Expected value and risk for alternatives under scenarios
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1.) Myers Business Systems is evaluating the introduction of a new product. The possible levels of unit sales and the probabilities of their occurrence are given below:
Possible Market Reaction Sales in Units Probabilities
Low response 20 .10
Moderate response 40 .30
High response 55 .40
Very high response 70 .20
a. What is the expected value of unit sales for the new product?
b. What is the standard deviation of unit sales?
5.) Five investment alternatives have the following returns and standard deviations of returns.
1.
Alternative Returns-Expected Value Standard Deviation
A $ 5,000 $1,200
B 4,000 600
C 4,000 800
D 8,000 3,200
E 10,000 900
Using the coefficient of variation, rank the five alternatives from lowest risk to highest risk.
14.) Mr. Monty Terry, a real estate investor, is trying to decide between two potential small shopping center purchases. His choices are the Wrigley Village and Crosley Square. The anticipated annual cash inflows from each are as follows:
Wrigley Village Crosley Square
Yearly Aftertax Cash Probability Yearly Aftertax Cash Probability
Inflow (in thousands) Inflow (in thousands)
$10 .1 $20 .1
30 .2 30 .3
40 .3 35 .4
50 .3 50 .2
60 .1
a. Find the expected value of the cash flow from each shopping center.
b. What is the coefficient of variation for each shopping center?
c. Which shopping center has more risk?
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Solution Summary
This post explains how to calculate the expected return and risk on investment, which provides different pay off under different scenarios. The concepts are explained by three examples (solved three book problems). The different measures of risk are calculated such as standard deviation and coefficient of variation.
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1. Myers Business Systems is evaluating the introduction of a new product. The
possible levels of unit sales and the probabilities of their occurrence are given
below:
Possible Market Reaction Sales in Units (X) Probability (p) x*p x-E(x) (x-E(x))^2*p
Low response 20 0.1 2 -30 90
Moderate response 40 0.3 12 -10 30
High response 55 0.4 22 5 10
Very high ...
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