2.1.3 Endpoints and payoffs
You can now complete all the branches with endpoints, since there is no further branch information to represent. Draw a small triangle (
) at the end of each branch to represent
the endpoint. Write the payoff value at the endpoint. In
business applications the payoff is usually a monetary
value equal to the anticipated net profit, or return on investment. Net profit
(or net loss) is the difference between the investment
cost and the total revenue. A positive value indicates
a net profit, while a negative value indicates a net
loss. In other words, if revenue exceeds investment,
then the effort is profitable. Otherwise the effort is
a net loss, or a break-even result if the payoff is
zero.
For Really Big Ideas, a successful smoke and fire detector project will earn $1,000,000 in gross revenue. The resulting net profit therefore equals the sum of the gross revenue and the investment cost. Recall that cost can be represented as a negative number. The calculation is therefore $1,000,000 + (-$100,000) = $900,000 net profit, or payoff. Write $900,000 at the end of the branch for success of the smoke and fire detector.
However, if the smoke and fire detector project is not successful, then no revenue will be earned and all the investment will be lost. The calculation for this event is $0 + (-$100,000) = (-$100,000), a loss or negative payoff. Write (-$100,000) at the end of the branch for failure of the smoke and fire detector.
Perform a similar calculation for the success and failure payoffs for the motion detector. Your results should show a $390,000 payoff if successful, and a (-$10,000) payoff (a loss) if it fails. Write these values at the endpoints of their respective branches.
The payoff for the decision branch to not develop either project is simply $0.
Write these payoff values near the endpoints as shown in figure 2.1.3.
Fig 2.1.3 Use endpoints, shown by small triangles with one point connecting to the branch, to indicate that there are no further outcomes or decisions to consider. Write payoff values (net profits or net losses) for each terminated branch are to the right of the endpoints.
This concludes the basic structure of the decision tree for the Really Big Ideas alternatives. We can now incorporate the likelihood of success and failure and use that to analyze the decision alternatives.
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