Joker stock has a sustainable growth rate of 7 percent, ROE of 10 percent, and dividends per share of $1.20. If the P/E ratio is 15.0, what is the value of a share of stock?

P/E ratio = Market price per share

Earnings per share

15 = Market price per share

$4

Market price per share = 15 x $4 = $60

Growth rate = Retention rate x ROE

0.07 = Retention rate x 0.10

0.07 = Retention rate

0.10

Retention rate = 0.7 = 70%

Dividend pay-out ratio = 100% - 70%

Dividend pay-out ratio = 30%

Earnings per share = 100/30 x $1.20 = $4

Explanation:

In this case, we will apply the formula of price-earnings ratio, which is market price per share divided by earnings per share. The P/E ratio was given while the earnings per share is derived. The market price per share becomes the subject of the formula.

In order to determine the earnings per share, we need to obtain the retention ratio by applying the formula of growth rate. In this case, growth rate and ROE were provided in the question with the exception of retention rate. Thus, the retention rate is made the subject of the formula. Having obtained the retention rate, we will now obtain the dividend payout ratio which is 100% minus retention rate.

Then, we will obtain the earnings per share by dividing 100 by the pay-out ratio multiplied by the dividend per share.