Question

In: Finance

The common stock of Leaning Tower of Pita Inc., a restaurant chain, will generate payoffs to...

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

$

9

$

255

  Normal economy

5

85

  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 $75.

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

%

Solutions

Expert Solution

a1.

In order to calculate the 1 year return, we need to use general return calculation methodology:

Return % = (Ending Stock Price - Beginning Stock Price + Dividend)/Beginning Stock Price

Dividend

Ending Stock Price

Current Stock Price

Return

% Return

Boom

9

255

75

(255-75+9)/75

252.00%

Normal

5

85

75

(85-75+5)/75

20.00%

Recession

0

0

75

(0-75)/75

-100.00%

a2.

Expected Return of Stock

E(R) = (252% * 33.3%) + (20% * 33.3%) + (-100% * 33.3%) = 57.33%

% Return Probability Probability * Return
Boom 252.0% 33.3% 84.00%
Normal 20.0% 33.3% 6.67%
Recession -100.0% 33.3% -33.33%

X Y
Probability % Return [% Return - Expected Return]^2 X * Y
Boom 33.3% 252.0% 378.95% 126.32%
Normal 33.3% 20.0% 13.94% 4.65%
Recession 33.3% -100.0% 247.54% 82.51%

Therefore standard dev =

= 146.11%


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