Question

Joker stock has a sustainable growth rate of 9 percent, ROE of 15 percent, and dividends per share of $3.15. If the P/E ratio is 19.7, what is the value of a share of stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Solution:

As per the information given in the question we have:

1. Sustainable growth rate = 9 % ;
2. ROE = 15 % ;
3. Dividends per share = $ 3.15    ;
4. P/E ratio = 19.7

Calculation of Dividend Payout ratio:

We know that

Sustainable growth rate = ROE * (1 - Dividend Payout ratio)

Applying the information available in the formula we have:

9 % = 15 % * ( 1 - Dividend Payout ratio)

9 / 15 = ( 1 - Dividend Payout ratio)

0.6 = ( 1 - Dividend Payout ratio)

Dividend Payout ratio = 1 – 0.6 = 0.4

Thus the Dividend Payout ratio = 0.4          

Calculation of Earnings per share:

We know that

Dividend Payout ratio = Dividend per share / Earnings per share

Applying the information available in the formula we have:

0.4 = $ 3.15 / Earnings per share

Earnings per share = $ 3.15 / 0.4

= $ 7.8750

Thus the Earnings per share = $ 7.8750

Calculation of value of a share of stock:

We know that P/E Ratio = Value of a share or Price per share / Earnings per share

Applying the information available in the formula we have:

19.7 = Value of a share or Price per share / $ 7.8750

Value of a share or Price per share = 19.7 * $ 7.8750

= $ 155.1375

Thus the value of a share of Joker stock = $ 155.1375

=$ 155.14 ( when rounded off to two decimal places )