The P/E ratio (price-to-earnings ratio) of a stock is a measure of the price paid for a share relative to the annual net income or profit earned by the firm per share. It is a financial ratio used for valuation. P/E ratio shows current investor demand for a company share. P/E ratio has units of years. P/E is the most popular metric of stock analysis. The reciprocal of the PE ratio is known as the earnings yield.

There are various P/E ratios, all defined as:

P/E ratio =

PRICE PER SHARE ANNUAL EARNINGS PER SHARE

Earnings per share (EPS) are the earnings returned on the initial investment amount. Calculating EPS

EPS(basic formula) EPS= Profit / Weighted average common share EPS(net income formula) EPS= Net Income/Weighted average common share EPS(continuing operations formula) EPS= Income from continuing operations / Weighted average common share

Example: The market price of a share is $30 and earning per share is $5.

Calculation:

Price earnings ratio = 30 / 5 = 6

The P/E ratio can alternatively be calculated by dividing the company's market capitalization by its total annual earnings. For example, if a stock is trading at $24 and the earnings per share for the most recent 12 month period is $3, then stock A has a P/E ratio of 24/3 or 8.

Is derived from the dividend discount model. Constant growth dividend discount model, P = D / r-g Where, D = E(1-b)

=> P = E(1-b) / r-g

=> P/E = (1-b) / r-g

Where, (1-b)= dividend payout ratio b= ploughback ratio r= required rate of return g= expected growth rate Growth rate Internal growth rate, g= RoA * b / 1-(RoA * b ) where, RoA= m * Asset turnover m= net profit margin asset turnover= sales/asset

External growth rate, g= RoE * b / 1-(RoE * b ) Where, RoE= m * assets/equity * asset turnover m= net profit margin asset turnover= sales/asset

P/E ratio & b: an increase in b leads to increase in P/E. P/E ratio & interest rate: an increase in interest rate decreases P/E ratio P/E ratio & risk: Riskier stocks have lower P/E. P/E ratio & liquidity: Highly liquid stocks command higher P/E. Highly illiquid stocks command lower P/E. Others: Size of company: a large company tend to command higher P/E. Reputation of management: High reputed management are likely to command high P/E.

1.The following information are available for ‘A’ corporation Ploughback ratio is 0.7 Required rate of return is 15% The firm enjoys 9% growth rate over a period of 10 years. Calculate the P/E rattio

Solution Given: b=0.7 r=15% g=9%

P/E = (1-b) / r-g

=> P/E = (1- 0.7) / 0.15-0.09 => P/E = 5.

2.The following information is available for ‘B’ corporation Dividend payout ratio is 0.7 Required rate of return is 16% Asset to equity is 2.5 times Asset turnover is 1 time Profit margin is 0.05 Calculate the P/E ratio.

Solution Given: 1-b=0.7, => b=0.3 r=15% asset/equity= 2.5 asset turnover=1 m=0.05 Internal growth, g= RoA * b / 1-(RoA * b ) RoA= m * Asset turnover = 0.05 * 1 = 0.05. g= 0.05*0.3 / 1-(0.05*0.3) = 0.0152.

External growth rate, , g= RoE * b / 1-(RoE * b ) RoE= m * assets/equity * asset turnover = 0.05 * 2.5 * 1 = 0.125. g= 0.125 * 0.3 / 1-(0.125*0.3) = 0.038.

Hence, g= 0.0152+0.038= 0.0532= 5.32%

Now,

P/E = (1-b) / r-g = (1-0.3) / 0.16- 0.0532 = 6.55.

Two stage growth model This model assumes that the extraordinary growth will continue for a finite number of years & thereafter the normal growth rate will prevail indefinitely.

P= EPS(Payout ratio)(1+g)[1-(1+g)n/(1+ke,hg)] + (EPS)(Payout ration)(1+gn)(1+g)n ke,hg – g (k e,st-gn)(1+ke,hg)n

EPS = Earnings per share in year 0 (Current year) g = Growth rate in the first n years ke,hg = Cost of equity in high growth period ke,st = Cost of equity in stable growth period Payout = Payout ratio in the first n years gn = Growth rate after n years forever...