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# Business Finance - Distribution of Returns

Consider the following probability distribution of returns estimated for a proposed project that involves a
new ultrasound machine:

State of the Probability Rate of
Economy of occurrence Return
Very poor 0.1 -10%
Poor 0.2 0%
Average 0.4 10%
Good 0.2 20%
Very good 0.1 30%

a. What is the expected rate of return on the project?
b. What is the project's standard deviation of returns?
c. What is the project's coefficient of variation (CV) of returns?
d. What type of risk does the standard deviation and CV measure?
e. In what situation is this risk relevant?

#### Solution Preview

a.

Expected return = 0.1 X -10 + 0.2 X 0 + 0.4 X 10 + 0.2 X 20 + 0.1 X 30 = 10%.

b.

Variance = 0.1 X (-0.1 - 0.1)^2 + 0.2 X (0 - 0.1)^2 + 0.4 X (0.10 - 0.10)^2 + 0.2 X (0.20 - 0.10)^2 + 0.1 x (0.3 - 0.1)^2 = 0.012

Std. Dev. = sqrt(variance) = 0.1095

c.

CV = std dev/mean = 0.1095/0.1 = 1.095

d.

The std. dev. measures the absolute risk ...

#### Solution Summary

Business finance for distribution of returns are examined. The expected rate of return on the projects are determined.

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