 In modern day corporate world, significant discussion on stock price valuation concentrates on price earning multiples or the price earning ratio. Now this price earning ratio is the ratio between a stock's market price and the company's earning per share. Let's see why financial analysts focus more on price earning multiples. Let's see the relationship between price earning and the growth opportunities. The price earning multiple is a useful indicator of expectations of growth opportunities. Let's see how. We have price earning ratio of Firm A and Firm B. For Firm A it is a times and Firm B it is 11.4 times. So apparently Firm B have more growth opportunities than the Firm A. We know that the price is equal to value of the firm with no growth opportunities plus the present value of growth opportunities. If we put the value, quantify this equation we can see that P0 is equal to 1 plus K 1 over K plus present value of growth opportunities. If we rearrange this equation, we get present price earning ratio to reflect growth opportunities. Now we see the model which is that the price earning ratio is equal to 1 over K into 1 plus present value of growth opportunities over E divided by K. Now this equation shows the relationship between growth opportunities of the firm and its assets in place. A high price earning multiple indicates ample growth opportunities for the firm and price earning multiples vary with growth prospects. Price earning multiples reflect the market's expectations on the firm's growth prospects. Analysts decision must not be subject to the market multiples in buying recommendations to their clients. Now what these insights can be quantified? Let's see. We have constant growth dividend discount model formula which says that P0 is equal to D1 over K divided by G. K minus G. If dividend equals earnings then D1 is equal to E1 into 1 minus B which is a flowing back ratio. D1 is equal to E1. In this particular case where dividend is equal to earnings, B is equal to 0, D1 is equal to E1. Dividend and earnings are equal to each other. We also know that growth rate or G is equal to return on equity R or E multiplied by P. So we can substitute these for the D1 and G, we will get P0 is equal to E1 into 1 minus B over K minus R oE into B. So our D1 is replaced with E1 into 1 minus B and our G is replaced with R oE into B. So we implying the price earning ratio, we can say that P0 over E1 or price earning ratio is equal to 1 minus B over K minus R oE multiplied by B. We see that price earning ratio increases with R oE because higher R oE projects give a firm good growth opportunities. Price earning ratio also increases for higher B as long as the return on equity exceeds K. So if return on equity is greater than K then the price earning ratio will be higher than the flowing bag ratio. When R oE is less than K the investors don't like retention, the firm value will be fall and the flowing bag will be on decline. When E expected return on equity is greater than K the firm will be offering pretty reinvestment opportunities to its owners, firm value will be increased owing to the increased flowing bag of the earnings. And where the return on equity is equal to the cost of capital or the K then the firm offers its break even reinvestment opportunities both inside and outside the firm to its shareholders. This means that there will be no change in the firm's stock price and it will remain unaffected. So conclusion here is that higher flowing bag may yield higher growth rate but higher flowing bag may not yield higher flowing price earning ratio for the firm. So now see what is the relationship between price earning and the growth rates? There is a Wall Street rule of thumb that says that growth rate ought to be roughly equal to price earning ratio. This means that price earning to growth or known as peg ratio should be equal to 1. Now how it is equal to 1? Let's see we have RF or risk rate of 8% market return of 6% flowing bag or B of 40% beta of the firm equal to 1 and K is equal to we assume that K is equal to return on equity of the firm which is equal to 16%. So computing the value of G we have G equal to 6.4% and when we put these values to determine the price earning multiples we have an amount equal to 6.26%. So we see that our growth rate is 6.4 whereas our price earning ratio is equal to 6.23 a 6.26 or 6.3 which is nearest to the growth rate. So price earning ratio in this case equals the growth rate that we have computed using our assumptions. But remember that this rule of thumb may not work under certain cases. For that purpose let's say another example now assume that long term T bonds have yield of 2.5% and we assume that K is equal to ROE which is equal to risk pre rate plus market risk premium and that comes to in total of 10.5%. So our G will be equal to 4.2% and putting these values into our price earning model the value come to 9.5%. So we have growth of 4.2% and the price earning multiple of 9.5 times this means that price earning ratio and G are now diverging and the peg ratio is 2.3 that we have determined by dividing the price earning over the growth rate. So this means that while valuing a company primarily through the growth opportunities such type of values can be very sensitive to the reassessment of the growth prospects. Now see the relationship between price earning ratios and the stock riskiness remember that high risk firm will have lower price earning ratio holding all else equal. This means that P0 over P1 or the price earning multiple is equal to 1 minus B over K minus ROE into B. The resulting value is equal to 1 minus B over K minus G here G is replaced with ROE into B. This shows that riskier firm will have higher K the price earning multiple will be lower because the value of the K goes higher the price earning multiple due to this high value will go down. So due to this the lower present value of the expected earnings and the expected dividends for the riskier firm will be there and ultimately the current stock price of such firm and the price earning ratio will also be lower. But there is an exception and that says that a small and risky startup company may have very price earning multiples due to higher growth opportunities and market expectations of this higher growth opportunities during their earlier phase.