Question

Greengage, Inc., a successful nursery, is considering several expansion projects. All of the alternatives promise to produce an acceptable return. Data on four possible projects follow:
Project Expected Return Range Standard deviation
A 12.0% 4.0% 2.9%
B 12.5 5.0 3.2
C 13.0 6.0 3.5
D 12.8 4.5 3.0

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 pusrposes of this comparison.
C. Calculate the coefficient of variation for each project. Which project do you think Greengage's owners should choose? Explain why?

Answer 1

Answer:

A. Project A

B. Project A has lowest Standard Deviation

C. Project D

Explanation:

A.

The higher the range, the more risky the project is. Based on the table, project A has the smallest range, and therefore is the least risky based on range.

B.

The standard deviation is not scale-free, i.e. it is not adjusted for the level of returns. Hence, a project that has the same distribution of returns, but a higher average return, will have a higher standard deviation. But the project is not any more risky. Hence, the standard deviation might not be an appropriate measure of risk.

C.

The Coefficient of Variation (CV) is calculated as follows:

CV = Standard deviation / expected return

Applying this formula, the coefficient of variation for each project is:

Project A: 2.9% / 12.0% = 0.242

Project B: 3.2% / 12.5% = 0.256

Project C: 3.5% / 13.0% = 0.269

Project D: 3.0% / 12.8% = 0.23 4

Based on the coefficient of variation, project D has the lowest coefficient. It means that the project has the lowest risk per unit of return generated, and thus is the best project and should be chosen.