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# Calculating Expected return and standard deviation

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Swift Manufacturing must choose between 2 asset purchases. The annual rate of return and the related probabilities are given in the attached table summarize the firm's analysis to this point.

Project 257 Project 432
Rate of return Probability Rate of return Probability
-10% 0.01 10.0% 0.05
10 0.04 15.0% 0.1
20 0.05 20.0% 0.1
30 0.1 35.0% 0.15
40 0.15 30.0% 0.2
45 0.3 35.0% 0.15
50 0.15 40.0% 0.1
60 0.1 45.0% 0.1
70 0.05 50.0% 0.05
80 0.04
100 0.01

a) For each project compute:
1. the range of possible rates of return
2. the expected value of return
3. the standard deviation of the returns
4. the coefficient of the variation of the returns

b) Construct a bar chart of each distribution of rates of return.
c) Which project would you consider less risky? why?

#### Solution Preview

Please refer attached file for graphs and formulas which are not printed here.

Solution:
a) For each project compute:
1. the range of possible rates of return
Possible Range of Return for Project 257 is -10% to 100%
Possible Range of Return for Project 432 is 10% to 50%

2. the expected value of return
Expected value of return for project 257 =45.00%
Expected value of return for project 432 =30.00%

3. the standard deviation of the returns
Standard Deviation of return for project 257 =16.5378%
Standard Deviation of return for project 432 =10.60660%

4. the coefficient of the variation of the returns
coefficient for variation for projecr 257 = CV1= Standrad deviation/Expected Value=0.3675
coefficient for variation for projecr 432 = CV2= Standrad deviation/Expected Value=0.3536

b) Construct a bar ...

#### Solution Summary

Solution describes the steps in finding expected return, standard deviation and coefficient of variation for two assets and then determines which is less risky.

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