Question

The common stock of Leaning Tower of Pita Inc., a restaurant chain, will generate payoffs to investors next year, which depend on the state of the economy, as follows: Dividend Stock Price Boom $ 10 $ 215 Normal economy 6 110 Recession 0 0 The company goes out of business if a recession hits. Assume for simplicity that the three possible states of the economy are equally likely. The stock is selling today for $100. a-1. Calculate the rate of return to Leaning Tower of Pita shareholders for each economic state. (Negative amounts should be indicated by a minus sign. Enter your answers as a percent rounded to 2 decimal places.) Rate of return Boom % Normal economy % Recession % a-2. Calculate the expected rate of return and standard deviation of return to Leaning Tower of Pita shareholders. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) Expected return % Standard deviation %

Answer 1

SOLUTION:-

Given information:

State of Economy	Dividend	Ending Market Stock Price	Beginning Market stock price
Boom	$10	$215	$100
Normal Economy	$6	$110	$100
Recession	$0	$0	$100

a).  Calculate the rate of return to Leaning Tower of Pita shareholders for each economic state

  Rate of return to Leaning Tower of Pita shareholders for each economic state can be calculated by the following   formula:-

Rate Of Return (Ending Market price +Dividend) / (Beginning Market Price) - 1

By substituting the values from the above table we get:-

1. Rate of return (Boom) = ($215+$10)/ $100- 1

=2.25 - 1

= 1.25 or 125%

2. Rate of return (Normal Economy) = ($110+$6)/ $100- 1

=1.16 - 1

= .16 or 16%

3. Rate of return (Recession) = ($0+$0)/ $100- 1

=0 - 1

= -1 or -100%

b). Calculate the expected rate of return and standard deviation of return to Leaning Tower of Pita shareholders

1. Expected Return

equation for Expected Return :

   Expected Rate Of Return =(probability of Boom * Rate of Return of Boom) + (probability of Normal Economy * Rate of Return of Normal Economy) + (probability of Recession * Rate of Return of Recession)

   Here,

The possible outcome of all three states of economy is equal therefore, the probability of each one will be:

1 / 3 = .333 each

  By substituting the values from the above answer we get:-

Expected Rate Of Return = (.333 * 1.25) + (.333 * .16) + (.333 * -1)

Expected Rate Of Return   = .41625 + 0.05328 + (-.333)

Expected Rate Of Return     = .13653 or 13.65%

2. Standard Deviation

equation for Standard Deviation :

Where,

= Rate Of Return

= Expected Rate Of Return

Standard Deviation      

..9182 or 91.82%

Expected Rate Of Return     = .13653 or 13.65%

  Standard Deviation = .9182 or 91.82%