Incremental Values

Now, let us complicate the coin toss game a little. Just as before, you will win $100 if heads comes up, and nothing for tails. However, your options are to pay $40 to play this game or don’t play at all. This game is illustrated using the following tree.

The first thing you might notice is that each node has three lines instead of two. Just as before, the top line contains the node name and the bottom line contains the calculated EMV. The middle line is new. This line contains the amount of cash you will pay or receive as a result of jumping to that node from its parent--the incremental value.

For example, if you decide to play the game, you will pay $40. This means that the Play Game node has an incremental value of -40. The value is negative because it is a cash outflow. Similarly, if you win the coin toss, you will receive $100. Therefore, Win has an incremental value of 100 (positive). Note that if you win the coin toss, you will not have earned $100. Instead, you will have a net profit of $60 ($100 winnings minus $40 to play). The net profit is shown in the EMV line.

When you build a decision tree in DecisionPro, you enter node names, incremental values, and outcome probabilities. DecisionPro calculates the EMVs.