Question

Asked Mar 8, 2019

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- 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?

Step 1

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

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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