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# Two business projects: Coefficient, standard deviation, and expected value

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A firm is considering two business projects. Project A will return a loss of \$45 if conditions are poor, a profit of \$35 if conditions are good, and a profit of \$155 if conditions are excellent. Project B will return a loss of \$100 if conditions are poor, a profit of \$60 if conditions are good, and a profit of \$300 if conditions are excellent. The probability distribution of conditions follows:

Conditions : Poor Good Excellent
Probabilities: 40% 50% 10%

(i) Calculate the expected value of each project and identify the preferred project according to this criterion.
(ii) Calculate the standard deviation of each project and identify the project that has the higher level of risk.
(iii) Calculate the coefficient of variation for each project and identify the preferred project according to this criterion.

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Solution:

(i) Calculate the expected value of each project and identify the preferred project according to this criterion.
Project A Project B
P Profit X1 Profit X2 P*X1 P*X2
Poor 0.4 -45 -100 -18 -40
Good 0.5 35 60 17.5 30
Excellent 0.1 155 300 15.5 ...

#### Solution Summary

The solution describes the steps needed for choosing a project from given alternatives based upon expected profit, standard deviation and coefficient of variation.

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