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		$	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	%

Answer 1

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%