An amusement park is considering installing an outdoor ice-skating rink, which costs $950,000. Expenses for operating and maintaining the ice-skating rink are estimated at $2,500 each day it is used. The outdoor skating rink can only be used when the weather is sufficiently cold, so its usage is limited. The US weather service estimates that there is a 50% probability of 80-day suitable weather per year, 30% probability of 100 days per year, and 20% probability of 120 days per year. The operators of the amusement park estimate that during the first 80 days of use in a season, an average of 500 people will skate each day, at a fee of $20 each. If 20 additional days are available, the rink will be used by only 400 people each day during the extra period, and if 20 more days of skating are available, only 300 people per day will use the rink during those days. The management of the amusement park wish to recover any invested capital within three years and want at least a 22% per year rate of return before taxes. Based on before tax analysis, should the outdoor ice-skating rink be installed

Yes, the outdoor ice skating rink should be installed.

Step-by-step explanation:

We can reach this conclusion after simulating the profit for each possible scenario made by The US weather service estimates:

For 80-day suitable weather per year:

total invested capital = $950,000 + $200,000 (total operating and maintaining cost) = $1,150,000per day revenue= 500 x $20 = $10,000total revenue per season = $10,000 x 80 days = $800,000total operating and maintaining cost = $2,500 x 80 = $200,000total profit (returns) in a season = $800,000-$200,000 = $600,000per year rate of return before taxes =  52% (total profit / total invested capital *100; $600,000/$1,1150,000 *100 = 52%

For 100 days suitable weather per year:

total invested capital = $950,000 + $200,000 (total operating and maintaining cost) = $1,150,000per day revenue= 400 x $20 = $8,000total revenue per season = $8,000 x 100 days = $800,000total operating and maintaining cost = $2,500 x 100 = $250,000total profit (returns) in a season = $800,000-$250,000 = $550,000per year rate of return before taxes =  52% (total profit / total invested capital *100; $550,000/$1,1150,000 *100 = 47%

For 120 days suitable weather per year:

total invested capital = $950,000 + $200,000 (total operating and maintaining cost) = $1,150,000per day revenue= 300 x $20 = $6,000total revenue per season = $6,000 x 120 days = $720,000total operating and maintaining cost = $2,500 x 120 = $300,000total profit (returns) in a season = $800,000-$250,000 = $420,000per year rate of return before taxes =  52% (total profit / total invested capital *100; $420,000/$1,1150,000 *100 = 58%

Threfore, we notice that the 22% per year rate of return before taxes criteria was met in each of the possible scenarios, making the endeavor worthwhile.