Joker stock has a sustainable growth rate of 9 percent, ROE of 17 percent, and dividends...

Joker stock has a sustainable growth rate of 9 percent, ROE of 17 percent, and dividends per share of $1.55. If the P/E ratio is 15.5, what is the value of a share of stock? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Share of stock $________

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Expert Solution

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=9%
Return of equity or ROE=17%
So, dividend payout ratio=1-9%/17%=1-0.529411765=0.470588235 or 47.06% (Rounded up to 2 decimal places)

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=$1.55
Substituting the values in the above equation we get:
Earnings per share=$1.55/0.470588235=$3.293750002

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=$3.293750002
Given that the P/E ratio=15.5
Price per share =$3.293750002*15.5=$51.05312503 or $51.05 (Rounded up to 2 decimal places)

jeff jeffy answered 1 year ago

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