Question

Please assist in solving all parts

Standard deviation versus coefficient of variation as measures of risk Greengage, Inc., a successful nursery, is considering several expansion projects. All the alternatives promise to produce an acceptable return. Data on four possible projects appear in the following table: a. Which project is least risky, judging on the basis of range? b. Which project has the lowest standard deviation? Explain why standard deviation may not be an entirely appropriate measure of risk for purposes of this comparison. c. Calculate the coefficient of variation for each project. Which project do you think Greengage's owners should choose? - X Data Table a. Which project is least risky, judging on the basis of range? (Select the best answer below.) O A. Project B O B. Project A (Click on the icon located on the top-right corner of the data table below in order to copy its contents into a spreadsheet.) O C. Project D Standard deviation Expected D. Project C Project Range return A 12.7% 6.2% 3.5% В 13.3% 4.3% 3.9% 11.7% 5.8% 3.8% с 11.7% 4.7% 3.7%

Answer 1

a) Project B is the least risky project as the range is the minimum. Range is a measure of dispersion. More the range, more risky is the project, and vice versa.

b) Project A has the lowest standard deviation. Standard measure is not an appropriate measure of risk as it is an absolute measure of dispersion. Risk should be compared together with returns of the project so as to know risk per unit of expected return.

c) Coefficient of Variation = (Standard Deviation/ Expected Returns) x 100

Project A - C.V = (3.5 / 12.7) x 100 = 27.56%

Project B - C.V = (3.9 / 13.3) x 100 = 29.32%

Project C - C.V = (3.8 / 11.7) x 100 = 32.48%

Project D - C.V = ( 3.7/ 11.7) x 100 = 31.62%

Greengage's owner should select Project A as the Coefficient of Variation is the minimum, which means the relative risk, when compared together with expected returns, is the minimum.