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 $ 200 Normal economy 6 90 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 $80.
a. 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.
b. 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

Answer:

a) Boom = 162.50%

Normal =20.00%

Recession = - 100.00%

b) Expected return = 27.50%

Standard deviation = 107.30%

Explanation:

a) To find the rate of return for each economy state, let's use:

Rate of return = (Dividend +Stock price next year-stock price today)/stock price today

i) For Boom:

$\frac{10 + 200 - 80}{80} = 1.625$ = 162.50%

ii) Normal:

$\frac{6 + 90- 80}{80} = 0.2$ = 20.00%

iii) Recession :

$\frac{0 + 0 - 80}{80} = - 1$ = -100%

b) To calculate the expected rate of return, let's use:

Expected return = Sum of expected return in different scenario / number of economy states

$= \frac{162.5 + 20 - 100}{3} = 27.50$

Standard deviation:

To find the standard deviation, let's use:

Standard deviation = √[(sum of square of expected return in each scenario -average return)/n]

$= \sqrt{\frac{(162.50-27.50)^2+(20-27.50)^2+(-100-27.50)^2}{3}}$

$= \sqrt{\frac{(135)^2 + (-7.50)^2 + (-127.50)^2}{3}}$

$= \sqrt{\frac{18225+56.25+16256.25}{3}$

= 107.30%

Standard deviation = 107.30%