equal to the Change in Residual Earnings AEG t = [ earn t + (ρ E – 1)d t-1 ] - ρ E earn t-1 By the stocks and flows equation for accounting for the book value of equity (Chapter 2), B t-1 = B t-2 + earn t-1 d t-1 , so earn t-1 – d

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