An investor is considering a short-term investment in a resort property on a Caribbean island. If the weather is reasonably stable over the next year, the value of the investment is expected to be $1.2 million; however, if this proves to be a heavy hurricane year, the value is expected to be $0.5 million. According to the experts, there is a 40% chance that this will be a year of many hurricanes.
-Refer to the information above. If this investment is purchased for its fair market value, what is the expected return if there is a heavy hurricane season? Round your answer to the nearest
Tenth of a percent.
A)-62.5%
B)-45.7%
C)-37.5%
D)-54.3%

Question

Quizplus · Accepted Answer

The expected return in the event of a heavy hurricane season is calculated as follows:

Expected return = (Probability of a heavy hurricane season x Return in a heavy hurricane season) 
               + (Probability of a stable year x Return in a stable year)

Expected return = (0.4 x 0.5) + (0.6 x -0.2)
Expected return = -0.2
Expected return as a percentage = -20%
Therefore, the expected return if there is a heavy hurricane season is -20%, which is equivalent to -0.2. The answer closest is -37.5% (choice C). The expected return if there is a heavy hurricane season can be calculated as follows:

Expected return = (probability of heavy hurricane season * value in heavy hurricane season) - (probability of no heavy hurricane season * cost of investment)
Expected return = (0.4 * 0.5 million) - (0.6 * 1.2 million)
Expected return = -0.2 million

To convert this to a percentage, we divide by the cost of investment and multiply by 100:

Expected return as a percentage = (-0.2 million / 1.2 million) * 100
Expected return as a percentage = -16.7%

Rounded to the nearest tenth of a percent, the expected return is -16.7%, which is equivalent to -16.7/100 = -0.167 or -16.7%. The closest answer choice to this is C, -37.5%, which is the best choice.

An Investor Is Considering a Short-Term Investment in a Resort