### 2.4.2 Recalculate the expected values (EV)

You are now ready to find the EV for the chance event node representing the UL safety certification.Recall that for any chance node,

EV

_{chance node}= [EV

_{branch1}+ EV

_{branch2}+ . . . +EV

_{branchN}].

Therefore,

($895,000 x 0.3) + ($695,000 x 0.6) + [(-$105,000) x 0.1] = $675,000.

This chance node is thus resolved or collapsed into a single EV, in this case $675,000. Now use this amount as the payoff value for the “submit application” branch of its decision node.

You may notice that the “don’t submit application” branch also can have an expected value, in this case (-$100,000). For a decision node you accept only the branch with the largest EV and disregard all the lower value branches. Use double-hatch marks to indicate a branch from a decision node that is disregarded, as in figure 2.4.2.

You can now calculate the chance event node for the smoke and fire detector development outcome. The input from the “success” branch is $675,000 x 0.5. And the input from the “failure” branch remains at: (-$100,000) x 0.5. Therefore,

EV = ($675,000 x 0.5) + (-$100,000 x 0.5) = $287,500.

Fig. 2.4.2

The calculation in figure 2.4.2 is an example of successively calculating the expected values from endpoints back through branches and nodes. Such a rollback calculation takes the EV from a given node and uses that value as a payoff input for the prior node.

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