1) The outcomes for three potential investments (A, B or C) have been reduced to
ID: 1203457 • Letter: 1
Question
1) The outcomes for three potential investments (A, B or C) have been reduced to the information below describing the Net Present Worth of the investment, along with associated probabilities NPW Investment Return Probabilities $1,000 $2,000 $3,000 $4,000 $5,000 $6,000 0.3 0.4 0.3 0.7 0.2 0.2 0.2 0.2 0.2 What is the Expected Value of the return from Investment A? What is the Variance associated with Investment C? Based on Expected Value and Variance analyses, which investment (if any) should be selected and why?Explanation / Answer
(1) Expected value, A ($) = 0.3 x 1,000 + 0.4 x 3,000 + 0.3 x 5,000 = 300 + 1,200 + 1,500 = 3,000
(2) Expected value, C ($) = 0.1 x 1,000 + 0.2 x 2,000 + 0.2 x 3,000 + 0.2 x 4,000 + 0.2 x 5,000 + 0.1 x 6,000
= 100 + 400 + 600 + 800 + 1,000 + 600 = 3,500
Variance, C ($) = 0.1 x (1,000 - 3,500)2 + 0.2 x (2,000 - 3,500)2 + 0.2 x (3,000 - 3,500)2 + 0.2 x (4,000 - 3,500)2 + 0.2 x (5,000 - 3,500)2 + 0.1 x (6,000 - 3,500)2
= 0.1 x 6,250,000 + 0.2 x 2,250,000 + 0.2 x 250,000 + 0.2 x 250,000 + 0.2 x 2,250,000 + 0.1 x 6,250,000
= 625,000 + 450,000 + 50,000 + 50,000 + 450,000 + 625,000
= 2,250,000
(3)
Expected value, B ($) = 1,000 x 0.7 + 5,000 x 0.2 + 6,000 x 0.1 = 700 + 1,000 + 600 = 2,300
Since B has highest expected value, B should be chosen.
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