Question

Given is a Decision Tree Diagram. The Payoffs 1-14 are given in the table below 1/3 1/3 0.50 PayOff s Altem ative A Payoff s 1/3 1/3 Altem atre Payoff 10 0.50 0.20 1/2 Payoff 14 a) The value at node 1 is b) The value at node 3 is c) The value at node 5 is (in 1 decimal place) (in 1 decimal place) in 1 decimal place) d) The value at node 7 isin 1 decimal place) (in 1 decimal place) e) The value at node 8 is 1) The best course of action or decision is to select altemative

Answer 1

Solution :

Solution: Decision Tree Diagram. 1 Value at Node 1 (1/3 payoff 1)(1/3 payoff 2)(1/3 payoff 3) (1/3 6)+(1/3 10) +I(1/3)-(-6)). i.e. 3.3 2 Value at Node 3 (1/2 payoff 13)+(1/2 payoff 14) i.e $5.5 3 Value at Node 5 Value at Node 2 or Value at payoff 10 whichever is higher Node 2 (1/3 payoff 7)(1/3 payoff 8)(1/3 payoff 9) i.e. S(2) Value at payoff 10 $8 Therefore, value at Node 5 $8 4 Value at Node 7 Value at Node 4: Value at Node 1 or Value of payoff 4 whichever is higher e 3.3or 3 whichever is higher i.e $3.3 Therefore, Value at Node 7-(0.3 Value at Node 4)+(0.5 Payoff at 5)+(0.2 Payoff at 6) i.e. (0.3 3.3)+(0.5 8)+(0.2 4) i.e $5.8 5 Value at Node 8 Value at Node 5: (1/3 payoff 7)+(1/3 payoff 8)+(1/3 payoff 9)] or payoff at 10 whichever is higher i.e. S (-2) Payoff 10-$8 Therefore, Value at Node 5-(2) or 8 whichever is higher $8 Value at Node 6 Payoff 12 or Value at Node 3 whichever is higher i.e 5 or 5.5 i.e $5.5 Therefore, Value at Node 8-(0.3 Value at Node 5)+(0.5 Payoff at 11)+(0.2 Value at Node 6) i.e. $ 0.5 6 Best Course of action to select Value at Node 7 or Node 8 whichever is higher e $5.8 or $0.5 whichever is higher i.e $5.8 Hence, we should choose alternative A as it has highest profit. (NPV)