Question

The common stock of Perforated Pool Liners, Inc. now sells for $44.00 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	0.110	$56	$3
High growth	0.196	$56	$3
Normal growth	0.399	$56	$2
Low growth	0.193	$49	$2
No growth	0.102	$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              %

Answer 1

State	Probability	Current Price	End Price	Dividend	HPR
	p(s)	P0	P1	D	(P1 + D - P0) / P0
Super High	0.11	44	56	3	34.09%
High	0.196	44	56	3	34.09%
Normal	0.399	44	56	2	31.82%
Low	0.193	44	49	2	15.91%
No	0.102	44	46	0	4.55%

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 34.09%
High growth 34.09%
Normal growth 31.82%
Low growth 15.91%
No growth 4.55%

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 = 0.11 x 34.09% + 0.196 x 34.09% + 0.399 x 31.82%+ 0.193 x 15.91% + 0.102 x 4.55% = 26.66%

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 = 0.11 x (34.09% - 26.66%)² + 0.196 x (34.09% - 26.66%)² + 0.399 x (31.82% - 26.66%)²+ 0.193 x (15.91% - 26.66%)² + 0.102 x (4.55% - 26.66%)² = 0.009970371

Hence, Standard deviation = Variance^1/2 = 0.009970371^1/2 = 9.99%