Question

You are a manager at a certain factory that designs small gadgets. The factory has been quite successful in the past years. Your CEO is wondering whether or not it is a good idea to expand the factory this year. The cost to expand the factory is $1.5M. Doing nothing will result in expected $3M in revenue if the economy stays good and people continue to buy plenty of gadgets, but only $1M in revenue is expected if the economy is bad. On the other hand, expanding the factory carries an expected $6M in revenue if economy is good and $2M if the economy is bad. Assume there is a 40% chance of a good economy and a 60% chance of a bad economy. Also, assume the costs of operating the factory account to $.5M if the factory is expanded and $.3M if not.

a. Illustrate a Decision Tree showing these choices.

b. What should you do?

* Please typewrite and explain how to tackle this type of problem. Thank you*

Answer 1

The expected returns if the factory expands will be .4 ( 3M-1.5M-.5M )+ .6 ( 1M-1.5M-.5M ) which is -.2M , here M is for Millions.

The expected returns if the factory doesn't expands would be .4 ( 6M-.3M ) + .6 ( 2M-.3M ) which is 3.3M.

Clearly, it is not a good idea to expand. Please note that in the above calculations we are simply subtracting costs from the revenue. For the case of expanding we are also subtracting the expanding costs from the revenue, if we don't take it as a one time payment in the account the expected returns would be .4 ( 3M-.5M ) + .6 ( 1M-.5M ) which is 1.3M. Expanding is still not a favorable decision. Since there are two possibilities: Good and Bad economy, we are taking into account both with the assigned probabilities which is .4 for Good economy and .6 for bad economy.