Question

Joker stock has a sustainable growth rate of 7 percent, ROE of 16 percent, and dividends...

Joker stock has a sustainable growth rate of 7 percent, ROE of 16 percent, and dividends per share of $3.40. If the P/E ratio is 19.7, what is the value of a share of stock? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)

  Share of stock $ __________
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Answer #1

Sustainable growth rate is calculated as ROE*(1-dividend payout ratio)
=>1-Dividend payout ratio=Sustainable growth rate/ROE
=>Dividend payout ratio=1-Sustainable growth rate/ROE
Given that,
Sustainable growth rate=7%
Return of equity or ROE=16%
So, dividend payout ratio=1-7%/16%=1-0.4375=0.5625 or 56.25%


Now, dividend payout ratio is equal to dividend per share/earnings per share.
=>Earnings per share = Dividend per share / Dividend payout ratio
Given that, dividends per share=$3.40
Substituting the values in the above equation we get:
Earnings per share=$3.40/0.5625=$6.044444444

Price to earnings ratio (PE ratio) is calculated as (price per share)/(earnings per share).
=>Price per share = earnings per share * PE ratio
Earnings per share=$6.044444444
Given that the P/E ratio=19.7
Price per share =$6.044444444*19.7=$119.0755555 or $119.08 (Rounded up to 2 decimal places)

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