Question

WTVCA Inc. may invest in new equipment and there are three possible outcomes with the following new present values of $48,570, $33,214 and $15,989, respectively. The outcomes have probabilities of 0.3, 0.5, and 0.2, respectively. Calculate risk (measured by the standard deviation) associated with this proposal.

Answer 1

Let X be the New present values. Let P(x) be the probabilities associated with each present value.

X	48,570	33,214	15,989
P(X)	3/10	5/10	2/10

Stanadard Deviation=

Variance of X = E(X2) - [E(X)]2

E(X) means the expected value of X . E(X2) means expected value of X2.

To find the E(X), we will first Mutilply each X with its probability i.e P(X) and then find the summation pof these products.

X	48570	33,214	15989
P(X)	3/10	5/10	2/10
X* P(X)	14,571	16,607	3197.8

E(X2) can be found using the same formula used in finding E(X) . We need to know one thing before that. The chances or probability of X2 taking place will be same as the chances of X taking place. P(X) = P (X2 ).

X	48570	33,214	15989
P(X)	3/10	5/10	2/10
X2	2,359,044,900	1,103,169,796	255,648,121
X2 P(X)	707,713,470	551,584,898	51,129,624.2

=

=

=

  

The risk associated with is of $11,346.0286 .