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The common stock of Perforated Pool Liners, Inc. now sells for $50.00 per share. The table below shows the anticipated stock price and the dividend to be paid one year from now. Both the price and the dividend will depend on the level of growth experienced by the firm.
State Probability, p(s) End-of-Year Price Annual Dividend
Super high growth 0.095 $62 $3
High growth 0.188 $60 $3
Normal growth 0.401 $56 $2
Low growth 0.207 $51 $2
No growth 0.109 $46 $0
a. Calculate the holding period return (HPR) for each of the possible states, assuming a one-year holding period. (Use a negative sign to indicate a negative answer. Round your answer to 2 decimal places.)

Super high growth %
High growth %
Normal growth %
Low growth %
No growth %
b. What is the expected return for a holder of Perforated Pool Liners stock? (Round your answer to 2 decimal places.)
Expected HPR              %
c. What is the standard deviation of the returns? (Round your answer to 2 decimal places.)
Standard deviation              %

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Answer #1
State Probability Current Price End Price Dividend HPR
p(s) P0 P1 D (P1 + D - P0) / P0
Super High 0.095 50 62 3 30.00%
High 0.188 50 60 3 26.00%
Normal 0.401 50 56 2 16.00%
Low 0.207 50 51 2 6.00%
No 0.109 50 46 0 -8.00%

a. Calculate the holding period return (HPR) for each of the possible states, assuming a one-year holding period. (Use a negative sign to indicate a negative answer. Round your answer to 2 decimal places.)

Super high growth 30.00%
High growth 26.00%
Normal growth 16.00%
Low growth 6.00%
No growth -8.00%

b. What is the expected return for a holder of Perforated Pool Liners stock? (Round your answer to 2 decimal places.)
Expected HPR = Sum (Probability x HPR) over all states = 0.095 x 30% + 0.188 x 26% + 0.401 x 16% + 0.207 x 6% + 0.109 x (-8%) = 14.52%


c. What is the standard deviation of the returns? (Round your answer to 2 decimal places.)
Variance = Sum [Probability x (HPR - Expected HPR)2] over all states = 0.095 x (30% - 14.52%)2 + 0.188 x (26% - 14.52%)2 + 0.401 x (16% - 14.52%)2 + 0.207 x (6% - 14.52%)2 + 0.109 x (-8% - 14.52%)2 = 0.011872542

Hence, Standard deviation = Variance1/2 = 0.0118725421/2 = 10.90%

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