Brandon is considering expansion of a store. If he expands, the interest rate at which he borrows the money is the important factor. He is not sure what kind of interest rate will be obtained. If he does not expand, the only factor influencing the outcome is future economy. The following table summarizes the situation:                                                                        Probabilities          Payoff Expand Large                        Favorable interest               .3             $60k                                Neutral interest                   .5             $30k                                Unfavorable interest           .2             ‑$70k                               Expand Small                        Favorable interest               .3             $50k                                Neutral interest                   .5             $30k                                Unfavorable interest           .2             ‑$30k Do not expand                      Economy up                          .3             $30k                                Economy same                     .5             $20k                                Economy down                    .2             $0Draw the decision tree showing all nodes and expected values. Use square for decision node, and circle for chance node. What should he do?

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Asked Mar 8, 2019
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  1. Brandon is considering expansion of a store. If he expands, the interest rate at which he borrows the money is the important factor. He is not sure what kind of interest rate will be obtained. If he does not expand, the only factor influencing the outcome is future economy. The following table summarizes the situation:

                                                                        Probabilities          Payoff

 

Expand Large                        Favorable interest               .3             $60k

                                Neutral interest                   .5             $30k

                                Unfavorable interest           .2             ‑$70k

                               

Expand Small                        Favorable interest               .3             $50k

                                Neutral interest                   .5             $30k

                                Unfavorable interest           .2             ‑$30k

 

Do not expand                      Economy up                          .3             $30k

                                Economy same                     .5             $20k

                                Economy down                    .2             $0

Draw the decision tree showing all nodes and expected values. Use square for decision node, and circle for chance node. What should he do?

check_circle

Expert Answer

Step 1

The decision tree has been represented as shown in the diagram.

fullscreen
Step 2

The expected values are given as below:

Expand large

Expected value = 0.3x60 + 0.5x 30 – 0.2 x 70 = $47

Expand small

Expected value = 0....

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