Question

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?

Answer 1

Answer:

a. Expected rate of return on the project = 10%

b. Project's standard deviation of returns = 10.95%

c. Project's coefficient of variation (CV) of returns = 1.10

d. The type of risk does the standard deviation and CV measure is referred to as the total risk of the project.

e. he risk is relevant when there is a need to assess the influence of the market and internal factors on the project.

Explanation:

Note: See the attached excel file for the calculations of Expected Rate of Return on the Project and Variance of Returns.

a. What is the expected rate of return on the project?

From the attached excel file, we have:

Expected rate of return on the project = Total of Expected Return Rate = 10%

b. What is the project's standard deviation of returns?

From the attached excel file, we have:

Project's variance of returns = Total of (P * D^2) = 1.20%

Therefore, we have:

Project's standard deviation of returns = Project's variance of returns^0.5 = 1.20%^0.5 = 10.95%

c. What is the project's coefficient of variation (CV) of returns?

Project's coefficient of variation (CV) of returns = Project's standard deviation of returns / Expected rate of return on the project = 10.95% / 10% = 1.10

d. What type of risk does the standard deviation and CV measure?

The type of risk does the standard deviation and CV measure is referred to as the total risk of the project.

Total risk is a metric that indicates all of the risks that come with accepting a project.

e. In what situation is this risk relevant?

The risk is relevant when there is a need to assess the influence of the market and internal factors on the project.

Download xlsx