# How to Calculate Expected Value in Decision Trees

by Kristyn Hammond; Updated September 26, 2017Decision tress help you make investment decisions, maximizing your profits and predicting possible losses. A decision tree is a graphical display of the initial investment in a decision and the potential gains, losses and chance to achieve either. Once you know how to calculate the expected value of each decision, you can use this information to determine which investments have the greatest chance to earn the most money in return for the investment. This technique is effective for any decision that requires an initial investment and has a number of predictable conclusions.

Isolate the expected gain value, expected loss value other expected outcome values and the percent change for each event to occur. For instance, a decision tree referring to the business decision to open a new store may include two branches. The first represents a $125,000 income from the branch, with a 45 percent interest from the community in the store. The second represents an operating cost of -$65,000 for the startup cost, with a 55 percent disinterest from the community.

Multiply the dollar value listed for each outcome by the percent chance for that outcome to occur. As an example, the first branch ($125,000 x .45 = $56,250) has an expected value of $56,250. The second branch (-$65,000 x .55 = -$35,750) has an expected loss of -$35,750. Write these new values to the right of the appropriate branch, in parentheses, showing the expected value for each branch.

Add the expected value for each branch together. For instance, the expected value for this decision tree is ($56,250 + [-$35,750] = $20,500). Write this value between the two branches, remembering to keep the negative sign if your final value is negative. For instance, write the $20,500 value between the two branches, representing the overall expected value for the decision to open the new store.

Refer to the initial investment for the decision, usually written to the left of each decision tree. Divide the investment by the expected value from the investment, determining how soon the company can expect a positive return on the initial investment. As an example, if the initial startup cost for the store would be $82,000, the company can expect a positive reimbursement on the initial investment in four years ($82,000 / $20,500 = 4).

#### Tips

Evaluate each decision branch separately. Remember that most decision branches will contain one value for gain and one for loss; note the difference as the gain is usually a positive figure and the loss is a negative figure. Remember to keep the negative value of cost listed as a negative value, to ensure that your other calculations are correct.

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