What's the formula of PE?

Energy Star, a leading renewable energy producer, paid out dividends of $2.4 per share on earnings per share of $4.8 in 2014. The firm is expected to have a return on equity of 25% between 2015 and 2018, after which the firm is expected to have a stable growth rate of 6% a year (the return on equity is expected to drop to 15% in the stable growth phase.) The dividend payout ratio is expected to remain at the current level from 2015 to 2018. Energy Star has a debt to equity ratio of 1.5. We do not have enough information to calculate the historical beta of the stock. However, we know Energy Innovation, another leading company in the renewable energy sector, has the same business structure and operating leverage as Energy Star. Energy Innovation has a cost of equity of 13% and a debt to equity ratio of 1. The marginal tax rates for Energy Star and Energy Innovation are both 30%. The Treasury bond rate is 4%, and the equity risk premium is 6%. (a). What is the current equity beta and cost of equity of Energy Star? (3 mark) First, calculate the equity beta of Energy Innovation: 0.13=0.04+ beta * 0.06. As a result, beta=1.5. (0.5 mark) Then calculate the asset beta of Energy Innovation: (1 mark) Asset beta = 1.5/(1+ (1-0.3) *1) =0.8823 Third, calculate the equity beta of Energy Star: (1 mark) Equity beta = 0.8823* (1+(1-0.3)*1.5)=1.81 Fourth, calculate the cost of equity of Energy Star: (0.5 mark) Cost of equity = 4%+ 1.81* 0.06=14.86% (b). Estimate the P/E ratio for Energy Star in 2014, based upon fundamentals. (3 marks) Payout Ratio = 2.4/4.8= 50% (0.5 mark) In the first 4 years, 50%=1-(g/ROE) = 1-(g/0.25); g= 12.5%; (0.5 mark) After year 4, Payout ratio in year 5 = (1-g/ROE)=1-6%/15%=60% (0.5 mark) 1 PE (1.125)4 0.5 * (1.125) * (1 (1.1486) (0.1486 0.125) 8.513 0.6* (1.125)4 * (1.06) + (0.1486 -0.06) * 1.14864 1.9067 + 6.6063 =