Compare the expected value of the profit of the company with and without the expansion.
See solution.
Practice makes perfect
We are trying to decide whether we should expand a business. If the business is not expanded, the revenue will be $2 million if the economy remains good and $0.5 million if the economy is bad. Expanding the business would cost $1 million and increase the revenue to $4 million in a good economy and to $1 million in a bad economy.
Revenue
Is The Business Expanded?
In Good Economy
In Bad Economy
Expanded
$4 million
$1 million
Not Expanded
$2 million
$0.5 million
The probability that the economy remains good is 30 %, or 0.3. The probability that the economy turns bad is 70 %, or 0.7. We want to use a probability tree to find whether we should expand the company. First, note that to compare the results of the company if it is expanded and if it is not, it is necessary to subtract the cost of expansion from the revenue of the expanded company.
Profit
Is The Business Expanded?
In Good Economy
In Bad Economy
Expanded
$3 million
$0 million
Not expanded
$2 million
$0.5 million
To know whether we should expand the company, we will find the expected value of the profit in the case of an expanded and not expanded business.
The expected value in each case is the profit in a good economy times 0.3 plus the profit in bad economy times 0.7.
Expected Profit of an Expanded Company:
0.3($3 million) + 0.7($0 million) = $0.9million
Expected Profit of an Unexpanded Company:
0.3($2 million) + 0.7($0.5 million) = $0.95million
As we can see, the expected profit is greater when the company is not expanded. Therefore we should not expand the company.
