Maka Gudiashvili Grigol Robakidze University
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1 DECISION TREE METHOD IN ENERGY MANAGEMENT Maka Gudiashvili Grigol Robakidze University Decision Tree Method is frequently used in Energy Management. It implies the energy project analysis in uncertainties. Decision tree analysis method connects present and future results and enables facilitates managers to make decision via grosser NPV. In the article is elaborated production and demand of transformers and generators, probabilities of demand (high or low) and cash flows for each combination. There is represented 2 year business- process decision tree, when a manager would choose the best result and make decision. Net present value of investment: r NPV= -Yx NPVx * Px x= 1 Yx Investment of each x period; NPVx- Net Present Value (NPV) of investment each x period; Px- Probability of demand each x period; r- Series of cash flow. A schematic tree-shaped diagram is used to determine a course of action or show a statistical probability. Each branch of the decision tree represents a possible decision or occurrence. The tree structure shows how one choice leads to the next, and the use of branches indicates that each option is mutually exclusive. A decision tree can be used to clarify and find an answer to a complex problem. The structure allows users to take a problem with multiple possible solutions and display it in a simple, easy-to-understand format that shows the relationship between different events or decisions. The furthest branches on the tree represent possible end results. A decision tree is a diagram of nodes and connecting branches. Nodes indicate decision points, chance events, or branch terminals. Branches correspond to each decision alternative or event outcome emerging from a node. The root node represents the first set of decision alternatives. For each decision alternative draws a line, or branch, extending to the right from the root node. Some branches may split into additional decision alternatives or outcomes. Let us label each branch with the decision and its associated investment cost. The root node is the small square at the left. Branch lines emerge from the root towards the right. Each branch represents one decision alternative.
2 Pict.1. Tree-shaped diagram business- process In the Picture 1 is represented a schematic tree-shaped diagram of 2 year business- process of production and demand transformers and generators. Production of transformers requires 1 st year investment costs GEL. Production of generators requires 1 st year investment costs GEL and for the second year additional investment costs GEL.
3 Pict.2. Tree-shaped diagram business- process of production and demand transformers and generators A schematic tree-shaped diagram shows production and demand of transformers and generators, probabilities of demand (high or low) and cash flows for each combination. Based on discount rate 10%, cash flows will be (see Table 1, 2):
4 Table 1. I year Cash flow Probability Demand Transformers GEL 0,6 High Transformers GEL 0,4 Low Generators GEL 0,6 High Generators GEL 0,4 Low Table 2. II year Cash flow Probability Demand Transformers GEL 0,8 High Transformers GEL 0,2 Low Transformers GEL 0,6 High Transformers GEL 0,4 Low Generators GEL 0,8 High Generators GEL 0,2 Low Generators GEL 0,4 High Generators GEL 0,6 Low Payoff calculates as: (probability high demand * payoff with high demand) (probability low demand * payoff with low demand). We calculate expected cash flows and discount: ( 0,6*150000) (0,4* 30000) NPVtransf = ,6*[(0,8* ) (0,2* )] 0,4 *[(0,4*930000) 2 () (0,6*140000)] = = _ = GEL ()
5 ( 0,6*100000) (0,4* 50000) NPVgenerat = _ ,6*[(0,8* ) (0,2*180000)] 0,4*[(0,4* ) 2 () (0,6 *100000)] =52000 GEL NPV comparative analysis shows: NPVtransf = GEL NPVgenerat = GEL P Conclusion: investment for transformer production via grosser NPV is more attractive then investment for generator production. If we expand and invest additionally GEL, choice would be different, because investment for generator production and its further expansion will bring more net present value (NPV) of investment. Investment for generator production according to high demand (80%) would guarantee cash flow GEL, or GEL according to low demand (20%). In this case cash flow would be: Present value of expanding: (0,8* ) (0,2* )= GEL NPVgenerat= = GEL If we choose investment for generator production we expect to receive cash worth GEL in year 1 if demand is high: GEL ( cash flow NPV) And cash worth GEL if it is low: NPVgenerat= ( 0,4* ) (0,6*100000) = GEL GEL ( cash flow NPV) The present value of investment in the generator production is:
6 ( 0,6* ) (0,4*185000) NPVgenerat= = GEL A schematic tree-shaped diagram business-process of production and demand transformers and generators, probabilities of demand (high or low) and cash flows for each combination, gives opportunity to choose the best result and make the decision: investment for generator production and its expansion is more attractive via the net present value (NPV) of investment. References 1. Brealey R. A., Myers S.C Principles of Corporate Finance. London. 2. Turrner E.C Energy Management. Handbook. Published by Fiarmont Press.
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