Question 18.10: Calculating Expected Values for MedEQuipt Decision Tree If M...

Expected value analysis, or rolling back, begins at the nodes furthest out in Exhibit 18.5. In this case, these are the nodes for the expected return from normal development (node 2) and from accelerated development (node 3). The results are summarized in Exhibit 18.6 and explained in the following text.

The expected value for normal development is calculated as a present value as follows:

E_{normal   returns} = .05(0) + .95(100,000)(P/A,.12,10)(P/F,.12,1)

= 0 + .95(504,484) = $479,260

If MedEQuipt were to select the branch for normal development, costs of $450,000 at time 0 are incurred and the annual returns have an expected present worth of $479,260. The expected net present worth for normal development is $479,260 minus $450,000, or $29,260.

If MedEQuipt were to select accelerated development, the probabilities differ and the potential $50,000 in revenue for year 1 must be included, but the principles are identical. To simplify the formulas, the present worth of the returns are first calculated.

PW_{accelerated   returns} = (P/F,.12,1)[50,000 + 125,000(P/A,.12,10)]

= (50,000 + 706,278)/1.12 = $675,248

Now, it is easy to calculate the expected value for node 3:

E_{accelerated   returns} = .4(0) + .6(675,248) = $405,149

If MedEQuipt selects accelerated development, costs of $250,000 at time 0 are incurred and returns have an expected present worth of $405,149. The expected net present worth for accelerated development is $405,149 minus $250,000, or $155,149.

Since accelerating is the best alternative, this last value is entered into node 1. Notice that the branch for the accelerated branch is bold, since that is the best decision. Chance branches are not bold, since it is not possible to control the states of nature.