Question

Instruction:   The table consists of information about 2 competing investments.                  
                      
Economy    Probability   Project A           Project B  
       Profit     Expected Value       Profit     Expected Value
Weak   15.0%   $10.00           -$25.00  
OK   55.0%   $30.00           $0.00  
Good    20.0%   $50.00           $100.00  
Excellent   10.0%   $70.00           $200.00  
   100%                  
                      
Part 1 - calculate the expected value for each project.           3 points per answer          
                      
part 2 - which do you select?           Why?          
                      
                      

Answer 1

Expected Value (EV) of Project = RP_{1 +} RP_{2 +} RP_{3 +} RP₄ , where, R = Profitability and P = Probability

EV of project A = 10 (0.15) + 30 (0.55) + 50 (0.20) + 70 (0.10) = 1.5 + 16.5 + 10 + 7 = $ 35

EV of project B = -25 (0.15) + 0 (0.55) + 100 (0.20) + 200 (0.10) = -3.75 + 0 + 20 + 20 = $ 36.25

The expected value of project B is more than that of project A. However, the difference between EVs is quite less, i.e. only 1.25 $ and hence, to select the most profitable project, we need to consider the risk associated with each of them.

Thus, we compute standard deviation for each of these projects:

Standard Deviation

Returns (Project A) XA	(XA - MeanA)2	Returns (Project B) XB	(XB - MeanB)2
10	900	25	3164.0625
30	100	0	6601.5625
50	100	100	351.5625
70	900	200	14101.5625
Total - 160	Total - 2000	Total - 325	Total - 24218.75

Standard Deviation (SD) =

SD of project A =

SD of project A = 22.36

SD of project B =

SD of project B = 77.81

Therefore, as the Standard Deviation of Project B is much higher than Project A, it means that the risk associated with Project B is quite high. Considering only negligible margin in expected values of both the projects and a much higher risk associated with investment in project B, I would select Project A for investing.