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DECISION-TREE APPROACH
The Decision-tree Approach (DT) is another useful alternative for evaluating investment proposals. The outstanding feature of this method is that it takes into account the impact of all probabilistic estimates of potential outcomes. In ot her words, every possible outcome is weighted in probabilities terms and then evaluated. The DT approach is especially useful for situations in which decisions at one point of time also affect the decisions of the firm at some later date. Another useful application of the DT approach is for projects, which require decisions to be made in sequential parts.
A decision tree is a pictorial representation in tree from which indicates the magnitude, probability and inter-relationship of all possible outcomes. The format of the exercise of the investment decisions has an appearance of a tree with branches and, therefore, this method is referred to as the decision-tree method. A decision tree shows the sequential cash flows and the NPV of the proposed project under different circumstances.
To illustrate, suppose that a firm has a two-year project that requires an initial investment of Rs.100,000. The cash flows expected in each of the years along with their probabilities are given in following figure. It may be noted that in this example both the cash flows and the probabilities are conditional (a case where the cash flows are not independent) on what happen in the first year.
It is evident from this figure that the decision tree show nine different combinations of outcomes as possible. One possibility is that the first year will have an inflow of Rs.40,000 which shall be followed by a Rs.60,000 cash flow in the second year. As shown in the figure, the net present value associated with this set of cash flows, discounted using a rate of 8%, is 40000 X (1.08)-1 + 60000 X
(1.08) -2 – 100,000 = -11,526. In a similar manner, the net present value of each of the other eight combinations is given. The (joint) probability of each combination is obtained by multiplying the probabilities of occurrences. For example, for the first combination, the probability is 0.08 (=0.2 X 0.4)
By multiplying the joint probability for each of the nine combinations times their associated NPVs and summing, we obtain the project‘s expected net present value, E (NPV). The standard deviation of the project equals Rs.18,684 approximately, obtained as follows:
NPV J = NPV of the jth combination
Pj = Probability of the jth combination
= ((-11526-20177) 2 x0.08 + (-2953 – 20177) 2 x 0.08 +…)1/2 = Rs.18,
Although useful for setting out all possible combinations of a proposed project, the decision-tree approach suffers from a shortcoming that in situations involving a large number of possible outcomes, it may be too complex to handle.
NPVxProb
Year 2 NPV Prob.= (11526)x0.08=
- Year (922.08) - Rs.60, - 0. - 0. Rs.40,000 70,000 (2953)x0.08=(236.24) - 0.3 80, - 0. - 5620x0.04=224. - Rs.60,
- Year 0 0.3 6992x0.09= 629.
- (Rs.100,000) Rs.60, - 70,000 15565x0.15=2334. - 0.3 0. - 80, - 0.2 24138x0.06=1448. - Rs.50, - 7678x0.05=383. - Rs.70,000 0. - 0.3 70,000 24824x0.25=6206. - 0.
- 100,000 50543x0.20=10108.
Expected NPV = 20177.
